JP2015161838A - Optical resonator, and coupled optical resonator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make an optical resonator small-sized.SOLUTION: An optical resonator 1 includes a first input/output port 2, a second input/output port 3 and a resonator wall 4. The resonator wall 4 is formed in such a manner that a direction vertical to a lamination direction becomes a normal direction, and includes a plurality of reflection parts 41 for fully reflecting light inputted from the first input/output port 2 multiple times and outputting the fully reflected light from the second input/output port 3. A first optical resonator is characterized in that there is a portion where tracks cross each other, on a track of light inputted from the first input/output port 2 until outputted from the second input/output port 3. In a second optical resonator, Q is an integer equal to or greater than 5, P is an integer greater than 1 and smaller than Q/2, Q and P are primary to each other and Q pieces of points circumferentially disposed at equal intervals in a core layer are defined as apexes. The second optical resonator is characterized in that a track of light inputted from the first input/output port 2 until outputted from the second input/output port 3 becomes a track connecting the apexes which are separated for the unit of P apexes.

Description

  The present invention relates to an optical resonator and a coupled optical resonator that can be used as an optical delay device of an optical chaos generating circuit.

  Optical resonator technology that realizes low loss and long optical path length in a limited space is, for example, return optical chaos that outputs high-speed random signals used for high-speed physical random number generation and secret communication. It is required for miniaturization of generators. In Non-Patent Document 1, an external resonator for realizing a long path length in a return light chaos generator is miniaturized by realizing it with a monolithically integrated semiconductor element.

Takahisa Harayama, Satoshi Sunada, Kazuyuki Yoshimura, Peter Davis, Ken Tsuzuki, Atsushi Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers”, Physical Review A, Vol.83, p.031803 (R), 2011.

  The return light chaos generator of Non-Patent Document 1 is a relatively small return light chaos generator, but its length is about 1 cm, and about 90% of the return light chaos generator is an external resonator for creating an optical delay. is occupying. That is, it is effective to use a space-saving external resonator for downsizing the return light chaos generator.

  An object of the present invention is to reduce the size of an optical resonator for producing an optical delay.

  In the optical resonator of the present invention, a core layer through which light propagates and two cladding layers sandwiching the core layer to confine light in the core layer are laminated. A first input / output port, a second input / output port, and a resonator wall are provided. The first input / output port and the second input / output port are two input / output ports for inputting / outputting light in a direction perpendicular to the stacking direction to / from the core layer. The resonator wall is formed such that the direction perpendicular to the stacking direction is the normal direction, and the light input from the first input / output port is totally reflected a plurality of times and output from the second input / output port. A plurality of reflecting portions. In the first optical resonator of the present invention, there are portions where the trajectories intersect in the trajectory until the light input from the first input / output port is output from the second input / output port. In the second optical resonator of the present invention, Q is an integer greater than or equal to 5, P is an integer greater than 1 and less than Q / 2, Q and P are relatively prime, and Q is arranged in the core layer at equal intervals circumferentially. A trajectory connecting light points input from the first input / output port to the light output from the second input / output port is a trajectory connecting apexes separated by P pieces.

  The coupled optical resonator of the present invention includes M optical resonators of the present invention, and the second input / output port of the mth optical resonator and the first input / output port of the (m + 1) th optical resonator are coupled. The light input to the first input / output port of the first optical resonator is output from the second input / output port of the Mth optical resonator. However, M is an integer of 2 or more, and m is an integer of 1 to M-1.

  According to the first optical resonator of the present invention, since the light is totally reflected by the resonator wall so that the trajectories of light intersect, the path length can be increased while suppressing optical loss even in a narrow range. Therefore, the optical resonator can be reduced in size. According to the second optical resonator of the present invention, since the light reflecting position and the design guideline for the order are shown, it is easy to realize a small optical resonator. Further, since the coupled optical resonator of the present invention is a combination of a plurality of the optical resonators of the present invention, the path length can be increased while suppressing optical loss even in a narrow range.

The perspective view which shows the external appearance of the optical resonator of this invention. Sectional drawing which cut | disconnected the core layer of the optical resonator by the surface perpendicular | vertical to az axis. The figure which shows the orbit of the light in the case of FIG. The figure which shows the example of the coupling optical resonator which couple | bonded nine optical resonators. The figure which shows the example of the coupling optical resonator which couple | bonded 25 optical resonators.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the structure part which has the same function, and duplication description is abbreviate | omitted.

  FIG. 1 is a perspective view showing the appearance of the optical resonator of the present invention. In the optical resonator 1, a core layer 8 in which light propagates and two clad layers 9 sandwiching the core layer 8 in order to confine light in the core layer 8 are laminated. In FIG. 1, the stacking direction is the z-axis direction. FIG. 2 is a cross-sectional view of the core layer of the optical resonator taken along a plane perpendicular to the z-axis. FIG. 2A is a diagram showing a shape viewed from the stacking direction, and FIG. It is a figure for demonstrating. FIG. 3 is a diagram showing the trajectory of light in the case of FIG. 2, FIG. 3A is an example in which light input from the input / output port 2 is output from the input / output port 3, and FIG. An example in which a mirror is arranged at the input / output port 3 is shown.

The optical resonator 1 includes an input / output port 2, an input / output port 3, and a resonator wall 4. The input / output ports 2 and 3 are two input / output ports that input / output light in the direction perpendicular to the stacking direction (z direction) (light parallel to the xy plane) to the core layer 8. The resonator wall 4 is a boundary between materials having different refractive indexes, and is formed so that a direction perpendicular to the stacking direction (a direction parallel to the xy plane) is a normal direction. A plurality of reflecting portions 41 for totally reflecting the emitted light a plurality of times and outputting from the input / output port 3 are provided. In the following, the refractive index inside the resonator wall 4 (the side through which light passes) is n ₁ , and the refractive index outside is n ₂ . The optical resonator 1 may be formed of a laminated structure of the core layer 8 and the clad layer 9 with a semiconductor such as GaAs or Si.

Q is an integer of 5 or more, P is an integer greater than 1 and less than Q / 2, Q and P are relatively prime, and Q points arranged in the core layer 8 are vertices C ₁ ,..., C _Q. The resonator wall 4 has a distance from the center point O when viewed from the stacking direction (z direction).

Where φ is an angle formed by a half line in the positive direction of the x axis starting from the center O and a line segment connecting the center O and one point of the resonator wall 4, r ₀ is a predetermined length, and ε Is formed in a shape shown like a predetermined parameter. The vertices C ₁ ,..., C _Q are points where the curvature is minimized, that is,
φ = (2m−1) π / Q (m = 1, 2,..., Q)
It is a position. The (Q-2) number of vertices are on the resonator wall 4, and the light input from the input / output port 2 passes through one vertex other than the (Q-2) number of vertices, and the input / output port. The light output from 3 passes through the other apex other than the (Q-2) apexes. The light (beam) input from the input / output port 2 generally spreads as it travels. However, by adjusting the curvature of the reflection portion 41 in the resonator wall 4, the expanded beam is condensed and reaches the input / output port 3. , There can be no loss due to spreading. Specifically, the track connecting the input / output port 2 and the input / output port 3 may be stabilized. ε is a parameter for stabilizing the orbit of light, and the orbit can be stabilized by appropriately selecting this value (Reference 1: Takuhisa Harayama and Katsuhiro Nakamura, “Quantum Chaos-Quantum Billiard Niwa, Bafukan, 2000). For example, r ₀ = 100 μm, ε = 0.005, d = 20 μm.

The example of FIG. 2 is a shape when Q = 10 and P = 3. The eight vertices C ₂ ,..., C ₇ , C ₉ , C ₁₀ are on the resonator wall 4, the vertex C ₁ is a position through which light input from the input / output port 2 passes, and the vertex C ₈ is The light output from the input / output port 3 is in a position where it passes. Since the light has a spread, the reflector 41 has a predetermined range including any one of the vertices C ₂ ,..., C ₇ , C ₉ , C ₁₀ (the reflected light sufficient for the incident beam). Range in which power can be obtained).

In the optical resonator 1, the trajectory until the light input from the input / output port 2 is output from the input / output port 3 is a trajectory connecting apexes separated by P pieces, and the incident angle is at the apex where the light is reflected. The critical angle should be exceeded. Since Q and P are relatively prime, the light passing through the vertex C ₁ repeats reflection and follows the vertex as follows.

In the example of FIG. 2, since Q = 10 and P = 3,
C ₁ → C ₄ → C ₇ → C ₁₀ → C ₃ → C ₆ → C ₉ → C ₂ → C ₅ → C ₈ → C ₁
become that way. Further, in the example of FIG. 2, there are input and output ports 2 to the position of the apex C _1, since the input and output port 3 to the position of the vertex C _8, as shown in FIG. 3 (A), input and output ports The light input from 2 is output from the input / output port 3 after repeating reflection eight times. The input / output port selection need not be limited to the above example, and any two vertices may be selected. However, as the number of reflections on the resonator wall 4 increases, the effect of increasing the path length increases. In particular, since P is an integer greater than 1, the vertex can be selected so that the light trajectories intersect. At this time, it is easy to obtain the effect of increasing the path length in a narrow space. Specifically, when the number of reflections is R, the relationship between Q, P, and R is (R + 1) P> Q
In this case, since the tracks intersect at least once, it is easy to obtain the effect of increasing the path length. That is, the number of reflections R is R> Q / P−1.
If the vertices of the input / output ports 2 and 3 are selected so that

<Evaluation of the road head>
The distance s between vertices separated by P is

It is. (Q-2) When the reflection is performed, the path length L from the vertex of the input / output port 2 to the vertex of the input / output port 3 is

It becomes. Therefore, by increasing the value of Q, by selecting the values of P such that the value of P / Q is close to its maximum value 1/2, r ₀ tends to ensure a longer path length is also the same. However, in order to physically guarantee the existence of the path, the distance between adjacent vertices Δs≈ (2πr ₀ ) / Q is determined by the wavelength λ = λ ₀ / n ₁ (λ ₀ of the light in the optical resonator 1. Is a wavelength in vacuum and n ₁ is sufficiently larger than the refractive index inside resonator 1), so there is an upper limit for Q,

Must be met. For example, when r ₀ = 100 (μm) GaAs semiconductor resonator (refractive index n ₁ = 3.3, oscillation wavelength λ ₀ = 0.86 μm),
(2πr ₀ ) /λ≈2.4×10 ³
It is.

On the other hand, the theoretical minimum value of Q for the present invention is 5, and P in that case is 2. When P = 2, it is reflected like a star. However, in this case, since the incident angle to the resonator wall 4 is an acute angle and the conditions for total reflection described later must be satisfied, it is necessary to form the optical resonator 1 with a material having a high refractive index. Considering these, it is appropriate to set Q = 10 when the refractive index n ₁ = 3.3 inside the optical resonator 1.

In the above has been described using a GaAs-based semiconductor as a material for forming an optical resonator, small absorption of light, as long as it is a substance having a higher refractive index than the outer refractive index n _2, the optical resonator Other substances may be formed. For example, using a material containing a semiconductor of Si, Ge, AlAs, SiC, InP, InAs, GaP, GaN, AlN, GaAs, ZnSe, or ZnO, or a mixed crystal semiconductor of any of these semiconductors, A laminated structure of the layer 8 and the clad layer 9 may be formed.

<Total reflection conditions>
For total reflection, the critical angle θ _c is

(Where n ₁ is the refractive index inside the resonator wall 4 and n ₂ is the refractive index outside). On the other hand, the incident angle θ of light at the vertex where the light is reflected is

So, it may be selected Q and P such that θ> θ _c. In other words, Q and P are

It may be selected so as to satisfy. If Q and P are selected in this way, a long path length can be secured in a narrow area while maintaining a low loss. In the case of the example in FIG. 2, the light incident angle θ is 36 degrees at the vertices C ₂ ,..., C ₇ , C ₉ , C ₁₀ where the light is reflected. When the optical resonator 1 is formed of a GaAs-based semiconductor and the outside of the resonator wall 4 is air, n ₁ = 3.3 and n ₂ = 1, so that the critical angle θ _c for total reflection is obtained. Is about 17.6 degrees. Therefore, since the incident angle is larger than the critical angle, the reflection at the resonator wall 4 becomes total reflection, and loss due to transmission can be suppressed.

<When a mirror is placed>
FIG. 3B shows an example in which a mirror is arranged at the input / output port 3. The mirror can be formed, for example, by depositing metal or the like on the end face of the input / output port. As described above, the mirror 7 may be disposed in the input / output port 3, and the light reflected by the mirror 7 may be input from the input / output port 3 and output from the input / output port 2. In this case, the path length is doubled, and the path length 2L of the light input from the input / output port 2, reflected by the mirror 7 and output from the input / output port 2 is

It becomes. For example, when r ₀ = 100 μm, Q = 10, P = 3, n ₁ = 3.3,
2L≈29.2 × r ₀ ≈2.92 (mm)
Is obtained.

<Extraction of superordinate concepts>
In the above description, the shape of the formula (1) is shown. And if it is this shape, since total reflection is repeated so that the track | orbit of light cross | intersects in the space inside the resonator wall 4, a path length is lengthened using the space inside the resonator wall 4 efficiently. Yes (first effect). In addition, since the position where light is reflected and the design guideline for the order are shown, it is easy to realize a small optical resonator (second effect). However, it is possible to slightly deform this shape within a range in which the above effect can be obtained. Therefore, for each effect, a point where the effect is obtained is shown, and a superordinate concept is extracted.

  Considering only to obtain the first effect, the resonator wall 4 does not have to be limited to the shape represented by the equation (1). For example, the portion other than the portion necessary for light reflection (reflecting portion 41) may not have the shape described above, and the effect of the present invention can be obtained without the resonator wall 4. In other words, the resonator wall 4 is “for the light input from the input / output port 2 (first input / output port) to be totally reflected a plurality of times and output from the input / output port 3 (second input / output port)”. The first effect is obtained by satisfying the feature that the trajectory having a plurality of reflecting portions 41 and the light input from the input / output port 2 is output from the input / output port 3 has a portion where the trajectories cross each other. Can be obtained.

  The second effect is that “Q is an integer of 5 or more, P is an integer greater than 1 and less than Q / 2, Q and P are relatively prime, and Q points arranged circumferentially at equal intervals in the core layer 2 or more (Q-2) or less so that the trajectory connecting the vertices separated by P is the trajectory from the first input / output port until the light input from the first input / output port is output from the second input / output port. It is easy to obtain by following the design guideline “disposing the reflective portion 41”.

  FIG. 4 shows an example of a coupled optical resonator in which nine optical resonators are coupled, and FIG. 5 shows an example of a coupled optical resonator in which 25 optical resonators are coupled. In this embodiment, a plurality of optical resonators 1 are connected as a basic structure (referred to as “cell”). The coupled optical resonators 10 and 20 couple the input / output ports and the input / output ports of adjacent cells so that the tracks are connected. In other words, M is an integer of 2 or more, m is an integer of 1 to M-1, and the second input / output port of the mth optical resonator and the first input / output port of the (m + 1) th optical resonator. Join. Accordingly, light input to the input / output ports 12 and 22 (first input / output port) of the first optical resonator is input from the input / output ports 13 and 23 (second input / output port) of the Mth optical resonator. Is output. Further, a mirror is disposed at the input / output ports 13 and 23, and the light reflected by the mirror is input from the input / output ports 13 and 23 of the Mth optical resonator, and the input / output port 12 of the first optical resonator. , 22 may be output.

An amount τ obtained by summing the path lengths of all the cells constituting the coupled optical resonator of the present embodiment is given by the following equation (5). When mirrors are arranged at the input / output ports 13 and 23, the path length is 2τ.

Here, N is the number of cells per vertical and horizontal direction, and coefficients α and β are defined by equations (6) and (7).

  FIG. 4 is an example in which nine optical resonators 1 are coupled, and FIG. 5 is an example in which 25 optical resonators 1 are coupled. However, it is not necessary to limit to these numbers, and coupling is performed according to the path length that must be secured. The number of optical resonators 1 may be determined as appropriate. According to this method, each cell itself realizes a long-distance total reflection path, and further, by laying them two-dimensionally, a two-dimensional region can be efficiently used to realize a long-distance total reflection path. . Therefore, the path length can be increased even in a narrow range.

  The present embodiment is a return optical chaos generator using the optical resonator of the first embodiment or the coupled optical resonator of the second embodiment as an external resonator. The basic configuration of the return light chaos generating device is composed of a laser resonator and an external resonator for returning a part of the output light. An external resonator that requires a long path length is realized by the optical resonator of the first embodiment or the coupled optical resonator of the second embodiment.

  It has been experimentally and theoretically shown that a sufficiently long external resonator is required in order to generate stable high-speed random fluctuations by the return light chaos generator. For example, although the exact path length is not shown, it has been experimentally confirmed that stable high-speed random fluctuations can be generated if the path length is about 1 cm (see Non-Patent Document 1).

If the radius parameter of the resonator corresponding to a single cell in FIG. 4 is r ₀ = 100 μm, the overall length of the coupled optical resonator is 600 μm, and the path length τ from the input / output port 12 to the input / output port 13 is Is 1.07 cm. When the light is reflected at the input / output port 13, the return light path is doubled. Therefore, it is possible to form a path length that is long enough to generate stable high-speed random fluctuations using an area of 1 mm square or less.

In the above equation (5), the coefficient α itself is a large number, and is proportional to the number N ² of cells. Therefore, when the vertical and horizontal lengths of the system according to this method are set to D, the coefficient α is proportional to D ^2. You can earn a path head.

According to the present invention, as shown in the first embodiment, a semiconductor microresonator having a low loss and a long distance path can be realized. Further, as shown in Example 2, using the method of combining a plurality of micro-resonators, for the length D of the device, the path length increases in proportion to D ^2, effectively a two dimensional area It can be used to earn a path length.

  The present invention is not limited to the above-described embodiment, and it goes without saying that modifications can be made as appropriate without departing from the spirit of the present invention.

  The high-speed random fluctuation of the laser output obtained by the return light chaos generating device can be applied to, for example, high-speed physical random number generation and secret communication. Therefore, according to the return light chaos generator using the optical resonator of the present invention as an external resonator, high-speed physical random number generation and a secret communication device can be reduced in size. Further, the optical resonator of the present invention can be applied to an optical gyro, an optical delay device, an optical memory, and the like that require a long path length in addition to a return optical chaos generator.

DESCRIPTION OF SYMBOLS 1 Optical resonator 2, 3, 12, 13, 22, 23 Input / output port 4 Resonator wall 7 Mirror 8 Core layer 9 Clad layer 10, 20 Coupled optical resonator 41 Reflection part

Claims (8)

A core layer through which light propagates;
Two cladding layers sandwiching the core layer to confine light in the core layer;
Are stacked,
A first input / output port and a second input / output port which are two input / output ports for inputting / outputting light in a direction perpendicular to the stacking direction to / from the core layer;
A resonator wall formed so that the direction perpendicular to the stacking direction is the normal direction,
The resonator wall has a plurality of reflecting portions for totally reflecting the light input from the first input / output port a plurality of times and outputting the light from the second input / output port,
An optical resonator characterized in that there is a portion where the trajectories intersect in the trajectory until the light input from the first input / output port is output from the second input / output port. A core layer through which light propagates;
Two cladding layers sandwiching the core layer to confine light in the core layer;
Are stacked,
A first input / output port and a second input / output port which are two input / output ports for inputting / outputting light in a direction perpendicular to the stacking direction to / from the core layer;
An optical resonator including a resonator wall formed so that a direction perpendicular to the stacking direction is a normal direction,
Q is an integer greater than or equal to 5, P is an integer greater than 1 and less than Q / 2, Q and P are relatively prime, and Q points arranged at equal intervals in a circle in the core layer are apexes,
The resonator wall has two or more (Q-2) reflecting portions that totally reflect light within a predetermined range including any one of the vertices,
The reflection unit totally reflects the light input from the first input / output port so as to pass through any one of the vertices a plurality of times, and passes through any one of the vertices. 2 Output from the input / output port,
An optical resonator in which a trajectory until light input from the first input / output port is output from the second input / output port is a trajectory connecting the apexes separated by P pieces. A core layer through which light propagates;
Two cladding layers sandwiching the core layer to confine light in the core layer;
Are stacked,
A first input / output port and a second input / output port which are two input / output ports for inputting / outputting light in a direction perpendicular to the stacking direction to / from the core layer;
An optical resonator including a resonator wall formed so that a direction perpendicular to the stacking direction is a normal direction,
Q is an integer of 5 or more, P is an integer greater than 1 and less than Q / 2, Q and P are relatively prime, and Q points arranged in the core layer are vertices,
The resonator wall has a distance from a central point when viewed from the stacking direction.

Where φ is an angle formed by a predetermined half line starting from the center and a line segment connecting the center and one point of the resonator wall, r ₀ is a predetermined length, and ε is predetermined. It is formed in the shape shown as a parameter,
The vertex is
φ = (2m−1) π / Q (m = 1, 2,..., Q)
The position
(Q-2) vertices are on the resonator wall,
The light input from the first input / output port passes through one apex other than the (Q-2) apexes,
The light output from the second input / output port passes through the other vertex other than the (Q-2) vertexes,
The trajectory until the light input from the first input / output port is output from the second input / output port is a trajectory connecting the apexes separated by P pieces,
An optical resonator, wherein an incident angle is not less than a critical angle at an apex where light is reflected. The optical resonator according to claim 2 or 3, wherein
The number of times the light input from the first input / output port is reflected before being output from the second input / output port is Q / P-1.
Optical resonator characterized by more. An optical resonator according to any one of claims 2 to 4,
The inside refractive index of the resonator wall is n ₁ , the outside refractive index is n ₂ ,
Q and P are

An optical resonator characterized by satisfying An optical resonator according to any one of claims 1 to 5,
A mirror is disposed at the second input / output port;
The light reflected by the mirror is input from the second input / output port and output from the first input / output port. A coupled optical resonator comprising M optical resonators according to any one of claims 1 to 5,
M is an integer of 2 or more, m is an integer of 1 to M-1,
The second input / output port of the mth optical resonator and the first input / output port of the (m + 1) th optical resonator are coupled,
The light input to the first input / output port of the first optical resonator is output from the second input / output port of the Mth optical resonator. The coupled optical resonator according to claim 7, wherein
A mirror is disposed at the second input / output port of the Mth optical resonator;
The light reflected by the mirror is input from the second input / output port of the Mth optical resonator and output from the first input / output port of the first optical resonator. .

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