JP2006195427A - Photonic crystal directional coupler - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To make the coupling length and the high extinction ratio coexist by breaking through the relation of trade off between the coupling ratio and the extinction ratio. <P>SOLUTION: The photonic crystal directional coupler is composed of three directional coupler waveguides of A, B, and C, and each of them is provided with a common reflective symmetry plane. The A and C are the directional couplers of small energy distribution difference between odd/even modes, and the B is the directional coupler of large energy distribution difference between the odd/even modes. Because, the A, B, and C are provided with a common reflective symmetry plane, in the connection between A and B and the connection between B and C, the excitation is performed at only from the odd mode to the odd mode, and from the even mode to the even mode, and neither performed from the even mode to the odd mode nor from the odd mode to the even mode. The serially connected three directional coupler wave guides are constituted of photonic crystal. Boundaries between the central directional coupler wave guide and its both sided two directional coupler wave guides are directly connected or provided with connection regions of prescribed lengths while keeping the reflection symmetry. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a photonic crystal directional coupler that achieves both a high extinction ratio and a short bond length.

  A directional coupler is an optical device in which two symmetric waveguides are arranged in parallel (hereinafter referred to as symmetric parallel waveguides) and have a certain optical coupling. A directional coupler typically has four terminals as shown in FIG. The light incident from the terminal 1 propagates through the symmetric parallel waveguide while transferring energy to the waveguide 2-4 side, and is finally output from the terminals 3 and 4 at a certain fixed ratio. The output ratio is determined by the length of the directional coupler and the optical coupling strength between the waveguides. The optical coupling strength varies depending on the frequency of light.

  The output ratio of the terminals 3 and 4 periodically varies with respect to the length of the directional coupler when the frequency of light (coupling strength determined thereby) is constant. A state in which light is evenly output to the terminals 3 and 4 is referred to as a 50% coupled state, and a state in which the output from the terminal 4 is maximum is referred to as a fully coupled state. The length of a directional coupler in a completely coupled state is called a coupling length. In the fully coupled state, the output ratio of the terminals 4 and 3 is ideally 100%: 0%, but in practice, a certain amount of light is also output from the terminal 3. The output ratio of the terminals 3 and 4 in this completely coupled state is called the extinction ratio. The extinction ratio is often expressed in decibels (output of 3) / (output of 4), and its absolute value is large, i.e., when the output of 3 is small compared to the output of 4, the extinction ratio is It's expensive.

In general, in a directional coupler composed of a simple symmetric parallel waveguide, the coupling length decreases as the coupling rate increases. On the contrary, the extinction ratio deteriorates and the output from the terminal 3 increases (see [Trade-off relationship] section).
In the above description, the input from terminal 1 was described. However, since the structure is symmetric, when the input from terminal 1 is in a fully coupled state, the input from terminals 2, 3, and 4 are also complete. In the coupled state, the outputs to terminals 3, 2, and 1 are maximized.

  In the conventional parallel waveguide directional coupler, when the optical coupling between the waveguides is strong, the coupling length is shortened, but the extinction ratio is deteriorated. Conversely, when the coupling between the waveguides is weak, the extinction ratio is improved, but the coupling length is increased. Thus, the bond length and the extinction ratio were in a trade-off relationship. In order to incorporate the directional coupler as a part of the optical circuit, it is preferable that the length of the directional coupler, that is, the coupling length is short. However, in a directional coupler having a simple structure, the extinction ratio deteriorates when the coupling length is shortened.

  An object of the present invention is to solve such problems and to overcome the trade-off relationship between the coupling length and the extinction ratio and to achieve both a high extinction ratio and a short coupling length.

  The directional coupler of the present invention has three directional coupler waveguides connected in cascade with the same mirror symmetry plane. The two directional coupler waveguides located on both sides are directional coupler waveguides having a small difference in energy distribution between the even mode and the odd mode, and the directional coupler waveguide located in the center is The directional coupler waveguide has a large difference in energy distribution between the even mode and the odd mode. In the connection between the directional coupler waveguide located in the center and the two directional coupler waveguides located on both sides of the directional coupler waveguide, the even mode excites only the even mode and the odd mode excites only the odd mode, Excitation from the even mode to the odd mode and from the odd mode to the even mode cannot be generated. The three directional coupler waveguides connected in cascade are constituted by a photonic crystal. In addition, the boundary between the directional coupler waveguide located in the center and the two directional coupler waveguides located on both sides of the directional coupler waveguide is directly connected or predetermined while maintaining mirror symmetry. It has a connection area of the length.

  According to the present invention, it is possible to overcome the trade-off relationship between the bond length and the extinction ratio and to achieve both a high extinction ratio and a short bond length.

  Hereinafter, the present invention will be described based on examples. FIG. 4 is a diagram illustrating a directional coupler structure that embodies the present invention for eliminating the trade-off relationship. It consists of three directional coupler waveguides, A, B, and C, each with the same mirror symmetry plane. A and C are directional couplers with a small difference in energy distribution between even and odd modes, and B is a directional coupler with a large difference in energy distribution between even and odd modes. Since A, B, and C have the same mirror symmetry, even mode between AB and BC, even mode only excites even mode, odd mode only odd mode, even mode to odd mode, and even mode to odd mode. There can be no excitation to the mode.

Thus, the present invention prepares two directional coupler structures composed of symmetric parallel waveguides having a desired extinction ratio (A, C). A directional coupler B composed of a symmetric parallel waveguide having a shorter coupling length than the directional couplers A and C is prepared. (As mentioned in the prior art section, the extinction ratio of B is worse than that of A and C.)
By performing the cascade connection while maintaining the mirror symmetry in the order of the directional couplers A, B, and C, a directional coupler having an extinction ratio of A and C and a coupling length of B can be obtained.
When cascading directional couplers A, B, and C, the transmittance between eigenmodes with the same symmetry of each symmetric parallel waveguide is equalized at the interface from A to B and from B to C. There is a need to.

An eigenmode is a propagation mode that is a unit that represents the state of light propagating through a waveguide structure. In the case of a symmetric parallel waveguide, light is distributed symmetrically in each waveguide (even mode) and antisymmetric. There is a state in which light is distributed (odd mode) (FIG. 2). All of the light propagating through the parallel symmetric waveguide can be represented by the superposition of this eigenmode. In other words, light entering the parallel symmetric waveguide is decomposed into eigenmodes and propagates. The transmissivity between modes in the above text is the transmissivity through which the even mode of symmetric parallel waveguide A is transmitted to the even mode of symmetric parallel waveguide B, and the odd mode of A is transmitted to the odd mode of B. This means that the transmittance is equal (the same applies to the connection between B and C). By the way, if the symmetry between the connected waveguides is maintained, the even mode and the odd mode overlap, and the integral becomes 0, so transmission from the even mode to the odd mode, and conversely, transmission from the odd mode to the even mode occurs. I don't get it.
When cascading A, B, and C, it is possible to install a connection area to compensate for the equal transmission between eigenmodes. As a structure of the connection region, it is necessary to have the same mirror symmetry plane as that of the symmetric parallel waveguides A, B, and C in order to avoid mixing between even mode and odd mode.

ここで、+,‐は偶モード、奇モードを意味している(以後全て複合同順)。

は偶・奇モードの振幅を表す関数で、次の対称性をもつ。

また、ｋ_±は偶・奇モードの伝播定数を表す。
(フォトニック結晶の場合は、さらに並進対称性が加わるので、

が成り立つ。Tは導波路進行方向の周期)
なお、座標軸は図３に示すようにとっている。 [Trade-off relationship]
Light propagating through a directional coupler composed of two parallel waveguides is represented by a linear combination of two eigenmodes. The two eigenmodes are as follows:

Here, + and-mean even mode and odd mode (all in the same composite order).

Is a function representing the amplitude of the even / odd mode and has the following symmetry.

K _± represents the propagation constant of the even / odd mode.
(In the case of photonic crystals, translational symmetry is added.

Holds. T is the period of the waveguide travel direction)
The coordinate axes are as shown in FIG.

  A directional coupler is a parallel waveguide in which light that is concentrated in one waveguide is propagated by a certain distance (coupling length), and light is transferred to the remaining waveguide. It is a device. A state where the extinction ratio is high in the directional coupler means a state where light is distributed only on one side of the parallel waveguide. A directional coupler with a low extinction ratio cannot completely fulfill the purpose of transferring light to the opposite side of the parallel waveguide, so the extinction ratio is an important value that represents the performance of the directional coupler. is there.

を満たせばよい。ここで、

であれば、式(2)の対称性から

が成立する。
そこで、

を満たす係数を用いて線形和をとれば、

となり、ｘ＜０のみに光が存在し、高消光比が獲られることがわかる。
ここで、式(5)と式(2)をあわせて考えると、

となる。これは、

が等しくなることが高消光比を得る条件であることを意味する。 In order to obtain a high extinction ratio, it is necessary that the light is concentrated only on one side of the waveguide, that is, x> 0 or x <0 in FIG. The light in the parallel waveguide can be expressed by a linear sum of eigenmodes as described above. Therefore, a condition for obtaining a form in which a value exists only at x <0 as a linear sum at a certain position z = z ₀ is a condition for obtaining a high extinction ratio. That means

Should be satisfied. here,

Then, from the symmetry of equation (2)

Is established.
Therefore,

If we take a linear sum using coefficients that satisfy

It can be seen that light exists only at x <0 and a high extinction ratio is obtained.
Here, when combining Equation (5) and Equation (2),

It becomes. this is,

Means that it is a condition for obtaining a high extinction ratio.

であれば、偶モードと奇モードの和は

となるため、式(10)を満たすようなＬが結合長ということになる。式(10)をＬに付いて解くと

となる(nは整数)。ここで、結合長を短くする（Ｌを小さくする）条件に付いて述べる。式(12)より、｜ｋ_＋−ｋ₋｜が大きくなればＬが小さくなることがわかる。伝播定数ｋは、

とすると、以下の関係式が成り立つ

フォトニック結晶導波路に於いては、一般にブリルアンゾーンでの折り返しを受けるために適当な逆格子ベクトルＧと、伝播方向の単位ベクトルｉを用いて

で表すことができる。いずれの場合も、同じ周波数の光については、伝播定数は平均屈折率に比例することがわかる。すなわち、偶モード・奇モードの伝播定数差を大きくするためには、各モードの平均屈折率の差を大きくすればよいといえる。平均屈折率は、伝播光の屈折率が高い部分と低い部分に広がる比率で決定される。このため、平均屈折率の差を広げるということは、各モードのエネルギー分布の差を広げるということを意味する。 Next, the bond length, which is another important performance index, will be described. The bond length (L) is such that light localized at x < ₀ at the initial position z = z ₀ is localized only at x> 0 at the position z = z ₀ + L propagated by the bond length. Say that length. if,

Then, the sum of even mode and odd mode is

Therefore, L satisfying equation (10) is the bond length. Solving equation (10) with L

Where n is an integer. Here, the condition for shortening the coupling length (decreasing L) will be described. From equation (12), it can be seen that L decreases as | k ₊ −k ₋ | increases. The propagation constant k is

Then, the following relational expression holds:

In a photonic crystal waveguide, generally, an appropriate reciprocal lattice vector G and a unit vector i in the propagation direction are used to receive folding in the Brillouin zone.

It can be expressed as In either case, it can be seen that for light of the same frequency, the propagation constant is proportional to the average refractive index. That is, it can be said that in order to increase the propagation constant difference between the even mode and the odd mode, the difference in the average refractive index of each mode should be increased. The average refractive index is determined by the ratio of spreading to a portion where the refractive index of propagating light is high and a portion where it is low. For this reason, widening the difference in average refractive index means widening the difference in energy distribution in each mode.

  In summary, in order to increase the extinction ratio, the even / odd mode energy distributions should match, and in order to shorten the coupling length, there should be a difference in the even / odd mode energy distributions. That is. That is, the extinction ratio and the coupling length are in a trade-off relationship.

[Technology to achieve both]
A directional coupler with a large difference in energy distribution between the even and odd modes has a poor extinction ratio. This occurs because light that is localized in the waveguide on one side cannot be expressed well by linear combination of even / odd modes. However, the phase difference between the even mode and the odd mode continuously changes between 0 and 2π as light propagates through the directional coupler. Therefore, if this phase difference can be converted into a localized form of light, both a short coupling length and a high extinction ratio can be achieved.

とする。各振幅関数の対称性は以下のようになる。 The directional coupler structure described above with reference to FIG. 4 includes three directional coupler waveguides A, B, and C, each having the same mirror symmetry plane. A and C are directional couplers with a small difference in energy distribution between even and odd modes, and B is a directional coupler with a large difference in energy distribution between even and odd modes. Since A, B, and C have the same mirror symmetry, even mode between AB and BC, even mode only excites even mode, odd mode only odd mode, even mode to odd mode, and even mode to odd mode. There can be no excitation to the mode. The eigenmodes of regions A, B, and C

And The symmetry of each amplitude function is as follows.

AB間、BC間の各モードの透過率を

境界を通過することによる振幅関数の絶対値の変動割合と、各モードの位相の変動割合が含まれる複素数であり、振幅関数間には次の関係が成り立つ。

A, Cは高消光比の得られる方向性結合器であるので、

の関係が成り立つ。

The transmittance of each mode between AB and BC

It is a complex number that includes the variation rate of the absolute value of the amplitude function due to passing through the boundary and the variation rate of the phase of each mode, and the following relationship is established between the amplitude functions.

A and C are directional couplers with high extinction ratios.

The relationship holds.

の関係が成り立つように、方向性結合器を作製する。このとき、AB界面のA側に光がx<0の範囲に分布するように入力した場合、つまり

で線形結合された光

を入力すると、AB間の界面、B、BC間の界面を通った光は次のようになる。

とし、方向性結合器Bの長さをLとしている。このとき、位相項が

すなわち、

(nは整数)の条件を満たす場合、伝播してきた光は

となる。これは最初x<0にあった光がx>0側に完全に乗り移っていることを意味し、高消光比の方向性結合器が実現できることを意味している。このときの結合長は式(23)で表される。式の分子は位相角を表しているので、適当な整数nを考えることにより−πからπの範囲に納めることができる。そのため、結合長は主に分母の項で決まるが、最初に構造として、B領域においては偶・奇モードのエネルギー分布差が大きく、伝播定数差が大きいものを取り上げているので、必然的に結合長は短くなる。 here

A directional coupler is manufactured so that At this time, if light is input to the A side of the AB interface so that the light is distributed in the range of x <0, that is,

Light linearly combined with

Is input, the light passing through the interface between AB and the interface between B and BC is as follows.

And the length of the directional coupler B is L. At this time, the phase term is

That is,

When the condition of (n is an integer) is satisfied, the transmitted light is

It becomes. This means that the light that was initially at x <0 has completely shifted to the x> 0 side, which means that a directional coupler with a high extinction ratio can be realized. The bond length at this time is expressed by equation (23). Since the numerator of the formula represents a phase angle, it can be set in the range of −π to π by considering an appropriate integer n. For this reason, the bond length is mainly determined by the denominator term. First, as the structure, in the B region, the energy distribution difference between the even and odd modes is large and the propagation constant difference is large. The length is shortened.

  Up to this point, we have described the situation where AB and BC are directly connected. However, the boundary area between AB and BC has a certain length of connection area while maintaining mirror symmetry. (Fig. 5). In this case, the transmittance in the above equation is the transmittance of each mode that reaches the region B from the region A beyond the connection region, and the transmittance of each mode that reaches the region C from the region B beyond the connection region. Just as in the case where there is no connection region, a directional coupler having both a high extinction ratio and a short coupling length can be designed.

  In summary, as shown in FIGS. 4 and 5, a directional coupler having a short coupling length is sandwiched between directional couplers having a high extinction ratio while maintaining mirror symmetry. At that time, if the absolute values of the even mode and odd mode transmittances at each boundary are designed to be equal, a directional coupler having both a short coupling length and a high extinction ratio can be obtained.

  FIG. 6 shows a directional coupler structure composed of a GaAs two-dimensional slab type air circular triangular lattice array photonic crystal. In order to perform a two-dimensional simulation, the effective refractive index of the GaAs region is 2.76. The lattice constant of the triangular lattice arrangement is a, and the radius is r.

FIG. 7 shows a schematic diagram of a simple parallel waveguide used for dispersion relation calculation. Calculation is performed for a structure in which this structure is periodically repeated in the vertical direction.
FIG. 8 shows the waveguide mode dispersion relationship calculated for the simple symmetric parallel waveguide shown in FIG. 7 when the circular hole radii are r = 0.3a and 0.33a. Looking at the normalized frequency of 0.274, in the symmetric parallel waveguide of r = 0.3a (◯ in the graph), the wave numbers at which the even mode and the odd mode are 0.274 almost overlap. On the other hand, the symmetrical parallel waveguide of r = 0.33a (● in the graph) differs greatly from about 0.35 when the wave number is about 0.42 and the odd mode because the even mode has a normalized frequency of 0.274. That is, for light with a normalized frequency of 0.274, a directional coupler with a good extinction ratio but a long coupling length at r = 0.3a, and a directional coupler with a short coupling length but a poor extinction ratio at r = 0.33a. It is expected to become a vessel. Therefore, in this embodiment, a symmetric parallel waveguide with r = 0.3a is used in the A and C regions, and a symmetric parallel waveguide with r = 0.33a is used in the B region. In addition, as the connection region, by changing the circular hole radius continuously over 5a and propagating from A to B and B to C adiabatically, the even mode transmittance and the odd mode transmittance are equal. It was made to become.

  FIG. 9 shows the relationship of the extinction ratio with respect to the frequency obtained by the finite differential time domain (FDTD) method. It is designed to be completely connected at 0.274. For comparison, the characteristics of a directional coupler composed of a simple parallel waveguide with r = 0.33a and a directional coupler composed of a simple parallel waveguide with r = 0.33a are also shown. Here, the extinction ratio means the intensity of light exiting the waveguide 3 relative to the sum of the intensity of light exiting the waveguide 2 and waveguide 3, and the smaller the value, the higher the extinction ratio. is doing. In the case of the structural design based on the present invention, the coupling length is 18a and the extinction ratio is -24.4 dB. In the case of a conventional directional coupler using a simple parallel waveguide, a photonic crystal directional coupler with an r = 0.3a hole has a coupling length of 91a and an extinction ratio of -23.2 dB, and the extinction ratio is good. Long bond length. On the other hand, in the photonic crystal directional coupler with r = 0.33a circular hole, the coupling length is 11a, the extinction ratio is -10.9 dB, and the coupling length is short, but the extinction ratio is poor. Although the coupling length is slightly longer than that of r = 0.33a due to the coupling region, the extinction ratio of the regions A and C (r = 0.3a) and the region B (r = 0. A directional coupler having a coupling length of 33a) has been designed, indicating the effectiveness of the present invention.

  FIG. 10 shows an example of a directional coupler design that is completely coupled at a normalized frequency of 0.274. (a) shows a structure consisting of r = 0.3a, (b) shows a structure based on the present invention, and (c) shows a structure consisting of r = 0.33a.

The characteristics when each region deviates from the mirror symmetry plane will be described. FIG. 11 is a schematic diagram of a structure in which the region B of the structure of FIG. 6 is shifted in parallel to the connection boundary surface. FIG. 12 shows the extinction ratio when the shift amount of the structure of FIG. 11 is changed from 0a (a is a lattice constant) to 0.03a. It can be seen that when the deviation is 0.02247317a or less, an extinction ratio of up to -20 dB (10 ^-2 ) can be obtained.

It is a schematic diagram of a general directional coupler. It is a figure for demonstrating a natural mode. It is a figure for demonstrating how to take a coordinate axis. It is a figure which illustrates a directional coupler structure. It is a figure which illustrates the directional coupler structure with a connection area | region. It is a figure which shows the structural example by a photonic crystal. It is a figure explaining a simple parallel waveguide. FIG. 7 is a diagram showing a dispersion relation of a photonic crystal parallel waveguide (FIG. 7) when the circular hole radii are r = 0.3a and r = 0.33a. It is a figure which shows the relationship of the extinction ratio with respect to a frequency. It is a figure which shows the example of a directional coupler design. It is a figure which shows the example of the directional coupler which shifted the mirror symmetry. It is the figure which showed the value of the extinction ratio with respect to deviation | shift amount in the directional coupler which shifted the mirror symmetry.

Claims (3)

Having three cascaded directional coupler waveguides having substantially the same mirror symmetry plane;
The two directional coupler waveguides located on both sides are directional coupler waveguides having a small difference in energy distribution between the even mode and the odd mode, and the directional coupler waveguide located in the center is A directional coupler waveguide with a large difference in energy distribution between the even mode and the odd mode,
In the connection between the directional coupler waveguide located in the center and the two directional coupler waveguides located on both sides of the directional coupler waveguide, the even mode excites only the even mode and the odd mode excites only the odd mode, A directional coupler configured so that excitation from the even mode to the odd mode or from the odd mode to the even mode does not occur substantially.   The boundary between the directional coupler waveguide located in the center and the two directional coupler waveguides located on both sides of the directional coupler waveguide is directly connected or remains substantially mirror-symmetric. The directional coupler according to claim 1, comprising a connection region having a predetermined length. 3. The directional coupler according to claim 1, wherein the three directional coupler waveguides connected in cascade are configured by a photonic crystal. 4.

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