JP4213020B2 - Optical circuit - Google Patents

Description

  The present invention relates to an optical circuit, and more particularly, to an optical circuit using a medium (holographic wave transmission medium) that transmits waves holographically by multiple scattering according to a two-dimensional refractive index distribution.

  In a technical field such as optical communication, integrated optical components using an optical waveguide structure have been developed in order to construct an optical circuit for easily realizing branching / interference of light. Integrated optical components using such properties as waves can adjust the length of the optical waveguide and facilitate the fabrication of optical interferometers, etc., and apply circuit processing technology in the semiconductor field. As a result, integration of optical components is also possible.

  However, in such an optical waveguide circuit, each component of the optical circuit is configured by an “optical confinement structure” that realizes spatial optical confinement of light propagating in the optical waveguide using the spatial distribution of the refractive index. In order to configure, a cascaded circuit design using optical wiring or the like is required. For this reason, the optical path length of the optical waveguide circuit must be longer than the optical path length required for causing an interference phenomenon in the optical circuit, and as a result, the optical circuit itself becomes extremely large. There was a problem.

For example, taking a typical arrayed waveguide grating as an example, light of multiple wavelengths (λ _j ) input from an input port is repeatedly demultiplexed and multiplexed by a star coupler having a slab waveguide. Although the output light is output from the output port, the optical path length required to demultiplex the light with a resolution of about one thousandth of the wavelength is tens of thousands of the wavelength of the light propagating through the waveguide. Further, it is necessary to perform processing for providing a wave plate for correcting circuit characteristics depending on the polarization state, including waveguide patterning of an optical circuit. (For example, refer nonpatent literature 1).

  In addition, in order to reduce the size of the optical circuit, it is necessary to confine the light strongly in the waveguide. Therefore, in order to control the optical confinement state by the spatial distribution of the refractive index, an extremely large refractive index difference is generated in the optical waveguide. For example, in a conventional step index type optical waveguide, the optical waveguide is designed to have a spatial distribution of the refractive index so that the relative refractive index difference is a value larger than 0.1%. It had been. If optical confinement is performed using such a large refractive index difference, there arises a problem that the degree of freedom of the circuit configuration is limited. In particular, when the refractive index difference in the optical waveguide is to be realized by local ultraviolet irradiation, thermo-optic effect, electro-optic effect, etc., the obtained refractive index variation is at most about 0.1%. In many cases, when changing the propagation direction of light, the direction must be gradually changed along the optical path of the optical waveguide, and the optical circuit length is inevitably extremely long. As a result, it is difficult to reduce the size of the optical circuit.

  Furthermore, a circuit in which a grating-like circuit is added to an optical waveguide circuit constitutes an optical circuit by a periodic structure or a periodic change of the dielectric refractive index in a direction substantially parallel to the light propagation direction, and in an actual design. Since the characteristics of the optical circuit are obtained by a structure with a strong periodicity that can be evaluated by a Fourier transform or a chirp structure with a slight distortion of the periodicity, the propagation direction becomes a substantially uniform structure with respect to the wavefront. It becomes difficult to control light in the direction perpendicular to the direction (the direction along the wavefront). For example, in the optical circuit disclosed in Non-Patent Document 2, light that is transmitted without being reflected in the optical circuit spreads in the circuit and cannot be used as signal light. Further, in a circuit that changes the spot position greatly in a direction perpendicular to the propagation direction, such as a branch circuit, it is necessary to greatly expand the “field” (field) formed by light in the direction perpendicular to the propagation direction, and the circuit does not become large. I do not get. Furthermore, in actual circuit design, since only a design method almost equivalent to a conventional one-dimensional grating circuit design method such as a fiber grating can be realized, a structure with a strong periodicity (that is, a wave number in the propagation direction) It is limited to circuits with a low degree of freedom in design, such as a large circuit scale, a tendency to be sensitive to wavelengths, and a continuous distribution of input / output positions in the order of wavelengths. There was a problem.

Y. Hibino, “Passive optical devices for photonic networks”, IEIC Trans. Commun., Vol.E83-B No. 10, (2000). T. W. Mossberg, “Planar holographic optical processing”, Optics Letters, Vol. 26, No. 7, pp 414-416 (2001). H. Rao, et. Al, “A bidirectional beam propagation method for multiple dielectric interfaces”, IEEE PTL Vol.11, No.7, pp 830-832 (1999). T. Baba and Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions”, Quantum Electronics, IEEE Journal of, Vol. 28 No. 7, pp 1689 -1700 July (1992). Charls Kittel ed. “Introduction to solid state physics 6th” John Wily & Sons, Inc., New York, U.S.A. (1986).

  The present invention has been made in view of such problems, and the object of the present invention is smaller than an optical circuit using a conventional optical waveguide circuit or planar holographic circuit and capable of inputting and outputting light. A highly efficient and compact optical circuit can be realized by using a wave transmission medium that can be set as freely as possible, and that enables sufficiently efficient optical signal control even with a gentle refractive index distribution (small height difference). It is in.

In order to solve such a problem, the present invention provides a light waveguide region comprising a clad layer formed on a substrate and a core layer embedded in the clad layer. In the cross section perpendicular to the light propagation direction, the cross section of the light field is a port on the circuit where the cross section of the light field is to be given, and the light is incident from any one port. In order to emit input light as output light from another port, a wave transmission medium in which a spatial refractive index distribution is formed instead of the core layer having a uniform refractive index is provided, and the spatial refraction is performed. The rate distribution indicates that when the input light propagates along the light propagation direction from the arbitrary one port, the input field of the input light is converted into the output field of the output light, and the other One or more inputs output from the port Determined by the refractive index of each core of the pixels defined by the mesh to propagate through each set of force fields, the refractive index of each pixel's core being a coordinate z of the light propagation direction, The phase of the forward propagation field of the input field and the phase of the output field at the location (z, x) of the cross section X when the coordinate x in the direction perpendicular to the light propagation direction is set in the light guiding region. It is determined by repeatedly calculating the refractive index of the core of each of the pixels as a variable so that the phase difference between the back-propagated field and the phase of the field is equal to or less than a predetermined error. , J-th input field ψ ^j (x) and output field φ of the set of input / output fields based on the refractive index profile {n _q-1 } obtained by the (q−1) -th calculation. ^{When j} (x) is the forward propagation field ψ ^j (z, x, {n _q-1 }) and the back propagation field φ ^j (z, x, {n _q-1 }), The refractive index n _q (z, x) at (z, x) is
n _q (z, x) = n _q-1 (z, x) −αΣ _j Im [φ ^j (z, x, {n _q-1 }) ^* · ψ ^j (z, x, {n _q-1 })]
Where the symbol “*” is a complex conjugate, the symbol “·” is an inner product operation, Im [] is the imaginary component of the field inner product operation result in [], and α is the convergence of the calculation Σ _j represents the sum of j, and the field of the input light is refracted in the cross section X along the propagation direction from the one arbitrary port to the other port. By receiving the phase change in multiple stages due to the rate distribution, it propagates while changing the shape of the light field due to the interference phenomenon caused by the multiple scattering of the propagation waves generated in the wave transmission medium, and the output from the other port It is emitted as an output field of light.

According to a second aspect of the present invention, in the optical circuit according to the first aspect, the pixels defined by the mesh are constituent elements of a unit cell that forms the waveguide region by periodic repetition. And

  According to a third aspect of the invention, in the optical circuit of the first or second aspect, the unit cell has a shape that forms a quasi-periodic structure.

According to a fourth aspect of the present invention, there is provided an optical circuit comprising an optical waveguide region comprising a clad layer formed on a substrate and a core layer embedded in the clad layer, wherein the optical circuit In a cross section perpendicular to the propagation direction, a place on the circuit where a cross section of the light field is to be given is a port, and input light incident from any one port is emitted as output light from another port. As described above, a wave transmission medium in which a spatial refractive index distribution is formed in place of the core layer having a uniform refractive index is provided, and the spatial refractive index distribution is such that the input light is the arbitrary one A set of one or more input / output fields output from the other port by converting the input field of the input light into the output field of the output light. To propagate each of The refractive index of each of the pixel cores defined by the cache, and the refractive index of each of the pixel cores is determined by a coordinate z of the light propagation direction, the light propagation direction in the light guiding region. Between the phase of the forward propagation field of the input field and the phase of the field propagated back to the phase conjugate of the output field at the location (z, x) of the cross-section X when the coordinate x is in the direction perpendicular to The phase difference between the pixels is determined by repeatedly calculating the refractive index of the core of each pixel as a variable, and this calculation is obtained by the (q−1) th calculation. and _{V q-1 (z, x} ) and on the basis of the refractive index distribution {n _q-1}, the input-output field sets the j-th input field [psi ^j (x) and the output field phi ^j (x ) Propagation field ^{ψ j (z, x, {} n q-1}) and the field phi ^j of the back propagation _{(z, x, {n q} -1}) when the value v q _(z given by the following formula _{, x) = v q-1} (z, x) -αΣ j Im [φ j (z, x, {n q-1}) * · ψ j (z, x, {n q-1})]
Where the symbol “*” is a complex conjugate, the symbol “•” is an inner product operation, Im [] is the imaginary component of the field inner product operation result in [], and α is the convergence of the calculation Σ _j represents the sum of j, and corresponds to the low refractive index portion n _clad corresponding to the refractive index of the cladding layer and the refractive index of the core layer higher than the refractive index of the cladding layer. the two types of the refractive index of the high refractive index portion _{n core,} the refractive index of the core of the pixels in each location (z, x),
When v _q (z, x)> (n _core + n _clad ) / 2, n _q (z, x) = n _core
When v _q (z, x) <(n _core + n _clad ) / 2, n _q (z, x) = n _clad
And then, and,
The field of the input light is subjected to a change in phase in multiple stages by the refractive index distribution of the cross section X along the propagation direction from the arbitrary one port to the other port. And propagating while changing the shape of the field of light due to the interference phenomenon caused by multiple scattering of the propagation waves generated in step 1, and emitted from the other port as an output field of the output light .

The invention according to claim 5 is the optical circuit according to claim 4, wherein the size of the core having the high refractive index is set to be equal to or less than the wavelength of light propagating in the waveguide region. And

According to a sixth aspect of the present invention, in the optical circuit according to the fourth or fifth aspect, the value given by (λq) / (πna) is 0.1 or less. Here, lambda: propagation light wavelength, n: refractive index value of the core of set pixels refractive index n _core, a: height of the core of set pixels refractive index n _core, q: propagating light Is a coefficient given by q = ( z _L / a) where z _L is the average distance propagating through the part other than the core .

According to a seventh aspect of the present invention, in the optical circuit according to any one of the fourth to sixth aspects, a cross-sectional shape parallel to the substrate of the pixel core in which the refractive index is set to n _core is an n square ( n is an integer of 3 or more), and the pixels are arranged so that each side thereof is inclined with respect to the propagation direction of light propagating through the waveguide region.

  The invention according to claim 8 is the optical circuit according to claim 7, wherein the polygonal shape is a square and the inclination angle is 45 degrees.

The invention of claim 9 is the optical circuit according to any one of claims 4 to 6, the core before Kipi Kuseru, at least one recess on the surface of the core layer of the uniform refractive index the facilities Succoth a relief-like patterning provided, the refractive index of the concave portion and the low refractive index portion n _clad, the refractive index of the convex portion other than the recess as the high refractive index portion n _core, that make up a pixel It is characterized by that.

The invention of claim 10 is the optical circuit according to claim 9, wherein the relief-like patterning, characterized in that it applied to both sides of the front SL core layer.

The invention described in claim 11 is characterized in that the relief-like patterns applied to both surfaces of the optical circuit according to claim 10 are different from each other.

According to a twelfth aspect of the present invention, in the optical circuit according to the tenth or eleventh aspect , the depths of the concave portions of the relief pattern provided on both surfaces of the core layer are equal. .

According to a thirteenth aspect of the present invention, in the optical circuit according to any one of the first to third aspects, the pixel core has a high refractive index (n _H ) or a low refractive index (n _L ) of 2 The pixel is divided into a plurality of subpixels having a binarized refractive index, and the refractive index of the pixel is determined by an array of the binarized subpixels.

According to a fourteenth aspect of the present invention, in the optical circuit according to any one of the fourth to sixth aspects, a cross-sectional shape parallel to the substrate of the core of the pixel in which the refractive index is set to n _core is a circle. It is characterized by that.

According to a fifteenth aspect of the present invention, in the optical circuit according to the fourteenth aspect , the cross-sectional shape perpendicular to the substrate of the pixel core in which the refractive index is set to n _core has a smoothly changing curve. It is characterized by being.

According to a sixteenth aspect of the present invention, in the optical circuit according to any one of the first to fifteenth aspects, the spatial refractive index distribution includes a field intensity distribution and a phase distribution that enable spot size conversion of output light. It is set so that it may be realized.

  The present invention is smaller than an optical circuit using a conventional optical waveguide circuit or a planar holographic circuit, can freely set input / output of light as much as possible, and has a gentle refractive index distribution (small refractive index height difference). However, by using a wave transmission medium that enables sufficiently high-efficiency optical signal control, a highly efficient and compact optical circuit can be realized.

  Embodiments of the present invention will be described below with reference to the drawings. In addition, the same code | symbol is attached | subjected to the location which has the same function in each drawing, and duplication of description is abbreviate | omitted. Further, the same code may be used for the input light and the input port, and for the output light and the output port.

(Basic concept of holographic wave transmission medium)
The basic concept of the holographic wave transmission medium constituting the optical circuit of the present invention will be described below. In this explanation, the “wave” propagating in the holographic wave transmission medium is coherent like laser light. It is assumed that the holographic wave transmission medium is used as an optical circuit. Note that the basic theory described below specifies the characteristics of a medium based on a general wave equation, and can also hold in principle for general waves. Therefore, this basic concept is applicable not only to general media that can transmit holographic waves of "electromagnetic waves" in a broad sense, but also to electron waves that can ignore many-body effects or those that have macroscopic coherence. Is possible.

  In the following explanation, the property of wave transmission medium is defined by "refractive index", but "refractive index" is the rate at which a wave is refracted in the propagation of a general planar wave as defined by the wording. This means (ratio of deflecting the direction of the plane wave) and defines the property of the medium with respect to the optical signal. In the case of an optical signal, it is mainly a dielectric constant.

  Furthermore, this wave transmission medium is said to be a “holographic” wave transmission medium because the holographic control at the global level of the entire circuit by the wave transmission medium is different from the local holographic control. This is achieved by the set (controlled multiple scattering). More specifically, the term “holographic wave transmission medium” refers to a combination of forward-propagating light and back-propagating light propagating in this medium in order to input a coherence light pattern and output it as a desired light pattern. A global holographic control is realized by arranging the refractive index so that the phase difference becomes small at any place in the medium and repeatedly repeating the holographic control at the local level. .

  1A to 1C are diagrams for explaining the basic concept and basic structure of a holographic wave transmission medium. First, terms will be described with reference to FIG. In FIG. 1A, reference numeral 1 denotes an optical circuit board, and reference numeral 1-1 denotes an optical circuit design area constituted by a holographic wave transmission medium. One end face of the optical circuit is an incident surface 2-1 on which the input light 3-1 is incident, and this input light 3-1 is in the optical circuit having a spatial refractive index distribution composed of a holographic wave transmission medium. Is output while being output from the exit surface 2-2 which is the other end face. Here, it is assumed that the holographic wave transmission medium is made of a dielectric, and the spatial refractive index distribution is set based on the theory described later for the local refractive index of the dielectric that constitutes the medium. To be realized.

The “field” (input field) formed by the input light 3-1 is modulated in accordance with the spatial distribution of the refractive index of the holographic wave transmission medium constituting the optical circuit to form the output light 3-2. Converted to “field” (output field). In other words, the holographic wave transmission medium is an (electromagnetic) field conversion means for correlating the input field and the output field according to the spatial refractive index distribution. For these input field and output field, the light field in the cross-section (cross-section along the x-axis in the figure) perpendicular to the propagation direction (z-axis direction in the figure) in the optical circuit is represented by its location (x, This is called a (forward) propagation image (propagation field or propagation light) in z) (see FIG. 1B). Coordinate z in FIG. 1 (a) coordinate (z = 0 is the incident surface, z = z _e is output surface) of the propagation direction of the light is, the coordinate x is the horizontal coordinate relative to the propagation direction of the light.

  Here, “field” means what is generally called an electromagnetic field (electromagnetic field) or a vector potential field of an electromagnetic field, and the control of the electromagnetic field is a spatial refractive index distribution (that is, an optical circuit). This corresponds to considering the distribution of dielectric constant). Although the dielectric constant is given as a tensor, since the transition between the polarization states is usually not so large, it is an approximation that may be a scalar wave approximation for only one component of the electromagnetic field. Therefore, in this description, the electromagnetic field is treated as a complex scalar wave. Since the “state” of light includes an energy state (wavelength) and a polarization state, when the “field” is used to express the state of light, the light wavelength and polarization state are also included. Will get.

  In general, in an optical circuit that does not cause amplification or attenuation of propagating light, when the spatial distribution of the refractive index is determined, an image (input field) of the input light 3-1 other than the focal point is an image of the output light 3-2. (Output field) is determined uniquely. Such a field of light traveling from the exit surface 2-2 side to the entrance surface 2-1 side is referred to as a back propagation image (a back propagation field or back propagation light) (see FIG. 1C). Such a backpropagation image can be defined for each location in the optical circuit. That is, when a light field at an arbitrary place in the optical circuit is considered, if the place is considered as an emission point of a virtual “input light”, the image of the output light 3-2 can be obtained in the same manner as described above. The back-propagation image at that location can be considered. In this way, a back propagation image can be defined for each location in the optical circuit. Here, in particular, in a single optical circuit, when the outgoing field is a propagation field of the incident field, the propagation field and the reverse propagation field at an arbitrary point of the optical circuit coincide. The field is generally a function on the entire target space, but the term “incident field” or “exit field” means a cross section of the field on the incident surface or the exit surface. In addition, even in the case of “field distribution”, when a discussion is made regarding a specific cross section, it means a cross section of the field with respect to that cross section.

In order to explain the method of determining the refractive index distribution, it is better to use symbols, so the following symbols are used to represent each quantity. Note that the target light (field) is not limited to light in a single state. Therefore, an index j is assigned to light in each state so that light in which light in a plurality of states is superimposed can also be targeted. In general.
ψ ^j (x): j-th incident field (complex vector value function, defined by intensity distribution and phase distribution set on the incident surface, and wavelength and polarization).
φ ^j (x): j-th outgoing field (complex vector value function, defined by intensity distribution and phase distribution, wavelength and polarization set on the outgoing face).

Note that ψ ^j (x) and φ ^j (x) have the same total light intensity (or negligible loss) unless intensity amplification, wavelength conversion, or polarization conversion is performed in the circuit. Their wavelength and polarization are the same. Therefore,
{Ψ ^j (x), φ ^j (x)}: Input / output pair (a set of input / output fields)
Is defined by the intensity distribution and phase distribution, wavelength and polarization at the entrance and exit surfaces.

{n _q }: Refractive index distribution (a set of values for the entire optical circuit design region).
When one refractive index distribution is given for a given incident field and outgoing field, the field of light is determined, so it is necessary to consider the field for the entire refractive index distribution given by the qth iteration. Therefore, the entire refractive index distribution may be expressed as n _q (x, z) with (x, z) as an indefinite variable, but it is distinguished from the refractive index value n _q (x, z) at location (x, z). _Therefore, {n _q } is used for the entire refractive index distribution.
n _core : A symbol indicating a high refractive index value with respect to the surrounding refractive index, such as a core portion in an optical waveguide.
n _clad : A symbol indicating a low refractive index value with respect to n _core , such as a clad portion in an optical waveguide.
ψ ^j (z, x, {n _q }): The field at location (z, x) when the j-th incident field ψ ^j (x) is propagated to z in the refractive index profile {n _q }. value.
φ ^j (z, x, {n _q }): field at the location (z, x) when the j-th outgoing field φ ^j (x) is propagated back through the refractive index profile {n _q } to z The value of the.

Method of determining the refractive index profile described below, all j for _{^{ψ j (z e, x,}} {n q}) method of obtaining a = φ ^j (x) or, as a state close to it {n _q} Is to give.

  “Input port” and “output port” are “areas” where the fields at the entrance end face and the exit end face are concentrated. For example, by connecting an optical fiber to the area, an area where the light intensity can be propagated to the fiber. It is. Here, since the field intensity distribution and phase distribution can be designed to be different for the j-th and k-th ones, it is possible to provide a plurality of ports on the entrance end face and the exit end face. Furthermore, when considering a pair of an incident field and an outgoing field, the phase generated by the propagation between them differs depending on the frequency of light. Therefore, for light having different frequencies (that is, light having different wavelengths), the field shape including the phase Can be configured as different ports regardless of whether they are the same or orthogonal. As the reference numerals, alphabetic capital letters A, B, C,... Are assigned to the incident port side, and alphabetic small letters a, b, c,.

  In addition, α, γ, g, and w are appropriate coefficients in numerical calculation, and the degree thereof will be appropriately indicated in the text. For example, “scheme stability used in ordinary computational fluid dynamics” The actual numerical calculation should be adjusted slightly according to the “sex argument”.

Propagation direction z, expressed in a direction perpendicular x to the propagation direction, 0 the value of z at the incident surface 2-1, the value of z at the exit surface 2-2 and z _e. As will be described later, sequential numbers are assigned to the distinguishable light states. At this time, the j-th incident field and the corresponding desired emission field to be emitted are ψ ^j (x) and φ ^j (x), respectively. Here, the electromagnetic field is a field of a real vector value, and has the wavelength and polarization state as parameters, but the value of the component is displayed as a complex number that is easy to handle in general, and the electromagnetic wave solution is expressed. To do. In the following calculation, it is assumed that the strength of the entire field is normalized to 1. Note that the j-th incident field and output field are appropriately ordered with respect to elements of a set of light having attributes that are distinguished from each other by the intensity distribution and phase distribution of the field or wavelength and polarization.

As shown in FIG. 1B and FIG. 1C, for the jth incident field ψ ^j (x) and the output field φ ^j (x), the propagation field and the back propagation field are respectively represented by complex vector values. As functions, ψ ^j (z, x, {n}) and φ ^j (z, x, {n}) are written. Since the values of these functions vary depending on the refractive index distribution {n}, the refractive index distribution {n} is a parameter. According to the definition of the symbols, ψ ^j (x) = ψ ^j (0, x, {n}) and φ ^j (x) = φ ^j (z _e , x, {n}). The values of these functions can be easily calculated by a known method such as a beam propagation method if an incident field ψ ^j (x), an outgoing field φ ^j (x), and a refractive index distribution {n} are given. . The state of each of these fields will be described using a more specific example as follows.

FIG. 2 is a diagram for explaining a configuration example of a conventional arrayed waveguide grating circuit. An optical circuit design area 1-1 includes two star couplers (optical multiplexer / demultiplexers) 4-1 and 4-2. And the wave plate 6 provided at the center of the arrayed waveguide 5 is formed. Considering a 1 × N wavelength demultiplexer (N is the number of wavelengths) in wavelength division multiplexing communication as shown in this figure, for example, substantially the same field intensity and phase distribution for one input port 3-1. , Λ _N are numbered, and the j-th wavelength light is transmitted to a desired individual output port 3-2 in an incident field having a wavelength of λ ₁ , λ ₂ , λ ₃ ,. Output from. At this time, in order to demultiplex the light, it is required that the intensity and phase distribution of the j-th wavelength light in the cross section of the exit surface of the waveguide is an independent output field pattern. Called the j-th outgoing field. Assuming the case where the demultiplexed light is output to the optical fiber, the field pattern to be output is a set of fields in which each independent emission field is spatially different. In order to construct an optical circuit that outputs a given set of incident fields in a desired outgoing field, the pattern of the incoming field or outgoing field has the same intensity and phase distribution at the jth and kth. It may be.

In the following, a general algorithm for determining the spatial refractive index distribution will be described.
FIG. 3 is a flowchart for explaining a calculation procedure for determining the spatial refractive index distribution of the holographic wave transmission medium. Since this calculation is repeatedly executed, the number of repetitions is represented by q, and the state of the q-th calculation when the calculation is executed up to the (q−1) -th is shown.

Based on the refractive index distribution {n _q-1 } obtained by the (q-1) th calculation, the jth incident field ψ ^j (x) and the outgoing field φ ^j (x) are opposite to the propagation field. The propagation field is obtained by numerical calculation, and the results are expressed as ψ ^j (z, x, {n _q-1 }) and φ ^j (z, x, {n _q-1 }), respectively (step S220). .

Based on these results, the refractive index n _q (z, x) at each location (z, x) is obtained by the following equation (step S240).
n _q (z, x) = n _q-1 (z, x) −αΣ _j Im [φ ^j (z, x, {n _q-1 }) ^* · ψ ^j (z, x, {n _q-1 })] ... (1)
Here, the symbol “·” in the second term on the right side means an inner product operation, and Im [] means an imaginary number component of the field inner product operation result in []. The symbol “*” is a complex conjugate. The coefficient α is a value obtained by dividing a value less than a fraction of n _q (z, x) by the number of field pairs, and is a small positive value. Σ _j means that the sum is taken for the index j.

Step S220 and repeat the S240, the value in the exit plane of the propagation field _{^{ψ j (z e, x,}} {n}) the absolute value of the difference between the exit field φ ^j (x) is becomes smaller than a desired error d _j (Step S230: YES) The calculation ends.

The basis for obtaining the refractive index n _q (z, x) as in the above equation (1) is as follows, which corresponds to obtaining the refractive index distribution by the steepest descent method.

First, the difference between the field ψ ^j (z _e , x, {n _q-1 }) in which the incident light is propagated by the refractive index distribution {n _q-1 } and the output φ ^j (x) to be finally obtained is to become minimum, the residual ^{_{R = Σ j | φ j (}} x) -ψ j (z e, x, {n q-1}) | 2 may if minimized. Note that φ ^j (x) or the like represents a function of x, and does not mean a specific coordinate of x. Also, a weight may be assigned to each pair, but for simplicity, all are summed with the same weight.

  Here, it is considered that the light fields can be overlapped, and the inner product is defined by the field overlap integration. This superposition of light fields has a finite energy, and the field handled is limited to a spatially finite range. Therefore, the field here forms a Hilbert space, and the propagation of light is defined as a unitary transformation having the following properties.

Specifically, as a unitary transformation operator U from z ₀ to z,
ψ ^j (z, x, {n _q-1 }) = U (z, z ₀ , {n _q-1 }) ψ ^j (z ₀ , x, {n _q-1 }) (2)
Here, if the reflection is negligible, from the additivity of the propagation process,
U (z, z ₀ , {n _q-1 }) = U (z, z ₁ , {n _q-1 }) U (z, z ₀ , {n _q-1 }) (3)
It becomes.

Furthermore, since it has unitarity for the inner product defined by the overlap integral,
U (z, z ₀ , {n _q-1 }) ^* U (z, z ₀ , {n _q-1 }) = U (z, z ₀ , {n _q-1 }) ^-1 U (z, z ₀ , {n _q-1 })
= | U (z, z ₀ , {n _q-1 }) | ² = 1 (4)
It becomes. Here, U (z, z ₀ , {n _q-1 }) ^* is a self-adjoint operator of U (z, z ₀ , {n _q-1 }). U (z, z ₀ , {n _q-1 }) ⁻¹ is an inverse operator of U (z, z ₀ , {n _q-1 }), that is, an operator that gives propagation in the reverse direction. .

In a range where the difference between z ′ and z (| z′−z |) is sufficiently small, U (z ′, z, {n _q−1 }) is a matrix that provides a conversion of just one step in the beam propagation method or the like. What is necessary is just to think that there is U (z, z ₀ , {n _q-1 }) or the like obtained by appropriately dividing the propagation direction and repeating this calculation.

Rewriting the residual R using these results,
^{_{R = Σ j | φ j (}} x) -U (z e, z ', {n q-1}) U (z', 0, {n q-1}) ψ j (x) | 2
_{= Σ j | U (z e} , z ', {n q-1}) | 2 | U (z e, z', {n q-1}) -1 φ j (x) -U (z ', 0, {n _q-1 }) ψ ^j (x) | ²
_{= Σ j | U (z e} , z ', {n q-1}) -1 φ j (x) -U (z', z, {n q-1}) U (z, 0, {n q _-1 }) ψ ^j (x) | ²
= Σ _j | φ ^j (z ′, x, {n _q−1 }) − U (z ′, z, {n _q−1 }) φ ^j (z, x, {n _q−1 }) | ² ... (5)
It becomes.

In the limit of | z′−z | → 0, the change (δ _x U (z ′, z, {n _q )) of U (z ′, z, {n _q−1 }) at a specific x coordinate location x. _-1 })) is also the change of n _q-1 (z, x) at the location x of the specific x coordinate (δ _x n _q-1 (z, x)),
δ _x U (z ′, z, {n _q−1 }) = − iκδ _x n _q−1 (z, x) (6)
Have the relationship. Note that κ is a value that is approximately a propagation constant in vacuum and an appropriate positive coefficient, but will not be discussed in detail here because it is combined with other coefficients for calculation.

From the above results, the change in the residual R (δ _x R) at the location x of the specific x coordinate is
δ _x R = Σ _j {−iκδn _q−1 (z, x) φ ^j (z ′, x, {n _q−1 }) ^* ψ ^j (z, x, {n _q−1 }) + c.c .}
_{= 2κδn q-1 (z,} x) ImΣ j φ j (z ', x, {n q-1}) * ψ j (z, x, {n q-1}) ··· (7)
Is obtained.

here,
δn _q-1 (z, x) =-αImΣ _j φ ^j (z ', x, {n _q-1 }) ^* ψ ^j (z, x, {n _q-1 }) (α> 0) (8)
Then, δ _x R <0, and if it is changed in this direction, it will go to the minimum value. This is the reason for changing the refractive index distribution in the direction of the above formula (1).

In the above calculation, the initial value {n ₀ } of the refractive index distribution may be set appropriately. However, if this initial value {n ₀ } is close to the expected refractive index distribution, the calculation converges faster accordingly ( Step S200). When calculating φ ^j (z, x, {n _q-1 }) and ψ ^j (z, x, {n _q-1 }) for each j, , J (that is, φ ^j (z, x, {n _q-1 }) and ψ ^j (z, x, {n _q-1 })). Thus, calculation efficiency can be improved (step S220). If the computer is configured with a relatively small memory, an appropriate j is selected for each q in the sum of the index j in equation (1), and φ ^j (z, x, { It is also possible to calculate only n _q-1 }) and ψ ^j (z, x, {n _q-1 }) and repeat the subsequent calculations (step S220).

In the above ^{operation, φ j (z, x,} {n q-1}) in the case of values and ^{ψ j (z, x, {} n q-1}) and the value of the near, the formula (1) Im [φ ^j (z, x, {n _q-1 }) ^* · ψ ^j (z, x, {n _q-1 })] is a value corresponding to the phase difference, and by reducing this value, It is possible to obtain a desired output.

  FIG. 4 is a diagram showing an example of the state of the field in the holographic wave transmission medium in order to facilitate understanding of the calculation procedure described above. At an arbitrary position (x, z) of the optical circuit design area 1-1 made of a holographic wave transmission medium, a minute area having a width (Δz) that is substantially parallel to the wavefront of the propagating light and that can be substantially ignored. Assume that X is a cross section of this minute region. Here, the “substantially negligible width” means that when the light propagates through the medium having no refractive index distribution by the distance Δz, the phase of the propagating light is substantially the same as the original wavefront. It means distance. If the optical circuit on the incident surface 2-1 side of the cross section X is an A circuit and the optical circuit on the output surface 2-2 side is a B circuit, the cross section X is an interface between the A circuit and the B circuit.

Now, considering each desired input / output set, j = 1 to N are assigned to each set, and the j-th set incident field ψ ^j (x) and output field φ ^j (x) are assumed. When the incident field ψ ^j (x) is input to the A circuit and propagated, the sum of each of the guided light, diffracted light and scattered light at the interface X is the field ψ ^j (z _X , x, {n _q }). In addition, as phase conjugate light of light propagating in the A circuit, each of the fields of the guided light, the diffracted light, and the scattered light in which the outgoing field φ ^j (x) is propagated in the B circuit in the opposite direction to the A circuit. The sum is the field φ ^j (z _X + Δz, x, {n _q }). A value P obtained by averaging (or weighted average) the phase differences of these fields ψ ^j (z _X , x, {n _q }) and φ ^j (z _X + Δz, x, {n _q }) for each group. The refractive index distribution on the interface X is determined so as to cancel out the phase difference P as much as possible within a desired refractive index range. Since such a refractive index distribution is determined for each interface X, if the calculation is executed by changing the position of the interface X from 0 (incident surface) to z _e (exit surface) on the z-axis, holographic The refractive index distribution of the entire wave transmission medium is determined.

The spatial distribution of the refractive index is determined by defining a virtual mesh in the holographic wave transmission medium and determining the refractive index of a minute region (called “pixel” or “pixel”) defined by this mesh for each pixel. It can be paraphrased as something to do. In principle, such a local refractive index can be set to an arbitrary (desired) value for each location. However, a system having a simple base has a low refractive index (n _L ). And a system consisting of only pixels having a high refractive index (n _H ), and the overall refractive index distribution is determined by the spatial distribution of these two types of pixels. In this case, the place where the low refractive index pixel exists in the medium is considered as a gap of the high refractive index pixel, and conversely, the place where the high refractive index pixel exists is considered as the gap of the low refractive index pixel. Is possible. That is, the holographic wave transmission medium can also be expressed as a desired place (pixel) in a medium having a uniform refractive index replaced with a pixel having a different refractive index.

  The calculation contents for determining the refractive index distribution described above are summarized as follows. That is, an input port and an output port are provided in a medium (dielectric in the case of light) capable of transmitting a wave in a holographic manner, and the field distribution 1 (propagating light) of propagating light incident from the input port and the input port A field distribution 2 (reverse propagation light) of phase conjugate light in which an output field expected when an incident optical signal is output from the output port is propagated backward from the output port side is obtained by numerical calculation. Then, based on these field distributions 1 and 2, a spatial refractive index distribution in the medium is obtained so as to eliminate the phase difference at each point (x, z) of the propagating light and the counter propagating light. If the steepest descent method is adopted as a method for obtaining such a refractive index distribution, the refractive index is calculated by changing the refractive index in the direction obtained by the steepest descent method using the refractive index of each point as a variable. By changing as in (1), the difference between the two fields can be reduced. If such a holographic wave transmission medium is applied to an optical component that emits light incident from an input port to a desired output port, it is effective due to an interference phenomenon caused by multiple scattering of propagation waves generated in the medium. Thus, an optical circuit having a sufficiently high optical signal controllability can be configured even with a gradual refractive index change (distribution).

  In the following, an optical circuit configured using the above-described holographic wave transmission medium will be described by way of an example. In the following embodiments, unless otherwise specified, an optical circuit having a refractive index distribution in the height direction from the substrate, similar to that of the embedded silica-based optical waveguide formed on the substrate. The thickness (layer thickness) of is assumed to be approximately the same as that of a single mode optical waveguide. Furthermore, a silicon substrate is used as a substrate, and a film whose refractive index is adjusted by adding an additive to quartz is deposited thereon, and an optical circuit is patterned by a fine processing technique used in a semiconductor manufacturing process. . Therefore, the optical circuit pattern is two-dimensional and is formed so as to exhibit the function as an optical circuit in the horizontal direction with respect to the substrate.

  However, when a circuit composed of a high refractive index portion and a low refractive index portion is two-dimensionally developed in the substrate surface, it is simply assumed that there is no portion corresponding to the core of the optical waveguide. As a result, a loss in the optical circuit occurs. Therefore, it goes without saying that the optical circuit should be designed in consideration of the substrate height direction even if it is two-dimensional.

  As described above, since the semiconductor microfabrication technology is applied to the fabrication of the optical circuit of the present invention, the refractive index distribution of the optical circuit is a binarized pattern unless otherwise specified. In the pattern in the substrate surface, a portion having a high refractive index is called a high refractive index portion, and a portion having a low refractive index is called a low refractive index portion. In addition, since the refractive index change is given by the deposition of the film whose refractive index is adjusted, the high refractive index portion in the substrate height direction is called the high refractive index layer and the low portion is called the low refractive index layer. If there is no particular problem, the high refractive index portion is referred to as “core” and the low refractive index portion is referred to as “cladding” in accordance with the customary structure of the optical waveguide. Further, when discussing the pattern in the horizontal plane of the substrate, the basic unit of the pattern is called “pixel”, and a macro pattern is formed by combining these “pixels” in a block shape. In the simplest case, such a pixel is arranged on a lattice point having a period of a pixel size defined by a virtually provided mesh, and a pattern is formed by a high refractive index portion and a low refractive index portion. It is formed. However, these pixels are not necessarily arranged on the lattice points, and may be intentionally shifted from the lattice points in order to obtain a desired refractive index distribution.

  In the case of a so-called step index type optical circuit, since the value that the refractive index can take is limited, it is not obvious whether or not the optical circuit can be designed based on the above formula (1). However, even if the values that the refractive index can take are limited, it is possible to globally adjust the phase of light by repeatedly adjusting the local refractive index. Therefore, assuming a step-like refractive index distribution having an upper limit value of the refractive index of the dielectric constituting the optical circuit and a finite number of refractive index values reaching the upper limit value, and using these refractive indexes as limit values, the optical circuit It is possible to design an optical circuit by calculating the refractive index distribution of the optical circuit. In this embodiment, an optical circuit is designed based on such an idea.

  In the present embodiment, this is an optical waveguide having a structure similar to that of a step index type planar optical waveguide, and having a structure in which the core of the waveguide is patterned in a dot shape in the optical circuit design region. The wavelength division filter of 1.31μm and 1.55μm was designed to adapt to the waveguide.

  In this embodiment, a quartz optical waveguide is assumed. In calculating the spatial distribution of the refractive index, only two types of refractive index are considered: the refractive index of the core (high refractive index portion) and the refractive index of the cladding (low refractive index portion). The refractive index distribution obtained by distributing the refractive index within the optical circuit design region was calculated.

Further, in the algorithm for calculating the refractive index distribution described with reference to FIG. 3, the refractive index value as a parameter can take any value, but here, the value v _q given by the following equation (9): From this v _q value, the refractive index was determined by the following equations (10) and (11).
v _q (z, x) = v _q-1 (z, x) −αΣ _j Im [φ ^j (z, x, {n _q-1 }) ^* · ψ ^j (z, x, {n _q-1 })] ... (9)
When v _q (z, x)> (n _core + n _clad ) / 2, n _q (z, x) = n _core (10)
When v _q (z, x) <(n _core + n _clad ) / 2, n _q (z, x) = n _cladd (11)
Here, n _core is a refractive index corresponding to the core, and n _clad is a refractive index corresponding to the _clad . Therefore, the refractive index distribution in the optical circuit design region is obtained by spatially distributing these two types of refractive indexes. In general, the relationship n _core > n _clad is established. By such calculation, an optical waveguide capable of sufficiently obtaining a desired light output can be designed as will be described below. Further, for simplification, the refractive index (n _core ) corresponding to the core pattern of the above two types of refractive indexes was used as the effective refractive index, and the calculation was performed as one dimension in the traveling direction and one dimension in the lateral direction.

FIG. 5A and FIG. 5B are diagrams for explaining the setting of the optical circuit design in the present embodiment. First, by adjusting the refractive index distribution by outputting the polarization multiplexed light input from the input port 3-1 from the output port 3-2, as shown in FIG. A pair of an incident field ψ ¹ (x) and an outgoing field φ ¹ (x) (that is, j = 1 in the above symbol) and an incident field ψ ² (x) having a wavelength of 1.55 μm as shown in FIG. And the output field φ ² (x) (that is, j = 2 in the above symbol). The field is defined for the entire area of the incident surface 2-1 and the output surface 2-2, but in this drawing, only the portion where the field intensity is concentrated is illustrated for easy understanding. Such a pair of incident / exit fields {ψ ^j (x), φ ^j (x)} is hereinafter referred to as an input / output pair.

  FIGS. 6A and 6B are diagrams for explaining the refractive index distribution (FIG. 6A) and the transmission spectrum (FIG. 6B) according to this example. An optical circuit having the refractive index distribution shown in FIG. 6A is obtained by repeating the calculation of the refractive index according to the above algorithm about 200 times. Here, the black portion (1-11) in the optical circuit design region (1-1) in the figure is a high refractive index portion (dielectric multiple scattering portion) corresponding to the core, and the portions other than the black portion are cladding. This is a low refractive index portion corresponding to. As the refractive index of the clad, the refractive index of quartz glass is assumed, and the refractive index of the core is assumed to have a value higher by 1.5% than that of quartz glass. The size of the optical circuit is 300 μm in length and 140 μm in width.

  The mesh used in the calculation for obtaining the refractive index distribution is 140 × 300 (= 42000). Accordingly, since the number of parameters of the refractive index distribution is 42000, it is necessary to optimize these parameters. If the parameters are optimized by simply applying the steepest descent method and obtaining a numerical derivative for each of these parameters, the propagation of 42000 light is needed to perform the calculation for one step. It is necessary to calculate. On the other hand, in this embodiment, it is only necessary to calculate the propagation of light twice, so that an optical circuit can be designed with a short time calculation that does not impede practical use.

  The transmission spectrum of the optical circuit designed in this way is as shown in FIG. 6B. Light having a wavelength of 1.31 μm is output from the output port a, while light having a wavelength of 1.55 μm is output from the output port b. Show the characteristics. That is, it can be seen that a wavelength demultiplexer is formed. The light input direction and output direction shown in FIGS. 5 (a) and 5 (b) are reversed, and each of the two wavelengths of light is input from the output ports a and b, and these lights are combined. Since it can be output from the incident surface 2-1, it can be operated as a multiplexer. That is, it can be seen that the optical circuit described in the present embodiment has an effect as a multiplexer / demultiplexer depending on the wavelength of light.

  By the way, in order to secure the function as an optical circuit, it is necessary that light propagating in the optical circuit is sufficiently confined in the optical circuit. In the refractive index distribution shown in FIG. 6A, the core that is the high refractive index portion is distributed in the form of dots in the optical circuit design region, and light confinement in the thickness direction of the substrate becomes insufficient. Is concerned.

  Therefore, the high refractive index portion is composed of two high refractive index portions (a first high refractive index portion and a second high refractive index portion), and the high refractive index portion is sandwiched from above and below by the low refractive index portion. Assuming an optical circuit with the above structure, the refractive index distribution was obtained.

  FIG. 7A is a conceptual cross-sectional view of an optical circuit having a planar lightwave circuit-like refractive index distribution and capable of optical confinement in the direction perpendicular to the substrate. The high refractive index portion 1-11 of this optical circuit is shown in FIG. Is composed of two high refractive index portions (a first high refractive index portion 1-11a and a second high refractive index portion 1-11b), and the second high refractive index portion 1-11b is a first high refractive index portion 1-11b. The refractive index is higher than that of the refractive index portion 1-11a. The high refractive index portion 1-11 is sandwiched between the upper and lower low refractive index portions 1-12 to form an optical circuit. In this optical circuit, the second high refractive index portion 1-11b functions as a so-called “core”. The first high refractive index portion 1-11a transmits light propagating in the core to the substrate. It is for confining in the thickness direction (vertical direction). In this figure, the relative refractive index difference between the low refractive index portion 1-12 and the first high refractive index portion 1-11a, and the first high refractive index portion 1-11a and the second high refractive index portion. The calculation is performed assuming that the relative refractive index difference of 1-11b is 1.5%. The effective refractive index profile in the vertical direction of the optical circuit is shown on the right side of FIG. 7A, and the effective refractive index profile in the horizontal direction in the high refractive index portion 1-11 is shown on the lower side.

  According to the optical circuit having such a structure, optical confinement in the substrate thickness direction is performed by the second high refractive index portion 1-11a provided around the second high refractive index portion 1-11b that is the core. It can be easily realized.

  In providing an optical input / output unit in such an optical circuit, light is guided by the first high refractive index portion 1-11a (FIG. 7B) and the second high refractive index portion 1-11b. It can be considered that light is guided (FIG. 7C). Further, by optimizing the shape of each of the first high refractive index portion 1-11a and the second high refractive index portion 1-11b, or by combining them, the field diameter is adjusted and the optical fiber can be adjusted. The optical coupling can be optimized.

  Since the output field is calculated as a complex value, the phase of the output field can be obtained. Therefore, for example, when the phase of the light is also required, such as when an external resonator laser is manufactured by combining the above-described optical circuit and a semiconductor optical amplifier with a non-reflective coating, The optical field calculation procedure is applicable.

  Although the beam propagation method has been used for the calculation of the optical field described so far, the time domain difference method may be used when the memory capacity of the computer used for the calculation is sufficient. In general, since the beam propagation method calculates the light output in a linear direction, the position of the output port is limited. For example, in the case of the present embodiment, the opposite surface of the incident surface is the exit surface. On the other hand, if the time-domain difference method is used for calculation, the position of the output port can be freely selected. Therefore, it is possible to easily design an optical circuit or the like having an optical path having a sharp bend. it can. The same applies to the following embodiments. Further, when such a circuit is realized by a combination of directional couplers, an optical circuit portion of several hundred μm is required only for the directional coupler portion. An optical circuit configuration having a size of about 1 / min can be achieved, and miniaturization can be achieved.

  The optical circuit of the present embodiment is a 1.31 μm / 1.55 μm wavelength filter using Rayleigh scattering having low directivity and high wavelength dependency.

  Scattering by an object having a size of about one-tenth or less of the wavelength of light is generally called Rayleigh scattering and has low directivity and high wavelength dependency (proportional to 1/4 of the wavelength). It is done. In this embodiment, the pixel size of the high refractive index portion of the holographic wave transmission medium constituting the optical circuit is set to a size not more than the length of the wavelength component of the light propagating in the optical circuit in the direction perpendicular to the propagation direction. As a result, a refractive index distribution (dielectric distribution) that satisfies the conditions for generating Rayleigh scattering is realized, and a sufficiently large light controllability is obtained.

  FIG. 8 is a diagram for explaining a configuration example of the 1.31 μm / 1.55 μm wavelength filter of this embodiment. FIG. 8A is a plan view of this optical circuit, and FIG. 8B is a high refractive index. It is a figure for demonstrating the mode of arrangement | positioning of the pixel of a part, and the pixel of a low refractive index part.

  The black part in FIG. 8A means a high refractive index part. Lights having wavelengths of 1.31 μm and 1.55 μm are input from the input port 3-1, and light having a wavelength of 1.31 μm is output from the output port a. Light of 1.55 μm is output from the output port b. The optical circuit has a length in the light propagation direction of 1000 μm and a width of 160 μm. As shown in FIG. 8B, the refractive index distribution of this optical circuit is such that each pixel has a pixel size W and is a high refractive index portion pixel (shaded portion) and a low refractive index portion (white portion). Is determined.

  The field radius w of light formed in a waveguide structure (that is, an optical confinement structure) configured by arranging a large number of dielectrics having a pixel size W is a variation by one-dimensional Gaussian approximation. By law,

The following conditions are required. Here, k ₀ is the wave number in vacuum, n is the refractive index, and Δ is the relative refractive index difference of the pixel portion.

  On the other hand, a dielectric pixel constituting this optical circuit is considered as a light scattering point, and a field radius w by this pixel is defined as an opening radius w (FIG. 9). At this time, if the diffraction angle (far viewing angle) from this opening is θ, the wave number λ in vacuum is used,

(FIG. 9). Wave number in the direction perpendicular to the light propagation direction in the medium

And wave number in the propagation direction

And the ratio

Is obtained. here,

Is the wavelength of the light propagation direction component,

Is the wavelength of the direction component perpendicular to the propagation direction.

  Here, assuming that most of the wave number of light (equivalent to momentum) is concentrated in the propagation direction,

And

Is obtained. As a condition of Rayleigh scattering,

Because

Furthermore, from equation (15),

Substituting into equation (12) as

Get the condition.

  The parenthesis part (coefficients other than λ) in the right side of Expression (16) is, for example, a silica-based optical waveguide (n = 1.5, Δ = 0.01) or a semiconductor waveguide (n = 3.5, Δ = 0.05) but about 1 so

Then, the Rayleigh scattering condition is satisfied.

  FIGS. 10A and 10B show pixel size dependence of transmission loss characteristics and crosstalk characteristics when an optical circuit of a wavelength filter of 1.31 μm / 1.55 μm is configured by changing the pixel size W as a parameter. (FIG. 10B) is a diagram for explaining the optical circuit in which the length in the light propagation direction is 600 μm, and the distance between the output port a and the output port b is 30 μm (FIG. 10A). .

  From the result shown in FIG. 10 (b), when the pixel size W is about the wavelength level (shown in FIG. 10 (b)) or less, crosstalk is suppressed very efficiently and excellent transmission loss characteristics are obtained. It can be seen that it is effective to set the pixel size W so as to satisfy the Rayleigh scattering condition as in this embodiment.

  The optical circuit of the present embodiment is an optical circuit that can suppress light loss by suppressing light emission in the substrate height direction (direction perpendicular to the substrate surface).

  In a pixel pattern obtained by binarizing the refractive index distribution of an optical circuit with a high refractive index portion and a low refractive index portion, if the low refractive index portion is considered to be a hole (void) in the high refractive index portion, the high refractive index The low refractive index portion that exists between the pixels corresponding to the index portion corresponds to a radiation portion (gap between the waveguides) to the clad portion in the optical waveguide. When designing an optical circuit, light in the substrate lateral direction (direction parallel to the substrate surface) can be controlled by multiple scattering. However, in the case of a planar optical circuit, light leaking in the height direction of the substrate is usually emitted as it is and causes (light) loss.

  FIG. 11 is a diagram for explaining light confinement levels in the substrate vertical direction and the substrate horizontal direction in a planar optical circuit. A solid line indicates light in the substrate vertical direction, and a broken line indicates light in the substrate horizontal direction. As shown in this figure, the light spreading in the horizontal direction of the substrate is confined in the optical circuit while repeating reflection and scattering in the optical circuit, but the light in the vertical direction of the substrate is directly emitted outside the optical circuit. Is done.

  FIG. 12 is a diagram for explaining the field radius dependence of the radiation loss (coupling loss) per point when the minimum pixel unit is 3 μm square. As shown in this figure, the light radiated in the optical circuit greatly depends on the field diameter of light, and generally has a large radiation angle due to the influence of diffraction when the field diameter is small. Conversely, by increasing the field diameter, light emission can be suppressed, and loss as an optical circuit can be suppressed. Assuming a circuit size of about several thousand μm, several hundred scattering points may be generated. Therefore, in order to suppress the loss of the entire optical circuit, the light loss at each scattering point is sufficiently low. There is a need.

  A field of light propagating in a single mode optical waveguide having a weak optical confinement effect such as a silica-based optical waveguide can have a Gaussian distribution with a good approximation. The light field can be approximated by F (x, y) = f (x) g (y) obtained by variable separation of the light amplitude distribution F (x, y) in the wavefront. Here, the substrate plane direction is x, the substrate vertical direction is y, and the coordinates are represented by (x, y). That is, assuming a Gaussian distribution as the light field, the variables are separated into functions in the x and y directions.

  Here, there is no problem because f (x), which is a function in the horizontal direction of the substrate, is controlled by multiple scattering and can be confined in the optical circuit. On the other hand, for g (y), which is a function in the direction perpendicular to the substrate, the emitted light deviates from the high refractive index region and becomes a radiation loss. Therefore, in order to suppress the light loss at each scattering point sufficiently low, a method for reducing the radiation diffraction loss due to the g (y) component may be considered.

  Assuming a Gaussian distribution for g (y),

Can be written. Here, w is a field radius. It is well known that the field radius w can be controlled mainly by the size and refractive index of the core. Therefore, on the premise that the controllability of the parameter w is high, conditions necessary for sufficiently suppressing the light loss at each scattering point are obtained.

Assuming the case where the high refractive index portions shown as “pixels” in FIG. 11B are divided and arranged, a gap of the high refractive index portions is generated between the high refractive index portions. It is assumed that a field of light having a Gaussian distribution is emitted outside the waveguide due to the existence of this gap. In this case, although the Gaussian distribution of the shape of the optical field is maintained, the field radius changes and the wavefront is curved. The field distribution in this state is formally expressed as g (y, z). Here, z is a parameter given as an average value of the distance z _L of the radiation part.

  Of the optical field radiated to the outside of the waveguide by the gap portion, the amount of coupling to the high refractive index portion is given by the overlap integral of the following equation.

Here, λ is the wavelength of light, and n is the refractive index of the high refractive index portion.

Here, it is assumed that the height of the high refractive index portion of the optical circuit shown in FIG. 11 is a, and that the field diameter is substantially the same as this a and w = a / 2. Also, assuming that the average value of the distance of the radiating part is z _L = qa by an appropriate coefficient q, the expected value <η> of loss per gap is

It is represented by The value of this equation (19) can be normalized by (λq / na). Since the light propagating in the optical circuit of the present invention is generally scattered about 100 times, when a loss of about 1/100 dB is expected,

If the above condition is satisfied, the light loss at each scattering point can be suppressed sufficiently low.

  In FIG. 12, when the gap width is set to 3 μm, q = 1, λ = 1.55 μm, and n = 1.45, the field radius is changed using the thickness a of the high refractive index portion as a parameter, and the field radius of the coupling loss is changed. This is the result of the dependency. A sufficiently low loss was obtained at a position corresponding to a field radius of 3 μm (about 6 μm in terms of the film thickness a of the high refractive part).

  As described in the second embodiment, the pixel size in the in-plane direction of the optical circuit has a great influence on the light propagating in the optical circuit. In this embodiment, efficient light control can be performed by arranging the pixels so as to be inclined with respect to the light propagation direction.

  FIG. 13A is a diagram for explaining an optical circuit in which pixels are arranged in the light propagation direction, and FIG. 13B is a diagram for explaining an optical circuit in which pixels are inclined with respect to the light propagation direction. FIG. As shown in FIG. 13B, when the pixels are arranged so as to be inclined with respect to the light propagation direction, a lattice plane having a period shorter than the pixel size is formed in the direction perpendicular to the light propagation direction. Light control is possible. Here, if the inclination angle is shallower (or deeper) than 45 degrees, it is possible to form a grating surface with a shorter period, but the interval between the center positions of the reflecting surfaces constituting the grating surface is increased, and reflection is performed. The function as a surface is reduced. In particular, since the refractive index of this circuit changes with a size of several pixels, about 45 degrees is suitable for functioning as a Bragg reflecting surface at such a distance.

  In the embodiments described so far, the pixels of the high refractive index portion (or low refractive index portion) that define the refractive index distribution are arranged on the lattice points defined by the virtual mesh, and the refractive index distribution Since the size of each pixel is limited so as to be easily patterned, the lattice point interval cannot be made smaller than each pixel size. For this reason, optical circuit characteristics may be deteriorated due to digitizing errors relating to pixels and scattering of propagating light at pixel edges. Furthermore, the regular periodicity of the refractive index in the direction (y direction: transverse to the light propagation direction) perpendicular to the light propagation direction (x direction) in the waveguide plane (in the xy plane) Depending on the pixel size, the controllability of light is also limited in order to generate a spatial cutoff frequency. In the optical circuit according to the present embodiment, only the minimum unit of the pixel size and the minimum unit of the pixel interval are set as a condition in the lateral direction with respect to the light propagation direction, so that the high refractive index portion (or the low refractive index portion) is arbitrarily set. The refractive index distribution is formed by arranging the pixels of the index part.

  FIG. 14A is a diagram for explaining an optical circuit in which pixels are arranged at lattice points defined by a virtual mesh to form a refractive index distribution, and FIG. 14B is a diagram illustrating positions of such lattice points. It is a figure for demonstrating the optical circuit which performed the pixel arrangement | positioning in the y direction irrespective of 1 and formed the refractive index distribution. In the waveguide shown in FIG. 14A, each pixel is arranged at a lattice point position defined by a virtual mesh, whereas in the present embodiment shown in FIG. In the waveguide, each pixel is arranged at a lattice point position defined by a virtual mesh in the light propagation direction (x direction), but in the lateral direction (y direction) with respect to the light propagation direction. (Not necessarily) each pixel is not arranged at a lattice point position defined by a virtual mesh, and a pixel of a high refractive index portion or a low refractive index portion is arranged at an arbitrary position.

  In this embodiment, the refractive index distribution determined by the pixel arrangement is calculated with an interval sufficiently smaller than the minimum pixel size (grating point interval) as the minimum unit of the arrangement parameter. When the interval between pixels is larger than this minimum unit, an appropriate boundary is defined, and the value of the high refractive index portion or the low refractive index portion is set to each pixel so that the refractive index value changes at the boundary. On the other hand, if the interval between the pixels is smaller than the minimum unit, the average of the refractive index is calculated within the range of the region, and the value of the high refractive index portion or the low refractive index portion is the closest. We are going to adopt it.

  FIGS. 15A and 15B show actual optical circuits (1.31 μm and 1.55 μm wavelength filters manufactured corresponding to the pixel arrangements of FIGS. 14A and 14B, respectively. ) Is a diagram for explaining the refractive index distribution, and the left side of these figures is an overall image of the circuit, and the right side is an enlarged image of a part of the circuit. In these figures, the white portion is the high refractive index portion, the black portion is the low refractive index portion, and the relative refractive index difference is 1.5%. The optical circuit has a circuit length of 1200 μm and a minimum pattern rule (minimum unit of arrangement parameter) of 3 μm.

  Comparing FIG. 15A and FIG. 15B, it can be seen that the refractive index pattern is smoothed in the optical circuit of this example. The optical circuit with the refractive index profile shown in FIG. 15A has a loss of 2 dB, whereas the optical circuit with the refractive index profile in FIG. 15B has a loss improvement of about 0.5 dB. Admitted. This fact indicates that, by smoothing the refractive index distribution as in the optical circuit of the present embodiment, loss due to strong scattering, which cannot be controlled by the optical circuit having the refractive index distribution as shown in FIG. This is due to the fact that the controllability of propagating light is improved. Specifically, in the optical circuit as shown in FIG. 15A, for example, since the pixel structure is a rectangular pixel structure having sides substantially perpendicular to the wavefront traveling direction, As the light is diffracted, intense interference occurs and the design accuracy of the optical circuit is lowered. In addition, light having a large wave number is generated, and light control cannot be performed with a refractive index distribution having a small refractive index difference. On the other hand, by using an optical circuit having a smooth refractive index distribution like the optical circuit of this embodiment, it is possible to suppress intense interference and generation of light with a large wave number in the optical circuit. It is an effect by becoming.

  In the optical circuit of Example 3, as described with reference to FIGS. 11 and 12, the thickness a of the high refractive index layer is increased in order to suppress light emission from the high refractive index portion to the low refractive index portion. However, when the low refractive index portion is long and continuous (that is, when the gap interval is long), a large loss is generated in principle. Therefore, in the optical circuit of this embodiment, the optical confinement in the direction perpendicular to the substrate is made possible even in the low refractive index portion, and an optical circuit structure is provided which has a low loss even when the gap interval is long.

FIG. 16 is a diagram for explaining the manufacturing procedure of the optical circuit of the present embodiment. First, in the same manner as the manufacturing of a normal optical waveguide, for example, a clad portion (low refractive index portion) which is a lower portion of a core is formed on a Si substrate. The first high refractive index layer corresponding to the core is deposited on the low refractive index portion (FIG. 16A). Here, when the refractive index of the low refractive index portion is n, the refractive index of the first high refractive index layer is n (1 + Δ ₂ ).

  Next, a part of the first high refractive index layer is patterned by etching (FIG. 16B). The pattern at this time is a pattern corresponding to the high refractive index portion and the low refractive index portion of the optical circuit, and the portion where the first high refractive index layer is left by etching becomes the high refractive index portion of the optical circuit. If the first high refractive index layer is left so as to have a waveguide pattern, a waveguide structure can be formed in the remaining portion. In this patterning step, it is applied to the surface portion of the low refractive index portion directly under the first high refractive index layer to be removed by etching, and will be described later so that the low refractive index portion of the portion has a desired thickness. The etching is stopped at an appropriate height.

Further, a second high refractive index layer having a constant film thickness is deposited, and patterning is performed on the second high refractive index layer as necessary, and a waveguide is formed using the second high refractive index layer. May be executed. The refractive index of the second high refractive index layer is n (1 + Δ ₁ ), and n (1 + Δ ₂ )> n (1 + Δ ₁ ) compared to the refractive index n (1 + Δ ₂ ) of the first high refractive index layer. (That is, Δ ₂ > Δ ₁ ). Finally, an upper clad (not shown) is deposited to fill the first and second high refractive index layers.

The optical circuit thus obtained can have an optical circuit structure with low loss and no increase in loss even by an optical circuit including many low refractive index portions by adjusting parameters described later. Hereinafter, using the relative refractive index difference of these high refractive index layers, the first high refractive index layer is referred to as “high refractive index layer Δ ₂ ”, and the second high refractive index layer is referred to as “high refractive index layer Δ _1. ". Hereinafter, a parameter setting method will be described.

  As already described in the third embodiment, in the optical circuit, light can be propagated without loss if the field shape at each interface of the pixel is the same. In the following, description will be given focusing on only the field distribution of light in the direction perpendicular to the substrate.

As shown in FIG. 17, the region where the high refractive index layer Δ ₂ is removed by etching is referred to as “low refractive index region”, and the region where the high refractive index layer Δ ₂ is left without etching is referred to as “high refractive index region”. In other words, in the high refractive index region, the thickness of the portion corresponding to the “waveguide core” corresponding to the sum of the high refractive index layer Δ ₁ and the high refractive index layer Δ ₂ is smaller than that in the low refractive index region. It is thick. The optical field propagating in the waveguide can suppress the kinetic energy when it is distributed and propagated throughout the waveguide. Therefore, the above-described high refractive index region has the effect of reducing the kinetic energy by spreading the optical field distribution over the entire waveguide. On the other hand, paying attention to the potential energy of the optical field, the high refractive index layer Δ ₂ and the high refractive index layer Δ ₁ have a higher refractive index than the high refractive index layer Δ _{2. Since the} potential energy is lower when concentrated on ₂ , there is a tendency to concentrate on the high refractive index layer Δ2 as much as possible. Thus, the action of widely distributing the optical field over the entire waveguide competes with the action of concentrating on a part of the waveguide. Moreover, the action to try to concentrate on the high refractive index layer delta ₂ serves the central position of the light field to shift the substrate side. Utilizing the property resulting from the energy minimization of the light field, the light field in the high refractive index region has the same field radius and the same center position as the light field in the low refractive index region. Thus, the parameters may be adjusted.

FIG. 18 is a diagram for explaining a calculation example for parameter adjustment in the present embodiment, and the parameters in this case include n, Δ ₁ and Δ ₂ described above, as shown in FIG. thickness W ₁ of the high refractive index layer delta _1, the thickness W ₂ of the high refractive index layer delta _2, the distance x _c from the layer upper surface of the high refractive index layer delta ₂ to the field center position of the low refractive index _region, the field radius w, the wavelength λ of light (that is, wave number k ₀ = 2π / λ). Usually, since the refractive index n and the wavelength λ are determined at the time of circuit design, the remaining six parameters are determined. Here, these parameters are obtained using a variational method. For convenience, the subscripts fill and gap are used to denote the wave function in the high refractive index region as u _fill , the wave function in the low refractive index region as u _gap , and the like.

The wave function u _fill in the high refractive index region is given by the following equation (21):

The wave function u _fill in the high refractive index region is given by the following equation (22).

  Fresnel equation obtained by paraxial wave approximation of wave equation

For the field radius w and the high refractive index layer Δ ₂ , the variation equation for determining the distance x _c from the upper surface of the high refractive index layer Δ ₂ to the field center position (center position) of the low refractive index region is set as follows and the calculation proceeds. Finally, three equations are derived as in the following equation (27).

The result is just the field radius w are the same, corresponds to the condition that there is an appropriate center position x _c. Therefore, as a result, the system of the optical field is determined by giving the remaining three parameters.

FIG. 19 is a diagram for explaining the characteristics (wavelength dependence of transmission loss) of the 1.31 / 1.55 μm WDM circuit which is the optical circuit of the present embodiment. Here, Δ ₁ = 1.5%, Δ ₂ = 2%, and W ₁ = 5.5 μm are set. The ratio of the low refractive index region to the total circuit area was about 50%, and the circuit length was 1200 μm. An optical circuit including a relatively large number of interfaces between a high refractive index region and a low refractive index region and a continuous low refractive index region. As shown in FIG. 19, a good transmission loss of about 2 dB is obtained. was gotten.

  In manufacturing the optical circuit of the present invention, in addition to the usual process that has been generally used in the past, the technique of changing the refractive index and structure by light irradiation is a recently developed technique. Can be employed as part of the optical circuit manufacturing process. In this embodiment, several embodiments of manufacturing an optical circuit using such light irradiation will be described. According to the present embodiment, the number of manufacturing steps can be greatly reduced as compared with a commonly used process, and the desired structure can be easily manufactured.

(Example 7-1)
FIG. 20 is a diagram for explaining the manufacturing method of the optical circuit according to the first embodiment of the present embodiment. First, the lower clad layer 22 and the core layer are formed on the silicon substrate 21 by the flame deposition method (FHD method). 23 and the upper clad layer 24 were sequentially formed (FIG. 20A). As the lower clad layer 22 and the upper clad layer 24, a material obtained by doping a base material based on quartz glass (SiO ₂ ) with an oxide such as B or P is used. As the core layer 23, a material doped with an oxide of Ge in addition to an impurity of an oxide such as B or P is used. By such material selection, the core layer 24 is set to have a higher refractive index than the lower cladding layer 22 and the upper cladding layer 24. The thickness of the lower cladding layer 22 was 20 μm, the thickness of the core layer 23 was 7 μm, and the thickness of the upper cladding layer 24 was 10 μm. The upper clad layer 24 is designed to have a slightly thinner thickness than the structure of a normal optical circuit in order to suppress diffraction spread when UV light is irradiated.

  Next, after forming a silicon thin film 25 as a light-shielding film for light irradiation as shown in FIG. 20B on the upper clad layer 24, a pattern is formed with a photosensitive resist, and silicon is formed by a dry etching process. Pattern formation was performed by partially removing the film (FIG. 20B). The photosensitive resist is removed after the silicon pattern is formed. In addition, when forming this light-shielding mask pattern, the process dependency and the spread of irradiation light are taken into consideration so that a refractive index pattern necessary for obtaining desired circuit characteristics is finally obtained. A slight correction is added to the design value of the core shape obtained without considering the dependency and the like.

  Next, in order to improve photosensitivity, hydrogen diffusion into the sample was performed in a high-pressure hydrogen atmosphere. Specifically, the sample was placed in a sealed container and left in a hydrogen atmosphere of 150 atm at room temperature for one week.

  Following this hydrogen diffusion, the ArF excimer laser was used to irradiate UV light having a wavelength of 193 nm, thereby changing the refractive index of the core layer 23 so as to have a refractive index larger than that before irradiation. A region (23 ′) indicated by oblique lines in FIG. 20B is a region in which a refractive index change is caused by laser irradiation. The irradiation power at this time is 120 mJ, and the irradiation time is 10 minutes. After removing the light-shielding film by etching after light irradiation, heat treatment is performed to remove hydrogen diffused in the sample and to stabilize the refractive index by eliminating the unstable state of the glass caused by light irradiation. It was.

  By such a process, the refractive index of the core layer in the region where the light shielding mask 25 is not formed is selectively changed so that the refractive index is different from the refractive index of the core layer in the region where the light shielding mask 25 is formed. it can. The degree of such refractive index change is estimated to be about 0.3% from the measurement of a wide irradiation region set as a reference.

  A (1 × 4) branch circuit was manufactured by the manufacturing process described above. Although the loss characteristic was about 2 dB larger than the characteristic expected from the circuit design, the basic branching operation was confirmed. The reason why the loss characteristic deviates from the design value is considered to be that the amount of change in the refractive index is different from the design value.

  The manufacturing method described above is merely an example. It is an essential element that the manufacturing process includes the formation process of the lower cladding layer 22, the core layer 23, and the upper cladding layer 24, the formation process of the light shielding mask layer 25, and the light irradiation process. It goes without saying that various changes can be made for each process including the process. For example, the lower clad layer 22, the core layer 23, and the upper clad layer 24 can be formed by a film forming method such as a CVD method, a sputtering method, or a spin coating method. In the example shown in FIG. 20, each layer is made of a material having a single composition. However, a single layer of a multilayer structure obtained by stacking and stacking a plurality of glasses having different compositions. It doesn't matter if you treat it as

  As the light-shielding mask layer 25, another material other than silicon may be used as long as the material has an effect of shielding the light to be irradiated. In addition, as an example of a method for forming a light-shielding mask, a method of forming the mask on the upper clad 24 has been described. However, a mask is formed on another glass substrate, and the glass substrate is adhered to the sample and irradiated with light. The same result can be obtained by. Furthermore, as a technique for improving the photosensitivity, in addition to a hydrogen addition method under a high pressure, a technique such as hydrogen treatment at a high temperature for a short time or addition of deuterium is also possible. In addition to 193 nm UV excimer laser light, light from other lasers such as KrF excimer laser and XeF excimer laser, short pulse visible light laser light, etc. can be used as the irradiation light. A circuit structure can be produced.

(Example 7-2)
FIG. 21 is a diagram for explaining the method of manufacturing the optical circuit according to the second mode of this example. Since this embodiment is substantially the same as the first embodiment (Example 7-1), only the differences will be described. In the first embodiment, since the lower clad layer 22 and the upper clad layer 24 are not doped with Ge oxide, the refractive index change in the upper clad layer 24 and the lower clad layer 22 when irradiated with light is as follows. No or almost negligible. On the other hand, in the present embodiment, the upper cladding layer 24 and the lower cladding layer 22 are formed with a Ge-doped glass composition so that these layers also become photosensitive layers like the core layer 23, and light It is supposed that a refractive index change due to irradiation is induced.

  As in the first embodiment, a lower clad layer 22, a core layer 23, and an upper clad layer 24 are sequentially formed (FIG. 21A), and silicon as a light-shielding film for light irradiation is formed on the upper clad layer 24. A thin film 25 is formed and patterned (FIG. 21B). When a region not masked by the light shielding mask 25 is irradiated with light, not only the core layer 23 but also the upper cladding layer 24 and the lower cladding layer 22 are exposed, and a refractive index change corresponding to the Ge doping amount occurs. A region (23 ′) indicated by oblique lines in FIG. 21B is a region in which a refractive index change is caused by laser irradiation. As a result of producing a (1 × 4) branch circuit by the above-described manufacturing process, it was confirmed that a loss characteristic superior to that of the branch circuit of the first embodiment was obtained.

  That is, by selecting the composition so that both the core layer 23 and the clad layer (22 and 24) are photosensitive layers, the light propagation direction in the high refractive index region and the low refractive index region formed by light irradiation. The difference in field distribution is reduced, and the loss characteristics of the element can be improved.

(Example 7-3)
FIG. 22 is a diagram for explaining the manufacturing method of the optical circuit according to the third mode of the present embodiment. This embodiment corresponds to the combination of the first and second embodiments (Example 7-1 and Example 7-2). Therefore, only the process parts added to these embodiments will be described below.

  In this embodiment, a local refractive index change is caused by UV light irradiation using a phase mask, and a (1 × 2) branch circuit as shown in FIG. The UV light irradiation method using a phase mask is used in the manufacture of fiber gratings and the like, and a periodic and fine structure such as a grating structure can be produced relatively easily and accurately. There is an advantage. In addition, by using a plurality of phase masks, even a somewhat complicated structure can be manufactured relatively easily. However, if the structure is complicated as in the optical circuit of the present invention, it is difficult to achieve a desired refractive index distribution completely only by UV light irradiation using a phase mask. It is necessary to use it together with the manufacturing method described in the embodiment.

  As in the first embodiment, a lower cladding layer 22, a core layer 23, and an upper cladding layer 24 are sequentially formed (FIG. 22A), and a patterned light shielding pattern for light irradiation is formed on the upper cladding layer 24. A mask 25 was formed and UV light irradiation was performed (FIG. 22B). A region (23 ′) indicated by hatching in FIG. 22B is a region where a refractive index change is caused by UV light irradiation. After the light shielding mask 25 is removed, a grating filter is formed in a partial region near the output port as shown in FIG. Specifically, a patterned phase mask 26 as shown in FIG. 22 (c) is formed in the vicinity of the output port in the region where the grating filter is to be formed (corresponding to 27 in FIG. 22 (d)). UV irradiation is performed through the phase mask 26 to expose the desired region 23 ″ in the core layer 23 to form a grating filter. After this step, heat treatment is performed in the same manner as in Example 7-1 to remove hydrogen diffused in the sample and to stabilize the refractive index by eliminating the unstable state of the glass caused by light irradiation. I planned.

  In the output port in which the grating is additionally formed (the output port in the region indicated by 27 in FIG. 22D), it has been confirmed that the transmission wavelength characteristic is changed by the filter operation. In this example, the UV light irradiation process corresponding to FIG. 22C is interrupted during the manufacturing process of Example 7-1 to simplify the manufacturing process. After completing all the steps, the UV light irradiation step corresponding to FIG. 22C may be performed.

(Example 7-4)
FIG. 23 is a diagram for explaining a method of manufacturing the optical circuit according to the fourth mode of this example. Also in this embodiment, the lower clad layer is formed on the silicon substrate 21 as in Example 7-1. 22, the core layer 23, and the upper cladding layer 24 were sequentially formed by a flame deposition method (FHD method) (FIG. 23A).

  Subsequently, the wafer on which each of the above layers is formed is fixed on a XYZ direction triaxial movable stage (not shown), and the laser light 28 is condensed near the core by the lens 29 to perform light irradiation. The refractive index was changed (FIG. 23 (b)). A region (23 ′) indicated by hatching in FIG. 23B is a region where the refractive index change is caused by laser irradiation. As shown in this figure, the size of the region where the refractive index is changed is not constant, and the size of each region can be determined so that a desired refractive index distribution is realized.

  The extent of these regions in the lateral direction (XY direction) is determined by the amount of drive and the amount of laser power in the XY plane of the stage during laser light irradiation. On the other hand, the spread (thickness) in the vertical direction (Z direction) is determined by controlling the condensing state of the laser light 28 by controlling the laser power amount and the driving amount of the stage in the Z direction, and is the same as the core layer 23. It is possible to have a thickness, or to make the thickness thinner or thicker than the core layer 23. Further, the amount of change in the refractive index of the irradiated region is mainly controlled by controlling the laser power amount. In this embodiment, a femtosecond pulse laser having a wavelength of 775 nm is used as the laser light, and the pulse width is 150 fs. In this way, a (1 × 4) branch circuit was manufactured and the basic branch operation was confirmed.

  When the laser beam is focused and drawn by the above-described method to realize the spatial distribution of the refractive index, there is no need to perform mask formation or the like in advance. Since it is necessary to perform irradiation, it tends to take time to fabricate an optical circuit. For this reason, it is effective to use this method in combination with the refractive index distribution forming method by batch drawing described in Example 7-1 or Example 7-2.

  Further, the laser light is not limited to the femtosecond laser, and UV excimer laser light, CW UV laser light, or the like can also be used. Also in this case, as described in Example 7-1, it is effective to perform sensitization to UV light using hydrogenation or the like in order to obtain a large refractive index change.

  Furthermore, in this embodiment, the three-layer structure of the lower clad layer 22, the core layer 23, and the upper clad layer 24 is used, but this method uses a change in refractive index near the condensing point of the laser beam. Therefore, it can be applied to a single composition material such as bulk glass.

(Example 7-5)
An example in which an optical circuit is manufactured by the method described in Examples 7-1 and 7-2 will be described.

  24A and 24B are waveguide cross-sectional views for explaining the state of the refractive index distribution of the manufactured optical circuit. FIG. 24A shows the refractive index distribution before light irradiation, and FIG. 24B shows the embodiment 7-1. FIG. 24C shows the refractive index distribution formed by the method of Example 7-2. In these drawings, the refractive index distribution pixel size is 3 × 3 μm, and the thickness of the core layer is 4.5 μm.

  In any refractive index distribution shown in FIGS. 24A to 24C, the high refractive index portion and the low refractive index portion have the same effective refractive index difference (high refractive index portion: Δ = 1.5%, low refractive index). Rate part: Δ = 1.3%) and can be directly compared.

  FIG. 25 is a diagram for explaining the loss characteristics (transmittance) of the 1.31 μm / 1.55 μm (1 × 2) branch circuit having the structure shown in FIGS. It is. The circuit size is 1200 μm × 120 μm. The characteristics of the optical circuit of the structure corresponding to FIG. 24A (conventional structure) are indicated by broken lines, and the optical circuit characteristics of the structure corresponding to FIG. 24B and FIG. 24C are respectively represented by (A) and It is indicated by (B).

  As can be seen from this figure, the loss characteristic of the optical circuit of the present invention is improved by about 1 dB as compared with the loss characteristic of the optical circuit of the conventional structure, and an optical circuit with good characteristics is obtained.

  In this embodiment, the refractive index is handled as a complex refractive index. The imaginary part of the complex refractive index means the gain or loss of light in the medium. Therefore, it is assumed that the wave transmission medium has an absorption or amplification effect. In the optical circuit of the present embodiment, the characteristic that the complex refractive index of the normal material changes depending on the wavelength is effectively used. As an optical circuit structure, an example of the 1.31 μm / 1.55 μm (1 × 2) branching circuit described in the second embodiment is considered.

  FIG. 26 is a schematic diagram for explaining the configuration of the optical circuit of the present embodiment. FIG. 26 (a) is a conceptual diagram of the entire circuit, and FIGS. 26 (b) and 26 (c) are diagrams on the output side. It is a conceptual diagram of the complex refractive index distribution, and these figures respectively show the states of the complex refractive index distribution in the vicinity of the 1.31 μm port (a in the figure) and the 1.55 μm port (b in the figure). .

  In addition to the usual circuit design, this optical circuit has a complex refractive index profile near the 1.31 μm output port that is almost transparent to the 1.31 μm band light and 1.55 μm band light. On the other hand, it is designed to have a large loss (FIG. 26B), while the complex refractive index distribution in the vicinity of the output port of 1.55 μm is substantially transparent to light in the 1.55 μm band, and It is designed to have a large loss for light in the 1.3 μm band (FIG. 26C). That is, in this optical circuit, the complex refractive index distribution is determined so that the signal light of the wavelength to be output is transparent and unnecessary signal light is absorbed and output in the optical circuit.

  Although not shown in detail, between the 1.31 μm output port (a) and the 1.55 μm output port (b), there is a complex refractive index distribution so as to have a large loss for light of both wavelengths. And is designed to prevent crosstalk caused by scattering of unnecessary signal light. As a constituent material of the optical circuit of this embodiment, a semiconductor-doped glass-based material is selected, and as a result, an output of 1.55 μm is obtained as compared with a case where an optical circuit is manufactured only with a material transparent to light. The crosstalk of 1.3 μm band signal light to the port was greatly reduced. In addition, the crosstalk of 1.55 μm band signal light to the 1.31 μm output port was slightly reduced. Note that almost no increase in the loss of signal light was observed. In addition, when comparing an optical circuit having a refractive index distribution of only a real number with the optical circuit of the present embodiment having a complex refractive index distribution, it is possible to shorten the circuit length for obtaining the same circuit characteristics. Become.

  In the present embodiment, a semiconductor material is used for configuring the circuit. However, any material that provides a complex refractive index may be used, and various materials such as an organic material, a metal, and a dielectric material can be used.

  The circuit of the present invention has the feature that it can realize a wide variety of functions because it uses multiple diffraction and interference phenomena, but it realizes sufficient circuit characteristics with a refractive index distribution of only real numbers. It can also be difficult. In such a case, if it is designed to give a complex refractive index distribution in part or all of the circuit as in this embodiment, the circuit characteristics can be improved or the element length can be increased. A short circuit can be manufactured.

  The optical circuit of the present embodiment is a circuit in which a refractive index distribution is formed by processing a layer having a high refractive index in a relief shape as a high refractive index portion and a low refractive index portion of the optical circuit described so far.

  FIGS. 27A to 27C are cross-sectional views for explaining the configuration of the optical circuit of the present embodiment. FIG. 27A shows the basic structure of the optical circuit, and has a low refractive index. By removing a part of the upper part of the core layer 23 having a thickness of 5 μm, which is a high refractive index layer sandwiched between clad layers (22, 24) which are layers, by a depth of 2 μm, and performing relief patterning, A refractive index distribution is formed by forming effective "high refractive index portion" 23a and "low refractive index portion" 23b.

  Such pattern formation can be performed by reactive ion etching. In general, in pattern formation by etching, as the processing depth increases, the degree of pattern deformation increases and the controllability of pattern formation decreases. Therefore, if deep etching is performed, the pattern size that can be formed must be large. There is a problem of not getting. The inventors have found that the pattern size formed by etching is an extremely important parameter in the optical circuit of the present invention. This is because the spatial refractive index distribution determined by the pattern size affects the controllability of light, and thus affects the characteristics of the optical circuit itself.

  Therefore, in order to increase the controllability of the pattern size and enable the formation of a pattern with a smaller size, a relief pattern with a relatively shallow etching depth is applied by a method as described below to achieve a desired refraction. We decided to realize the rate distribution. FIG. 27B is a diagram for explaining an example. In the structure of FIG. 27A, the unevenness is formed only from one surface of the core layer 23 which is a high refractive index layer. In the structure shown in this figure, unevenness is formed from both surfaces of the core layer 23, and thereby an equivalent refractive index distribution is realized with an etching depth applied to each unevenness being 1/2 of 1 μm.

  In order to fabricate the circuit structure shown in FIG. 27B, first, a low refractive index glass is deposited as a lower clad portion on a silicon substrate (not shown), and a groove is formed in a part thereof by reactive ion etching. The lower cladding layer 22 is formed. As will be described later, this groove portion corresponds to a high refractive index portion of the core layer 23 of the present optical circuit. Here, the relative refractive index difference Δ with respect to the cladding layers (22, 24) of the core layer 23, which is a high refractive index layer, is 1.5%, and the thickness of the high refractive index portion of the finally obtained core layer 23 is 5 μm. Therefore, a groove of about 1 μm is formed so that sufficient step coverage can be obtained for this layer thickness.

  Following the formation of the grooves in the lower cladding layer 22, a glass layer having a high refractive index is deposited on the lower cladding layer 22 and heated at a high temperature. By this heating, the high refractive index glass is filled in the vicinity of both ends (stepped portions) of the groove of the lower clad layer 22 without gaps, and the surface of the high refractive index layer is also flattened. The high refractive index glass is deposited so that the thickness of the high refractive index glass layer on the groove corresponding to the high refractive index portion of the core layer 23 of the optical circuit is 6 μm.

  Here, the thickness of the high refractive index glass layer is set to 6 μm because a groove is formed by etching on the upper surface of the high refractive index glass layer, and the final high refractive index portion has a thickness of 5 μm. In order to obtain the above, it is because the “trim” by etching is set to 1 μm.

  In the groove formed on the surface of the high refractive index glass layer, as shown in FIG. 27B, the concave portion (convex portion) provided in the lower cladding layer 22 becomes the convex portion (concave portion) of the high refractive index glass layer. In other words, the low refractive index portion and the high refractive index portion formed on the front surface and the back surface of the core layer 23 are provided at positions corresponding to each other. This is because the shape of the field of light propagating in the core layer 23 is symmetric with respect to a straight line extending in the light propagation direction, so that it is formed on the front and back surfaces of the core layer 23 in order to avoid extra losses. This is based on the inventors' knowledge that the low refractive index portion and the high refractive index portion should be symmetric with respect to a straight line extending in the light propagation direction.

  After the core layer 23 having such a relief pattern is formed, an upper cladding layer 24 is provided on the core layer 23 that is a waveguide portion, and the core layer 23 has a high refractive index portion 23a and a low refractive index portion 23b. Are embedded in the upper and lower cladding layers, and a 1.31 / 1.55 μm WDM optical circuit is formed as in the second embodiment.

  Conventionally, in the case of an optical waveguide having a relative refractive index difference Δ of about 1.5% between the cladding layer and the core layer, the thickness of the core is about 4.5 μm in order to achieve a single mode in the substrate thickness direction. Therefore, as compared with an etching depth of about 1 μm in a normal semiconductor process of the same level, a considerably deep etching is required and it is difficult to process a fine pattern. On the other hand, by using a relief structure like the optical circuit of this embodiment, the etching depth can be reduced to 1 .mu.m and a fine pattern of about 0.5 .mu.m can be formed.

  In the optical circuit having the structure shown in FIG. 27B, the effective refractive index difference Δ ′ between the high refractive index portion and the low refractive index portion of the core layer 23 is calculated by calculating the low refractive index glass and the core forming the cladding. Is estimated to be about 20% of the relative refractive index difference Δ (about 1.5%) of the high refractive index glass forming the effective refractive index difference Δ ′ for forming the spatial refractive index distribution of the optical circuit of this embodiment. Is only about 0.3%.

  As a result of designing an optical circuit based on this effective refractive index difference Δ ′ (about 0.3%), even when the pixel size is set to 3 μm, the design is performed with a relative refractive index difference of Δ1.5%. Compared with the optical circuit of Example 1, it was possible to reduce the circuit length to about 1.5 times as long. In the optical circuit of this embodiment, the pixel size can be set as small as 0.5 μm. If the optical circuit is designed with a pixel size of 0.5 μm, an optical field with a large wave number in the horizontal direction can be obtained. Therefore, the circuit length can be approximately half that of the optical circuit of the first embodiment.

  That is, in the optical circuit of this embodiment, even if the light propagation region is formed with a refractive index difference as low as about 0.3%, for example, it is relatively large using multiple scattering by the waveguide structure having a relief pattern. Reflection and scattering can be generated, and light interference can be generated with high efficiency. For this reason, it is possible to greatly reduce the size of the optical circuit.

  The shape of the relief provided on the core layer 23 can be freely changed according to the desired refractive index distribution. For example, as shown in FIG. In addition to the high refractive index portion 23a and the low refractive index portion 23b, an intermediate refractive index portion 23c may be provided.

  As already described in the fifth embodiment, in the optical circuit as shown in FIG. 15A, the pixel structure is a rectangular pixel structure having sides substantially perpendicular to the traveling direction of the wavefront. Just as light is diffracted by a knife edge, severe interference occurs and the design accuracy of the optical circuit is reduced. In addition, light having a large wave number is generated, and light control is performed in a refractive index distribution with a small refractive index difference. However, if the above-described relief pattern is applied to the core layer 23, the refractive index pattern is caused by the presence of pixels having a low refractive index interposed between pixels having a high refractive index. Is effectively smoothed, and it is possible to suppress intense scattering of propagating light.

  The optical circuit of the present embodiment realizes optical confinement by forming a clad with a multilayer film in which films having different refractive indexes are laminated in multiple layers.

  FIG. 28 is a cross-sectional view of the waveguide portion of the optical circuit of the present embodiment. The lower cladding layer 22 and the upper cladding layer 24 sandwiching the core layer 23 are films having different refractive indexes (22a to d and 24a to 24a). It is composed of a multilayer film in which d) is laminated in multiple layers.

  In the optical circuit described so far, the field pattern of the low refractive index portion is usually radiating like the optical circuit of the second embodiment, and even in the circuit configuration of the sixth and eighth embodiments, In principle, loss occurs. In order to solve this problem, the optical circuit of this example is a multilayer film in which films having different refractive indexes are laminated in a multilayer so as to completely suppress light leaking up and down the substrate. is there. The optical circuit design method is the same as in Non-Patent Document 4.

  If media having different refractive indexes are incorporated in multiple layers, total reflection and non-reflection conditions can be realized. In particular, when the wave number in the lateral direction is small, it is possible to form the total reflection condition relatively easily (see, for example, Non-Patent Document 4).

  Therefore, the clad layer is composed of the multilayer film, and by arranging these layers so that total reflection (or sufficiently high reflectance) is obtained on both the upper and lower sides of the core layer 23 in the low refractive index region, Even in an optical circuit in which the ratio between the refractive index region and the high refractive index region is approximately the same, a sufficiently low-loss circuit can be realized.

  Such a circuit configuration is effective if the Bragg condition is satisfied only in the vertical direction of the substrate (not shown). Therefore, a multilayer film having a periodic structure only in the vertical direction of the substrate as in the configuration shown in FIG. In addition to the structure, the same effect can be obtained by forming the upper and lower cladding layers using photonic crystals.

  In the optical circuit of this embodiment, a refractive index distribution is designed by dividing one pixel into a plurality of sub-pixels, thereby realizing an optical circuit with a lower loss than the circuit described in the third embodiment.

  In general, as a rough approximation, when light interacts with an object having a structure smaller than its wavelength, the refractive index averaged over a region of the order of wavelength is effectively used due to diffraction phenomena. Perceived as a good refractive index. Therefore, among the plurality of subpixels constituting the unit pixel, unit pixels having different effective refractive indexes are arbitrarily created depending on the distribution method of the number of subpixels having a high refractive index and the number of subpixels having a low refractive index. be able to.

  FIGS. 29A and 29B are top views showing examples of such sub-pixels, and FIG. 29C shows an optical circuit in which a refractive index distribution is designed using pixels divided by the sub-pixels. It is a top surface conceptual diagram of a part. The unit pixel has a size of 1 μm square, and the case where this pixel is divided into two (FIG. 29A) and the case where it is divided into four (FIG. 29B) is illustrated. By such pixel division, the effective value of the gap becomes about 0.5 μm (in the case of FIG. 29A) or 0.25 μm (in the case of FIG. 29B), and the light propagating in such a medium is Almost no sense of the existence of the gap. Also, when designing the refractive index distribution, the amount of data necessary for the calculation can be reduced to 1/2 or 1/4, for example, so that 10,000 pixels × 10,000 pixels (in this case, 1 cm square) Even a large-scale circuit corresponding to the above can be easily formed.

  In the optical circuit of the present embodiment, the pixel is divided into a plurality of subpixels. When designing the refractive index distribution, the calculation of the refractive index distribution is facilitated by executing the calculation for each pixel. In addition, when realizing a fine pattern, if calculation is performed using many unit pixels having the same division state by sub-pixels, a diffraction correction process using a phase shift mask in a photo process or an etching amount correction process using a process This makes it easier to set the correction conditions.

  As already described in the fifth embodiment, in the optical circuit as shown in FIG. 15A, the pixel structure is a rectangular pixel structure having sides substantially perpendicular to the traveling direction of the wavefront. Just as light is diffracted by a knife edge, severe interference occurs and the design accuracy of the optical circuit is reduced. In addition, light having a large wave number is generated, and light control is performed in a refractive index distribution with a small refractive index difference. There is a problem of being unable to fill.

  In order to solve this problem, in the optical circuit of this embodiment, the pixel shape is changed from the conventional rectangle. Such pixel shape deformation modes include a case where the pixel shape is deformed in a direction horizontal to the substrate and a case where the pixel shape is deformed in a direction perpendicular to the substrate. When calculating the refractive index distribution, it is only necessary to assume two refractive indexes, high and low, having an effective refractive index difference as in the case of the eleventh embodiment.

  FIG. 30A is a conceptual diagram of the refractive index distribution of a waveguide having a structure in which the refractive index changes in a horizontal direction with respect to the substrate, and FIG. 30B shows the refraction shown in FIG. It is a figure for demonstrating the mode of reflection attenuation at the time of propagating a plane wave in rate distribution. In FIG. 30B, the horizontal axis represents the gradient of the refractive index (the rate of spatial change of the propagation constant), and the vertical axis represents the return loss due to the propagation constant mismatch. The spatial length is normalized by the wavelength of light in the medium, and the refractive index of each place is the reference refractive index (n = 1.45: refractive index of the silica-based waveguide at a wavelength of 1.55 μm). ) To obtain the relative refractive index difference.

  As can be seen from these figures, the return loss is improved by making the gradient of the refractive index smaller than 1. That is, the pixel shape may be gradually changed. For example, assuming a pixel with a refractive index distribution of 3 μm square, this pixel size is about 2 wavelengths for light with a wavelength in vacuum of 1.55 μm, so the gradient is about 1/2. When the refractive index is changed so that it becomes, it is expected that the scattering can be attenuated by several dB.

  FIG. 31A is a conceptual diagram for explaining the state of the refractive index distribution in a unit pixel when the pixel shape is circular, and FIG. 31B uses the circular pixel shown in FIG. FIG. 31C is a schematic top view of a part of the circuit configured as described above, and FIG. 31C is a top view of a part of the circuit when the arrangement of the high refractive index portion and the low refractive index portion in FIG. It is a conceptual diagram.

  Assuming that the extent of the field spread is the same as the pixel size, the local effective refractive index is considered to change approximately in proportion to the cross-sectional area of the circular pixel. Here, a circular region having a diameter of about 3 μm has the same refractive index as that of the cladding, and the periphery of the circular region is formed of a high refractive index film. That is, in the circuit shown in FIG. 31 (b), a high refractive index portion made of a film having a high refractive index is uniformly formed, and a partial region of the high refractive index portion is cut into a circular shape so that the portion has a low refractive index. The refractive index portion is provided. On the contrary, in the circuit shown in FIG. 31 (c), a low refractive index portion made of a film having a low refractive index is uniformly formed, and a partial region of the low refractive index portion is hollowed out in a circle. The portion is provided with a high refractive index portion.

  In the case of a circuit configuration in which the refractive index changes in the direction perpendicular to the substrate, first, after depositing an underclad on the substrate, a film having a higher refractive index than the clad is deposited. When the core pattern is formed by reactive ion etching using a photoresist as a mask, a film having a different thickness can be left as a core by spatially changing the thickness of the photoresist as a mask. For example, if a photoresist is applied and then heated to about 130 ° C. to melt the resist, the edge of the pattern is rounded by surface tension, and the resist in this state is used as an etching mask, the periphery of the resist pattern is etched away. Thus, the pattern finally transferred to the high refractive index film is also a pattern in which the outer periphery of the pattern is rounded.

  For example, if an AZ-based photoresist is used, it is possible to remove the resist having a depth substantially proportional to the exposure amount. Therefore, if different patterns are exposed in a plurality of times, a desired pattern can be finally formed. Also in this case, the outer peripheral portion of the finally obtained pattern can be smoothed.

  The arrangement of the pixels constituting the optical circuit can be defined by a method of dividing the planar area of the optical circuit. In other words, in the same manner as in crystallography, the arrangement position of the pixels can be defined by the symmetry of the unit cell. Here, it is assumed that the unit cell is composed of one or more pixels. If handled in this way, the entire circuit will have the same periodicity as the crystal. When an ideal plane wave that is spatially widened in the lateral direction is incident on a circuit having such periodicity, strong scattering occurs for a specific wave number component. However, since a medium having a low refractive index or a high refractive index is appropriately arranged at the pixel arrangement position, there is no complete periodicity (for example, see Non-Patent Document 5).

  In this case, the optical circuit characteristics differ depending on how the crystallographic orientation of the circuit is set with respect to the size and arrangement of the pixels and the incident direction (or outgoing direction) of light. The light incident direction and wave number are important. If strong scattering with respect to the specific wave number component described above is used, the circuit can be downsized and the characteristics can be improved.

  The simplest unit cell is composed of a single pixel, and the shape of this pixel can be round or n-gonal (n is an integer of 3 or more).

  FIG. 32 is a diagram for explaining the state of the pixel arrangement when this pixel shape is a honeycomb shape. When this pixel arrangement is used, a relatively isotropic diffractive surface is obtained. Therefore, in an optical circuit that inputs and outputs light from a plurality of directions as indicated by arrows in the figure, it is easy to generate large reflections in various directions, and circuit characteristics are improved.

  Further, as shown in FIG. 13, even if the pixel arrangement structure is the same, the characteristics can be improved by changing the orientation state of the pixels.

  As shown in FIG. 33, an incomplete periodic structure called a “quasi-periodic structure” is also known. In this case, the diffraction spectrum has a fractal shape, and the spectrum is distributed over a relatively wide range. Therefore, there is an advantage that favorable scattering can be obtained in constructing the circuit.

  Conventionally, in an optical circuit having a plurality of input / output ports, a circuit configured to simultaneously distribute signals from each port to other ports and receive signals from the same port has a simple optical power. An optical multiplexer / demultiplexer that only multiplexes and demultiplexes has been used. For this reason, when a signal is received from only one port, there is a problem that light is attenuated to 1 / N in a circuit composed of N ports. The cause of such a problem is that the circuit design considering the phase of light is not made. On the other hand, if the holographic wave transmission medium of the present invention is used, the combining / distributing function including the phase can be realized, so that the light can be combined / distributed without generating extra loss.

  FIG. 34 is a diagram for explaining a configuration example of an optical circuit having a mutual broadcast / simultaneous reception configuration, and FIG. 35 is a diagram schematically illustrating a signal flow between each port of the optical circuit. . This optical circuit has four ports, and each port emits light toward the other three ports, while receiving a signal output independently from the other three ports. When such an optical circuit is manufactured on a substrate, an optical fiber is connected to these ports, and each port is connected to a termination device or an optical amplification device.

  If the signal flow between the ports schematically shown in FIG. 35 is modified without breaking the logical signal flow, it is as shown in FIG. In this figure, the upper and lower ports facing each other are actually the same port, but in order to clarify the signal flow, the lower side is shown as a transmission port and the upper side is shown as a reception port. . However, since these are configured by the same circuit, they merely show a logical configuration.

  At this time, in the normal power branch circuit, the power is reduced to 1/3 by the three branches on the transmission side, and the power is reduced to 1/3 by the multiplexer on the reception side, so that the power is eventually reduced to 1/9. That is, as much as 8/9 loss occurs. Among these, the loss on the receiving side is a loss that occurs because light that is phase-matched from the other two ports is not input. Therefore, it is considered that if the branching method is devised so that it can be received independently of the light from the other two ports, the loss is eliminated. This can be realized by performing distribution to each port in consideration of the phase of each light as shown below.

  First, the phase of each port is represented as a set of four numbers (ie, vectors). Here, the amplitude is 1. However, when there is no light distribution to a specific port, the component is set to zero. For example, if the phase is 0 for port 1, π for port 2, π for port 3, and no light for port 4,

Let's consider the vector Considering this representation method, the field overlap integral can be calculated just as an inner product of vectors, and this can be used to find a desired set of vectors.

  Assuming that a signal is evenly distributed from one port to all other ports, the component corresponding to the distributing port is 0, and the absolute value of the other ports is

Think of the field that becomes. If all vectors are orthogonal to each other by adjusting their phases, each port can receive light independently from signals from other fields, and the optical signal is received only with a branch loss. be able to.

  In fact, in this case

Is one such combination. As a result, the principle loss on the conventional receiving side can be eliminated, and an optical signal can be received with three times the intensity.

  Further, as in the non-uniform distribution circuit shown in FIG. 37, by distributing (branching) light non-uniformly, it is possible to compensate for the loss associated with the transmission distance and reduce the loss by selecting an appropriate phase. Thus, a low-cost optical communication system that does not use an optical amplifier or the like can be realized. In FIG. 37, simultaneous transmission / reception from the base station and communication between the terminals are also performed.

  The present embodiment is an optical circuit having the same configuration as that of the fourteenth embodiment, but is a configuration example of an optical circuit for minimizing the overlap of output signals when there is no orthogonal state. Here, consider the case of a three-port optical circuit. In this case, since there are only three ports, the orthogonal state cannot be realized. However, as shown below, a configuration with less loss can be realized by selecting a state as close to an orthogonal state as possible.

  As in Example 14, the output of the port

And Here, there is an output in itself, but this can be handled as reflected return light.

  As a result, 4/9 = 3.5 dB of light can be obtained at a necessary port. This is a loss that is 2.5 dB lower than when two conventional 3 dB couplers are combined.

  FIG. 38 is an applied conceptual diagram of such an unequal distribution circuit. As shown in this figure, a tap circuit can be realized by cascading three-port optical circuits. Here, the inorganic glass material constituting the optical circuit is doped with an Er element to have an amplification function in the 1.5 μm wavelength band. Since the loss of the circuit is sufficiently lower than in the prior art, it can be amplified with a small amount of power consumption and in a short distance, so that a small and low power consumption tap circuit can be configured. This is shown as a loss compensation circuit in the figure.

  In the waveguide diffraction grating, as shown in FIGS. 39A and 39B, when the position of the incident waveguide in the incident side slab is fixed, the output position is shifted in the direction A depending on the wavelength (FIG. 39A )). Further, when the position B of the incident waveguide is shifted, the output position is shifted in the direction C (FIG. 39B). If the center position of the field on the incident waveguide side is shifted in the direction B according to the wavelength by utilizing such a property, the movement in the direction A and the movement in the direction C cancel each other, and the field does not move.

  When the center position of the field on the incident waveguide side is periodically changed at the wavelength interval between the output ports when the center position of the field on the incident waveguide side does not move, a plateau is formed as shown in FIG. If the optical waveguide of the output port is arranged at this plateau portion, a rectangular wavelength filter characteristic can be obtained.

  In order to realize this, a proposal has been proposed in which a directional coupler is arranged in the incident waveguide portion and a branch delay circuit is arranged in the preceding stage. At this time, since the swing width that the center position of the field swings is required to be about the field diameter, the core width of the directional coupler cannot be reduced. Therefore, the field shape becomes wider than the required spot diameter, and the field shape is distorted. This distorts the light output image on the output side, which is the conjugate image, and as a result, there is a problem that optical coupling deteriorates.

  Therefore, in this embodiment, by using the holographic wave transmission medium of the present invention, the light from a plurality of incident ports is shaped and output, respectively, and the waves are superposed to obtain a good incident field. The center position of the field was adjusted by obtaining the shape and adjusting the phase between the incident ports. In this embodiment, there are two incident ports.

Here, the coordinates are represented by x, the images of the incident ports are respectively represented by f ₀ (x) and f ₁ (x), and the phase difference between the ports is represented by φ. At this time, the superimposed image f (x, φ) is

It becomes. The desired field shape is a function where the function x _c (φ) of the phase difference φ is the center position and θ (φ) is the phase.

Suppose that Here, x _c (0) = 0 and θ (0) = 0 are set for simplicity. At this time, when comparing the first order coefficient with respect to φ,

It becomes. This is an expression that the functions g (x) and h (x) must satisfy. Since φ is an amount corresponding to the wavelength difference, as shown later,

Corresponds to the speed at which the center position should move, and is an amount determined by design conditions.

From the orthogonal condition and normalization condition of f ₀ (x) and f ₁ (x),

It becomes. Where G is

Where s is an amount not exceeding 1,

It is the amount decided by. In addition,

Is the square root of the norm.

  As long as the holographic wave transmission medium used in the present invention is an orthogonal field, the shape of each field including the phase can be arbitrarily set. Therefore, these output fields are assigned to each input port using the holographic wave transmission medium. Can be set. Now, as shown in FIG. 41 (only the incident part excluding the arrayed waveguide grating is shown), the phase difference in the previous stage is given by the delay of the waveguide circuit, and the output repetition period and the output side with respect to the wavelength of the delay circuit When the output wavelength interval between the waveguides is the same, the waveguide interval D between the output ports is used.

As long as the desired field F is determined, all parameters are determined.

  For example, assuming a Gaussian function as F and the field radius is w,

It is.

  FIG. 42 is an example showing how the center position moves when a Gaussian function is assumed as the field shape. The field shape of the portion before entering the arrayed waveguide grating is observed with a near-field image so that the motion of the field can be seen. It is a configuration including the delay circuit shown in FIG. 41, and it can be seen that the center position of the field periodically changes at intervals of about 10 nm. However, although there are two peaks in the transition region, which are not approximated, this portion is a transition region from one output port to the next output port and is not related to coupling. The delay circuit portion can be set freely according to the length of the waveguide, and the branching ratio of the two-branch circuit can also be set freely. Wave characteristics are obtained.

  In the above embodiment, the input side waveguide is two input waveguides. However, in order to improve the accuracy, the number of input side waveguides may be increased. The general theory for that is shown below.

  For a desired function F (x; η) with η as a parameter, approximation up to the first order is obtained in the same manner as described above, and when expanded up to the second order,

It becomes. Therefore,

Transform

If you

Can be determined in an appropriate manner in the same manner as in the above embodiment. Here, in the case of the above embodiment, φ is a parameter for the sake of simplicity. However, for the sake of clarity, a conditional expression is described with a parameter η of a desired field. Also,

Is

The field should be orthogonal to The phase term to be added to the third waveguide is

It becomes.

  As described above, the desired function is Taylor-expanded and summarized into the previous order term, and apparently, the coefficient of the term of the first order is made parameter dependent, and the first order approximation is performed for that term. By applying, it is possible to increase the approximation sequentially. Similarly, when there are a plurality of parameters, the parameters may be similarly set so as to match one parameter, and thereafter, the above method may be used to perform approximation in the order of setting another parameter.

  In general, a silica-based optical waveguide and a semiconductor optical waveguide have different field diameters. Therefore, in an optical fiber and an optical semiconductor laser, optical coupling loss is reduced through a lens. However, in order to use a lens, it is necessary to provide a sufficient space between the optical waveguide structure and the lens, so that it is not suitable for miniaturization. Therefore, a method for optically coupling the optical waveguide and the optical semiconductor element without using a lens has been tried. As shown in FIG. 43A, the optical waveguide has a substantially plane wave equiphase surface inside the circuit. Therefore, light is diffracted by radiation from the opening and loss in optical coupling occurs. Furthermore, since there is generally an optical coupling loss when there is a difference in field diameter, for example, in the optical coupling system of a quartz optical waveguide and a semiconductor optical waveguide, it is necessary to reduce the field diameter of the silica optical waveguide.

  In this embodiment, optical coupling is improved by simultaneously controlling the wavefront and the field shape using the holographic wave transmission medium. Since holographic wave transmission media use multiple scattering of light, unlike optical waveguides, it is possible to control light with a high transverse wave number, which is usually radiated light, so that the field diameter is smaller than the value that can be narrowed by the waveguide structure. It can be made smaller. Furthermore, since the holographic wave transmission medium can control the phase distribution of the field, the equiphase surface may be concave as shown in FIG.

  FIG. 44 is a cross-section in the direction perpendicular to the substrate surface of the near-field image, although the spot diameter is shaped only in the horizontal direction of the substrate by a holographic wave transmission medium manufactured by a quartz-based planar lightwave circuit technology with a relative refractive index difference of 1.5%. is there. The holographic wave transmission medium is designed to form a beam waist about 5 μm away from the exit end, and a minimum field diameter of about 5 μm from the exit end is realized even in a near-field image. It can be seen that the reference is a field by an optical waveguide and coincides with the spread of the vertical field of the holographic wave transmission medium. On the other hand, the field in the horizontal direction of the substrate has a field diameter of about 3 μm, and a field diameter smaller than that of the optical waveguide structure can be realized. As a result, the conventional coupling loss with the semiconductor laser of about 8 dB can be improved to 4 dB.

  The present invention makes it possible to provide a small-sized optical circuit with sufficiently high efficiency even with a gentle refractive index distribution (small refractive index height difference).

It is a figure for demonstrating the basic concept and basic structure of a holographic wave transmission medium. It is a figure for demonstrating the structural example of the conventional array waveguide grating circuit. It is a flowchart for demonstrating the calculation procedure for determining the spatial refractive index distribution of a holographic wave transmission medium. FIG. 5 is a diagram showing an example of a state of a field in a holographic wave transmission medium in order to facilitate understanding of a calculation procedure. FIG. 6 is a diagram for explaining setting of optical circuit design in the first embodiment. It is a figure for demonstrating the refractive index distribution ((a)) and transmission spectrum ((b)) by Example 1. FIG. FIG. 3 is a diagram for explaining a refractive index profile of a planar lightwave circuit according to the first embodiment. 6 is a diagram for explaining a configuration example of a wavelength filter of 1.31 μm / 1.55 μm of Example 2. FIG. It is a figure for demonstrating the mode of the breadth of the light at the time of considering the pixel of the dielectric material which comprises the optical circuit of Example 2 as a light scattering point. It is a figure for demonstrating the pixel size dependence of a transmission loss characteristic and a crosstalk characteristic at the time of comprising the optical circuit of a wavelength filter of 1.31 micrometer /1.55 micrometer by changing pixel size W as a parameter. 10 is a diagram for explaining light confinement levels in a substrate vertical direction and a substrate horizontal direction in the planar optical circuit of Example 3. FIG. It is a figure for demonstrating the field radius dependence of the radiation loss per point (coupling loss) when a minimum pixel unit is 3 micrometers square. The figure for demonstrating the optical circuit which has arrange | positioned the pixel in the light propagation direction in Example 4 (a), and the figure for demonstrating the optical circuit which inclined the pixel with respect to the light propagation direction ((B)). FIG. 5A is a diagram for explaining an optical circuit in which pixels are arranged at lattice points defined by a virtual mesh to form a refractive index distribution in Example 5 (a), and is independent of the position of the lattice points. FIG. 6B is a diagram (b) for explaining an optical circuit in which a pixel distribution in the y direction is formed to form a refractive index distribution. It is a figure for demonstrating the refractive index distribution of the actual optical circuit (1.31 micrometer and 1.55 micrometer wavelength filter) produced corresponding to the pixel arrangement | positioning shown in FIG. FIG. 10 is a diagram for explaining a manufacturing procedure of an optical circuit in Example 6. An optical circuit configuration in which a region where the high refractive index layer Δ ₂ is removed by etching is referred to as a “low refractive index region” and a region where the high refractive index layer Δ ₂ is left without being etched away is referred to as a “high refractive index region”. It is a figure for doing. FIG. 20 is a diagram for explaining a calculation example for parameter adjustment in the sixth embodiment. It is a figure for demonstrating the characteristic (wavelength dependence of a transmission loss) of the 1.31 / 1.55 micrometer WDM circuit which is an optical circuit of Example 6. FIG. It is a figure for demonstrating the manufacturing method of the optical circuit of Example 7-1. It is a figure for demonstrating the manufacturing method of the optical circuit of Example 7-2. It is a figure for demonstrating the manufacturing method of the optical circuit of Example 7-3. It is a figure for demonstrating the manufacturing method of the optical circuit of Example 7-4. It is waveguide sectional drawing for demonstrating the mode of refractive index distribution of the optical circuit of Example 7-5. It is a figure for demonstrating each loss characteristic (transmittance) of a 1.31 micrometer /1.55 micrometer (1x2) branch circuit which has the structure shown in FIG. FIG. 10 is a schematic diagram for explaining a configuration of an optical circuit according to an eighth embodiment. FIG. 10 is a cross-sectional view for explaining the configuration of an optical circuit in Example 9. 10 is a cross-sectional view of a waveguide portion of an optical circuit according to Example 10. FIG. 22 is a top view illustrating an example of subpixels of an optical circuit according to Example 11. FIG. Conceptual diagram ((a)) of a refractive index distribution of a waveguide having a structure in which the refractive index changes in a direction horizontal to the substrate in Example 12, and when a plane wave is propagated in this refractive index distribution It is a figure for demonstrating the mode of reflection attenuation of (b). Conceptual diagram ((a)) for explaining the state of the refractive index distribution in the unit pixel when the pixel shape is circular, and a top conceptual diagram of a part of the circuit configured using the circular pixel ((b)) (C)). It is a figure for demonstrating the mode of the pixel arrangement | sequence when a pixel shape is made into a honeycomb shape. It is a figure for demonstrating the incomplete periodic structure called "quasiperiodic structure." It is a figure for demonstrating the structural example of the optical circuit made into mutual simultaneous delivery and simultaneous reception structure. FIG. 35 is a diagram schematically illustrating a signal flow between each port of the optical circuit in FIG. 34. It is a figure for demonstrating a mode that the flow of the signal between each port typically shown in FIG. 35 was deform | transformed without destroying the flow of a logical signal. It is a conceptual diagram of the communication network using an uneven distribution circuit. It is an application conceptual diagram of a non-uniform distribution circuit. It is a figure for demonstrating the property of a waveguide diffraction grating. It is a figure for demonstrating the relationship between an output spot center position and a wavelength. FIG. 20 is a diagram for explaining a configuration of an optical circuit in Example 16; It is a figure for demonstrating the mode of a movement of a center position when a Gaussian function is assumed as a field shape. (A) is a state of the equiphase surface of the emission field from the waveguide having the conventional configuration, and (b) is a diagram for explaining the state of the equiphase surface of the emission field from the waveguide having the circuit configuration of the present invention. . FIG. 5 is a cross-sectional view of a near-field image in a direction perpendicular to the substrate surface, although the spot diameter is shaped only in the horizontal direction of the substrate by a holographic wave transmission medium produced by a quartz-based planar lightwave circuit technology with a relative refractive index difference of 1.5%.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Optical circuit board 1-1 Optical circuit design area 1-11 High refractive index portion 1-11a First high refractive index portion 1-11b Second high refractive index portion 1-12 Low refractive index portion 2-1 Incident Surface 2-2 Output surface 3-1 Input light 3-2 Output light 4-1 and 4-2 Star coupler (optical multiplexer / demultiplexer)
5 Array Waveguide 6 Wavelength Plate 21 Silicon Substrate 22 Lower Cladding Layer 23 Core Layer 24 Upper Cladding Layer 25 Shading Mask Layer 26 Phase Mask 27 Partial Port Portion 28 Laser Light 29 Lens

Claims (16)

An optical circuit provided with a light waveguide region comprising a clad layer formed on a substrate and a core layer embedded in the clad layer,
In a cross section perpendicular to the light propagation direction, a place on the circuit to which a cross section of the light field is to be given is a port, and input light incident from any one port is output light from another port. A wave transmission medium in which a spatial refractive index distribution is formed instead of the core layer having a uniform refractive index so as to be emitted,
The spatial refractive index distribution is such that when the input light propagates along the propagation direction of the light from the arbitrary one port, the input field of the input light is converted into an output field of the output light. Determined by the refractive index of each core of pixels defined by the mesh to propagate through each of the one or more sets of input / output fields output from the other port,
The refractive index of the core of each pixel is defined by the location (z, X) of the cross-section X when the coordinate z in the light propagation direction and the coordinate x in the direction perpendicular to the light propagation direction in the light guiding region are used. x) each pixel so that the phase difference between the phase of the forward-propagating field of the input field and the phase of the field back-propagated to the phase conjugate of the output field is less than or equal to a predetermined error. This is determined by repeatedly calculating the refractive index of the core of the core as a variable. This calculation is based on the refractive index distribution {n _q−1 } obtained by the (q−1) -th calculation. For the j-th input field ψ ^j (x) and output field φ ^j (x) of the field set, the forward propagation field ψ ^j (z, x, {n _q-1 }) and the back propagation field φ ^j (z, x, {n _q-1 }), each location (z, x) The refractive index n _q (z, x)
n _q (z, x) = n _q-1 (z, x) −αΣ _j Im [φ ^j (z, x, {n _q-1 }) ^* · ψ ^j (z, x, {n _q-1 })]
Where the symbol “*” is a complex conjugate, the symbol “·” is an inner product operation, Im [] is the imaginary component of the field inner product operation result in [], and α is the convergence of the calculation Where Σ _j is the sum for j, and
The field of the input light is subjected to a change in phase in multiple stages by the refractive index distribution of the cross section X along the propagation direction from the arbitrary one port to the other port. An optical circuit which propagates while changing the shape of a light field due to an interference phenomenon caused by multiple scattering of propagation waves generated in, and is emitted from the other port as an output field of the output light.   The optical circuit according to claim 1, wherein the pixel defined by the mesh is a component of a unit cell that forms the waveguide region by periodic repetition.   The optical circuit according to claim 1, wherein the unit cell has a shape forming a quasi-periodic structure. An optical circuit provided with a light waveguide region comprising a clad layer formed on a substrate and a core layer embedded in the clad layer,
In a cross section perpendicular to the light propagation direction, a place on the circuit to which a cross section of the light field is to be given is a port, and input light incident from any one port is output light from another port. A wave transmission medium in which a spatial refractive index distribution is formed instead of the core layer having a uniform refractive index so as to be emitted,
The spatial refractive index distribution is such that when the input light propagates along the propagation direction of the light from the arbitrary one port, the input field of the input light is converted into an output field of the output light. Determined by the refractive index of each core of pixels defined by the mesh to propagate through each of the one or more sets of input / output fields output from the other port,
The refractive index of the core of each pixel is defined by the location (z, X) of the cross-section X when the coordinate z in the light propagation direction and the coordinate x in the direction perpendicular to the light propagation direction in the light guiding region are used. x) each pixel so that the phase difference between the phase of the forward-propagating field of the input field and the phase of the field back-propagated to the phase conjugate of the output field is less than or equal to a predetermined error. is determined by performing repeatedly the core refractive index as a variable calculated, this calculation, (q-1) th V _q-1 obtained by the calculation _(z, x) and refractive index distribution {n _{q −1} }, the forward propagation field ψ ^j (z, x, {n _q− ) for the ^jth input field ψ ^j (x) and output field φ ^j (x) of the set of input / output fields ₁ }) and the reverse propagation field φ ^j (z, x, {n _q-1 }) The value v _q (z, x) = v _q−1 (z, x) −αΣ _j Im [φ ^j (z, x, {n _q−1 }) ^* · ψ ^j (z , x, {n _q-1 })]
Where the symbol “*” is a complex conjugate, the symbol “•” is an inner product operation, Im [] is the imaginary component of the field inner product operation result in [], and α is the convergence of the calculation Σ _j represents the sum of j, and corresponds to the low refractive index portion n _clad corresponding to the refractive index of the cladding layer and the refractive index of the core layer higher than the refractive index of the cladding layer. the two types of the refractive index of the high refractive index portion _{n core,} the refractive index of the core of the pixels in each location (z, x),
When v _q (z, x)> (n _core + n _clad ) / 2, n _q (z, x) = n _core
When v _q (z, x) <(n _core + n _clad ) / 2, n _q (z, x) = n _clad
And then, and,
The field of the input light is subjected to a change in phase in multiple stages by the refractive index distribution of the cross section X along the propagation direction from the arbitrary one port to the other port. It propagates while changing the shape of the field of light by the interference phenomenon caused by multiple scattering of the propagating wave between occurring in the optical circuit you characterized in that it is emitted from the other port as output field of the output light.   The optical circuit according to claim 4, wherein a size of the core having the high refractive index is set to be equal to or less than a wavelength of light propagating in the waveguide region. 6. The optical circuit according to claim 4, wherein a value given by the following equation is 0.1 or less.

(Lambda: propagation light wavelength, n: refractive index value of the core of set pixels refractive index n _core, a: height of the core of set pixels refractive index n _core, q: propagating light core Q = coefficient given by (z _L / a) where z _L is the average distance propagating through the other part) The cross-sectional shape of the pixel _core whose refractive index is set to n _core is parallel to the substrate, and has a polygonal shape of n-gon (n is an integer of 3 or more). The optical circuit according to claim 4, wherein the pixels are arranged so as to be inclined with respect to a propagation direction of light propagating through the region.   The optical circuit according to claim 7, wherein the polygonal shape is a square, and the inclination angle is 45 degrees. Before the core Kipi Kuseru by a relief-like facilities patterning Succoth provided with recesses on at least one surface of the core layer of the uniform refractive index, a low refractive index portion n the refractive index of the recess and _clad, the refractive index of the convex portion other than the recess as the high refractive index portion n _core, optical circuit according to any one of claims 4 to 6, characterized that you configure the pixels. Optical circuit of claim 9, wherein the relief-like patterning, characterized in that it applied to both sides of the front SL core layer.   The optical circuit according to claim 10, wherein the relief patterns provided on both surfaces of the core layer are different from each other.   12. The optical circuit according to claim 10, wherein the depths of the concave portions of the relief pattern provided on both surfaces of the core layer are equal to each other. The core of the pixel is divided into a plurality of sub-pixels having a binarized refractive index of either high refractive index (n _H ) or low refractive index (n _L ), and the binarized 4. The optical circuit according to claim 1, wherein a refractive index of the pixel is determined by an array of subpixels. 7. The optical circuit according to claim 4, wherein a cross-sectional shape of the pixel _core whose refractive index is set to n _core is parallel to the substrate. The optical circuit according to claim 14, wherein a cross-sectional shape perpendicular to the substrate of the pixel _core having the refractive index set to n _core is a shape having a smoothly changing curve. The spatial refractive index distribution according to any of claims 1 to 15, characterized in that it is set so as to realize the intensity distribution and the phase distribution of the field which enables the spot size conversion of the output light Optical circuit.

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