JP3333817B2 - Method for manufacturing multilayer filter using genetic algorithm - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for manufacturing an optical multilayer filter for appropriately multiplexing and demultiplexing wavelength-multiplexed signal light in an optical communication system for transmitting and receiving optical wavelength multiplex communication.

[0002]

2. Description of the Related Art With the development of optical wavelength division multiplexing communication, a multilayer multiplexing / demultiplexing filter having a narrow band and small side reflection characteristics has been demanded.

A method for designing a multilayer filter having a refractive index Ni of each layer and a film thickness Di based on desired optical characteristics is as follows.
As in Japanese Patent No. 2650048, the refractive index Ni of each layer constituting the filter is determined in advance, the film thickness Di is assumed, the optical characteristics are obtained for each wavelength, and the film thickness Di is determined.
In general, the film thickness Di is optimized by using a film thickness optimizing method so that the optical characteristic has a maximum value.
Further, as a further optimization method, there is only a trial and error method of changing the refractive index of a certain layer and optimizing the film thickness of all the films again.

[0004]

However, in the above method, since the refractive index Ni is determined in advance, not only the degree of freedom of design is impaired, but also the obtained result often falls into a local solution. . Also in multilayer filter
The number of combinations of Ni and Di is very large, and it takes a lot of time to extract the optimal combination, which is practically impossible. For this reason, conventionally, the local solution obtained by using the above-mentioned film thickness optimizing method had to be satisfied. An object of the present invention is to design a multilayer optical filter having a complex combination as described above, extracting an optimal combination of the refractive index Ni and the film thickness Di of each layer without falling into a local solution, and forming a multilayer optical filter. To manufacture.

[0005]

According to the present invention, there is provided a method for manufacturing a multilayer filter, comprising the steps of: forming a refractive index of an i (i is an integer of 1 or more) layer of an S (S is an integer of 1 or more) multilayer optical filter; Generating an initial pattern consisting of a matrix represented by the following formula 1: P = (X1, X2, X3..., XS) (1) with the matrix Xi having the film thickness as an element as one element; Based on the initial pattern, in any element Xi in the initial pattern, a growth / mutation method in which the refractive index in the initial pattern is increased or decreased by a predetermined value or the film thickness is increased or decreased by a predetermined value to generate a predetermined number of different mutation patterns. Process and
At least one set of a pair of patterns is selected from the mutation pattern group generated in the multiplication / mutation step and the initial pattern, and the matrix Xi and / or the matrix Xi in the patterns of the selected pair of patterns are determined by the predetermined number. A crossover step of generating a predetermined number of crossover patterns by exchanging matrices formed by value mutation, and a pattern group consisting of the mutation pattern group generated in the multiplication / mutation step, the crossover pattern group, and the initial pattern. A selection step of sequentially selecting a desired number of patterns whose optical characteristics are close to the desired optical characteristics; and, based on a predetermined number of patterns selected in the selection step in place of the initial pattern,
A series of algorithm steps including the mutation step, the crossover step, and the selection step, wherein the value of the optical property of the selection pattern immediately before obtained in the algorithm step is the value of the desired difference value with respect to the value of the desired optical property. And repeating the process until the value falls within the range.

According to the method for manufacturing a multilayer filter of the present invention, by repeating a series of algorithm steps,
Each layer of the multilayer optical filter can be set so that the value of the optical property falls within a desired range, and therefore, a better multilayer optical filter can be designed and manufactured as compared with the conventional design method.

[0007] When a series of algorithm steps including the multiplication / mutation step, the crossover step, and the selection step are repeatedly performed, the value of the optical characteristic of the selection pattern obtained in the algorithm step is changed to the value of the previous property. When the value of the optical characteristic of the selection pattern obtained in the algorithm step matches, a second initial pattern different from the initial pattern is set, and the algorithm step is repeatedly performed using the second initial pattern. Is desirable. According to such a method, even if the optical characteristics of the design obtained in the repetition of the series of algorithm steps are not improved, the algorithm can be restarted from the second initial pattern. It is possible to forcibly avoid a stagnant state.

The second initial pattern is a pattern generated by increasing or decreasing the refractive index in the selection pattern having the best optical characteristics obtained in the previous steps or increasing or decreasing the film thickness by a predetermined value. Is preferred. According to such a method, information of optical elements effective for improving the optical characteristics in the pattern created until the values of the optical characteristics match can be used for the second initial pattern. A multilayer filter having various optical characteristics can be designed.

Another method of manufacturing a multilayer filter according to the present invention is a method of manufacturing a multilayer optical filter having S (S is an integer of 1 or more) layers.
(I is an integer of 1 or more) A matrix Xi having the refractive index and the film thickness of the layer as one element is further expressed by the following equation 1: P = (X1, X2, X3..., XS) (1) Generating an initial pattern consisting of a matrix to be copied, and copying the initial pattern by a predetermined number, and in the element Xi in the copied pattern, increase or decrease the refractive index in the initial pattern by a predetermined value or increase or decrease the film thickness by a predetermined value. A first replication growth / mutation step to be performed, and a pattern in which a desired number of patterns whose optical properties are close to desired optical properties are selected in order from a pattern in a group consisting of a mutation pattern and an initial pattern generated in the step. And at least one set of a pair of patterns is selected from the selection pattern group generated in the selection selection step 1 and the selection pattern group generated in the selection selection step, and the matrix Xi and / or the matrix X in the pattern is selected among the selected pair of patterns. i
A crossover step of generating a predetermined number of crossover patterns by exchanging a matrix obtained by mutating the predetermined value, and selecting and duplicating at least one arbitrary pattern from a pattern group consisting of the crossover pattern group and the selection pattern group The matrix Xi and / or the matrix Xi in the replicated pattern
A second replication growth and mutation step of generating a mutation pattern by increasing or decreasing the refractive index by a predetermined value or increasing or decreasing the film thickness by a predetermined value in an element in the matrix obtained by mutating the predetermined value, and the mutation pattern group From a pattern group consisting of the cross pattern group and the selection pattern group, a second selection step of sequentially selecting a desired number of patterns whose optical characteristics are close to the desired optical characteristics, and Alternatively, based on the predetermined number of patterns selected in the second selection step, the first replication growth / mutation step, the first selection step, the crossover step, the second
A series of algorithm steps including the replication growth / mutation step and the second selection step, and the optical property value of the second selection pattern immediately before obtained in the algorithm step is the value of the desired optical property. Repeatedly until the difference falls within the range of a desired difference value. According to another method for manufacturing a multilayer filter of the present invention, by repeating a series of algorithm steps, each layer of the multilayer optical filter can be set such that the value of the optical property falls within a desired range. Therefore, a better multilayer optical filter can be designed and manufactured as compared with the conventional design method.

The first replication growth / mutation step;
The selection step, the crossover step, the second replication
When a series of algorithm steps including the mutation step and the second selection step are repeatedly performed, the value of the optical property of the second selection pattern obtained in the algorithm step is
If the value matches the value of the optical property of the second selection pattern obtained in the previous algorithm step, a second initial pattern different from the initial pattern used in the algorithm is set, and this second initial pattern is set. It is desirable to repeat the above algorithm step using the above. According to such a method, even if the optical characteristics of the design obtained in the repetition of the series of algorithm steps are not improved, the algorithm can be restarted from the second initial pattern. It is possible to forcibly avoid a stagnant state.

Further, the second initial pattern is formed by increasing or decreasing the refractive index in the second selection pattern having the best optical characteristics obtained in the previous steps or increasing or decreasing the film thickness by a predetermined value. Preferably, it is a pattern. According to this method, information on optical elements effective for improving the optical characteristics in the pattern created until the values of the optical characteristics match can be used for the second initial pattern, and at a high speed,
In addition, a multilayer filter having better optical characteristics can be designed.

The selection in the selection step or the first and second selection steps is represented by the following equation 2:

[0013]

(Equation 2)

(Where Rj (λ) is the matrix Xi
Indicates the reflection characteristics at each wavelength λ obtained from the combination pattern of the elements, and Rr (λ) indicates the desired reflection characteristics. ) Is desirably performed in the order from the larger value Qj to the smaller value Qj.

Even if the degree of deviation χ of the reflection characteristic of a certain combination pattern from the desired reflection characteristic, that is, the denominator of Q becomes smaller due to convergence and the difference in the value of χ between the patterns becomes smaller, Since the reciprocal Q is used as the fitness, the difference between the patterns can be further increased. Therefore, accurate extraction can be performed even when the difference in the value of χ between patterns is small.

The predetermined value for increasing or decreasing the refractive index in the second replication growth / mutation step is different from the predetermined value for increasing / decreasing the refractive index in the first replication growth / mutation step and the predetermined value for increasing / decreasing the film thickness. And the predetermined value for increasing or decreasing the film thickness is 2 to 50 times,
The convergence in the vicinity of the solution increases, and the optimal solution can be extracted more quickly.

The predetermined value for increasing or decreasing the refractive index in the second replication growth / mutation step is different from the predetermined value for increasing / decreasing the refractive index in the first replication growth / mutation step. And the predetermined value for increasing or decreasing the film thickness is set to 2 to 25 times,
The convergence is further improved, and the optimal solution can be extracted at high speed.

[0018]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS (First Embodiment) A first embodiment of the present invention will be described below with reference to the drawings. In the first embodiment, the first substrate formed on the substrate 1 shown in FIG.
The optimization calculation for a five-layer multilayer filter including layers 2 to 5 will be described. In the first embodiment, an initial pattern generation step, a first replication growth / mutation step,
, A crossover step, a second replication growth / mutation step, and the second selection step.

FIG. 2 shows a flowchart of designing a multilayer optical filter having a five-layer film structure according to the first embodiment of the present invention. The first replication growth / mutation step comprises:
The replication growth / small mutation step is the second replication growth / mutation step, the selection / replication growth / medium / large mutation step.

In this embodiment, a random number α (= A, B, C, D, E, F, G, H) is used in the operations of selection, selection, selection, crossover, and mutation in steps S2 to S8. Shall be used. As a method of generating the random number α, a congruence method represented by the following equations (3) and (4) is used. α = Mn + 2/10000 (3) Mn + 2 = MOD (Mn + 1 + Mn, 10000) (4) (where MOD is a function representing the remainder)

First, in step S1, initial values required for calculation (desired optical characteristics, total number of films, refractive index of substrate, incident angle of incident light, total number of patterns after replication growth / small mutation process, first selection)・ Total number of patterns after the selection step, total number of patterns after the crossover step, total number of patterns after selection / replication multiplication / medium / large mutation step, total number of patterns after the second selection / selection step, small amount of mutation , Medium / large-scale mutation amount, number of repetitions of medium / large-scale mutation process, fitness target value) or numerical range.

Thereafter, a matrix Xi in which the i-layer of the multilayer film j has the refractive index Ni and the film thickness Di as elements is represented by the following equation (5): Xi = (Ni, Di) (5) By inputting the initial value of the element Xi = (Ni, Di) of each layer, a matrix pattern Pj composed of a combination of Xi representing the multilayer film j and represented by Expression 6 is generated. (Step of generating initial pattern group) Pj = (X1, X2, ..., Xi, ...) (6)

In this embodiment, the values shown in Table 1 are used in step S
This is the initial value required for the calculation in 1. By the above operation, one element combination pattern P1 represented by Expression 7 is created. P1 = (X1, X2, X3, X4, X5)… (7)

[Table 1]

Next, in step S2, a copy of the initial pattern is first created to increase the total number of pattern groups to the number of patterns after the multiplication step (shown in FIG. 3).
In this embodiment, the entire pattern group is obtained by this operation.
P1 to P20, and all patterns are represented by Expression 8. P1 = P2 = P3 =... = P20 (8) Thereafter, small-scale mutations are given to the respective replication patterns P2 to P20 (shown in FIG. 4). First, a random number A in the range of 1 ≦ A ≦ 5 (= the number of layers) is generated, and one element Xi = {(Ni, Di)} in the pattern is selected from the random number A (step S2-2). ). Thereafter, a random number B is generated in the range of 0 ≦ B ≦ 1 (step S2-3),
If the random number B is 0.5 or more, Di (Step S2-4
a) If it is less than 0.5, select Ni (step S2-4b).
Then, a random number C is generated in the range of 0 ≦ C ≦ 1 (S
2-5a, S2-5b) If the random number C is less than 0.5, add +
(Steps S2-6a, S2-6d), if it is 0.5 or more,-is selected (Steps S2-6b, S2-6c). By the above-mentioned operation, a small-scale mutation (Δnz of + or-or Δdz of + or-) is given to Ni or Di. (Replication Proliferation / Small Mutation Step S2) In the present embodiment, the random number A = 3, the random number B = 0.2, and the random number C = 0.
Assuming that the above operation is performed, P2 is expressed by Expression 9 by the above operation. P2 = (X1, X2, X3 ', X4, X5) = {X1, X2, (N3 + Δnz, D3), X4, X5} ... (9)

Next, as shown in FIG. 2, in step S3, the optical characteristics are calculated for all the element combination patterns P1 to P20 generated up to step S2, and the difference from the desired optical characteristic value is calculated. As the optical characteristics, refer to the reflection characteristics of the incident light incident on the multilayer optical filter at an angle θ by the multilayer optical filter. Here, transmission characteristics instead of reflection characteristics may be used as optical characteristics. For each element combination pattern Pj, the reflection characteristic for each wavelength λ of the incident light is Rj (λ), the desired reflection characteristic is Rr (λ), and the desired reflection characteristic wavelength range is λ1 to λ2, Rj (λ) and Rr at λ1 ~ λ2
Assuming that the square of the difference of (λ) is χ, χ is given by Equation 10:

[0026]

(Equation 3)

The fitness Qj is given by the following equation 2:

[0028]

(Equation 4)

## EQU1 ## That is, the larger the value of Qj, the closer the optical characteristics of the multilayer optical filter having the element combination pattern to the desired value.

Next, as shown in FIG. 2, an element combination pattern is selected and eliminated based on the fitness Qj for the desired optical characteristic of the element combination pattern Pj calculated in step S3 (see FIG. 5). .). First, Pj is rearranged in descending order of the value of the fitness Qj, and the rearranged patterns are left in the order of the number of patterns after the selection / selection step from the top.
Patterns other than the surviving patterns are eliminated. (Primary selection / selection step S4) Fitness Q1 in the present embodiment
Assuming that Q20 is in the order of the size represented by the formula 11: Q20>Q19>Q18>...>Q3>Q2> 1 (11), the number of individuals after the selection process is 10, The element combination patterns extracted by the above operation are P11 to P20.

Next, as shown in step S5 of FIG. 2, pattern crossover is performed (shown in FIGS. 6 and 7). However, Figure 6 is 1
FIG. 7 is a diagram for explaining the generation of a pattern by the number of crossover steps, and FIG. 7 is a flowchart illustrating the crossover step including repetition. First, two random numbers D and E are generated within a range of 1 ≦ D, E ≦ 10 (= total number of patterns after the selection and selection process), and based on the two random numbers D and E, selection and selection are performed in step S4. Out of the element combination pattern groups P1 to P10
Two patterns Pj ′ and Pj ″ (where 1 ≦ j ′, j ″ ≦ j) are selected (step S5-1).

In the present embodiment, two patterns P
It is assumed that j ′ and Pj ″ are expressed as Expressions 12 and 13, respectively (Step S5-2). Pj '= (X1', X2 ', X3', X4 ', X5') ... (12) Pj '' = (X1 '', X2 '', X3 '', X4 '', X5 '') ... ( 13) In the two patterns Pj ′ and Pj ″, 1 ≦ F ≦ 4 (=
A random number F in the range of the number of films -1) is generated, and a position between elements giving an intersection of two patterns is determined based on the random number F (step S5-3).

Assuming that F = 3 in the present embodiment, the position between the elements giving the intersection of Pj ′ and Pj ″ is expressed by Expression 14.

[0034]

(Equation 5)

The two patterns are crossed at the position between the elements, and two combined patterns Ck and Ck + 1 shown in Expressions 16 and 17 are newly created (Steps S5-4 and S5-).
Five). Ck = (X1 ', X2', X3 ', X4'',X5'') ... (16) Ck + 1 = (X1'',X2'',X3'',X4', X5 ') ... (17) )

Thereafter, the operations in steps S5-1 to S5-5 are repeated until the total number of pattern groups reaches a predetermined total number of patterns after the crossover process. (Crossover process S
5) In the present embodiment, since the total number of patterns after the crossing step is 20 and the total number of patterns before the crossing step is 10, after that, C10 is generated by performing the operations of the above steps S5-1 to S5-5. (Step S5-6).

Next, in step S6 shown in FIG. 2, the patterns Pj and Ck after the crossover process are given medium / large-scale mutations,
A new pattern CRp is generated (shown in FIG. 8). However, the selection of the medium-scale or large-scale mutation in step S6 generates a random number G in the range of 0 ≦ G ≦ 1 at the end of the crossover process, and if the random number G is less than 0.8, it is a medium-scale mutation, and 0.8 or more. If so, it is decided to be a large-scale mutation.

In step S6, a random number H is first generated in the range of 0 ≦ H ≦ (j + k), and one pattern is selected from the patterns Pj and Ck after the crossing process based on the random number H, By duplicating the selected pattern, a new pattern CRp-a is generated. This selection and duplication operation is performed when the number of pattern groups is determined in advance.
Repeat until the total number of patterns after the large-scale mutation step reaches 40. CR1-a to CR20-a are generated by this selection / duplication operation. Thereafter, a pattern CRp having a medium / large mutation is generated by giving a medium / large-scale mutation to this CRp-a. (Selection, replication, medium / large-scale mutation step S6)

First, the case of giving a medium-scale mutation will be described. As shown in FIG. 9, in the medium-scale mutation process,
Generate a random number A in the range of ≦ A ≦ 5 (= number of layers), and
Xi = {(Ni, D
i)} is selected (step S6-1-2). Thereafter, a random number B is generated in the range of 0 ≦ B ≦ 1 (step S6-1-3), and the random number B is set to 0.5
If so, Di is selected (step S6-1-4a), and if less than 0.5, Ni is selected (step S6-1-4b). Then, a random number C is generated in the range of 0 ≦ C ≦ 1 (step S
6-1-5a, S6-1-5b) If the random number C is less than 0.5, choose + (S6-1-6a, S6-1-6d); if it is 0.5 or more, choose- (Steps S6-1-6b, S6-1-6c). By the above operation,
Give either Ni or Di a positive or negative medium-scale mutation (+ or -Δnc, or + or -Δdc). Steps S6-1-2 to S6-1-6 a, 6b, 6c, and 6d are repeated a predetermined number of times Nc (= 5 times) (step S6-1-
7) Generate a pattern CRp having a medium-scale mutation (step S6-8).

Next, the case of giving a large-scale mutation will be described (shown in FIG. 10). In the large-scale mutation process, first, 1 ≦ A ≦
A random number A in the range of 5 (= number of layers) is generated, and one element Xi = {(Ni, Di)} in the pattern CRp-a is selected from the random number A (step S6-2-2). ). Then random number B in the range of 0 ≦ B ≦ 1
(Step S6-2-3), and if the random number B is 0.5 or more, select Di (Step S6-2-4a), and if the random number B is less than 0.5, select Ni (Step S6-2-3). 4b). Then, a random number C is generated in the range of 0 ≦ C ≦ 1 (step S6-2-5a,
S6-2-5b), if the random number C is less than 0.5, select + (steps S6-2-6a, S6-2-6d), and if it is 0.5 or more, select-(step S6-2). -6b, S6-2-6c). By the above operation,
Give either Ni or Di a positive-negative mesoscale mutation (+ or-Δnd, or + or-Δdd). The operations from S6-2-2 to S6-2-6 a, 6b, 6c, 6d are repeated a predetermined number of times Nd (= 10 times) (step S6-2
-7), a pattern CRp having a large-scale mutation is generated (step S6-8).

Through the above middle / large-scale mutation process, a combination pattern group of elements having completely different element patterns can be incorporated into the pattern group.

After the selection / duplication / medium / large mutation process in step S6 is completed, the optical characteristics of the patterns Pj, Ck, and CRp that have passed through S6 are calculated in step S7, and the difference from the desired optical characteristic value is calculated. I do. As the optical characteristics, the above steps
Similar to S3, the reflection characteristic of the incident light incident on the multilayer optical filter at an angle θ is referred to by the multilayer optical filter. By the above method, the fitness Qm of each pattern (where 1 ≦ m ≦ j + k
+ p) is calculated.

Next, in step S8, element combination patterns are selected and selected based on the fitness Qm for the desired optical characteristics of the element combination patterns Pj, Ck, and CRp calculated in step S7 (see FIG. 11). .). First, Pj, Ck, C
After Rp is rearranged in the descending order of the value of the fitness Qm, the rearranged patterns are left in order from the top and the total number of patterns after the selection / selection step is left. Patterns other than the surviving patterns are eliminated. (Secondary Selection / Selection Step S8) In the present embodiment, assuming that the patterns are rearranged based on the fitness Qm and have the order shown in Expression 18, C1,..., C10, P11,. , CR20 (18) Since the number of individuals after the selection / selection step is 10, the element combination patterns extracted by the above operation are C1 to C10.

Steps S1 to S8 are performed as described above.
Generation. Here, when step S8 is completed, the element combination pattern having the maximum fitness Qm is set as the best combination pattern in the generation. In the present embodiment, C1
Is the best combination pattern of the first generation.

When the first generation is completed, the repetition of steps S2 to S8 is performed on the combination pattern group of ten elements obtained in step S8, and the best value Qm of the fitness of the combination pattern of each generation is obtained. , Until the predetermined value Q0 or more is reached. (Step S29) An element combination pattern having the best value Qm of the fitness obtained by repeating the above steps is set as the design value of the multilayer filter.

(Second Embodiment) In a second embodiment of the present invention, optimization calculation for a five-layer multilayer filter similar to that shown in FIG. 1 will be described. The second embodiment of the present invention compares the value of the optical property of the selection pattern obtained in a certain generation of the algorithm step with the value of the optical property of the selection pattern obtained in the previous generation of the algorithm step. If they match, a second initial pattern different from the initial pattern used in the previous algorithm process is set, and the algorithm process is repeated using the second initial pattern. here,
In order to mainly describe the process using the second initial pattern, in the case of the same content as in the first embodiment, the description is omitted.

FIG. 14 is a flow chart for designing a multilayer optical filter having a five-layer film structure according to the second embodiment of the present invention. In the second embodiment, step S2
Selection, selection, selection in the process from 1 to step S29,
The random number α (= A, B, C, D, E, F) is used in the operation of crossover and mutation. As a method for generating the random number α, a congruential method is used as in the first embodiment.

First, in step S21, initial values required for calculation (desired optical characteristics, total number of films, refractive index of substrate, incident angle of incident light, total number of patterns after replication growth / mutation process, amount of mutation, The number of repetitions, the total number of patterns after the crossover step, the total number of patterns after the selection / selection step, the number of comparison generations, the amount of mutation in the second initial pattern generation step,
The number of repetitions of the mutation step in the second initial pattern generation step, the target value of the fitness) or the numerical range is specified.

Thereafter, similarly to the first embodiment, the i-layer of the multilayer film j is converted into a matrix Xi having the refractive index Ni and the film thickness Di as elements.
= (Ni, Di) is used to generate an initial pattern Pj shown in Expression 6. (Step of generating initial pattern group) Pj = (X1, X2, ..., Xi, ...) (6)

In the second embodiment, the values shown in Table 2 are used as initial values required for the calculation in step S1. By the above operation, one element combination pattern P1 represented by Expression 7 is created. P1 = (X1, X2, X3, X4, X5)… (7)

[Table 2]

Next, in step S22, a copy of the initial pattern group is first created to increase the total number of pattern groups up to the number of patterns after the multiplication step (shown in FIG. 15). The whole pattern group is
P1 to P20, and all patterns are represented by Expression 8. P1 = P2 = P3 =... = P20 (8) Thereafter, mutations are given to the respective replication patterns P2 to P20.
(Shown in FIG. 16). First, random number A in the range of 1 ≦ A ≦ 5 (= number of layers)
Is generated, and one element of the pattern, Xi = {(Ni, Di)}, is selected by the random number A (step S22-2). Thereafter, a random number B is generated in the range of 0 ≦ B ≦ 1 (step S22-
3) If the random number B is 0.5 or more, Di
S22-4a) If it is less than 0.5, select Ni (step S
22-4b). After that, the random number is further reduced to C within the range of 0 ≦ C ≦ 1.
Are generated (S22-5a, S22-5b), and if the random number C is less than 0.5, + is added (steps S22-6a, S22-6d) to 0.5
If so, select-(Steps S22-6b, S22
-6c). By the above operation, either positive or negative mutation (+ or -Δn, or + or -Δ)
d) give. The operations from S22-2 to S22-6a, 6b, 6c, 6d are repeated a predetermined number of times Nh (step S22-2-7), and a mutated pattern Pj is generated (step S22-8). ). (Replication replication / mutation step: S22) In the present embodiment, a random number is assigned to the replication pattern P2.
Assuming that A = 3, random number B = 0.2, random number C = 0.6, and Nh = 1, P2 is expressed by Expression 9 by the above operation. P2 = (X1, X2, X3 ', X4, X5) = {X1, X2, (N3 + Δn, D3), X4, X5} ... (9)

Next, as shown in step S23 of FIG.
Crossover of patterns is performed (shown in FIGS. 17 and 18). However, FIG. 17 is a diagram illustrating the generation of a pattern by one crossing process, and FIG. 18 is a flowchart illustrating the crossing process including repetition. First, 1 ≦ D, E ≦ 20 (=
Two random numbers D and E are generated within the range of (the total number of patterns after the replication growth / mutation step), and based on the two random numbers D and E, from among the pattern populations P1 to P20 created up to step S22. , Two patterns Pj ′ and Pj ″ (where 1 ≦ j ′, j ″ ≦ j)
(Step S23-1).

In this embodiment, two patterns P
It is assumed that j ′ and Pj ″ are expressed as Expressions 12 and 13, respectively (Step S23-2). Pj '= (X1', X2 ', X3', X4 ', X5') ... (12) Pj '' = (X1 '', X2 '', X3 '', X4 '', X5 '') ... ( 13) In the two patterns Pj ′ and Pj ″, 1 ≦ F ≦ 4 (=
A random number F in the range of the number of films-1) is generated, and based on the random number F, the position between the elements giving the intersection of the two patterns is determined (step S23-3).

Assuming that F = 3 in the present embodiment, the position between the elements giving the intersection of Pj ′ and Pj ″ is expressed by Expression 14.

[0055]

(Equation 6)

The two patterns are crossed at the position between the elements, and two combined patterns Ck and Ck + 1 shown in Expressions 16 and 17 are newly created (Steps S23-4 and S2).
3-5). Ck = (X1 ', X2', X3 ', X4'',X5'') ... (16) Ck + 1 = (X1'',X2'',X3'',X4', X5 ') ... (17) )

Thereafter, the operations of steps S23-1 to S23-5 are repeated until the total number of pattern groups reaches a predetermined total number of patterns after the crossover process. (Crossover Step S23) In the present embodiment, the total number of patterns after the crossover step is 30
And the total number of patterns before the crossing process is 20, so that the operations of steps S23-1 to S23-5 are repeated until C10 is generated (step S23-6).

When the crossing process in step S23 is completed, the optical characteristics of the patterns Pj and Ck which have passed through S23 are calculated in step S24, and the difference from the desired optical characteristic value is calculated.
As the optical characteristics, the reflection characteristics of the incident light incident on the multilayer optical filter at an angle θ by the multilayer optical filter are referred to as in the first embodiment. The fitness Qm (where 1 ≦ m ≦ j + k) of each pattern is calculated by the above method.

Next, in step S25, element combination patterns are selected and eliminated based on the fitness Qm for the desired optical characteristics of the element combination patterns Pj and Ck calculated in step S24 (shown in FIG. 19). ). First, Pj and Ck are rearranged in descending order of the value of the fitness Qm, and then the rearranged patterns are left in order from the top, for the total number of patterns after the selection / selection step. Patterns other than the surviving patterns are eliminated. (Selection / Selection Step S25) In the present embodiment, the pattern is obtained by rearranging based on the fitness Qm to obtain the expression 1
Assuming the order shown in FIG. 9, C1,..., C10, P1,..., P20 (19) Since the number of individuals after the selection / selection step is 10, the element combination pattern extracted by the above operation is C1 to C10.

The above steps S21 to S25 are 1
Generation. Here, the element combination pattern having the maximum fitness Qm when step S25 is completed is set as the best combination pattern in the generation. In the present embodiment, C1
Is the best combination pattern of the first generation. When the first generation is completed, it is determined whether or not the best value Qm of the fitness is equal to or greater than a predetermined value Q0 for the combination pattern group of ten elements obtained in step S25 ( Step S26). When the best value Qm of the fitness of the combination pattern is equal to or greater than a predetermined value Q0, the element combination pattern having the best value Qm of the fitness is set as the design value of the multilayer filter.

If the best value Qm of the fitness of the combination pattern is not equal to or larger than the predetermined value Q0, the local convergence of the obtained combination pattern is determined. (Step S27) In step S27, it is determined whether or not the best value Qm of the fitness of the combination pattern matches the best value of the fitness of the combination pattern obtained from the current generation to the previous NN generation. Alternatively, it is determined whether the best value Qm of the fitness of the combination pattern is the same value during the NN generation up to the current generation.

The best value Qm of the fitness of the combination pattern
Is not the same as the best value of the fitness of the combination pattern obtained from the current generation to the NN generation before, it is determined that local convergence has not occurred, and 1 obtained in step S25
A combination pattern group of 0 elements is set as an initial pattern in step S22 of the next generation (step S28).

If a match is found, it is determined that the pattern has locally converged, and a second initial pattern is generated (step S29). The second initial pattern is generated by giving a mutation to the element combination pattern having the best fitness among the element combination patterns obtained from the first generation to the generation in which a match is found (FIG. 20). Shown). First, a random number A in the range of 1 ≦ A ≦ 5 (= the number of layers) is generated, and the random number A is used to generate one of the best fitness patterns.
Xi = {(Ni, Di)} which is one of the elements (Step S29-
2). Thereafter, a random number B is generated in the range of 0 ≦ B ≦ 1 (step S
29-3) If the random number B is 0.5 or more, Di is selected (step S29-4a), and if it is less than 0.5, Ni is selected (step S29-4b). After that, a random number is further set within the range of 0 ≦ C ≦ 1.
C is generated (steps S29-5a and S29-5b), and the random number C is 0.5
If it is less than + (steps S29-6a, S29-6d), 0.
If it is 5 or more, select-(Steps S29-6b, S29-6
c). Through the above operation, either Ni or Di is given a positive or negative mid-scale mutation (+ or −Δnss, or + or −Δdss). S29-2 to S29-6 a, 6b, 6c, 6d
The above operation is repeated a predetermined number of times Nss (step S29-7), and the second initial pattern with mutation
A PP1 is generated (step S29-8). Using the second initial pattern PP1 as the initial pattern in step S22 of the next generation, the operation from step S22 onward is performed. In the present embodiment, it is assumed that the optical characteristic of the best element combination pattern in a certain generation matches the optical characteristic of the pattern obtained in the selection / selection step of the algorithm 10 generations ago. The element combination pattern having the best optical characteristics up to the matched generation is C1 {= (X1 ', X2', X3 ', X4', X
5 ′)), the random number A = 4 in step S29,
Assuming that the random number B = 0.2, the random number C = 0.6, and Nh = 1, the second initial pattern PP1 is expressed by Expression 20 by the above operation. PP1 = {X1 ', X2', X3 ', (N4 + Δn, D4), X5'} ... (20)

The repetition of the above steps S22 to S29 is repeated until the best value Qm of the fitness of the combination pattern of each generation becomes equal to or more than the predetermined value Q0. The element combination pattern having the best fitness value Qm obtained by repeating the above steps is set as the design value of the multilayer filter.

The first embodiment of the present invention employs steps S27 and S29 in the second embodiment of the present invention, that is, a step of judging the local convergence of the pattern after step S26. Although not described, the step of determining the local convergence may be performed in the first embodiment of the present invention. Further, in the first embodiment of the present invention, the replication growth / mutation step and the selection step are each performed twice, but the first selection step is performed similarly to the second embodiment of the present invention. The step and the second replication growth / mutation step can be omitted.

As described above, according to the methods of the first and second embodiments of the present invention, the conventional method for optimizing the film thickness of a multilayer optical filter has a low degree of freedom in design and largely deviates from desired optical characteristics. Although only a multilayer structure having the above-mentioned optical characteristics can be obtained, a multilayer structure with little deviation from desired optical characteristics can be obtained.

[0067]

Embodiments of the present invention will be described below with reference to tables and drawings. First, an initial pattern generation step, a first replication growth / mutation step, the first selective selection step, the crossover step, the second replication growth / mutation step, and the second selective selection step An example (Example 1 and Example 2) using an algorithm will be described. Next, the value of the optical property of the selection pattern obtained in a certain algorithm step is compared with the value of the optical property of the selection pattern obtained in the previous algorithm step, and if they match, the initial pattern used in the algorithm is used. Second different from
An example (Embodiment 3) will be described in which the initial pattern is set and the second initial pattern is used to repeat the above algorithm process again. The initial value of the multilayer film structure used in this embodiment is an alternating multilayer film of a high refractive index layer and a low refractive index layer, and the thickness of each layer is a λ / 4 optical multilayer film having a reflection center wavelength at 550 nm. I did it. The target optical characteristics are that the reflectance is 200 to 450 nm and 650 to 1
It was 0.1 at 000 nm and 0.5 at 450-650 nm.

Embodiment 1 This embodiment shows the result of optimization performed on a five-layer multilayer film. Table 3 shows initial values of the five-layered multilayer structure used in this embodiment. Table 4 shows various parameters when optimization is performed using this method.

[Table 3]

[Table 4]

In the optimization by the film thickness optimizing method, the reflection peak intensity approaches the target value, but a large sub-reflection band occurs. The value of the maximum fitness Q by the film thickness optimization method is
It was 0.1618. Table 5 shows a five-layer multilayer structure optimized by the film thickness optimization method.

[Table 5]

On the other hand, when the method of the present invention was calculated using the parameters in Table 4, the fitness Q was the best at the 49th generation.
0.6090, which is larger than Q0. This fitness Q
Is larger than the film thickness optimizing method, and indicates that a multilayer film structure having optical characteristics close to the target optical characteristics is obtained by the present method as compared with the film thickness optimizing method. FIG. 12 shows an optical characteristic 10 of the optical multilayer film having the maximum fitness Q. For comparison, the result 9 of the film thickness optimization method and the target optical characteristic 7 are also shown.

FIG. 12 shows that the present method can provide a multilayer structure having smaller sub-reflection bands and optical characteristics close to the target optical characteristics as compared with the film thickness optimizing method. Table 6 shows a five-layer multilayer structure optimized by this method.

[Table 6]

(Embodiment 2) This embodiment shows the result of optimization performed on a 15-layer multilayer film. Table 7 shows the initial values of the 15-layer multilayer structure used in this embodiment. Table 4 shows various parameters for optimization.

[Table 7] FIG. 13 shows the optical characteristics 11 of the optical multilayer film having the maximum fitness Q when the optimization according to the present method is performed using the parameters in Table 4 for the 15-layer film. From FIG. 13, it can be seen that this method can be applied even when the number of layers of the multilayer structure is increased, and that by increasing the number of layers, a multilayer optical filter having optical characteristics closer to desired optical characteristics can be obtained. I understand. Table 8 shows the optimized values
1 shows a 15-layer multilayer structure. As described above, by using this method, a multilayer optical multiplexing / demultiplexing filter having desired optical characteristics can be easily obtained.

[Table 8]

(Embodiment 3) This embodiment shows the result of optimization performed on a three-layer multilayer film. Table 9 shows initial values of the three-layered multilayer structure used in the present embodiment. Table 10 shows various parameters for optimization.

[Table 9]

[Table 10]

FIG. 21 shows a change in the fitness with respect to the number of generations in the optimization calculation. If the second initial pattern is not generated, the optimization calculation stagnates in some generations, and if the stagnation is long, the fitness is saturated (dashed line 1).
2). On the other hand, in the present method, when stagnation is determined, a second initial pattern is generated and the algorithm is repeated. The second initial pattern is obtained by mutating the pattern having the best fitness up to the generation in which stagnation is determined. The change in the fitness with respect to the number of generations (solid line 13) in the present method, when a stagnation is determined, temporarily drops sharply, but can avoid a long-term stagnation of the fitness. Table 11 shows the three-layer optical multilayer structure having the maximum fitness Q when a long-term stagnation occurs without the second initial pattern and when long-term stagnation is avoided by the present method. By using the second initial pattern,
It can be seen that the saturation of the fitness can be avoided and a different multilayer structure is obtained.

[Table 11] By using this method as described above, it is possible to design and manufacture a multilayer optical multiplexing / demultiplexing filter having optical characteristics closer to desired optical characteristics.

[0075]

As described above, according to the method for manufacturing a multilayer filter of the present invention, when designing a multilayer filter having desired optical characteristics, the optimal Ni, An optical filter having a multilayer structure having Di can be provided.

[Brief description of the drawings]

FIG. 1 shows a 5 manufactured according to a first embodiment of the present invention.
It is sectional drawing which shows a multilayer optical filter.

FIG. 2 is a flowchart for explaining a first embodiment of the present invention.

FIG. 3 is a schematic diagram for explaining a replication growth / small-scale mutation process in the flowchart shown in FIG. 2;

FIG. 4 is a flowchart for explaining a small-scale mutation step in the flowchart shown in FIG. 2;

FIG. 5 is a schematic diagram for explaining a primary selection / selection step in the flowchart shown in FIG. 2;

FIG. 6 is a schematic diagram for explaining a crossover step in the flowchart shown in FIG. 2;

FIG. 7 is a flowchart for explaining a crossover step in the flowchart shown in FIG. 2;

FIG. 8 is a schematic diagram for explaining a selective duplication / medium / large-scale mutation step in the flowchart shown in FIG. 2;

FIG. 9 is a flowchart for explaining a medium-scale mutation process in the flowchart shown in FIG. 2;

FIG. 10 is a flowchart for explaining a large-scale mutation process in the flowchart shown in FIG. 2;

FIG. 11 is a schematic diagram for explaining a secondary selection / selection step in the flowchart shown in FIG. 2;

FIG. 12 is a graph showing a reflection characteristic as a result of optimization of a five-layer multilayer optical filter manufactured according to the first embodiment of the method of the present invention.

FIG. 13 is a graph showing reflection characteristics as a result of optimization of a 15-layer multilayer optical filter manufactured according to Embodiment 2 of the method of the present invention.

FIG. 14 is a flowchart for explaining a second embodiment of the present invention.

FIG. 15 is a schematic diagram for explaining a replication growth / mutation step in the flowchart shown in FIG. 14;

FIG. 16 is a flowchart for explaining a mutation step in the flowchart shown in FIG. 14;

FIG. 17 is a schematic diagram for explaining a crossing step in the flowchart shown in FIG. 14;

FIG. 18 is a flowchart for explaining a crossover step in the flowchart shown in FIG. 14;

FIG. 19 is a schematic diagram for explaining a selection / selection step in the flowchart shown in FIG. 14;

FIG. 20 is a diagram showing a second example in the flowchart shown in FIG.
5 is a flowchart for explaining the initial pattern generation step of FIG.

FIG. 21 is a graph showing a change in fitness with respect to the number of generations in an optimization calculation process of a three-layer multilayer optical filter obtained in Embodiment 3 of the method of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Substrate 2 1st layer 3 2nd layer 4 3rd layer 5 4th layer 6 5th layer S1, S21 Initial pattern generation process S2 1st replication growth / mutation process S4 1st selection selection process S5, S23 crossover process S6 Second replication growth / mutation step S8 Second selective selection step S22 Replication growth / mutation step S25 Selective selection step S29 Second initial pattern generation step

──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Hiroshi Mizuseki 1-4-13-104 Yonegabukuro, Aoba-ku, Sendai-shi, Miyagi Examiner Kimio Yoshino (56) References JP-A-10-232312 (JP, A) JP-A-8-160220 (JP, A) JP-A-6-167726 (JP, A) Patent 2650048 (JP, B2) (58) Fields investigated (Int. Cl. ⁷ , DB name) G02B 5 / 28 G02B 1/10

Claims (8)

(57) [Claims] 1. A matrix Xi having a refractive index and a film thickness of an i (i is an integer of 1 or more) layer of an S (S is an integer of 1 or more) multilayer optical filter as one element. Formula 1: P = (X1, X2, X3..., XS) A step of generating an initial pattern composed of a matrix represented by the following equation: (1), and based on the initial pattern, an arbitrary element Xi in the initial pattern In, a growth and mutation step of increasing or decreasing the refractive index in the initial pattern by a predetermined value or increasing or decreasing the film thickness by a predetermined value to generate a predetermined number of different mutation patterns.
At least one set of a pair of patterns is selected from the mutation pattern group generated in the multiplication / mutation step and the initial pattern, and the matrix Xi and / or the matrix Xi in the patterns of the selected pair of patterns are determined by the predetermined number. A crossover step of generating a predetermined number of crossover patterns by exchanging matrices formed by value mutation, and a pattern group consisting of the mutation pattern group generated in the multiplication / mutation step, the crossover pattern group, and the initial pattern. A selection step of sequentially selecting a desired number of patterns whose optical characteristics are close to the desired optical characteristics; and, based on a predetermined number of patterns selected in the selection step in place of the initial pattern,
A series of algorithm steps including the mutation step, the crossover step, and the selection step, wherein the value of the optical property of the selection pattern immediately before obtained in the algorithm step is the value of the desired difference value with respect to the value of the desired optical property. A method of manufacturing a multilayer filter using a genetic algorithm, comprising the steps of repeatedly performing the process until the value falls within the range. 2. When a series of algorithm steps including the proliferation / mutation step, the crossover step, and the selection step are repeatedly performed, the value of the optical characteristic of the selection pattern obtained in the algorithm step is changed. When the value of the optical property of the selection pattern obtained in the previous algorithm step matches, a second initial pattern different from the initial pattern is set, and the proliferation / mutation step, the crossover step, the selection step, 2. The method for manufacturing a multilayer filter using a genetic algorithm according to claim 1, wherein a series of algorithm steps comprising: 3. The genetic method according to claim 2, wherein the second initial pattern is a pattern generated by mutating a selection pattern having the best optical characteristics obtained in the previous steps. A method for manufacturing a multilayer filter using an algorithm. 4. A matrix Xi having a refractive index and a film thickness of an i (i is an integer of 1 or more) layer of an S (S is an integer of 1 or more) multilayer optical filter as one element. Formula 1: P = (X1, X2, X3..., XS) A step of generating an initial pattern composed of a matrix represented by the following equation: (1), copying the initial pattern by a predetermined number, and elements in the copied pattern Xi, a first replication growth / mutation step of increasing or decreasing the refractive index in the initial pattern by a predetermined value or increasing or decreasing the film thickness by a predetermined value, and a pattern in a group consisting of the mutation pattern generated in the step and the initial pattern. A first selection step of sequentially selecting a desired number of patterns whose optical characteristics are close to the desired optical characteristics, and selecting at least one pair of patterns from a selection pattern group generated in the selection step, Selected pair The matrices Xi and / or the matrix Xi in the pattern in the over down together
A crossover step of generating a predetermined number of crossover patterns by exchanging a matrix obtained by mutating the predetermined value, and selecting and duplicating at least one arbitrary pattern from a pattern group consisting of the crossover pattern group and the selection pattern group The matrix Xi and / or the matrix Xi in the replicated pattern
A second replication growth and mutation step of generating a mutation pattern by increasing or decreasing the refractive index by a predetermined value or increasing or decreasing the film thickness by a predetermined value in an element in the matrix obtained by mutating the predetermined value, and the mutation pattern group From a pattern group consisting of the cross pattern group and the selection pattern group, a second selection step of sequentially selecting a desired number of patterns whose optical characteristics are close to the desired optical characteristics, and Alternatively, based on the predetermined number of patterns selected in the second selection step, the first replication growth / mutation step, the first selection step, the crossover step, the second
A series of algorithm steps consisting of the replication growth / mutation step and the second selection step, and the value of the optical property of the second selection pattern immediately before obtained in the algorithm step is the value of the desired optical property Repeating the process until the difference falls within a range of a desired difference value of the multi-layer filter using a genetic algorithm. 5. A series of algorithms including the first replication growth / mutation step, the first selection / selection step, the crossover step, the second replication growth / mutation step, and the second selection selection step. When the steps are repeated, the value of the optical property of the second selection pattern obtained in the algorithm step is equal to the value of the optical property of the second selection pattern obtained in the previous algorithm step. If they match, a second initial pattern different from the initial pattern is set, and the first replication growth / mutation step, the first selective selection step, the crossover step, the second replication growth / mutation step, and 5. The method for manufacturing a multilayer filter using a genetic algorithm according to claim 4, wherein a series of algorithm steps including the second selection step is repeatedly performed. 6. The method according to claim 5, wherein the second initial pattern is a pattern generated by mutating the second selection pattern having the best optical characteristics obtained in the previous steps. A method for manufacturing a multilayer filter using the genetic algorithm of the present invention. 7. The selection in the selection step or the first and second selective selection steps is represented by the following equation 2: (Where Rj (λ) indicates the reflection characteristic at each wavelength λ obtained from the combination pattern of the elements of the matrix Xi, and Rr (λ) indicates the desired reflection characteristic.)
5. The method for manufacturing a multilayer filter using a genetic algorithm according to claim 1 or 4, wherein the processing is performed in the order from the larger value Qj represented by the following formula. 8. The method of increasing or decreasing the refractive index in the second replication growth / mutation step with respect to the predetermined value for increasing / decreasing the refractive index in the first replication growth / mutation step and the predetermined value for increasing / decreasing the film thickness. 5. The method according to claim 4, wherein the predetermined value and the predetermined value for increasing or decreasing the film thickness are each 2 to 50 times.