JP2019144537A - Data creation device, optical control device, data creation method, and data creation program - Google Patents

Abstract

To reduce a ratio to be led to a local solution, and to accurately calculate spectrum intensity and spectrum phase (or only the spectrum intensity) for approximating a time waveform of light to a desired waveform thereof.SOLUTION: An intensity spectrum design unit 23 has: an initial value setting unit 25 that sets a plurality of individual bodies of a first generation of an intensity spectrum function A(ω), and a phase spectrum function Ψ(ω); an evaluation calculation unit 26 that calculates an evaluation value about each of a plurality of individual bodies of an n-th generation; an individual body selection unit 27 that selects two or more individual bodies to be used in creating a plurality of individual bodies of a (n+1)-th generation from the plurality of individual bodies of the n-th generation on the basis of superiority of the evaluation value; a next generation creation unit 28 that creates the plurality of individual bodies of the (n+1)-th generation on the basis of the two or more individual bodies selected in the individual body selection unit 27. The evaluation calculation unit 26, the individual body selection unit 27 and the next generation creation unit 28 are configured to repeat processing as adding n one by one until a prescribed condition is satisfied.SELECTED DRAWING: Figure 7

Description

  The present invention relates to a data creation device, a light control device, a data creation method, and a data creation program.

  Patent Documents 1 and 2 disclose a technique for shaping an optical pulse by modulating at least one of a phase spectrum and an intensity spectrum using a spatial light modulator (SLM). In these documents, at least one of a phase spectrum and an intensity spectrum for obtaining a desired optical pulse waveform is calculated using a method obtained by improving the iterative Fourier method (Iterative Fourier Transform Algorithm; IFTA).

JP 2016-218141 A JP 2016-218142 A

  For example, there is a technique for modulating the spectral intensity and spectral phase (or only the spectral intensity) of an optical pulse by an SLM as a technique for controlling the time waveform of various lights such as ultrashort pulsed light. In such a technique, the SLM is caused to present a modulation pattern for giving a spectrum intensity (and spectrum phase) for making the time waveform of light close to a desired waveform to the light. In that case, it is desirable that the spectrum intensity (and spectrum phase) can be obtained by calculation so that an arbitrary time waveform can be easily realized.

  When obtaining the spectrum intensity (and spectrum phase) by calculation, as shown in Patent Documents 1 and 2, for example, an iterative Fourier method or a method obtained by correcting the iterative Fourier method is used. However, in the iterative Fourier method and the method in which the iterative Fourier method is modified, the ratio of being led to a local solution is relatively high, so a method that can calculate the optimum solution more accurately is required. One aspect of the present invention is a data creation device capable of calculating a spectral intensity and a spectral phase (or only a spectral intensity) for bringing a temporal waveform of light closer to a desired waveform while reducing the ratio of being led to a local solution. An object is to provide a light control device, a data creation method, and a data creation program.

  In order to solve the above-described problem, a data creation device according to an aspect of the present invention is a device that creates data for controlling a spatial light modulator, and an intensity spectrum function A (ω that is suitable for a desired time intensity waveform. ) To generate data based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum design unit. . The intensity spectrum design unit includes an initial value setting unit that sets a plurality of individuals of the first generation of the intensity spectrum function A (ω) and a phase spectrum function ψ (ω), and an nth generation (n is an integer of 1 or more). A plurality of first waveform functions in the frequency domain including each of the plurality of individuals and a phase spectrum function Ψ (ω) are respectively converted into a plurality of second waveform functions in the time domain including the time intensity waveform function and the time phase waveform function. An evaluation value calculation unit that converts and calculates an evaluation value indicating a degree of difference between the time intensity waveform function and a desired time intensity waveform for each second waveform function, and the nth generation based on the evaluation value excellence An individual selection unit that selects two or more individuals used to generate a plurality of (n + 1) generation individuals from among the plurality of individuals, and the (n + 1) th based on the two or more individuals selected by the individual selection unit ) Live multiple generations A next generation generation unit. In this data creation device, the evaluation value calculation unit, the individual selection unit, and the next generation generation unit repeat the process while adding n one by one until a predetermined condition is satisfied. The intensity spectrum design unit generates an intensity spectrum function A (ω) suitable for a desired time intensity waveform from a plurality of nth generation individuals when a predetermined condition is satisfied.

  A data creation method according to an aspect of the present invention is a method for creating data for controlling a spatial light modulator, and an intensity spectrum function generation step for generating an intensity spectrum function A (ω) suitable for a desired time intensity waveform. And a data generation step of creating data based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum function generation step. The intensity spectrum function generation step includes an initial value setting step of setting a plurality of individuals of the first generation of the intensity spectrum function A (ω) and a phase spectrum function Ψ (ω), an nth generation (n is an integer of 1 or more) ) And a plurality of first waveform functions in the frequency domain including the phase spectrum function Ψ (ω), respectively, and a plurality of second waveform functions in the time domain including the time intensity waveform function and the time phase waveform function, respectively. And an evaluation value calculation step for calculating an evaluation value indicating the degree of difference between the time intensity waveform function and the desired time intensity waveform for each second waveform function, and a plurality of nth generations based on the evaluation value An individual selection step of selecting two or more individuals used to generate a plurality of (n + 1) generation individuals from among the individuals, and the number (n) based on the two or more individuals selected in the individual selection step +1) a next generation generation step of generating a plurality of generations of individuals. In this data creation method, the evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until the predetermined condition is satisfied, and the predetermined condition is satisfied in the intensity spectrum function generation step. An intensity spectrum function A (ω) suitable for a desired time intensity waveform is generated from a plurality of nth generation individuals.

  A data creation program according to an aspect of the present invention is a program for creating data for controlling a spatial light modulator, and an intensity spectrum function generation step for generating an intensity spectrum function A (ω) suitable for a desired time intensity waveform. And a data generation step of creating data based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum function generation step. The intensity spectrum function generation step includes an initial value setting step of setting a plurality of individuals of the first generation of the intensity spectrum function A (ω) and a phase spectrum function Ψ (ω), an nth generation (n is an integer of 1 or more) ) And a plurality of first waveform functions in the frequency domain including the phase spectrum function Ψ (ω), respectively, and a plurality of second waveform functions in the time domain including the time intensity waveform function and the time phase waveform function, respectively. And an evaluation value calculation step for calculating an evaluation value indicating the degree of difference between the time intensity waveform function and the desired time intensity waveform for each second waveform function, and a plurality of nth generations based on the evaluation value An individual selection step of selecting two or more individuals used to generate a plurality of (n + 1) generation individuals from among the individuals, and the number (n) based on the two or more individuals selected in the individual selection step +1) a next generation generation step of generating a plurality of generations of individuals. In this data creation program, the evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the intensity spectrum function generation step. An intensity spectrum function A (ω) suitable for a desired time intensity waveform is generated from a plurality of nth generation individuals.

  In these data creation devices, data creation methods, and data creation programs, the next generation is based on the evaluation value indicating the degree of difference between the time intensity waveform function of the second waveform function and the desired time intensity waveform. Select two or more individuals to be used to generate a plurality of individuals. Then, a plurality of (n + 1) generation individuals are generated based on the two or more selected individuals. Such processing is repeated while adding n one by one until a predetermined condition is satisfied, and an intensity spectrum suitable for a desired time intensity waveform is obtained from a plurality of nth generation individuals when the predetermined condition is satisfied. A function A (ω) is generated. According to the study of the present inventor, the rate by which the intensity spectrum function A (ω) is led to the local solution is reduced by such a method as compared with the iterative Fourier method and the method obtained by correcting the iterative Fourier method. The optimal solution can be searched more accurately. That is, according to the data creation apparatus, the data creation method, and the data creation program, it is possible to accurately calculate the spectrum intensity for bringing the temporal waveform of light closer to a desired waveform.

In the data creation device, the initial value setting unit includes an initial individual generation unit that generates a plurality of individuals of the first generation, and the initial individual generation unit includes the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω ), The first replacement of the time intensity waveform function based on the desired time intensity waveform in the time domain after the Fourier transform, and the inverse Fourier transform performed after the first replacement. And the second replacement for constraining the phase spectrum function Ψ (ω) in the frequency domain after the inverse Fourier transform to generate the intensity spectrum function A _IFTA (ω), A plurality of first generation individuals may be generated by changing the intensity spectrum function A _IFTA (ω). According to the knowledge of the present inventor, setting of a plurality of individuals of the first generation is extremely important in order to more accurately search for an optimal solution in the above-described data creation device. Thus, by generating a plurality of first generation individuals using the iterative Fourier method, a plurality of first generation individuals can be set appropriately, and the calculation accuracy of spectrum intensity can be further improved. . Similarly, in the above data creation method and data creation program as well, the initial value setting step includes an initial individual generation step of generating a plurality of individuals of the first generation, and in the initial individual generation step, the intensity spectrum function Fourier transform for the third waveform function in the frequency domain including A (ω) and phase spectrum function ψ (ω), and a first replacement of the time intensity waveform function based on the desired time intensity waveform in the time domain after the Fourier transform And an inverse Fourier transform performed after the first replacement, and a second replacement for constraining the phase spectrum function Ψ (ω) in the frequency domain after the inverse Fourier transform, thereby performing an intensity spectrum. generate a function a _IFTA (ω), the first generation of a plurality of individuals by varying the said intensity spectral function a _IFTA (ω) Generation may be.

  In the above data creation device, the evaluation value calculation unit calculates an evaluation value indicating a degree of difference between the time intensity waveform function and a function representing a desired time phase waveform multiplied by a coefficient for each second waveform function. The calculated coefficient may have a value that makes the evaluation value after multiplication favorable compared to before multiplication of the coefficient. Thereby, the difference in magnitude between the desired time intensity waveform and the time intensity waveform function of the second waveform function is suppressed from affecting the calculation of the evaluation value, and the time intensity of the desired time intensity waveform and the second waveform function is suppressed. The evaluation value can be calculated mainly based on the difference in shape from the waveform function. Similarly to this, also in the evaluation value calculation step of the above data creation method and data creation program, the degree of difference between the time intensity waveform function and the function representing the desired time phase waveform multiplied by a coefficient is set. An evaluation value to be shown is calculated for each second waveform function, and the coefficient may have a value that makes the evaluation value after multiplication better than before the multiplication of the coefficient.

  In the data creation device, the two or more individuals selected by the individual selection unit include a first individual group consisting of at least one individual and a second individual group consisting of at least one other individual, The average evaluation value of the first population is superior to the average evaluation value of the nth generation individuals, and the average evaluation value of the second population is the average of the nth generation individuals. It may be inferior to the average of the evaluation values. According to the present inventor's many trials, it is possible to further increase the accuracy of calculating the final spectrum intensity by including an individual with an inferior evaluation value as a part of the selected individual. Similarly, in the above data creation method and data creation program, two or more individuals selected in the individual selection step include a first individual group consisting of at least one individual and at least one other individual. The average of the evaluation values of the first individual group is superior to the average of the evaluation values of the plurality of nth generation individuals, and the evaluation value of the second individual group May be inferior to the average of the evaluation values of a plurality of individuals of the nth generation.

  A light control device according to one aspect of the present invention includes a light source that outputs input light, a spectroscopic element that divides the input light, a spatial light modulator that modulates the intensity spectrum of the input light after the spectrum, and outputs the modulated light. And an optical system for collecting the modulated light. The spatial light modulator modulates the intensity spectrum of the input light based on the data created by any one of the data creation devices. According to this apparatus, it is possible to reduce the ratio led to the local solution, accurately calculate the spectrum intensity, and bring the time waveform of light closer to a desired waveform.

  A data generating apparatus according to another aspect of the present invention is an apparatus for generating data for controlling a spatial light modulator, and an intensity spectrum function A (for an optical pulse train including a plurality of optical pulses arranged at intervals of time. ω) and a spectrum design unit for generating a phase spectrum function Ψ (ω), and data generation for creating data based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum design unit A section. The spectrum design unit includes an initial value setting unit that sets a plurality of first generation individual pairs related to the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω), and an nth generation ( (n = 1, 2,...) based on the evaluation value calculation unit for calculating the evaluation value indicating the amount of loss caused by the intensity spectrum modulation based on a plurality of individuals for each individual pair, and the superiority of the evaluation value, An individual selection unit for selecting two or more individual pairs used for generating a plurality of (n + 1) th generation individual pairs from a plurality of individual pairs of the nth generation, and two or more individuals selected by the individual selection unit And a next generation generation unit that generates a plurality of (n + 1) generation individual pairs based on the pair. The evaluation value calculation unit, the individual selection unit, and the next generation generation unit repeat the process while adding n one by one until a predetermined condition is satisfied. The spectrum design unit generates an intensity spectrum function A (ω) and a phase spectrum function Ψ (ω) for generating an optical pulse train from a plurality of nth generation individual pairs when a predetermined condition is satisfied.

  A data creation method according to another aspect of the present invention is a method for creating data for controlling a spatial light modulator, and an intensity spectrum function A (appropriate for an optical pulse train including a plurality of optical pulses arranged at intervals of time. ω) and the phase spectrum function Ψ (ω) are generated, and data is created based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum function generation step. Data generation step. The spectral function generation step includes an initial value setting step for setting a plurality of first generation individual pairs related to the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω), and the nth generation of the intensity spectrum function A (ω). Based on the evaluation value calculation step for calculating the evaluation value indicating the amount of loss caused by the intensity spectrum modulation based on a plurality of individuals (n = 1, 2,...) For each individual pair, and the superiority of the evaluation value , An individual selection step of selecting two or more individual pairs to be used for generating a plurality of (n + 1) generation individual pairs from a plurality of individual pairs of the nth generation, and two or more selected in the individual selection step A next generation generation step of generating a plurality of (n + 1) generation individual pairs based on the individual pairs. In this data creation method, the evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the spectrum function generation step. In this case, an intensity spectrum function A (ω) and a phase spectrum function Ψ (ω) suitable for an optical pulse train are generated from a plurality of nth generation individual pairs.

  A data creation program according to another aspect of the present invention is a program for creating data for controlling a spatial light modulator, and an intensity spectrum function A (appropriate for an optical pulse train including a plurality of optical pulses arranged at intervals of time. ω) and the phase spectrum function Ψ (ω) are generated, and data is created based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum function generation step. And causing the computer to execute a data generation step. The spectral function generation step includes an initial value setting step for setting a plurality of first generation individual pairs related to the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω), and the nth generation of the intensity spectrum function A (ω). Based on the evaluation value calculation step for calculating the evaluation value indicating the amount of loss caused by the intensity spectrum modulation based on a plurality of individuals (n = 1, 2,...) For each individual pair, and the superiority of the evaluation value , An individual selection step of selecting two or more individual pairs to be used for generating a plurality of (n + 1) generation individual pairs from a plurality of individual pairs of the nth generation, and two or more selected in the individual selection step A next generation generation step of generating a plurality of (n + 1) generation individual pairs based on the individual pairs. In this data creation program, the evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the spectrum function generation step. In this case, an intensity spectrum function A (ω) and a phase spectrum function Ψ (ω) suitable for an optical pulse train are generated from a plurality of nth generation individual pairs.

  In these data creation devices, data creation methods, and data creation programs, based on the superiority of the evaluation value indicating the amount of loss caused by intensity spectrum modulation, two or more used for generation of a plurality of next-generation individual pairs Select individual pairs. Based on the two or more selected individual pairs, a plurality of (n + 1) generation individual pairs are generated. Such processing is repeated while adding n one by one until a predetermined condition is satisfied, and an intensity spectrum suitable for a desired optical pulse train from a plurality of nth generation individual pairs when the predetermined condition is satisfied. A function A (ω) and a phase spectrum function Ψ (ω) are generated. Similar to the above-described case, the intensity spectral function A (ω) and the phase spectral function Ψ (ω) are led to the local solution by this method as compared to the iterative Fourier method and the modified method of the iterative Fourier method. The optimal solution can be searched more accurately. That is, according to these data creation devices, data creation methods, and data creation programs, the spectrum intensity and spectrum for reducing the time waveform of the optical pulse train to a desired waveform while reducing the ratio of being guided to a local solution. The phase can be calculated. Furthermore, according to these data creation devices, data creation methods, and data creation programs, it is possible to accurately calculate the spectrum intensity and the spectrum phase for minimizing the amount of loss that occurs when generating an optical pulse.

  In the data creation device, the initial value setting unit includes an initial individual generation unit that generates a plurality of first generation individuals, and the initial individual generation unit has the same amplitude and timing of each optical pulse included in the optical pulse train. A plurality of first generation individuals may be generated by performing a Fourier transform on each of a plurality of delta function groups having amplitude and timing and different time phases. As described above, in order to search for the optimum solution more accurately, the setting of a plurality of individuals of the first generation is extremely important. In this way, a plurality of delta function groups having the same amplitude and timing as each optical pulse included in the optical pulse train and having different time phases are Fourier transformed to generate a plurality of first generation individuals. By doing so, it is possible to appropriately set a plurality of individuals of the first generation, and it is possible to further improve the calculation accuracy of the spectrum intensity and the spectrum phase. Similarly, in the above data creation method and data creation program, the initial value setting step includes an initial individual generation step of generating a plurality of first generation individuals, and in the initial individual generation step, the optical pulse train A plurality of first generation individuals may be generated by Fourier transforming a plurality of delta function groups having the same amplitude and timing as the amplitudes and timings of the included optical pulses and having different time phases.

  In the above data creation device, the evaluation value calculation unit normalizes the plurality of nth generation individuals related to the intensity spectrum function A (ω) so that the maximum values are equal, and each of the plurality of individuals after normalization The evaluation value may be calculated based on the integral value of. As a result, the variation in the size of the plurality of individuals related to the intensity spectrum function A (ω) is suppressed from affecting the calculation of the evaluation value, and the evaluation value is calculated mainly based on the difference in the shape of the plurality of individuals. be able to. Similarly, in the evaluation value calculation step of the above data creation method and data creation program, a plurality of nth generation individuals related to the intensity spectrum function A (ω) are standardized so that the maximum values are uniform. The evaluation value may be calculated based on the integrated value of each of the plurality of individuals after normalization.

  In the above data creation device, the two or more individual pairs selected by the individual selecting unit include a first individual pair group composed of at least one individual pair and a second individual pair composed of at least one other individual pair. The average of the evaluation values of the first individual pair group is superior to the average of the evaluation values of a plurality of individual pairs of the nth generation, and the average of the evaluation values of the second individual pair group is It may be inferior to the average of the evaluation values of a plurality of individual pairs of the nth generation. By including an individual pair having an inferior evaluation value as a part of the selected individual pair in this way, the final spectral intensity and spectral phase calculation accuracy can be further increased. Similarly, in the above data creation method and data creation program, two or more individual pairs selected in the individual selection step are at least one first pair of individuals consisting of at least one individual pair. A second individual pair group consisting of two other individual pairs, and the average of the evaluation values of the first individual pair group is superior to the average of the evaluation values of the plurality of individual pairs of the nth generation, The average of the evaluation values of the two individual pairs may be inferior to the average of the evaluation values of a plurality of nth generation individual pairs.

  A light control device according to another aspect of the present invention includes a light source that outputs input light, a spectroscopic element that splits the input light, a spatial light modulator that modulates the input light after the spectrum and outputs the modulated light, and a modulation An optical system for collecting light. The spatial light modulator modulates the intensity spectrum and the spectrum phase of the input light based on the data created by any one of the data creating devices. According to this apparatus, it is possible to calculate the spectral intensity and the spectral phase while reducing the ratio led to the local solution, and to approximate the time waveform of light to a desired waveform. Furthermore, according to this apparatus, it is possible to accurately calculate the spectrum intensity and the spectrum phase for minimizing the loss amount generated when generating the optical pulse.

  According to the data creation device, the light control device, the data creation method, and the data creation program according to the present invention, the spectral intensity and the spectrum phase for reducing the ratio led to the local solution and bringing the time waveform of light closer to the desired waveform (Or only the spectral intensity) can be calculated with high accuracy.

FIG. 1 is a diagram schematically showing a configuration of a light control apparatus 1A according to the first embodiment of the present invention. FIG. 2 is a diagram illustrating a configuration of the optical system 10 included in the light control apparatus 1A. FIG. 3 is a diagram showing the modulation surface 17 of the SLM 14. 4A shows a spectrum waveform (spectrum phase G11 and spectrum intensity G12) of the input light La having a single pulse shape as an example, and FIG. 4B shows a time intensity waveform of the input light La. Show. FIG. 5A shows, as an example, a spectrum waveform (spectrum phase G21 and spectrum intensity G22) of the output light Ld when rectangular wave-like phase spectrum modulation is given in the SLM 14, and FIG. The time intensity waveform of the output light Ld is shown. FIG. 6 is a diagram schematically illustrating a hardware configuration example of the modulation pattern calculation apparatus 20. FIG. 7 is a block diagram showing an internal configuration of the intensity spectrum design unit 23. FIG. 8 is a flowchart showing an intensity spectrum design method (data creation method) by the modulation pattern calculation apparatus 20. FIG. 9 is a diagram conceptually illustrating a method of calculating the intensity spectrum function A _IFTA (ω) in the initial individual generation unit 25a. FIG. 10 is a graph showing an example of the intensity spectrum function A _pulse (ω) and the intensity spectrum function A _IFTA (ω) of the input light La. FIG. 11 shows the function b _m (ω) when the intensity spectrum functions A _pulse (ω) and A _IFTA (ω) shown in FIG. 10 are used, the function b _m (ω) as the upper limit, and the function a _m (ω ) (= 0) is a graph exemplifying a probability function B _m (ω) generated randomly (so that the appearance probabilities are the same at random) within a range having a lower limit of (= 0). FIG. 12A shows, as an example, an intensity spectrum function A (ω) for generating 8-pulse output light Ld calculated by the modulation pattern calculation device 20 and the modulation pattern calculation method of the first embodiment. It is a graph to show. 12B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform. FIG. 13A is a graph showing, as a comparative example, an intensity spectrum function A (ω) for generating 8-pulse output light Ld calculated using only the iterative Fourier method. FIG. 13B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform. FIG. 14 is a graph plotting the relationship between the number of pulses at that time and the evaluation value (minimum value of the standard deviation shown in Equation (14)). FIG. 15 is a graph plotting the relationship between the number of pulses and the average pulse width (full width at half maximum) in the above example. FIG. 16 is a graph plotting the relationship between the number of pulses and the dispersion of peak values in the above embodiment. FIG. 17 is a graph showing how the evaluation value changes as the generation progresses. FIG. 18 illustrates the amount of change in evaluation values before and after the introduction of non-elite individuals. FIG. 19 is a diagram schematically showing a configuration of a light control device 1B according to the second embodiment of the present invention. FIG. 20 is a diagram schematically illustrating an example of an optical pulse train. FIG. 21 is a flowchart showing a design method (data creation method) of an intensity spectrum and a phase spectrum by the modulation pattern calculation device 30. FIG. 22 illustrates the first generation M individual pairs (A _m (ω), Ψ _m (ω)) (m = 1, 2,...) From the M delta function groups in the initial individual generation unit 25a. , M) conceptually shows an example of a method for calculating. FIG. 23 is a flowchart showing details of the initial individual generation step S36. FIG. 24A shows, as an example, an intensity spectrum function A (for generating an optical pulse train composed of 50 optical pulses calculated by the modulation pattern calculation device 30 and the modulation pattern calculation method of the second embodiment. It is a graph which shows (omega)) and phase spectrum function (PSI) ((omega)). 24B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform. FIG. 25 shows the number of operations of Fast Fourier Transform (FFT) required in the conventional method for exhaustively searching for the optimal combination of the time intensity waveform function and the time phase function of the optical pulse train, and is required in this embodiment. It is a graph which compares the frequency | count of a calculation of FFT. FIG. 26 is a graph comparing the loss amount due to the intensity spectrum modulation pattern calculated by the conventional method with the loss amount due to the intensity spectrum modulation pattern calculated by the method according to the present embodiment. FIG. 27 shows the evaluation as the generation progresses when calculating the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) (see FIG. 23A) for generating an optical pulse train of 50 pulses. It is a graph which shows a mode that a value changes. FIG. 28 is a diagram schematically illustrating a configuration of a light control apparatus 1C according to the third embodiment.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments of a data creation device, a light control device, a data creation method, and a data creation program according to the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.

(First embodiment)
FIG. 1 is a diagram schematically showing a configuration of a light control apparatus 1A according to the first embodiment of the present invention. FIG. 2 is a diagram illustrating a configuration of the optical system 10 included in the light control apparatus 1A. The light control apparatus 1A of the present embodiment generates output light Ld having an arbitrary time intensity waveform different from the input light La from the input light La. As shown in FIG. 1, the light control device 1 </ b> A includes a light source 2, an optical system 10, and a modulation pattern calculation device (data creation device) 20.

  The light source 2 outputs input light La input to the optical system 10. The light source 2 is a laser light source such as a solid laser light source or a fiber laser light source, and the input light La is, for example, coherent pulse light. The optical system 10 includes an SLM 14, and receives a control signal SC for controlling each pixel of the SLM 14 from the modulation pattern calculation device 20. The optical system 10 converts the input light La from the light source 2 into output light Ld having an arbitrary time intensity waveform. The modulation pattern is data for controlling the SLM 14 and is data in which the intensity of the complex amplitude distribution or the intensity of the phase distribution is output to a file. The modulation pattern is, for example, a computer-generated hologram (CGH).

  As shown in FIG. 2, the optical system 10 includes a diffraction grating 12, a lens 13, an SLM 14, a lens 15, and a diffraction grating 16. The diffraction grating 12 is a spectroscopic element in the present embodiment, and is optically coupled to the light source 2. The SLM 14 is optically coupled to the diffraction grating 12 via the lens 13. The diffraction grating 12 separates the input light La for each wavelength component. As the spectroscopic element, other optical components such as a prism may be used instead of the diffraction grating 12. The spectroscopic element may be a reflection type or a transmission type. The input light La is incident on the diffraction grating 12 at an angle, and is split into a plurality of wavelength components. The light Lb including the plurality of wavelength components is condensed for each wavelength component by the lens 13 and imaged on the modulation surface of the SLM 14. The lens 13 may be a convex lens made of a light transmitting member, or a concave mirror having a concave light reflecting surface.

  The SLM 14 simultaneously performs phase modulation and intensity modulation of the light Lb in order to generate output light Ld having an arbitrary time intensity waveform different from the input light La. The SLM 14 may perform only intensity modulation. The SLM 14 is, for example, a phase modulation type. In one embodiment, SLM 14 is of the LCOS (Liquid crystal on silicon) type. Alternatively, the SLM 14 may be an intensity modulation type SLM such as a digital micromirror device (DMD). The SLM 14 may be a reflection type or a transmission type. FIG. 3 is a diagram showing the modulation surface 17 of the SLM 14. As shown in FIG. 3, a plurality of modulation regions 17 a are arranged along a certain direction A on the modulation surface 17, and each modulation region 17 a extends in a direction B intersecting the direction A. A direction A is a spectral direction by the diffraction grating 12. The modulation surface 17 functions as a Fourier transform surface, and each wavelength component corresponding to the spectrum is incident on each of the plurality of modulation regions 17a. In each modulation region 17a, the SLM 14 modulates the phase and intensity of each incident wavelength component independently of other wavelength components. Since the SLM 14 of the present embodiment is a phase modulation type, intensity modulation is realized by a phase pattern (phase image) presented on the modulation surface 17.

  Each wavelength component of the modulated light Lc modulated by the SLM 14 is collected at one point on the diffraction grating 16 by the lens 15. The lens 15 at this time functions as a condensing optical system that condenses the modulated light Lc. The lens 15 may be a convex lens made of a light transmitting member, or a concave mirror having a concave light reflecting surface. The diffraction grating 16 functions as a multiplexing optical system, and multiplexes the modulated wavelength components. That is, the plurality of wavelength components of the modulated light Lc are condensed and combined with each other by the lens 15 and the diffraction grating 16 to become output light Ld.

  The region before the lens 15 (spectral region) and the region after the diffraction grating 16 (time region) are in a Fourier transform relationship with each other, and phase modulation and intensity modulation in the spectral region are performed in time in the time region. Affects the intensity waveform. Therefore, the output light Ld has a desired time intensity waveform different from the input light La according to the modulation pattern of the SLM 14. Here, FIG. 4A shows the spectrum waveform (spectrum phase G11 and spectrum intensity G12) of the monopulse input light La as an example, and FIG. 4B shows the time of the input light La. An intensity waveform is shown. FIG. 5A shows, as an example, a spectrum waveform (spectrum phase G21 and spectrum intensity G22) of the output light Ld when rectangular wave-like phase spectrum modulation is given in the SLM 14, and FIG. Indicates a time intensity waveform of the output light Ld. 4 (a) and 5 (a), the horizontal axis indicates the wavelength (nm), the left vertical axis indicates the intensity value (arbitrary unit) of the intensity spectrum, and the right vertical axis indicates the phase spectrum. The phase value (rad) is indicated. In FIG. 4B and FIG. 5B, the horizontal axis represents time (femtoseconds), and the vertical axis represents light intensity (arbitrary unit). In this example, by giving a rectangular wave-like phase spectrum waveform to the output light Ld, the single pulse of the input light La is converted into a double pulse with higher-order light as the output light Ld. 4 and 5 are only examples, and the time intensity waveform of the output light Ld can be shaped into various shapes by combining various phase spectra and intensity spectra.

  Refer to FIG. 1 again. The modulation pattern calculation apparatus 20 is a computer having a processor such as a personal computer, a smart device such as a smartphone and a tablet terminal, or a cloud server. The modulation pattern calculation device 20 is electrically connected to the SLM 14, calculates a phase modulation pattern for bringing the time intensity waveform of the output light Ld closer to a desired waveform, and sends a control signal SC including the phase modulation pattern to the SLM 14. To provide. The modulation pattern calculation apparatus 20 of the present embodiment includes a phase pattern for phase modulation that gives a phase spectrum for obtaining a desired waveform to the output light Ld, and an intensity that gives an intensity spectrum for obtaining a desired waveform to the output light Ld. A phase pattern including the phase pattern for modulation is presented to the SLM 14. For this purpose, the modulation pattern calculation apparatus 20 includes an arbitrary waveform input unit 21, a phase spectrum design unit 22, an intensity spectrum design unit 23, and a modulation pattern generation unit (data generation unit) 24. That is, the processor of the computer provided in the modulation pattern calculation apparatus 20 has the function of the arbitrary waveform input unit 21, the function of the phase spectrum design unit 22, the function of the intensity spectrum design unit 23, and the function of the modulation pattern generation unit 24. And realize. Each function may be realized by the same processor or may be realized by different processors.

  FIG. 6 is a diagram schematically illustrating a hardware configuration example of the modulation pattern calculation apparatus 20. As shown in FIG. 6, the modulation pattern calculation apparatus 20 physically includes a processor (CPU) 201, a main storage device such as a ROM 202 and a RAM 203, an input device 204 such as a keyboard, a mouse, and a touch screen, and a display (touch). Output device 205 (including a screen), a communication module 206 such as a network card for transmitting / receiving data to / from other devices, an auxiliary storage device 207 such as a hard disk, and the like.

  The processor 201 of the computer realizes the above functions (arbitrary waveform input unit 21, phase spectrum design unit 22, intensity spectrum design unit 23, and modulation pattern generation unit 24) by a modulation pattern calculation program (data creation program). be able to. Therefore, the modulation pattern calculation program causes the processor 201 of the computer to operate as the arbitrary waveform input unit 21, phase spectrum design unit 22, intensity spectrum design unit 23, and modulation pattern generation unit 24 in the modulation pattern calculation device 20. The modulation pattern calculation program is stored in a storage device (storage medium) inside or outside the computer such as the auxiliary storage device 207, for example. The storage device may be a non-transitory recording medium. Examples of the recording medium include a recording medium such as a flexible disk, a CD, and a DVD, a recording medium such as a ROM, a semiconductor memory, a cloud server, and the like.

  The arbitrary waveform input unit 21 receives an input of a desired time intensity waveform from the operator. The operator inputs information relating to a desired time intensity waveform (for example, pulse width, number of pulses, etc.) to the arbitrary waveform input unit 21. Information on the desired time intensity waveform is given to the phase spectrum design unit 22 and the intensity spectrum design unit 23. The phase spectrum design unit 22 calculates the phase spectrum of the output light Ld suitable for realizing the given desired time intensity waveform. The intensity spectrum design unit 23 calculates an intensity spectrum of the output light Ld suitable for realizing a given desired time intensity waveform. The modulation pattern generation unit 24 provides a phase modulation pattern (for example, a computer-generated hologram) for providing the output light Ld with the phase spectrum obtained by the phase spectrum design unit 22 and the intensity spectrum obtained by the intensity spectrum design unit 23. Is calculated. Then, a control signal SC including the calculated phase modulation pattern is provided to the SLM 14, and the SLM 14 is controlled based on the control signal SC.

  FIG. 7 is a block diagram showing an internal configuration of the intensity spectrum design unit 23. As shown in FIG. 7, the intensity spectrum design unit 23 includes an initial value setting unit 25, an evaluation value calculation unit 26, an individual selection unit 27, and a next generation generation unit 28. The initial value setting unit 25 includes an initial individual generation unit 25a. FIG. 8 is a flowchart showing an intensity spectrum design method (data creation method) by the modulation pattern calculation apparatus 20. Hereinafter, the operation of the modulation pattern calculation apparatus 20 of the present embodiment, that is, the intensity spectrum design method (data creation method) will be described with reference to FIGS.

  First, the intensity spectrum design unit 23 generates an intensity spectrum function A (ω) suitable for a desired time intensity waveform input from the arbitrary waveform input unit 21 (intensity spectrum function generation step S1). Specifically, the intensity spectrum function generation step S1 includes an initial value setting step S11, an evaluation value calculation step S12, an individual selection step S13, and a next generation generation step S14.

In the initial value setting step S11, the initial value setting unit 25 performs the first generation M individuals (genetic information) A ₁ (ω) to A ₁ related to the intensity spectrum function A (ω) (where M is an integer of 2 or more). Set _M (ω) and the phase spectral function ψ (ω). The individual A ₁ (ω) to A _M (ω) and the phase spectrum function Ψ (ω) are functions of the frequency ω. The phase spectrum function Ψ (ω) may be input by an operator, or may be calculated by the phase spectrum design unit 22. By this initial value setting step S11, the frequency domain including each of the first generation individuals A ₁ (ω) to A _M (ω) of the intensity spectrum function A (ω) and the phase spectrum function Ψ ₀ (ω) is obtained. M waveform functions (1) are defined. This waveform function (1) is the first waveform function in the present embodiment. However, i is an imaginary number.

The initial value setting step S11 of the present embodiment includes an initial individual generation step S11a. In the initial individual generation step S11a, the initial individual generation unit 25a generates the intensity spectrum function A _IFTA (ω) by the iterative Fourier method, and changes the intensity spectrum function A _IFTA (ω) to thereby change the first generation individual A. ₁ (ω) to A _M (ω) are generated. FIG. 9 is a diagram conceptually illustrating a method of calculating the intensity spectrum function A _IFTA (ω) in the initial individual generation unit 25a. As shown in FIG. 9, first, the initial individual generation unit 25a prepares an initial intensity spectrum function A _{k = 0} (ω) and a phase spectrum function Ψ ₀ (ω) (processing number (1) in the figure). ). In one example, the initial intensity spectrum function A _{k = 0} (ω) and the phase spectrum function Ψ ₀ (ω) are determined based on the spectrum intensity and the spectrum phase of the input light La. Next, the initial individual generation unit 25a prepares a frequency domain waveform function (2) including the intensity spectrum function A _k (ω) and the phase spectrum function Ψ ₀ (ω) (process number (2) in the figure). . This waveform function (2) is the third waveform function in the present embodiment.

The subscript k represents after the k-th Fourier transform processing. First in front of the Fourier transform processing (first time), the above initial strength spectral function A _{k = 0} (omega) is used as the intensity spectrum function A _k (omega). i is an imaginary number.

Subsequently, the initial individual generation unit 25a performs a Fourier transform from the frequency domain to the time domain for the function (2) (arrow A1 in the figure). Thereby, the time domain waveform function (3) including the time intensity waveform function b _k (t) and the time phase function Θ _k (t) is obtained (process number (3) in the figure).

Subsequently, the initial individual generation unit 25a determines that the difference between the waveform function b _k (t) after Fourier transform and the function Target ₀ (t) multiplied by the coefficient α (α × Target ₀ (t)) A coefficient α that is smaller than the difference between the function b _k (t) and the function Target ₀ (t) is obtained (process number (4) in the figure). In one example, as shown in the following formula (4), a coefficient α that minimizes the standard deviation σ of α × Target ₀ (t) with respect to the waveform function b _k (t) after Fourier transform is the minimum (σ _min ). Derived exploratively. Note that in equation (4), D represents the number of data _points, t s, _{t e} represents the start and end points of each time axis.

Subsequently, the initial individual generation unit 25a performs replacement based on a desired waveform for the time intensity waveform function b _k (t) included in the function (3) after the Fourier transform (first replacement). At this time, the initial individual generating unit 25a performs replacement using a function Target ₀ (t) representing a desired waveform multiplied by a coefficient α (α × Target ₀ (t)). In one example, it is replaced with Target _k (t) calculated by Equation (5) (processing numbers (5) and (6) in the figure).

Subsequently, the initial individual generation unit 25a performs inverse Fourier transform from the time domain to the frequency domain on the function (6) (arrow A2 in the figure). Thereby, the waveform function (7) in the frequency domain including the intensity spectrum function C _k (ω) and the phase spectrum function Ψ _k (ω) is obtained (process number (7) in the figure).

Subsequently, the initial individual generation unit 25a replaces the phase spectrum function Ψ _k (ω) included in the function (7) with the initial phase spectrum function Ψ ₀ (ω) (second replacement, FIG. Middle processing number (8)).

Further, the initial individual generation unit 25a performs a filtering process based on the intensity spectrum of the input light La on the intensity spectrum function C _k (ω) in the frequency domain after the inverse Fourier transform. Specifically, the portion of the intensity spectrum represented by the intensity spectrum function C _k (ω) that exceeds the cutoff intensity for each wavelength determined based on the intensity spectrum of the input light La is cut. In one example, the cutoff intensity for each wavelength is set to coincide with the intensity spectrum of the input light La (in this embodiment, the initial intensity spectrum function A _{k = 0} (ω)). In that case, as shown in the following equation (9), at a frequency where the intensity spectrum function C _k (ω) is larger than the initial intensity spectrum function A _{k = 0} (ω), the intensity spectrum function A _k (ω) The value of the initial intensity spectrum function A _{k = 0} (ω) is taken as the value. At a frequency where the intensity spectrum function C _k (ω) is equal to or less than the initial intensity spectrum function A _{k = 0} (ω), the value of the intensity spectrum function C _k (ω) is the value of the intensity spectrum function A _k (ω). Incorporated.

The initial individual generation unit 25a replaces the intensity spectrum function C _k (ω) included in the function (7) with the intensity spectrum function A _k (ω) after the filter processing according to the equation (9). Further, a method of defining a function C ′ _k (ω) _obtained by multiplying C _k (ω) by an arbitrary coefficient and relatively changing the cutoff intensity may be used (processing number (9) in the figure). ).

Thereafter, the initial individual generation unit 25a repeats the above processes (1) to (9) a plurality of times, whereby the intensity spectrum function A _k (ω) in the waveform function is converted into an intensity spectrum corresponding to a desired time intensity waveform. It can be close to the shape. Finally, the intensity spectrum function A _IFTA (ω) is obtained.

The initial individual generation unit 25a generates first generation individuals A ₁ (ω) to A _M (ω) by changing the intensity spectrum function A _IFTA (ω). Specifically, the initial individual generation unit 25a generates first generation individuals A ₁ (ω) to A _M (ω) using the following formula (10).

Here, m represents an individual number, and m = 1, 2,. B _m (ω) is a probability function that changes the intensity spectrum function A _IFTA (ω). By appropriately setting this probability function B _m (ω), it is possible to generate appropriate first generation individuals A ₁ (ω) to A _M (ω) according to the intensity spectrum function A _IFTA (ω). it can.

For example, A _IFTA (ω) × B _m (ω) cannot exceed the intensity spectrum function A _pulse (ω) of the input light La that is the modulated light. When the upper limit of the real number range that the probability function B _m (ω) can take is expressed as a function b _m (ω) and the lower limit as a function a _m (ω), these functions b _m (ω) and a _m (ω) are It can be expressed using the intensity spectrum functions A _IFTA (ω) and A _pulse (ω) as follows. Note that s in the equation is a minute value inserted for convenience so that the denominator does not become zero.

FIG. 10 is a graph showing an example of the intensity spectrum function A _pulse (ω) and the intensity spectrum function A _IFTA (ω) of the input light La. In FIG. 10, a graph G31 represents the intensity spectrum function A _pulse (ω), and a graph G32 represents the intensity spectrum function A _IFTA (ω). The horizontal axis represents wavelength (unit: nm), and the vertical axis represents intensity (arbitrary unit). Regarding the horizontal axis, the wavelength can be converted to the frequency ω and treated as the frequency ω as expressed in the formulas and figures in the text. As shown in FIG. 10, the intensity spectrum function A _pulse (ω) follows a Gaussian distribution. The intensity spectrum function A _IFTA (ω) is a realistic intensity spectrum function that does not exceed the intensity spectrum function A _pulse (ω) in the entire frequency range due to the action of the above-described equation (9) while repeating the maximum and minimum. It has become.

FIG. 11 shows the function b _m (ω) when the intensity spectrum functions A _pulse (ω) and A _IFTA (ω) shown in FIG. 10 are used, the function b _m (ω) as the upper limit, and the function a _m (ω ) (= 0) is a graph exemplifying a probability function B _m (ω) generated randomly (so that the appearance probabilities are the same at random) within a range having a lower limit of (= 0). In FIG. 11, a graph G41 represents a function b _m (ω), and a graph G42 represents a probability function B _m (ω). The horizontal axis represents the wavelength (unit: nm), and the vertical axis represents the value (real number) of the function b _m (ω) and the probability function B _m (ω). As shown in FIG. 11, by appropriately setting the upper limit and the lower limit of the probability function B _m (ω), the above equation (10) is used to randomly calculate a random number within the range of real values that can be actually taken. One generation of individuals A ₁ (ω) to A _M (ω) can be generated. Further, by arbitrarily narrowing the difference between the upper limit and the lower limit, that is, the difference between the function b _m (ω) and the function a _m (ω), the first generation individuals A ₁ (ω) to A _M (ω) The dispersion can be reduced. Note that the probability function B _m (ω) may not be random in a complete sense, and the appearance probability may follow a normal distribution, for example.

Refer to FIGS. 7 and 8 again. Next, in the evaluation value calculation step S12, the evaluation value calculation unit 26 uses a common phase spectrum function with each of the individuals A ₁ (ω) to A _M (ω) of the nth generation (n is an integer of 1 or more). M first waveform functions (12) in the frequency domain including Ψ (ω)

M waveform functions (13) in the time domain including time intensity waveform functions I ₁ (t) to I _M (t) and time phase waveform functions Φ ₁ (t) to Φ _M (t), respectively.

Convert to These waveform functions (13) are the second waveform functions in the present embodiment. Then, the evaluation value calculation unit 26 indicates the degree of difference between each of the time intensity waveform functions I ₁ (t) to I _M (t) and the desired time intensity waveform T (t) (= Target ₀ (t)). M evaluation values are calculated. For example, the evaluation value calculation unit 26 calculates each standard deviation of the time intensity waveform functions I ₁ (t) to I _M (t) with respect to a desired time intensity waveform T (t) as an evaluation value. At this time, if there is an energy difference between the desired time intensity waveform T (t) and the time intensity waveform functions I ₁ (t) to I _M (t), the evaluation value varies due to the energy difference. End up. In the present embodiment, an exploratory evaluation function is introduced to compensate for this energy difference. Specifically, the evaluation value calculation unit 26 represents each of the time intensity waveform functions I ₁ (t) to I _M (t) and a desired time phase waveform as represented by the following formula (14). M evaluation values indicating the degree of difference from the function T (t) multiplied by the coefficients α _{1 to} α _M are calculated.

The coefficients α _{1 to} α _M have values at which the respective evaluation values are good compared to before the multiplication of the coefficients α _{1 to} α _M. As an example of the evaluation value, Expression (14) is a time intensity waveform function I ₁ (t) to I _M (for a function T (t) representing a desired time phase waveform multiplied by coefficients α _{1 to} α _M. The standard deviation of t) is shown. In this example, α _{1 to} α _M are changed so that each standard deviation takes a minimum value. Then, the respective minimum values _{σ min1} ~σ minM standard deviation, and the time intensity waveform function _{I 1 (t) ~I M (} t) each evaluation value.

Subsequently, based on the M evaluation values calculated in the evaluation value calculation step S12 (specifically, the minimum values of standard deviations σ _{min1 to} σ _minM ), the individual selection unit 27 selects the plurality of nth generation individuals A ₁ (ω) to A _M (ω) are used to select two or more individuals used to generate a plurality of (n + 1) th generation individuals A ₁ (ω) to A _M (ω) (individual selection step) S13). In this individual selection step S13, two or more individuals are selected based on the superiority of the M evaluation values. Here, “based on excellence” means, for example, an individual group G1 (a first group consisting of at least one individual selected from _M individuals A ₁ (ω) to A _M (ω) of the nth generation. Means that the evaluation value is superior to all the other individuals not included in the individual group G1 among the _M individuals A ₁ (ω) to A _M (ω). Alternatively, the average of the evaluation values in the individual group G1 including one or more individuals selected from _M individuals A ₁ (ω) to A _M (ω) of the nth generation is M individuals A ₁ (ω ) To A _M (ω) may mean better than the average evaluation value. Hereinafter, this population G1 may be referred to as an “elite population”.

In the present embodiment, the two or more individuals selected by the individual selection unit 27 in the individual selection step S13 are, in addition to the elite individual group G1, an individual group G2 (second individual group) composed of at least one other individual. ) May be included. In this case, the average of the evaluation values of the population G2 is inferior than the average of the evaluation values _{σ min1} ~σ minM of M individuals A ₁ of the generation n _{(ω) ~A M (ω)} . Hereinafter, this population G2 may be referred to as a “non-elite population”. When the evaluation values of _M individuals A ₁ (ω) to A _M (ω) are arranged in order of superiority, the evaluation values of the non-elite individual group G2 are not continuous from the evaluation values of the elite individual group G1. That is, some of the M individuals A ₁ (ω) to A _M (ω) are inferior to the evaluation value that is inferior in the elite individual group G1, and are the best in the non-elite individual group G2. There are one or more individuals that have an evaluation value better than the evaluation value.

Subsequently, in the next generation generation step S14, the next generation generation unit 28, based on the two or more individuals selected by the individual selection unit 27 in the individual selection step S13, the M individuals A ₁ ( ω) to A _M (ω) are generated. Here, “generating a plurality of (n + 1) generation individuals based on two or more selected individuals” means, for example, processing such as crossover, mutation, proliferation, and the (n + 1) generation M It means that each of the individuals A ₁ (ω) to A _M (ω) includes at least a component of any one of the nth generation individuals. A part of the selected two or more individuals (for example, the most excellent individual group) may be directly used as any one of the (n + 1) th generation individuals A ₁ (ω) to A _M (ω).

In the intensity spectrum function generation step S1, the above-described evaluation value calculation step S12, individual selection step S13, and next generation generation step S14 are repeated while adding n one by one until a predetermined condition is satisfied (step S15). . In other words, the evaluation value calculation unit 26, the individual selection unit 27, and the next generation generation unit 28 repeat the process while adding n one by one until a predetermined condition is satisfied. Then, the intensity spectrum design unit 23 (in the intensity spectrum function generation step S1) obtains a desired value from _M individuals A ₁ (ω) to A _M (ω) of the nth generation when a predetermined condition is satisfied. An intensity spectrum function A (ω) suitable for the time intensity waveform is generated. For example, one individual A _m (ω) out of _M individuals A ₁ (ω) to A _M (ω) may be extracted and used as the intensity spectrum function A (ω). The predetermined condition is, for example, a case where the arbitrarily set number of repeated trials is completed or a case where an arbitrarily defined evaluation value is satisfied.

  After the above processing, in the data generation step S2, the modulation pattern generation unit 24, based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum function generation step S1, Data relating to a modulation pattern to be presented to the SLM 14 is generated. The modulation pattern generation unit 24 provides the generated data to the SLM 14 as the control signal SC.

  The effects obtained by the light control device 1A, the modulation pattern calculation device 20, the modulation pattern calculation method, and the modulation pattern calculation program of the present embodiment described above will be described. Conventionally, when light having a desired time waveform is realized using an SLM, an iterative Fourier method or a method in which the iterative Fourier method is modified in order to accurately calculate the spectral intensity corresponding to the desired time waveform (for example, Patent Documents) 1 and 2) are used. However, when trying to generate multipulses using this method, the waveform control accuracy is greatly improved. However, when the waveform shape is analyzed in detail, dispersion (variation) is confirmed in the peak value and pulse width of each pulse. It was done. This means that there is room for improvement as a design method of the waveform control pattern. In particular, when considering a microscope application or processing application of pulsed light, a change in pulse width or a change in peak value may greatly affect a change in signal S / N ratio or processing state. Therefore, a method capable of designing the waveform control pattern with higher accuracy is desired.

For such a problem, in the modulation pattern calculation device 20, the modulation pattern calculation method, and the modulation pattern calculation program of the present embodiment, the time intensity waveform functions I ₁ (t) to I _M (t) and a desired time Two or more individuals used to generate the next generation M individuals A ₁ (ω) to A _M (ω) based on the superiority of the evaluation value indicating the degree of difference from the intensity waveform T (t). Select. Based on the two or more selected individuals, the (n + 1) th generation M individuals A ₁ (ω) to A _M (ω) are generated. Such processing is repeated while adding n one by one until a predetermined condition is satisfied, and the nth generation M individuals A ₁ (ω) to A _M (ω) when the predetermined condition is satisfied. From this, an intensity spectrum function A (ω) suitable for a desired time intensity waveform T (t) is generated. As a result of the research, the inventor leads the intensity spectrum function A (ω) to a local solution by such a method (genetic algorithm) as compared with the iterative Fourier method and the method obtained by correcting the iterative Fourier method. It has been found that the optimal solution can be searched more accurately by reducing the ratio.

  FIG. 12A shows, as an example, an intensity spectrum function A (ω) for generating 8-pulse output light Ld calculated by the modulation pattern calculation device 20 and the modulation pattern calculation method of the present embodiment. It is a graph. The graph G61 shows the intensity spectrum function A (ω). A graph G62 shows the phase spectrum function Ψ (ω) used in this example. This phase spectrum function Ψ (ω) is calculated by the iterative Fourier method. 12B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform. FIG. 13A is a graph showing, as a comparative example, an intensity spectrum function A (ω) for generating the 8-pulse output light Ld calculated using only the iterative Fourier method. The graph G71 shows the intensity spectrum function A (ω). A graph G72 shows the phase spectrum function Ψ (ω) used in this comparative example. The shape of the phase spectrum function Ψ (ω) is the same as the graph G62 in FIG. FIG. 13B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform.

  Referring to (b) of FIG. 13, when the intensity spectrum function A (ω) is calculated using only the iterative Fourier method, the peak intensity of the eight pulses greatly varies in the time intensity waveform of the generated output light Ld. Is seen. On the other hand, referring to FIG. 12B, when the intensity spectrum function A (ω) is calculated by the modulation pattern calculation apparatus 20 and the modulation pattern calculation method of the present embodiment, the intensity loss amount is 39%, and iterative Fourier Although it is higher than 31% of the modulo, in the time intensity waveform of the output light Ld to be generated, variations in the peak intensity of the eight pulses are suppressed to be small. Regarding the evaluation value, the value according to the present embodiment is 1 / 8.7 of the value obtained by the iterative Fourier method, which is greatly improved.

  Thus, according to the modulation pattern calculation device 20 and the modulation pattern calculation method of the present embodiment, compared to the conventional device and method using only the iterative Fourier method, the ratio of being led to a local solution is reduced, The optimal solution can be searched more accurately. That is, according to this embodiment, it is possible to accurately calculate the spectrum intensity for bringing the time waveform of the output light Ld close to the desired waveform T (t), and to obtain the desired time waveform with high accuracy. In the present embodiment, the number of individuals of each generation is unified to M, but the number of individuals of each generation may be changed.

Here, in order to confirm the effectiveness of the present embodiment, a plurality of modulation patterns for generating the output light Ld having a time intensity waveform including multipulses were calculated while changing the number of pulses. Each pulse was a TL pulse (single pulse with a time width of 135 fs), and the pulse interval was equal to 1 ps. As the initial phase spectrum Ψ ₀ (ω), the one calculated using the iterative Fourier method was used. FIG. 14 is a graph plotting the relationship between the number of pulses at that time and the evaluation value (minimum value of the standard deviation shown in Equation (14)). In FIG. 14, a plot P11 shows a case where the intensity spectrum function A (ω) is calculated by a conventional method using only the iterative Fourier method, and a plot P12 shows the intensity spectrum function A (ω) by the method of this embodiment. The calculated case is shown. In the calculation of the intensity spectrum function A (ω) by the method of the present embodiment, steps S12 to S14 were sufficiently repeated until the evaluation value converged. The number of repetitions (number of generations) was 1700 generations. As shown in FIG. 14, the waveform control accuracy (evaluation value) is greatly improved according to the method of this embodiment at any number of pulses as compared with the conventional method. Although there is a difference depending on the number of pulses, it was confirmed that an improvement of about 3 to 24 times can be expected.

  FIG. 15 is a graph plotting the relationship between the number of pulses and the average pulse width (full width at half maximum) in the above embodiment. FIG. 16 is a graph plotting the relationship between the number of pulses and the dispersion of peak values in the above embodiment. 15 and 16, plots P21 and P31 show the case where the intensity spectrum function A (ω) is calculated by a conventional method using only the iterative Fourier method, and the plots P22 and P32 show the intensity by the method of this embodiment. The case where the spectrum function A (ω) is calculated is shown. From these figures, the improvement of the evaluation value shown in FIG. 14 is due to the fact that the pulse width is narrowed (close to the half-value width of the TL pulse) and the variation in peak value is small. It is thought.

As in the present embodiment, the initial value setting unit 25 (initial value setting step S11) includes an initial individual generation unit 25a (initial individual generation step) that generates first generation individuals A ₁ (ω) to A _M (ω). S11a) may be included. The initial population generation unit 25a (initial population generation step S11a) is repeated by the Fourier transform to generate an intensity spectrum function A _IFTA (omega), by varying the said intensity spectral function A _IFTA (omega) of the first generation Individuals A ₁ (ω) to A _M (ω) may be generated. According to the knowledge of the present inventor, in order to search the optimum solution more accurately in the modulation pattern calculation apparatus 20 of the present embodiment, the setting of the first generation individuals A ₁ (ω) to A _M (ω) is required. Very important. The iterative Fourier method is characterized in that a solution with an excellent evaluation value can be calculated in a short time. In addition, there may be a solution with a higher evaluation value in the vicinity of the solution. Therefore, by generating the intensity spectrum function A _IFTA (ω) that is the basis of the first generation individuals A ₁ (ω) to A _M (ω) using the iterative Fourier method, the first generation individual A ₁ ( ω) to A _M (ω) can be set appropriately.

Further, as in the present embodiment, the evaluation value calculation unit 26 (evaluation value calculation step S12) includes the time intensity waveform functions I ₁ (t) to I _M (t) and a function T representing a desired time phase waveform. calculating the M evaluation values indicating the degree of difference between multiplied by the respective coefficients alpha ₁ to? _M in (t), the coefficient alpha ₁ to? _M has a front multiplication of engagement several alpha ₁ to? _M In comparison, the evaluation value after multiplication may have a good value. This suppresses the difference in total energy between the desired time intensity waveform T (t) and the time intensity waveform functions I ₁ (t) to I _M (t) from affecting the calculation of the evaluation value, and the desired time. The evaluation value can be calculated mainly based on the difference in shape between the intensity waveform T (t) and the time intensity waveform functions I ₁ (t) to I _M (t).

Further, as in the present embodiment, the two or more individuals selected by the individual selection unit 27 (individual selection step S13) are an individual group G1 composed of at least one individual and an individual group composed of at least one other individual. G2 may be included. The average of the evaluation values of the individual group G1 is superior to the average of the evaluation values of the nth generation individuals A ₁ (ω) to A _M (ω), and the average of the evaluation values of the individual group G2 is It may be inferior to the average of the evaluation values of the n generation individuals A ₁ (ω) to A _M (ω).

In the genetic algorithm as in the present embodiment, as the number of generations progresses, a plurality of individuals A ₁ (ω) to A _M (ω) gradually approach evenly. Therefore, the evaluation value converges and no further improvement is observed, or the degree of improvement is significantly reduced. Therefore, in the present embodiment, the individual group G2 composed of non-elite individuals is included in the two or more individuals selected by the individual selection unit 27 (individual selection step S13). FIG. 17 shows how the evaluation value changes as the generation progresses when calculating the intensity spectrum function A (ω) (see FIG. 12A) for generating the 8-pulse output light Ld. It is a graph. The horizontal axis in FIG. 17 represents the generation, and the vertical axis represents the evaluation value (standard deviation minimum value σ _min ). In the example shown in FIG. 17, the evaluation value once converges around about 150 generations, but the evaluation value is obtained by introducing a non-elite individual (shown by arrow A3 in the figure) around about 250 generations. Is discontinuously decreasing (improving). Each time a non-elite individual is introduced thereafter, the evaluation value further decreases (improves). Thus, by introducing non-elite individuals into two or more individuals selected by the individual selection unit 27 (individual selection step S13), it is possible to get out of the once converged value and further improve the evaluation value. Become.

The inventor further investigated what non-elite individuals were effective. FIG. 18 illustrates the amount of change in evaluation values before and after the introduction of non-elite individuals. In this embodiment, non-elite individuals constituting the individual group G2 are divided into four groups (0.0025 <σ _min <0.003, 0.0035 <σ _min <0.004, 0.0045 < The calculation was performed separately for each of σ _min <0.005 and 0.0055 <σ _min <0.006). The introduction of non-elite individuals was performed for calculations that reached a convergence value with an evaluation value of approximately 0.0015 to 0.0025. In FIG. 18, a graph G51 shows an average of evaluation value change amounts when a calculation for each range is tried a plurality of times, and a graph G52 shows an existence range of evaluation value change amounts in each range at that time. Referring to FIG. 18, regardless of the evaluation value of the non-elite individual, the evaluation value changed significantly from the convergence value to a better direction. In addition, it was found that, under this calculation condition, the evaluation value of the non-elite individual is better (standard deviation is smaller), and the evaluation value changes greatly from the convergence value to the better direction, and a remarkable effect is obtained. .

  Thus, according to the trial of the present inventor, it is possible to further increase the accuracy of calculating the final spectrum intensity by including a non-elite individual having a relatively inferior evaluation value as part of the selected individual.

  Further, according to the light control apparatus 1A of the present embodiment, by providing the modulation pattern calculation apparatus 20, the spectral intensity is accurately calculated by reducing the ratio led to the local solution, and the time waveform of the output light Ld is desired. The waveform T (t) can be approximated.

  In the above description, the configuration of the intensity spectrum design unit 23 and the calculation method of the spectrum intensity are mainly described. However, the configuration of the phase spectrum design unit 22 and the calculation method of the spectrum phase are the same as the conventional configuration and method (for example, iterative Fourier transform). May be used, or the configuration and method similar to the configuration of the intensity spectrum design unit 23 and the spectrum intensity calculation method of the present embodiment may be used.

(Second Embodiment)
FIG. 19 is a diagram schematically showing a configuration of a light control device 1B according to the second embodiment of the present invention. The light control apparatus 1B according to the present embodiment generates, as output light Ld, an optical pulse train that includes a plurality of optical pulses arranged at time intervals from the input light La. The optical pulse train includes a plurality of optical pulses LP _{1 to} LP _N (N is an integer of 2 or more). Each of the light pulses LP _{1 to} LP _N has a very short time width, for example, 100 fs or less. The appearance timing of each of the optical pulses LP _{1 to} LP _N is arbitrary, and the time interval between the adjacent immediately preceding optical pulses may be equal to or different from each other in each of the optical pulses LP _{2 to} LP _N. Further, the peak intensities of the light pulses LP _{2 to} LP _N may be equal to each other or different from each other.

  The light control device 1B includes a light source 2, an optical system 10, and a modulation pattern calculation device (data creation device) 30. The configurations of the light source 2 and the optical system 10 are the same as those in the first embodiment (see FIG. 2). The hardware configuration of the modulation pattern calculation device 30 is the same as that of the modulation pattern calculation device 20 (see FIG. 4) of the first embodiment. The modulation pattern calculation device 30 is electrically connected to the SLM 14 and calculates a phase modulation pattern for bringing the time intensity waveform of the output light Ld closer to an optical pulse train having a desired peak intensity and time interval. A control signal SC2 including a pattern is provided to the SLM 14. The modulation pattern calculation apparatus 30 according to the present embodiment outputs a phase pattern for phase modulation that gives a phase spectrum for obtaining a desired optical pulse train to the output light Ld and an intensity spectrum for obtaining a desired optical pulse train for the output light Ld. A phase pattern including a phase pattern for intensity modulation to be applied is presented to the SLM 14. For this purpose, the modulation pattern calculation apparatus 30 includes an arbitrary waveform input unit 31, a spectrum design unit 32, and a modulation pattern generation unit (data generation unit) 33. That is, the processor 201 (see FIG. 4) of the computer provided in the modulation pattern calculation device 30 realizes the function of the arbitrary waveform input unit 31, the function of the spectrum design unit 32, and the function of the modulation pattern generation unit 33. To do.

  The arbitrary waveform input unit 31 receives an input of information related to a desired optical pulse train from the operator. The operator inputs information on the desired optical pulse train (number of optical pulses, peak intensity of each optical pulse, time interval, etc.) to the arbitrary waveform input unit 31. Information about the desired optical pulse train is given to the spectrum design unit 32. The spectrum design unit 32 calculates a phase spectrum and an intensity spectrum of the output light Ld suitable for realizing a given desired optical pulse train. The modulation pattern generation unit 33 calculates a phase modulation pattern (for example, a computer-generated hologram) for giving the phase spectrum and the intensity spectrum obtained by the spectrum design unit 32 to the output light Ld. Then, a control signal SC2 including the calculated phase modulation pattern is provided to the SLM 14, and the SLM 14 is controlled based on the control signal SC2.

  FIG. 20 is a block diagram showing the internal configuration of the spectrum design unit 32. As shown in FIG. 20, the spectrum design unit 32 includes an initial value setting unit 35, an evaluation value calculation unit 36, an individual selection unit 37, and a next generation generation unit 38. The initial value setting unit 35 includes an initial individual generation unit 39. FIG. 21 is a flowchart showing a design method (data creation method) of the intensity spectrum and the phase spectrum by the modulation pattern calculation device 30. Hereinafter, the operation of the modulation pattern calculation apparatus 30 according to the present embodiment, that is, the design method (data creation method) of the intensity spectrum and the phase spectrum will be described with reference to FIGS.

  First, the spectrum design unit 32 generates the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) suitable for the optical pulse train based on the information about the desired optical pulse train input from the arbitrary waveform input unit 31. (Spectral function generation step S3). Specifically, the spectrum function generation step S3 includes an initial value setting step S31, an evaluation value calculation step S32, an individual selection step S33, and a next generation generation step S34.

In the initial value setting step S31, the initial value setting unit 35 performs the first generation M individuals (genetic information) A ₁ (ω) to A ₁ regarding the intensity spectrum function A (ω) (where M is an integer of 2 or more). _M (omega), and sets the phase spectrum function [psi (omega) the first generation of the M individual related (genetic _{information) Ψ 1 (ω) ~Ψ M} (ω). Each individual A _m (ω) and each individual ψ _m (ω) (where m = 1, 2,..., M) constitute an m-th individual pair. That is, the individuals A ₁ (ω) to A _M (ω) and the individuals ψ ₁ (ω) to ψ _M (ω) constitute M individual pairs. The individuals A ₁ (ω) to A _M (ω) and the individuals ψ ₁ (ω) to ψ _M (ω) are functions of the frequency ω. By this initial value setting step S31, each of the first generation individuals A ₁ (ω) to A _M (ω) of the intensity spectrum function A (ω) and the first generation individual of the phase spectrum function Ψ ₀ (ω). M waveform functions (15) in the frequency domain including each of Ψ ₁ (ω) to Ψ _M (ω) are defined. However, i is an imaginary number.

The initial value setting step S31 of the present embodiment includes an initial individual generation step S36. In the initial individual generation step S36, the initial individual generation unit 39 generates M delta function groups having the same amplitude and timing as the amplitude and timing of each optical pulse included in the desired optical pulse train and having different time phases. By performing Fourier transformation, M individual pairs (A _m (ω), Ψ _m (ω)) (where m = 1, 2,..., M) of the first generation are generated.

FIG. 22 illustrates the first generation M individual pairs (A _m (ω), Ψ _m (ω)) (m = 1, 2,...) From the M delta function groups in the initial individual generation unit 25a. , M) conceptually shows an example of a method for calculating. Part (a) of FIG. 22 shows a time waveform of a desired optical pulse train. Parts (b) to (d) in FIG. 22 indicate the first, second, and Mth delta function groups, respectively. Note that FIG. 22 is the top of each unit number of the plurality of optical pulses (1, 2, · · ·, N) are the indicated, t _{1, t} 2 in FIG, · · ·, _{t N} each light A ₁ , A ₂ ,..., _AN are the peak intensities of the optical pulses. FIG. 23 is a flowchart showing details of the initial individual generation step S36. As shown in FIG. 23, the initial individual generation step S36 includes steps S36a to S36c.

In order to realize the time waveform of a desired optical pulse train shown in FIG. 22A, the initial individual generation unit 25a first receives input of parameters of the desired optical pulse train (step S36a). The parameters of the optical pulse train include, for example, the number N of optical pulses included in the optical pulse train, the peak intensity (A ₁ , A ₂ ,..., A _N ) of each optical pulse, and the appearance timing (t ₁ ) of each optical pulse. , T ₂ ,..., T _N ).

Next, in the initial individual generation step S36, M delta function groups as shown in FIGS. 22B to 22D are prepared using the above-described parameters relating to the optical pulse train (step S36b). The N optical pulses of each delta function group have the same amplitude and timing as the amplitude and timing of the N optical pulses included in the desired optical pulse train. Further, the time phases of the N optical pulses of each delta function group are arbitrary and different from each other. The time phase is a value corresponding to Θ _k (t) in Equation (3) described above. Specifically, as shown in FIGS. 22B to 22D, the magnitudes of the phases Φ _{1 to} Φ _N of the delta functions included in the delta function group are set.

Subsequently, the initial individual generation unit 25a performs a Fourier transform on each of these delta function groups (step S36c). As a result, M waveform functions in the frequency domain shown in Expression (15) are obtained, and as a result, the first generation individuals A ₁ (ω) to A _M (ω), Ψ ₁ (ω) to Ψ _M (Ω) is calculated.

Refer to FIGS. 20 and 21 again. Next, in the evaluation value calculation step S32, the evaluation value calculation unit 36 equalizes the maximum values of the individual A ₁ (ω) to A _M (ω) of the nth generation (n is an integer of 1 or more). Standardize as follows. In one example, the evaluation value calculation unit 36 normalizes each of the nth generation individuals A ₁ (ω) to A _M (ω) so that the maximum value is 1. Then, evaluation value calculation unit 36 calculates the evaluation value based on the individual _{A 1 (ω) ~A M (} ω) respectively integral. For example, the evaluation value calculation unit 36 may calculate M evaluation values indicating the amount of loss caused by intensity spectrum modulation based on the individuals A ₁ (ω) to A _M (ω). In this case, the evaluation value calculation unit 26 calculates the integrated values (area of the graph) Area _{1 to} Area _M of the normalized individuals A ₁ (ω) to A _M (ω) at the above-described equal value h. A value obtained by subtracting from the area Area of the intensity spectrum function A (ω) = h (for example, h = 1) and dividing the value by Area (that is, a value represented by the following equation (16)) is an evaluation value Loss ₁ It may be calculated as ~ Loss _M.

Subsequently, based on the _M evaluation values (for example, Loss _{1 to} Loss _M ) calculated in the evaluation value calculation step S32, the individual selection unit 37 sets the n-th generation M individual pairs (A _m (ω), Generation of (n + 1) th generation M individual pairs (A _m (ω), Ψ _m (ω)) from Ψ _m (ω)) (where m = 1, 2,..., M) Two or more individual pairs (A _m (ω), Ψ _m (ω)) used in the above are selected (individual selection step S33). In this individual selection step S33, two or more individual pairs are selected based on the superiority of the M evaluation values. Here, "based on the fineness", e.g., M-number of individual pairs of generation n _{(A m (ω), Ψ} m (ω)) of at least one individual pairs were selected from (A _m ( _{ω), Ψ m (ω)} ) consisting of individual pair group G3 (first individual pair group), M number of individual pairs _{(a m (ω), Ψ} m (ω)) the individual pair group of G3 This means that the evaluation value is superior to all other individual pairs not included in. Alternatively, the average of the evaluation values in the individual pair group G3 including one or more individual pairs selected from the M individual pairs (A _m (ω), Ψ _m (ω)) of the nth generation is M It may mean that it is superior to the average of the evaluation values of the individual pairs (A _m (ω), Ψ _m (ω)). Hereinafter, this individual pair group G3 may be referred to as an “elite individual pair group”.

In this embodiment, two or more individual pairs (A _m (ω), Ψ _m (ω)) selected by the individual selection unit 37 in the individual selection step S33 are at least 1 in addition to the elite individual pair group G3. An individual pair group G4 (second individual pair group) including two different individual pairs may be included. In this case, the average of the evaluation values of the individual pair group G4 is the average of the evaluation values of the M individual pairs (A _m (ω), Ψ _m (ω)) of the nth generation (for example, the average of Loss _{1 to} Loss _M ). ). Hereinafter, this individual pair group G4 may be referred to as a “non-elite individual pair group”. When the evaluation values of M individual pairs (A _m (ω), Ψ _m (ω)) are arranged in order of preference, the evaluation values of the non-elite individual pair group G4 are consecutive from the evaluation values of the elite individual pair group G3. Not. That is, some of the M individual pairs (A _m (ω), Ψ _m (ω)) are inferior to the evaluation value that is the worst in the elite individual pair group G3, and the non-elite individual pair group G4 There are one or more individual pairs having an evaluation value better than the best evaluation value among them.

Subsequently, in the next generation generation step S34, the next generation generation unit 38 is based on two or more individual pairs (A _m (ω), Ψ _m (ω)) selected by the individual selection unit 37 in the individual selection step S33. , (N + 1) generation M individual pairs (A _m (ω), Ψ _m (ω)) (m = 1, 2,..., M) are generated. Here, “generating a plurality of (n + 1) generation individual pairs based on two or more selected individual pairs” means, for example, processing such as crossover, mutation, and multiplication, and the (n + 1) generation the M individual pairs _{(a m (ω), Ψ} m (ω)) respectively, one of the individual pairs of generation n _{(a m (ω), Ψ} m (ω)) of at least some of the components of Is included. It should be noted that a part of the selected two or more individual pairs (A _m (ω), Ψ _m (ω)) (for example, the most excellent individual pair group) is directly used as the (n + 1) th generation individual pair (A _m (ω ), Ψ _m (ω)) (m = 1, 2,..., M).

In the spectrum function generation step S3, the above-described evaluation value calculation step S32, individual selection step S33, and next generation generation step S34 are repeated while adding n one by one until a predetermined condition is satisfied (step S35). In other words, the evaluation value calculation unit 36, the individual selection unit 37, and the next generation generation unit 38 repeat the process while adding n one by one until a predetermined condition is satisfied. Then, the spectrum design unit 32 (in the spectrum function generation step S3) performs the n-th generation M individual pairs (A _m (ω), Ψ _m (ω)) (m = 1, 2,..., M), the intensity spectrum function A (ω) suitable for the desired optical pulse train form (number of optical pulses, peak intensity of each optical pulse, appearance timing of each optical pulse, etc.) And a phase spectral function Ψ (ω). For example, M-number of individual pairs _{(A m (ω), Ψ} m (ω)) (m = 1,2, ···, M) 1 single individual pairs of the _{(A m (ω), Ψ} m (ω )) (M is an arbitrary integer) may be extracted and used as the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω). The predetermined condition is, for example, a case where the arbitrarily set number of repeated trials is completed or a case where an arbitrarily defined evaluation value is satisfied.

  After the above processing, in the data generation step S2, the modulation pattern generation unit 33 presents to the SLM 14 based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum function generation step S3. Data relating to the modulation pattern to be generated is generated. The modulation pattern generation unit 33 provides the generated data to the SLM 14 as the control signal SC2.

The effects obtained by the light control device 1B, the modulation pattern calculation device 30, the modulation pattern calculation method, and the modulation pattern calculation program of the present embodiment described above will be described. In the present embodiment, the next-generation M individual pairs (A _m (ω), Ψ _m (ω)) (m = 1, based on the superiority of the evaluation value indicating the amount of loss caused by intensity spectrum modulation. 2,..., M), two or more individual pairs (A _m (ω), Ψ _m (ω)) are selected. Based on the two or more selected individual pairs (A _m (ω), Ψ _m (ω)), a plurality of (n + 1) th generation individual pairs (A _m (ω), Ψ _m (ω)) Is generated. Such processing is repeated while adding n one by one until a predetermined condition is satisfied, and the n-th generation M individual pairs (A _m (ω), Ψ _m ( From ω)), an intensity spectrum function A (ω) and a phase spectrum function Ψ (ω) suitable for a desired optical pulse train are generated. Similar to the first embodiment, the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) are compared with a method in which the iterative Fourier method and the iterative Fourier method are modified by such a method (genetic algorithm). Is reduced to a local solution, and the optimal solution can be searched more accurately. That is, according to the present embodiment, the spectral intensity A (ω) and the spectral phase Ψ (ω) for approximating the time waveform of the optical pulse train to a desired waveform are calculated while reducing the ratio of being led to the local solution. can do. Furthermore, according to the present embodiment, it is possible to accurately calculate the spectral intensity A (ω) and the spectral phase Ψ (ω) for minimizing the amount of loss that occurs when generating the optical pulse train.

  FIG. 24A shows, as an example, an intensity spectrum function A (ω for generating an optical pulse train composed of 50 optical pulses calculated by the modulation pattern calculation device 30 and the modulation pattern calculation method of the present embodiment. ) And the phase spectrum function Ψ (ω). The graph G81 shows the intensity spectrum function A (ω). The graph G82 shows the phase spectrum function Ψ (ω). 24B shows the time intensity of the output light Ld obtained by causing the SLM 14 to present the modulation pattern based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) shown in FIG. It is a graph which shows a waveform. Referring to (b) of FIG. 24, the output light generated when the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) are calculated by the modulation pattern calculation device 30 and the modulation pattern calculation method of the present embodiment. It can be seen that in the time intensity waveform of Ld, variation in peak intensity of 50 optical pulses is suppressed to a small level.

Conventionally, when an optical pulse train having a desired form (number of optical pulses, peak intensity of each optical pulse, appearance timing of each optical pulse, etc.) is realized using an SLM, an intensity spectrum function A ( In order to calculate ω) and the phase spectrum function Ψ (ω), a method of exhaustively searching for an optimal combination of the time intensity waveform function and the time phase function of the optical pulse train is used. However, when an attempt is made to generate an optical pulse train using such a method, the amount of calculation increases exponentially with the increase in the number of optical pulses, and the optical pulse is limited due to the computer's computational power and calculation time constraints. It has been confirmed that the number of is substantially limited. On the other hand, according to the method of the present embodiment, the number of individual pairs (A _m (ω), Ψ _m (ω)) of each generation is limited to M, and the number of optical pulses increases. The increase in the amount of calculation associated with is small. Therefore, according to the present embodiment, the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) for realizing an optical pulse train having a desired form can be designed regardless of the number of optical pulses. .

  FIG. 25 shows the number of operations of Fast Fourier Transform (FFT) required in the conventional method for exhaustively searching for the optimal combination of the time intensity waveform function and the time phase function of the optical pulse train, and is required in this embodiment. It is a graph which compares the frequency | count of a calculation of FFT. The vertical axis represents the number of FFT operations, and the horizontal axis represents the number of optical pulses. Moreover, the circular plot P41 shows the system of this embodiment, and the rhombus plot P42 shows the conventional system. As shown in FIG. 25, in the conventional method, the number of FFTs exponentially increases as the number of optical pulses increases. On the other hand, in the method of this embodiment, the number of FFTs hardly depends on the number of pulses. This indicates that the method of this embodiment enables calculation of a modulation pattern for a desired optical pulse train without limiting the number of optical pulses.

  FIG. 26 is a graph comparing the loss amount due to the intensity spectrum modulation pattern calculated by the conventional method with the loss amount due to the intensity spectrum modulation pattern calculated by the method according to the present embodiment. The vertical axis represents the loss amount (arbitrary unit), and the horizontal axis represents the number of optical pulses. Moreover, the circular plot P51 shows the system of this embodiment, and the rhombus plot P52 shows the conventional system. In the conventional method, when the number of pulses exceeds 10, the amount of calculation becomes enormous and the calculation cannot be performed. Referring to FIG. 26, it can be seen that in the method of this embodiment, the loss amount is small at any number of pulses as compared with the conventional method. That is, according to the present embodiment, it is possible to create a modulation pattern with a small loss while suppressing a calculation amount to a small amount.

Further, as in the present embodiment, two or more individual pairs (A _m (ω), Ψ _m (ω)) selected by the individual selection unit 37 (individual selection step S33) are at least one individual pair (A _m (omega), and Ψ _{m (ω))} individual pair group G3 consisting of at least one other individual pairs _{(a m (ω), Ψ} m (ω)) individual pair group G4 and may contain consisting . The average of the evaluation values of the individual pair group G3 is superior to the average of the evaluation values of the M individual pairs (A _m (ω), Ψ _m (ω)) of the nth generation, and the individual pair group G4 May be inferior to the average of the evaluation values of the M individual pairs (A _m (ω), Ψ _m (ω)) of the nth generation.

Similar to the first embodiment, also in this embodiment, two or more individual pairs (A _m (ω), Ψ _m (ω)) selected by the individual selection unit 37 (individual selection step S33) are non-elite. An individual pair group G4 including individual pairs is included. FIG. 27 shows the evaluation as the generation progresses when calculating the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) (see FIG. 23A) for generating an optical pulse train of 50 pulses. It is a graph which shows a mode that a value changes. The horizontal axis in FIG. 27 represents the generation, and the vertical axis represents the evaluation value (loss amount due to intensity spectrum modulation). In the example shown in FIG. 27, the evaluation value has converged once around about 40 generations, but the evaluation was made by introducing a non-elite individual pair (indicated by arrow A4 in the figure) around about 100 generations. The value drops discontinuously (improves). Then, each time the non-elite individual pair is introduced thereafter, the evaluation value further decreases (improves). As described above, by introducing the non-elite individual pair into the two or more individual pairs (A _m (ω), Ψ _m (ω)) selected in the individual selection unit 37 (individual selection step S33), convergence is once achieved. It becomes possible to get out of the value and further improve the evaluation value.

  Further, according to the light control device 1B of the present embodiment, the modulation pattern calculation device 30 is provided, thereby calculating the spectrum intensity A (ω) and the spectrum phase ψ (ω) while reducing the ratio led to the local solution. The time waveform of the output light Ld can be made closer to the time waveform of the desired optical pulse train. Furthermore, according to the light control apparatus 1B of the present embodiment, it is possible to accurately calculate the spectrum intensity A (ω) and the spectrum phase Ψ (ω) for minimizing the amount of loss that occurs when generating the optical pulse train.

  In this embodiment, the number of individual pairs in each generation is unified to M, but the number of individual pairs in each generation may be changed.

(Third embodiment)
The modulation pattern calculation device 20, the modulation pattern calculation method, and the modulation pattern calculation program of the above embodiment are not limited to the design of an intensity spectrum modulation pattern (one-dimensional pattern) typified by time pulse shaping, but for example for beam intensity distribution shaping. It can also be used to design a representative two-dimensional intensity modulation pattern. In other words, it can also be used to design the intensity distribution of a pattern in a region such as a hologram that has a relationship of optical Fourier transform with a desired intensity pattern.

FIG. 28 is a diagram schematically showing a configuration of a light control apparatus 1C when effectively using a two-dimensional intensity modulation pattern according to the third embodiment of the present invention. In FIG. 28, illustration of the modulation pattern calculation device 20 (or 30) included in the light control device 1C is omitted. The light source may be a pulse light source like the light source 2 of each of the above embodiments, or may be a CW (Continuous Wave) laser light source. The light control apparatus 1 </ b> C displays a desired light intensity distribution on the screen 45 as an application of the above embodiments. The light control apparatus 1 </ b> C includes two SLMs 41 and 46, a pair of lenses 42 and 43, and a Fourier transform lens 44. The two SLMs 41 and 46 are optically coupled via a pair of lenses 42 and 43. The optical distance between the SLM 46 and the lens 42 is the focal distance f ₁ of the lens 42, and the optical distance between the SLM 41 and the lens 43 is the focal distance f ₂ of the lens 43. In one example, the focal length f ₁ and the focal length f ₂ are equal to each other. The optical distance between the lens 42 and the lens 43 is the sum of the focal length f ₁ and the focal length f ₂ . Fourier transform lens 44, SLM41 and are optically coupled, during which the optical distance is the focal length f ₃ of the Fourier transform lens 44. The light control device 1C is the Fourier transform lens 44 SLM41 for forming an output optical image on the screen 45 at a distance a focal length f ₃ on the opposite side. The SLM 46 is a two-dimensional intensity modulation SLM, and presents a modulation pattern for intensity modulation provided from the modulation pattern calculation device 20 (or 30). The SLM 41 is an SLM for two-dimensional phase modulation, and presents a modulation pattern for phase modulation provided from the modulation pattern calculation device 20 (or 30). The SLM 46 that displays a hologram pattern for intensity modulation and the SLM 41 that displays a hologram pattern for phase modulation may be interchanged.

  The data creation device, the light control device, the data creation method, and the data creation program according to the present invention are not limited to the above-described embodiments, and various other modifications are possible. For example, in the first embodiment described above, the initial value setting unit includes an initial individual generation unit, and the initial individual generation unit generates a plurality of first generation individuals using the iterative Fourier method. The determination method of a plurality of individuals is not limited to this, and any plurality of individuals may be input, for example. In the first embodiment described above, the evaluation value calculation unit indicates an evaluation value indicating the degree of difference between the time intensity waveform function of the second waveform function and the function obtained by multiplying the function representing the desired time phase waveform by a coefficient. (Equation (14)), but the calculation formula for the evaluation value is not limited to this, as long as it represents the degree of difference between the time intensity waveform function of the second waveform function and the desired time intensity waveform. Any calculation formula can be used.

DESCRIPTION OF SYMBOLS 1A, 1B, 1C ... Light control apparatus, 2 ... Light source, 10 ... Optical system, 12 ... Diffraction grating, 13, 15 ... Lens, 16 ... Diffraction grating, 17 ... Modulation surface, 17a ... Modulation area, 20, 30 ... Modulation Pattern calculation device, 21, 31 ... Arbitrary waveform input unit, 22 ... Phase spectrum design unit, 23 ... Intensity spectrum design unit, 24, 33 ... Modulation pattern generation unit, 25, 35 ... Initial value setting unit, 25a, 39 ... Initial Individual generation unit, 26, 36 ... evaluation value calculation unit, 27, 37 ... individual selection unit, 28, 38 ... next generation generation unit, 32 ... spectrum design unit, f ₁ , f ₂ , f ₃ ... focal length, La ... Input light, Lc ... modulated light, Ld ... output light, SC, SC2 ... control signal.

Claims (14)

An apparatus for creating data for controlling a spatial light modulator,
An intensity spectrum design unit that generates an intensity spectrum function A (ω) suitable for a desired time intensity waveform;
A data generation unit that creates the data based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum design unit;
The intensity spectrum design unit
A plurality of first generation individuals of the intensity spectrum function A (ω), and an initial value setting unit for setting the phase spectrum function Ψ (ω);
A plurality of first waveform functions in the frequency domain including each of a plurality of individuals of the nth generation (n is an integer equal to or greater than 1) and the phase spectrum function Ψ (ω), a time intensity waveform function and a time phase waveform function An evaluation value calculation unit that converts each of the plurality of second waveform functions in the time domain including the time waveform function and calculates an evaluation value indicating the degree of difference between the time intensity waveform function and the desired time intensity waveform for each second waveform function When,
An individual selection unit that selects two or more individuals used to generate a plurality of (n + 1) th generation individuals from a plurality of nth generation individuals based on the superiority of the evaluation value;
A next generation generation unit that generates a plurality of (n + 1) generation individuals based on the two or more individuals selected by the individual selection unit,
The evaluation value calculation unit, the individual selection unit, and the next generation generation unit repeat the process while adding n one by one until a predetermined condition is satisfied, and the intensity spectrum design unit satisfies the predetermined condition. A data creation device that generates an intensity spectrum function A (ω) suitable for the desired time intensity waveform from a plurality of nth generation individuals in the case of being performed. The initial value setting unit includes an initial individual generation unit that generates a plurality of individuals of the first generation,
The initial individual generation unit
A Fourier transform for a third waveform function in the frequency domain including the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω), and a time intensity waveform based on the desired time intensity waveform in the time domain after the Fourier transform. A first replacement of the function, an inverse Fourier transform performed after the first replacement, and a second replacement for constraining the phase spectrum function Ψ (ω) in the frequency domain after the inverse Fourier transform; generating an intensity spectrum function a _IFTA (omega) by performing iteratively, and generates a plurality of individuals of the first generation by varying the said intensity spectral function a _IFTA (ω), according to claim 1 Data creation device. The evaluation value calculation unit calculates the evaluation value indicating the degree of difference between the time intensity waveform function and a function representing the desired time phase waveform multiplied by a coefficient for each second waveform function,
The data creation device according to claim 1, wherein the coefficient has a value that makes the evaluation value after multiplication better than before multiplication of the coefficient. The two or more individuals selected by the individual selection unit include a first individual group consisting of at least one individual and a second individual group consisting of at least one other individual,
The average of the evaluation values of the first population is superior to the average of the evaluation values of a plurality of individuals of the nth generation,
The data creation device according to any one of claims 1 to 3, wherein an average of the evaluation values of the second individual group is inferior to an average of the evaluation values of a plurality of nth generation individuals. A light source that outputs input light;
A spectroscopic element for dispersing the input light;
A spatial light modulator that modulates the intensity spectrum of the input light after spectroscopy and outputs modulated light;
An optical system for collecting the modulated light;
With
The said spatial light modulator is a light control apparatus which modulates the intensity spectrum of the said input light based on the said data produced by the data production apparatus as described in any one of Claims 1-4. An apparatus for creating data for controlling a spatial light modulator,
A spectrum design unit for generating an intensity spectrum function A (ω) and a phase spectrum function Ψ (ω) for an optical pulse train including a plurality of optical pulses arranged at time intervals;
A data generation unit that creates the data based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum design unit,
The spectrum design unit includes:
An initial value setting unit for setting a plurality of first-generation individual pairs for the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω);
Evaluation value for calculating for each individual pair an evaluation value indicating an amount of loss caused by intensity spectrum modulation based on a plurality of individuals of the nth generation (n = 1, 2,...) Of the intensity spectrum function A (ω). A calculation unit;
An individual selection unit that selects two or more individual pairs used to generate a plurality of (n + 1) generation individual pairs from among the plurality of n generation individual pairs based on the superiority of the evaluation value;
A next generation generation unit that generates a plurality of (n + 1) generation individual pairs based on the two or more individual pairs selected in the individual selection unit,
The evaluation value calculation unit, the individual selection unit, and the next generation generation unit repeat the process while adding n one by one until a predetermined condition is satisfied, and the spectrum design unit satisfies the predetermined condition. A data generation device that generates the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) for generating the optical pulse train from a plurality of n-th generation individual pairs in the case of The initial value setting unit includes an initial individual generation unit that generates a plurality of individuals of the first generation,
The initial individual generation unit
A plurality of first generation individuals are generated by Fourier transforming a plurality of delta function groups having the same amplitude and timing as each of the optical pulses included in the optical pulse train and having different time phases. The data creation device according to claim 6.   The evaluation value calculation unit normalizes the plurality of nth generation individuals related to the intensity spectrum function A (ω) so that the maximum values are equal, and based on the integrated value of each of the plurality of individuals after normalization The data creation device according to claim 6 or 7, wherein the evaluation value is calculated by using a computer. The two or more individual pairs selected in the individual selection unit include a first individual pair group consisting of at least one individual pair and a second individual pair group consisting of at least one other individual pair,
The average of the evaluation values of the first individual pair group is superior to the average of the evaluation values of a plurality of individual pairs of the nth generation,
The data creation according to any one of claims 6 to 8, wherein an average of the evaluation values of the second individual pair group is inferior to an average of the evaluation values of a plurality of n-th generation individual pairs. apparatus. A light source that outputs input light;
A spectroscopic element for dispersing the input light;
A spatial light modulator that modulates the input light after spectroscopy and outputs the modulated light;
An optical system for collecting the modulated light;
With
The said spatial light modulator is a light control apparatus which modulates the said input light based on the said data produced by the data production apparatus as described in any one of Claims 6-9. A method for creating data for controlling a spatial light modulator, comprising:
An intensity spectrum function generating step for generating an intensity spectrum function A (ω) suitable for a desired time intensity waveform;
A data generation step of creating the data based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum function generation step;
The intensity spectrum function generation step includes:
An initial value setting step of setting a plurality of individuals of the first generation of the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω);
A plurality of first waveform functions in the frequency domain including each of a plurality of individuals of the nth generation (n is an integer equal to or greater than 1) and the phase spectrum function Ψ (ω), a time intensity waveform function and a time phase waveform function An evaluation value calculating step of converting each of the plurality of second waveform functions in the time domain including the time domain and calculating an evaluation value indicating a degree of difference between the time intensity waveform function and the desired time intensity waveform for each second waveform function When,
An individual selection step of selecting two or more individuals used to generate a plurality of (n + 1) generation individuals from a plurality of n generation individuals based on the evaluation value;
A next generation generation step of generating a plurality of (n + 1) generation individuals based on the two or more individuals selected in the individual selection step,
The evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the intensity spectrum function generation step. A data creation method for generating an intensity spectrum function A (ω) suitable for the desired time intensity waveform from a plurality of nth generation individuals. A method for creating data for controlling a spatial light modulator, comprising:
A spectral function generation step for generating an intensity spectral function A (ω) and a phase spectral function Ψ (ω) suitable for an optical pulse train including a plurality of optical pulses arranged at intervals of time;
A data generation step of creating the data based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum function generation step;
The spectral function generation step includes:
An initial value setting step of setting a plurality of first generation individual pairs related to the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω);
Evaluation value for calculating for each individual pair an evaluation value indicating an amount of loss caused by intensity spectrum modulation based on a plurality of individuals of the nth generation (n = 1, 2,...) Of the intensity spectrum function A (ω). A calculation step;
An individual selection step of selecting two or more individual pairs used for generating a plurality of (n + 1) generation individual pairs from the plurality of n generation individual pairs based on the superiority of the evaluation value;
A next generation generation step of generating a plurality of (n + 1) generation individual pairs based on the two or more individual pairs selected in the individual selection step,
The evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and in the spectrum function generation step, the evaluation value is the predetermined condition. A data creation method for generating the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) suitable for the optical pulse train from a plurality of nth generation individual pairs when A program for creating data for controlling a spatial light modulator,
An intensity spectrum function generating step for generating an intensity spectrum function A (ω) suitable for a desired time intensity waveform;
Based on the phase spectrum function Ψ (ω) and the intensity spectrum function A (ω) generated in the intensity spectrum function generation step, the data generation step of creating the data is executed by a computer,
The intensity spectrum function generation step includes:
An initial value setting step of setting a plurality of individuals of the first generation of the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω);
A plurality of first waveform functions in the frequency domain including each of a plurality of individuals of the nth generation (n is an integer equal to or greater than 1) and the phase spectrum function Ψ (ω), a time intensity waveform function and a time phase waveform function An evaluation value calculating step of converting each of the plurality of second waveform functions in the time domain including the time domain and calculating an evaluation value indicating a degree of difference between the time intensity waveform function and the desired time intensity waveform for each second waveform function When,
An individual selection step of selecting two or more individuals used to generate a plurality of (n + 1) generation individuals from a plurality of n generation individuals based on the evaluation value;
A next generation generation step of generating a plurality of (n + 1) generation individuals based on the two or more individuals selected in the individual selection step,
The evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the intensity spectrum function generation step. A data creation program for generating an intensity spectrum function A (ω) suitable for the desired time intensity waveform from a plurality of nth generation individuals. A program for creating data for controlling a spatial light modulator,
A spectral function generation step for generating an intensity spectral function A (ω) and a phase spectral function Ψ (ω) suitable for an optical pulse train including a plurality of optical pulses arranged at intervals of time;
Based on the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) generated in the spectrum function generation step, the data generation step of creating the data is executed by a computer,
The spectral function generation step includes:
An initial value setting step of setting a plurality of first generation individual pairs related to the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω);
Evaluation value for calculating for each individual pair an evaluation value indicating an amount of loss caused by intensity spectrum modulation based on a plurality of individuals of the nth generation (n = 1, 2,...) Of the intensity spectrum function A (ω). A calculation step;
An individual selection step of selecting two or more individual pairs used for generating a plurality of (n + 1) generation individual pairs from the plurality of n generation individual pairs based on the superiority of the evaluation value;
A next generation generation step of generating a plurality of (n + 1) generation individual pairs based on the two or more individual pairs selected in the individual selection step,
The evaluation value calculation step, the individual selection step, and the next generation generation step are repeated while adding n one by one until a predetermined condition is satisfied, and the predetermined condition is satisfied in the spectrum function generation step. A data creation program for generating the intensity spectrum function A (ω) and the phase spectrum function Ψ (ω) suitable for the optical pulse train from a plurality of n-th generation individual pairs.