JP2007304629A - Structure of anti-reflection film on two or three dimensional photonic crystal and method of forming same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reliably achieve antireflection on photonic crystals with a simpler method by eliminating defects in a conventional technique for forming an anti-reflection film on the photonic crystals. <P>SOLUTION: Two or three dimensional photonic crystals are obtained by regularly arranging materials with two or more kinds of different refractive indexes in two or three dimensional cycles; and have a structure of the anti-reflection film on the photonic crystals that enhances an incidence efficiency of light into the two or three dimensional photonic crystals, by adding a thin film made of a medium consisting of one of the medium composing the photonic crystals at the end surfaces of the photonic crystals for enhancing the incidence efficiency of light into the photonic crystals. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a structure of an antireflection film, and more particularly to a structure of an antireflection film for a photonic crystal and a method for forming the same.

  In recent years, photonic crystals have attracted attention because of their unique dispersion characteristics and their ability to strongly confine light in a sub-micron region.

  A photonic crystal is a medium in which two or more media having different refractive indexes are regularly arranged in a three-dimensional or two-dimensional periodic manner with a wavelength order of light, that is, a sub-μm period. In the case of one-dimensional, it is a so-called dielectric multilayer film, but it shows characteristic optical properties due to its periodicity, and useful information applicable to two-dimensional or three-dimensional is obtained from the result of theoretical analysis. For this reason, this one-dimensional case is also referred to as a photonic crystal.

  FIG. 10A shows a schematic structure of a two-dimensional triangular lattice photonic crystal as an example of the structure of the photonic crystal. As shown in FIG. 10A, this has a structure in which a cylindrical atomic medium 17 is embedded in a background medium 15 in a two-dimensional triangular lattice shape.

  FIG. 10B is a diagram showing a first Brillouin zone corresponding to the two-dimensional triangular lattice structure of FIG. As shown in FIG. 10B, the first Brillouin zone has a regular hexagonal shape, the vertex of which is the K point, the midpoint of each side is the M point, and the center of the regular hexagon is the Γ point. In such a photonic crystal, it is known that an energy band structure (photonic band structure) is formed with respect to a light wave existing in the photonic crystal.

  FIG. 11 is a diagram illustrating a calculation example of a photonic band for the photonic crystal structure of FIG. As shown in FIG. 11, here, the background medium is Si, the atomic medium is air, and the ratio of the diameter of the air cylinder: d to the lattice spacing: a is calculated as d / a = 0.867. In addition, the direction of the electric field vector of light was calculated in the case of being perpendicular to the paper surface. The vertical axis represents the normalized frequency, and is expressed as Ω = a / λ using the wavelength of light in a vacuum: λ. In FIG. 11, there is no light propagation mode in the energy region indicated by a broken line, which is called a photonic band gap (PBG).

  In the energy region other than PBG, light can propagate through the photonic crystal, and it is known that an energy region having strong chromatic dispersion exists in this. As an invention using this strong chromatic dispersion characteristic, it is disclosed in a wavelength demultiplexing circuit disclosed in Patent Document 1 (hereinafter referred to as Conventional Technology 1) and in Patent Document 2 (hereinafter referred to as Conventional Technology 2). Chromatic dispersion compensator.

  However, in order to put the devices disclosed in the prior arts 1 and 2 into practical use, light is highly efficient from the medium (generally air) in contact with the photonic crystal in the photonic crystals constituting these devices. It is necessary to make it incident. That is, a non-reflective coating on the photonic crystal is required.

In general, an antireflection film 19 shown in FIG. 12 is widely known as a method for reducing the reflectance at the boundary surface to zero when two types of uniform media having different refractive indexes are in contact with each other on a plane. This is because when the refractive index of the uniform medium 21 is n ₁ and the refractive index of the uniform medium 23 is n ₃ , the refractive index n ₃ and the film thickness d of the antireflection film 33 are set for light of wavelength λ. If the following equations 1 and 2 are used, respectively, it is theoretically possible to make the reflection non-reflective.

  From the formula 2, the antireflection film is sometimes called a λ / 4 film.

  However, in the case of a photonic crystal, the refractive index cannot be simply defined as in the case of a uniform medium, and the extent of the photonic crystal region cannot be simply defined. The method of the antireflection film cannot be used as it is.

  On the other hand, as an antireflection film for a photonic crystal, a photonic crystal structure with a protrusion described in Non-Patent Document 1 (hereinafter referred to as Conventional Technology 3) has also been proposed.

  FIG. 13 is a diagram showing a structure according to the prior art 3. Referring to FIG. 13, a semi-cylinder and a triangular prism are combined at the boundary between a two-dimensional triangular lattice photonic crystal region in which an air cylinder 27 is embedded in Si25 as a background medium and a uniform Si region. An air column projection structure 29 is provided. Due to the effect of the protrusion structure 29, the transmittance at the interface between the photonic crystal and Si in contact with the photonic crystal is improved by about 15 dB compared to the case without the protrusion structure.

  However, in the example according to the prior art 3, as a practical matter, the protrusion structure has a size of about 1 μm or less, and an air column with a very sharp angle of about 10 to 20 ° is required. When such a structure is actually manufactured by dry etching or the like, the corner is expected to be rounded due to processing accuracy, and it is considered extremely difficult to accurately manufacture the designed structure.

Japanese Patent Laid-Open No. 11-271541 JP 2000-121987 62nd JSAP Scientific Lecture Proceedings 1065 pages P. Yeh et al. , J. et al. Opt. Soc. Am. Vol. 67, 423 (1977) R. Bellman and G.M. M.M. Wing, An Introduction to Invariant Imbedding, New York, McGraw-Hill, 1975

  Thus, the conventional antireflection film method for a uniform medium cannot be applied to a photonic crystal as it is, and the antireflection method using the above-described photonic crystal with a protrusion structure is very realizable. It was difficult.

  Therefore, the technical problem of the present invention is that it is possible to remove the drawbacks in the conventional method of forming an antireflection film on a photonic crystal and to reliably prevent reflection on the photonic crystal by a simpler method. An object is to provide a structure of an antireflection film on a photonic crystal.

  The structure of the antireflection film on a two-dimensional or three-dimensional photonic crystal according to the present invention is a photonic crystal in which two or more substances having different refractive indexes are regularly arranged two-dimensionally or three-dimensionally. In order to increase the incident efficiency of light into the crystal, a thin film made of one of the media constituting the photonic crystal is added to the end face of the photonic crystal.

  Also, the structure of the antireflection film on the photonic crystal according to the present invention is added to the end face of the photonic crystal in order to increase the light incident efficiency in the structure of the antireflection film on the two-dimensional or three-dimensional photonic crystal. The film thickness of the medium is the film thickness obtained by the method described in the embodiment.

  Also, the structure of the antireflection film on the photonic crystal according to the present invention is added to the end face of the photonic crystal in order to increase the light incident efficiency in the structure of the antireflection film on the two-dimensional or three-dimensional photonic crystal. The medium is composed of a medium independent of the medium constituting the photonic crystal, and the refractive index and film thickness of the medium are obtained by the method described in the embodiments.

  Also, the structure of the antireflection film on the photonic crystal according to the present invention is added to the end face of the photonic crystal in order to increase the light incident efficiency in the structure of the antireflection film on the two-dimensional or three-dimensional photonic crystal. The medium is a multilayer film composed of two or more media having different refractive indexes independent of the medium constituting the photonic crystal.

  In addition, according to the method of forming an antireflection film on a photonic crystal according to the present invention, reflection on a two-dimensional or three-dimensional photonic crystal in which two or more kinds of substances having different refractive indexes are regularly arranged two-dimensionally or three-dimensionally is performed. A method for forming an anti-reflection film, wherein the end face of the photonic crystal is formed on one of the mediums constituting the photonic crystal in order to increase the light incident efficiency into the photonic crystal. A thin film is added.

  In addition, the method of forming an antireflection film on a photonic crystal according to the present invention is a method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal. The thickness of the medium to be added is a thickness obtained by a predetermined method.

  In addition, the method of forming an antireflection film on a photonic crystal according to the present invention is a method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal. The medium to be added is a medium independent of the medium constituting the photonic crystal, and the refractive index and film thickness of the medium are obtained by a predetermined method.

  Further, in the method of forming an antireflection film on a photonic crystal according to the present invention, in the method of forming an antireflection film on a two-dimensional or three-dimensional photonic crystal, the end face of the photonic crystal is increased in order to increase the light incident efficiency. The medium to be added is a multilayer film composed of two or more media having different refractive indexes independent of the medium constituting the photonic crystal.

  In the present invention, the input / output coupling efficiency of light to the photonic crystal is improved simply and effectively by adding an antireflection film having a certain thickness to the light incident / exit end face of the photonic crystal. It is possible to provide a photonic crystal antireflection film structure and a method for forming the same.

  Embodiments of the present invention will be described with reference to the drawings.

  First, a new principle of forming an antireflection film for a one-dimensional photonic crystal (periodic dielectric multilayer film) will be described. A one-dimensional photonic crystal refers to a photonic crystal having a periodic refractive index spatial change in one direction and a uniform refractive index distribution in a direction perpendicular to the direction. Consider a case where an antireflection film is formed on the surface of the one-dimensional photonic crystal cleaved. The basic concept of antireflection film formation is based on the conventional method of antireflection coating with λ / 4 film, but the refractive index in the photonic crystal changes periodically, which is used to design the antireflection film. The key point of the invention is how to handle it.

  Here, as described in the section of the prior art, an antireflection coating method for a uniform dielectric has already been established, but an antireflection film for a one-dimensional photonic crystal (periodic dielectric multilayer film) is The present invention is the first.

FIG. 1 is a diagram showing an antireflection film (single layer) on a one-dimensional photonic crystal. The crystal shown in FIG. 1 has a structure in which a one-dimensional photonic crystal 37 in which unit cells 35 are periodically arranged in a one-dimensional manner with a lattice constant Λ and an antireflection film or an antireflection film (film thickness d ₂ ) 39 are in contact with each other at a boundary 41. Have. Internal refractive index distribution 43 of unit cell 35 may have any spatial distribution in the one-dimensional direction, the refractive index of the homogeneous medium 45 on the side where the light in FIG. 1 enters n _1, the antireflection film 39 refractive index is assumed to be n _2. Further, all the substances constituting them are assumed to be transparent media. The method for obtaining the reflectance when light is incident on the photonic crystal of FIG. 1 from the uniform medium 45 includes the following three steps.

  As a first step, an electromagnetic field in each region of the uniform medium 45, the antireflection film 39, and the one-dimensional photonic crystal 37 is developed in an eigenmode in each region. As a second step, the electromagnetic fields are connected by Maxwell boundary conditions. The third step is to solve the linear simultaneous algebraic equations obtained from the boundary conditions. This procedure is exactly the same as the method in ordinary macroscopic electromagnetism, but since the target is a one-dimensional photonic crystal, the first question is how to find the eigenmode in the one-dimensional photonic crystal. Become.

  The eigenmode in the uniform medium 45 and the antireflection film 39 is a plane wave, and since the one-dimensional photonic crystal 37 has a periodic structure, the eigenmode is a Bloch wave. This Bloch wave is obtained as an eigenvector of a transfer matrix for one period.

  In general, a transfer matrix M having a one-dimensional periodic structure made of a transparent medium can be written as the following equation (3) (see Non-Patent Document 2).

Here, in the above equation 3, a, b, c, and d are real functions determined by the structure of the unit cell, and E and H are electromagnetic fields (y component of electric field and x component of magnetic field) parallel to the surface. To express. Further, the determinant det M = 1 from the energy conservation law. The eigenvalue λ _± of the transfer matrix M and the eigenvector v _± excluding the normalization constant can be written as in the following equations (4) and (5).

  Here, k is the Bloch wave number and is an index for designating the electromagnetic field mode. In addition, since Equation 5 is an eigenmode of the periodically arranged one-dimensional photonic crystal 37, when the amplitude reflectivity is calculated by using this to establish a linear simultaneous equation from the Maxwell boundary condition, the uniform medium 56 is obtained. Amplitude reflectivity when light is vertically incident is given by the following equations (6) and (7).

Here, in Equation (6), k ₂ is the wave number of light in the antireflection film 39. In addition, the above formulas 6 and 7 are formally the same as the amplitude reflectivity when there are uniform media of refractive index n ₁ and n ₃ on both sides of the uniform medium of refractive index n ₂ , respectively. However, since a one-dimensional photonic crystal is considered here, the difference is that n ₃ is not a real refractive index having a material constant. The definition of n _{3 in} the above formula 7 is obtained by using the value at the boundary 41 of the Bloch wave (formula 5), which is an eigenmode of light in the crystal 37 that periodically spreads, to obtain the following formula 8. It is done.

  Since all the effects on the very complex reflectivity created by the one-dimensional photonic crystal having a periodic structure can be expressed by the above formula 8, the formula 8 is the core part of the present invention. It is one of.

In general, n ₃ in the above formula 8 is a complex number, so that the film thickness d ₂ and the refractive index n ₂ at which the amplitude reflectivity (formula 6) becomes zero like an antireflection coating for a uniform dielectric are set as follows. In general, it cannot be selected, but the reflectance of the photonic crystal having one non-reflective film represented by the following formula 9 can be minimized.

That is, when designing the film thickness d ₂ and the refractive index n ₂ of the non-reflective film, the first-order partial differential coefficient for d ₂ and n ₂ of the reflectivity R ₁ is zero, and the second-order partial differential coefficient is positive. What is necessary is just to obtain some n ₂ and d ₂ . Based on the above principle, it is possible to design the optimum film thickness d ₂ and refractive index n ₂ of the anti-reflection film 39 of the one-dimensional photonic crystal having a single-layer anti-reflection film. Further, when the above equation 8 becomes a real number, that is, when the phase of the electric field and the magnetic field coincides, the reflection can be zeroed by the antireflection coating. When the boundary between the one-dimensional photonic crystal and the antireflection film is selected as the mirror surface of the infinite one-dimensional photonic crystal, the above equation (5) is always a real number, so the boundary is zero for reflection with a non-reflective coating. You can choose the face. Therefore, it is important to select the boundary like that. Even in the general case where there is no mirror surface, reflection can be minimized by the above-described method, and reflection can be made zero by a multilayer antireflection film described below.

  Next, the design method and principle of a single-layer antireflection film on the photonic crystal described above are extended to the formation of multilayer antireflection on a one-dimensional photonic crystal. At the same time, it is extended to the case where an arbitrary incident angle and arbitrary polarized light (TM polarized light (p polarized light) or TE polarized light (s polarized light)) are incident on the one-dimensional photonic crystal.

  FIG. 2 is a diagram illustrating a case where an N-1 antireflection film is formed on a one-dimensional photonic crystal and light is incident at an arbitrary angle and with an arbitrary polarization. In FIG. 2 (in the case of a multilayer antireflection film) and FIG. 1 (in the case of a single-layer antireflection film), (A) the point that the antireflection film changes from a single layer to a multilayer, and (B) the light has an arbitrary incident angle. Definition of the boundary 41 between the one-dimensional photonic crystal and the antireflection film, except for the three points (C) where the light has an arbitrary polarization (TM or TE). In the definition of the cell 35 and the unit cell 35, a crystal having the same conditions as in FIG.

Since the above equation 8 and the above equation 7 representing the amplitude reflectivity r ₂ , ₃ can determine the amplitude reflectivity when light is incident on the one-dimensional photonic crystal from a uniform medium having a refractive index n ₂ , reflectance _{R N-1} of the one-dimensional photonic crystal having an anti-reflection film of the N-1 layer of the following, applied as in equation 10, 11, 12, and 13 formula.

The above formula 11 is based on Non-Patent Document 3, and it should be noted that the calculation is performed recursively. k _i and d _i are the wave number and film thickness of light perpendicular to the boundary of the i-th antireflection film, and n _i (i = 1, 2,... N) is the refractive index in each region. Further, α = −1 (TM polarization), 1 (TE polarization), and β = ck _N / ωn _N ² (TM polarization), −ω / ck _N (TE polarization). It should be noted that E _k and H _{k in} Equation 13 are an electric field component and a magnetic field component parallel to the surface in each of TM polarized light and TE polarized light. Similar to the equation (Equation 6) of the reflectance of a one-dimensional photonic crystal having an antireflection film, Equation 11 is formally the same as the reflectance of the uniform dielectric multilayer film, but Equation 8 It is decisively different that the equation (13) corresponding to the equation is not a real refractive index that is a material constant. In addition, since the effect of the one-dimensional photonic crystal exhibiting very complicated behavior in the reflection of light is all incorporated into the formula 13, the formula 13 is also one of the core parts of the present invention. .

In addition, the first-order differential coefficient relating to n _i , d _i (i = 2, 3,..., N) of the reflectivity R _N-1 is zero using the above-described formula 10 to formula 13, and the second-order differential coefficient. If n _i , d _i (i = 2, 3,..., N) are obtained, the reflectivity of the one-dimensional photonic crystal having the N-1 reflective film is minimized using the design value. can do.

  The design method and the principle of the antireflection film composed of the N-1 layer and its refractive index do not depend on the incident angle and polarization direction of incident light, and do not depend on the number of antireflection films to be coated. Generally holds. Furthermore, as in the case of a single layer, since it does not depend on the type, number, shape, and thickness of the substance constituting the unit cell, it can be applied to a one-dimensional photonic crystal having any multilayer antireflection film.

Next, as a reference example, it has a single-layer antireflection film, and the unit cell of the periodic part is composed of two layers of SiO ₂ (refractive index 1.5) amorphous Si (refractive index 3.5) having the same film thickness. Consider the crystals that are being made.

FIG. 3 is a diagram showing a map of the film thickness d ₂ and the refractive index n ₂ of the antireflection film that minimizes the reflectance obtained using the above-described principle. In FIG. 3, the film thickness on the vertical axis is normalized by λ ₀ / 4n ₂ (λ ₀ is the wavelength in vacuum). B1 to B5 in FIG. 3 represent the first band to the fifth band in ascending order of energy, and the reason why each appears as a curve on the map is that the optimum film thickness d ₂ and refractive index n ₂ are photo. This is because it depends on the band of the nick crystal and the wavelength of light.

FIG. 4 shows the reflectance calculated using the optimum film thickness d ₂ and refractive index n ₂ obtained in FIG. The solid line in FIG. 4 represents the reflectance of the crystal coated with the antireflection film, and the dotted line represents the reflectance when no antireflection film is present. 4 (a), 4 (b), and 4 (c) show the minimum reflection when the normalized light frequency (Ω = Λ / λ) is 0.5, 0.7, and 0.9, respectively. The frequency is indicated by an arrow.

  As can be seen from FIG. 3, at the light frequency indicated by the arrow, the reflectance (solid line) with the antireflection film is very close to zero, and the reflectance without the antireflection film (dotted line) is reduced. You can see that

FIG. 5 shows the reflectivity of the antireflective coating used in the calculation of FIG. 4 (thickness d ₂ , refractive index n ₂ ) is indeed a value that minimizes the reflectivity. The thickness d ₂ and refractive index n ₂ dependence of the non-reflective film are plotted with contour lines. The contour lines are drawn with 10 lines at equal intervals between the maximum value and the minimum value. In addition, the maximum value of the reflectance is black, the minimum value is white, and a gradation is added. The point indicated by x is the optimum design value used in the calculation of the reflectance in FIG. 4, and it can be confirmed that the reflectance is indeed the minimum at the design value.

The first embodiment of the present invention has been described above based on the principle of the method for forming an antireflection film on a one-dimensional photonic crystal. Here, the result when the unit cell is made of SiO ₂ and amorphous Si having the same film thickness and coated with a single-layer antireflection film is shown. However, the design method and the principle of the antireflection film do not depend on the type, number, shape, and thickness of the substances constituting the unit cell, and the number of antireflection films to be coated, the incident angle of incident light, and the polarization direction can be determined. Therefore, it is possible to design an optimum antireflection film (with a minimum or zero reflectance) based on exactly the same principle for a one-dimensional photonic crystal made of any transparent medium.

  In the case of a single-layer antireflection film, a structure in which only one of the refractive index and film thickness of the antireflection film is optimized is also based on the operation principle of the present invention. Further, in the case of the antireflection film composed of the N-1 layer, the structure in which either the N-1 refractive index or the N-1 film thickness of the antireflection film is optimized is also based on the operation principle of the present invention. is there. That is, even if the film thickness and refractive index are not optimum values, it is based on the operation principle of forming the antireflection film of the present invention.

Next, the structure of the antireflection film for the two-dimensional or three-dimensional photonic crystal of the present invention will be considered. The calculation of the reflectance of a two-dimensional or three-dimensional photonic crystal has a huge amount of calculation compared to that of a one-dimensional one, and it is very difficult to calculate exactly. In the one-dimensional case, the reflectance increases rapidly as it approaches the PBG, which indicates that the value of n ₃ increases rapidly. On the other hand, the parameter that rapidly increases as it approaches the PBG is the group refractive index. Here, the group refractive index is the ratio of the light velocity in vacuum to the energy propagation velocity of light in the photonic crystal, and can be obtained from the energy band structure using the following equation (14).

Thus, the n ₃ strictly determined instead by calculation, is expected to be better approximated with the group index n _g is established when designing an anti-reflection film.

  Subsequently, an antireflection film forming method for a two-dimensional or three-dimensional photonic crystal according to the first embodiment of the present invention will be described.

In the case of a one-dimensional photonic crystal, the value of n ₃ can be strictly determined by a mathematical formula as described above. However, in the case of a two-dimensional or three-dimensional photonic crystal having a more complicated structure, this method is Not applicable. Therefore, as a first approximation of the value of n _3, a group refractive index _ng that can be easily obtained from a photonic band diagram may be used. A general method such as a plane wave expansion method or a finite difference time domain (FDTD) method can be applied to the calculation of the photonic band diagram. The group refractive index _ng can be derived from the photonic band diagram using the above equation (14). By substituting _ng into Equation 1 and Equation 2, the refractive index n ₃ and the film thickness d of the antireflection film can be derived.

These values, because they are designed based on the value of n _g as a first approximation as the value of n _3, should have shifted slightly from the optimum value of the antireflection film, it must be corrected There are cases. A specific correction method is as follows. Looking at FIG. 4 showing the dependence of the refractive index and the film thickness on the reflectivity in the case of a one-dimensional crystal, there is always a certain film thickness at which the reflectivity is minimum when the refractive index is fixed to a certain value. Accordingly, the same applies to the case of a two-dimensional or three-dimensional photonic crystal, and the refractive index n ₂ obtained as described above is fixed, and the value of d is changed around the approximate value obtained above. Then, an optimal value of d that maximizes the transmittance (minimum reflectance) may be obtained using numerical calculation such as the FDTD method.

By the way, since the refractive index is a material constant, there may be a case where there is no medium having a refractive index of n ₂ or it is difficult to actually manufacture even if it exists. In that case, even if a medium having a refractive index close to n ₂ is used as the antireflection film, a certain degree of antireflection effect can be obtained. At this time, the film thickness d is regarded as a variable, and a numerical value calculation such as the FDTD method or the like is performed by using a value that becomes a λ / 4 film as an initial value, and an optimum value d of the film thickness that maximizes the transmittance can be found.

  FIG. 6 is a diagram showing a second embodiment relating to the formation of an antireflection film on a two-dimensional or three-dimensional photonic crystal according to the present invention based on such a principle. As an example in this case, the photonic crystal 51 of FIG. 6 has a two-dimensional triangular lattice structure, the background medium is Si (refractive index 3.5) 53, and the atomic medium is air (refractive index 1.0) 55. Lattice constant a = 0.75 μm and air cylinder diameter d = 0.65 μm. At this time, d / a = 0.867, and the energy band structure for this photonic crystal is given in FIG. The photonic crystal has an incident end face 57 and an outgoing end face 59 for light. Here, the boundary of the photonic crystal region is defined as a cut surface in contact with the air cylinder of the photonic crystal that continues infinitely. Therefore, in the case of FIG. 6, the boundary surface of the photonic crystal region corresponds to the boundary (i) in FIG. In addition, the outside of the photonic crystal is an air layer in this case.

  Since a wavelength demultiplexer or the like uses a relatively high frequency (high energy) region, attention is now focused on a band having a propagation mode at a normalized frequency Ω of 0.456 to 0.496. When a = 0.75 μm, from Ω = a / λ, this band is a band corresponding to 1.512 μm to 1.645 μm in terms of wavelength.

  FIG. 7 is a diagram showing the group refractive index in the photonic crystal of the present invention, calculated from the photonic band diagram of FIG. The group index of refraction is at least about 10 and rapidly increases from about several tens to about 100 as the band edge is approached. Therefore, in this case, when the antireflection coating is not applied, the difference in refractive index from air (refractive index 1) is large, so that it is expected that large reflection occurs at the interface.

  FIG. 8 (i) shows the calculation result of the light transmission spectrum when the input / output end face is the boundary of the photonic crystal region (when there is no antireflection film). The FDTD method was used for the calculation. A transmission spectrum was calculated by making a short pulse incident from the outside of the incident end face, monitoring the time waveform outside the outgoing end face, and subjecting it to Fourier transform. From the calculation results, it can be seen that the light transmittance is at most several percent in the wavelength band of interest. Note that the vibration structure is seen in the transmission spectrum because a finite calculation region of 20 μm × 20 μm is set and the influence of multiple reflection of light occurs between the incident end face and the outgoing end face.

In this state, almost no light can be incident on the photonic crystal, so that it is necessary to provide an antireflection structure. Since the refractive index of the medium in contact with the photonic crystal is 1, assuming that the wavelength for preventing reflection is λ = 1.55 μm and the group refractive index at this time is _ng = 10 from FIG. Is used to derive n ₂ = (10 * 1) ^1/2 = 3.2 as the refractive index of the antireflection film. Since this is only an approximation, it is considered here that Si of the background medium having a refractive index of 3.5 is used as the antireflection film. At this time, the film thickness as the λ / 4 film is derived to be 0.11 μm. With this value as the center, transmittance calculation for several film thicknesses is performed using the FDTD method, and a film thickness that maximizes the transmittance may be found. In this case, the optimum value of the film thickness was 0.10 μm.

  FIG. 8 (ii) shows the transmittance when d = 0.10 μm which is the optimum value. If such a method is used, it is possible to realize a transmittance of 80% or more in the considered wavelength band, and the transmittance is improved by 10 times or more compared with (i).

  Thus, the transmittance can be increased to 80% or more simply by setting the thickness of the Si layer constituting the photonic crystal to a certain value at the light input / output end face. This method does not need to be provided with a fine protrusion structure on the incident / exit end face as in the conventional example, and simply provides a flat surface and can be easily realized.

FIG. 9 is a diagram showing a second embodiment relating to a structure for preventing reflection to a photonic crystal according to the present invention. In the reference example, the background medium of the photonic crystal functions as an antireflection film. In this case, the refractive index of the antireflection film is the same as the refractive index of the background medium of the photonic crystal. There were restrictions on the optimal design conditions. Therefore, in the second embodiment, in order to remove the restriction, the antireflection film can be made closer to the optimum condition as the antireflection film by using a medium independent of the background medium of the photonic crystal. FIG. 9 shows this structure. After processing the end face of the photonic crystal, a medium having an appropriate refractive index such as an amorphous Si thin film 65 is formed on both end faces by vapor deposition or the like. It is also possible to use a medium that forms a film different from the background medium of the photonic crystal. In this case, the refractive index of the antireflection film needs to be an intermediate value between the group refractive index of the photonic crystal and the medium in contact therewith. Furthermore, the refractive index of the antireflection film is more preferably a value close to the refractive index n ₂ obtained by the above equation (1). Based on this refractive index, the optimum design of the film thickness can be made by using the numerical value calculation by the FDTD method using the approximate value of the film thickness with respect to the design wavelength in Equation 2 as a starting point.

  In addition, if this method is used, even if the thickness of the antireflection film is deviated from the design in the first embodiment described above, the thickness of the film formed thereon can be adjusted. It is also possible to compensate for the deviation.

  In the case of a two-dimensional or three-dimensional photonic crystal, a multilayer film in which two or more layers having different refractive indexes are overlapped may be used as an antireflection film as in the one-dimensional case according to the reference example. In this case, the design method of the film thickness or the like may be expressed by the following expression (Expression 10) to Expression 13 in the case of a one-dimensional photonic crystal. The multilayer film may have a photonic crystal structure in which media having different refractive indexes are periodically arranged.

In this embodiment, Si and air are taken as examples of the medium constituting the photonic crystal, but any material that is transparent at the operating wavelength such as a compound semiconductor such as GaAs or an insulator such as SiO ₂ can be used. It may be a medium. In addition to the triangular lattice shown in the present embodiment, other two-dimensional photonic crystals such as a square lattice and a hexagonal lattice, or a three-dimensional photonic crystal such as a diamond structure may be used.

  Further, although the λ / 4 film is used as the antireflection film, the film thickness may be 3λ / 4, 5λ / 4,...

  Furthermore, in the present embodiment, a photonic crystal having a two-dimensional triangular lattice structure whose structure is sufficiently long in the direction perpendicular to the paper surface of FIG. 6 has been described as an example, but its thickness is approximately the same as the lattice constant. It may be a slab photonic crystal whose upper and lower sides are sandwiched between low refractive index media such as air. At this time, the band structure of the slab type photonic crystal is obtained, the group refractive index is further derived, and the FDTD method is also used to determine the Si layer thickness for realizing antireflection by the above procedure.

  As described above, the present invention is applied to an optical device or the like in an optical communication system such as a wavelength demultiplexing circuit or a wavelength dispersion compensator.

It is a figure for demonstrating the structure of the anti-reflective film (single layer) to a one-dimensional photonic crystal. It is a figure for demonstrating the structure of the antireflection film (N-1 layer) to a one-dimensional photonic crystal. It is the figure which mapped the film thickness and refractive index of the optimal antireflection film with respect to a one-dimensional photonic crystal. It is the figure which showed the reflectance with respect to the optimal anti-reflective film with respect to a one-dimensional photonic crystal. It is the figure which showed the refractive index and the film thickness dependence of the reflectance of a one-dimensional photonic crystal. It is a figure which shows 1st Embodiment of the photonic crystal which has the reflection preventing structure by this invention. It is the figure which showed the group refractive index with respect to the photonic crystal structure in 1st Embodiment by this invention. It is the figure which showed the change of the transmission spectrum by the difference in the incident / exit end surface of the light of the photonic crystal corresponding to (i) and (ii) in FIG. It is a figure which shows 2nd Embodiment of the photonic crystal which has an antireflection structure by this invention. (A) It is the figure which looked at the structural example of the two-dimensional photonic crystal from the upper surface.

(B) It is the figure which showed the 1st Brillouin zone with respect to a two-dimensional photonic crystal structure.
It is an example of a calculation of the energy band figure with respect to the structure of Fig.10 (a). It is a figure for demonstrating the design method of the anti-reflective film in the interface of two uniform media from which a refractive index differs. It is a figure for demonstrating the prior art example which has the reflection preventing structure with respect to a photonic crystal.

Explanation of symbols

15 Background medium 17 Atomic medium 19 Antireflection film 21 Uniform medium 23 Uniform medium 25 Si
27 air cylinder 29 projection structure 31 incident light 33 outgoing light 35 unit cell of photonic crystal 37 one-dimensional photonic crystal 39 antireflection film (non-reflection film)
41 Boundary between photonic crystal and uniform medium 43 Refractive index distribution 45 Uniform medium 47 Antireflection film (nonreflective film)
51 photonic crystal 53 Si
55 Air 57 Light incident end face 59 Light outgoing end face 61 Incident light 63 Outgoing light 65 Amorphous Si thin film

Claims (8)

  In a two-dimensional or three-dimensional photonic crystal in which two or more kinds of substances having different refractive indexes are regularly arranged two-dimensionally or three-dimensionally, in order to increase the incident efficiency of light into the photonic crystal, the photo A structure of an antireflection film for a two-dimensional or three-dimensional photonic crystal, wherein a thin film made of a medium made of one of the media constituting the photonic crystal is added to an end face of the nick crystal.   2. The structure of the antireflection film on the two-dimensional or three-dimensional photonic crystal according to claim 1, wherein a film thickness of a medium added to the end face of the photonic crystal is obtained by a predetermined method in order to increase light incident efficiency. The structure of an antireflection film on a two-dimensional or three-dimensional photonic crystal, characterized by having a different film thickness.   2. The structure of an antireflection film for a two-dimensional or three-dimensional photonic crystal according to claim 1, wherein the medium added to the end face of the photonic crystal in order to increase the light incident efficiency constitutes the photonic crystal A structure of an antireflection film on a two-dimensional or three-dimensional photonic crystal, which is made of an independent medium and whose refractive index and film thickness are obtained by a predetermined method.   4. The structure of an antireflection film for a two-dimensional or three-dimensional photonic crystal according to claim 3, wherein the medium added to the end face of the photonic crystal in order to increase the light incident efficiency constitutes the photonic crystal. A structure of an antireflection film on a two-dimensional or three-dimensional photonic crystal, characterized in that it is a multilayer film composed of two or more media having different refractive indexes.   A method of forming an antireflection film on a two-dimensional or three-dimensional photonic crystal in which two or more kinds of substances having different refractive indexes are regularly arranged two-dimensionally or three-dimensionally. 2D or 3D photonic crystal, characterized in that a thin film made of a medium made of one of the media constituting the photonic crystal is added to the end face of the photonic crystal in order to increase the incident efficiency of the photonic crystal. Of forming an antireflection film on the surface.   6. The method of forming an antireflection film on a two-dimensional or three-dimensional photonic crystal according to claim 5, wherein the film thickness of the medium added to the end face of the photonic crystal is increased by a predetermined method in order to increase the light incident efficiency. A method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal, wherein the film thickness is determined.   6. The method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal according to claim 5, wherein a medium added to an end face of the photonic crystal in order to increase light incident efficiency constitutes the photonic crystal. A method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal, comprising a medium independent of the medium, wherein the refractive index and film thickness of the medium are determined by a predetermined method.   8. The method of forming an antireflection film on a two-dimensional or three-dimensional photonic crystal according to claim 7, wherein a medium added to an end face of the photonic crystal in order to increase light incident efficiency constitutes the photonic crystal. A method for forming an antireflection film on a two-dimensional or three-dimensional photonic crystal, which is a multilayer film composed of two or more media having different refractive indexes independent of the medium.

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