Optical implementation method and device of fractional fourier transform

Abstract

The application provides an optical implementation method and device of fractional Fourier transform. The method comprises the following steps: decomposing a fractional Fourier transform matrix into a fixed base matrix and a diagonal matrix product; using an irregular micro-nano structure to realize the base matrix, and using a phase shifter array to realize the diagonal matrix, so as to realize the fractional Fourier transform on an integrated photonic chip, wherein the irregular micro-nano structure is obtained by designing the position distribution of the semiconductor material in the region based on the base matrix. The optical implementation method and device of fractional Fourier transform of the application retain the super-high operation speed and energy efficiency of light, can be integrated into a photonic chip with extremely small area, can be flexibly modulated into fractional Fourier transform of any order through the phase shifter array, and has high reconfigurability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of signal processing, in particular to a method and device for optical implementation of fractional Fourier transform. BACKGROUND

[0002] Fractional Fourier transform (FrFT) is a generalization of the traditional Fourier transform, which realizes signal analysis in the time-frequency domain between time domain and frequency domain by using linear chirp basis functions, and provides an additional order degree of freedom for signal transformation. The fractional Fourier transform can be realized on both electricity and light. There are many bottlenecks in realizing the fractional Fourier transform on both electricity and light.

[0003] For realizing the fractional Fourier transform on electricity, the first detected waveform needs to be quantized by an analog-to-digital converter. Due to the physical limitations of carrier migration rate and the like, the electronic analog-to-digital converter has rate and bandwidth bottlenecks, so that the rate and bandwidth of the fractional Fourier transform are limited at a relatively low level. In addition, a complex signal processing task needs to occupy a large storage space and computing resources, and the performance of the electronic digital signal processor (DSP) is limited, so that the calculation delay of the fractional Fourier transform with higher complexity than the traditional FT is difficult to reduce.

[0004] For realizing the fractional Fourier transform on light, although the existing spatial optical equipment can be used to simply realize the fractional Fourier transform in theory, the system is too large in size and poor in stability, which is difficult to be practically applied, and the determined system can only correspond to a specific order, and it is difficult to flexibly adjust according to the demand. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a method and device for optical implementation of fractional Fourier transform, which retains the ultra-high operation speed and energy efficiency of light and can be integrated into a very small photonic chip. The phase shifter array can be flexibly modulated to any order of fractional Fourier transform, thereby having high reconfigurability.

[0006] Specifically, the present application is realized by the following technical scheme:

[0007] In a first aspect, the present application provides a method for optical implementation of fractional Fourier transform, which comprises: decomposing a fractional Fourier transform matrix into a fixed basis matrix and a diagonal matrix product; using an irregular micro-nano structure to realize the basis matrix, and using a phase shifter array to realize the diagonal matrix, so as to realize the fractional Fourier transform on an integrated photonic chip, wherein the irregular micro-nano structure is a micro-nano structure obtained by designing the position distribution of the semiconductor material in the region based on the basis matrix.

[0008] Further, the non-regular micro-nano structure is obtained by optimizing the position distribution of the semiconductor material in the micro-nano device structure based on the base element matrix, which comprises: defining the input and ideal light field output in the micro-nano device structure containing the semiconductor material based on the base element matrix to obtain an electromagnetic field distribution satisfying Maxwell equations, determining the position distribution of the semiconductor material based on the actual electromagnetic field distribution, so that the light field output result is equivalent to the matrix transformation result of the non-regular micro-nano structure.

[0009] Further, the decomposition of the fractional Fourier transform matrix into a fixed base element matrix and a diagonal matrix product form comprises: based on the principle of discrete fractional Fourier transform, the fractional Fourier transform matrix is decomposed into a fixed base element matrix and a diagonal matrix product form by singular value decomposition (SVD).

[0010] Further, the optimization of the position distribution of the semiconductor material based on the ideal distribution of the light field comprises: updating the gradient formula of different positions by using methods including adjoint method, neural network training or heuristic training.

[0011] Further, the method further comprises: after designing the base element matrix, the fractional Fourier transform matrix under any order is designed by changing the numerical value of the diagonal matrix.

[0012] Further, the method further comprises: a fractional Fourier transform cascade structure composed of a phase shifter array, a transpose of the base element matrix and the base element matrix is used to realize the fractional Fourier transform.

[0013] Further, the method further comprises: the phase shifter comprises a thermo-optic phase shifter, an electro-optic phase shifter and a non-volatile phase change material.

[0014] Further, the method further comprises: the semiconductor material comprises silicon, silicon dioxide and silicon nitride.

[0015] In a second aspect, the present application provides an optical implementation device of fractional Fourier transform, which comprises: a matrix decomposition unit, which decomposes a fractional Fourier transform matrix into a fixed base element matrix and a diagonal matrix product form; a fractional Fourier transform unit, which realizes the base element matrix by using a non-regular micro-nano structure and realizes the diagonal matrix by using a phase shifter array, so as to realize the fractional Fourier transform on an integrated photonic chip, wherein the non-regular micro-nano structure is a micro-nano structure obtained by optimizing the position distribution of the semiconductor material in the design region based on the base element matrix.

[0016] The application can realize fractional Fourier transform on an integrated photonic chip by decomposing a fractional Fourier transform matrix into a base matrix and a diagonal matrix, and using irregular micro-nano structures and a phase shifter array to realize the base matrix and the diagonal matrix respectively. The application retains high operation speed and energy efficiency of light and can be integrated into a photonic chip with extremely small area, and can be flexibly modulated into fractional Fourier transform of any order through the phase shifter array, and has high reconfigurability. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0018] Figure 1 is a flow chart of an optical implementation method of fractional Fourier transform according to an embodiment of the present application;

[0019] Figure 2 is a micro-nano structure diagram of a base matrix according to an embodiment of the present application;

[0020] Figure 3 is an optical implementation structure diagram of fractional Fourier transform according to the present application;

[0021] Figure 4 is a schematic diagram of an optical implementation device of fractional Fourier transform according to an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below with reference to the drawings in the present application. Obviously, the described embodiments are some embodiments of the present application, but not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0023] Figure 1 is a flow chart of an optical implementation method of fractional Fourier transform according to an embodiment of the present application. With reference to Figure 1 , the method can include the following steps:

[0024] Step 101: decompose a fractional Fourier transform matrix into a fixed base matrix and a diagonal matrix product form;

[0025] Step 102: implementing the base matrix with non-regular micro-nano structure, and implementing the diagonal matrix with phase shifter array, thereby implementing the fractional Fourier transform on an integrated photonic chip, wherein the non-regular micro-nano structure is obtained based on a position distribution of semiconductor material in a design region of the base matrix.

[0026] Specifically, in the present embodiment, it is to be noted that before implementing the method for implementing the fractional Fourier transform according to one embodiment of the present application, the conventional continuous fractional Fourier transform matrix needs to be transformed into a discrete fractional Fourier transform matrix. For example, the conventional continuous fractional Fourier transform matrix can be transformed into a discrete fractional Fourier transform matrix with reference to the document Discrete fractional Hartley and Fourier transforms by Soo-Chang Pei et al. published on Institute of Electrical and Electronics Engineers, wherein the matrix result is related to the dimension n and the transform order a (value range 0 to 4).

[0027] In step 101, the fractional Fourier transform matrix can be decomposed into the form of product of a fixed base matrix and a diagonal matrix. Specifically, when the matrix dimension n is fixed, the fractional Fourier transform matrix can be decomposed into the form of product of singular values and mutually orthogonal Hermite eigenvectors based on the principle of discrete fractional Fourier transform by singular value decomposition (SVD):

[0028]

[0029] The singular values are sorted by column to form the base matrix U, and the Hermite eigenvectors form the diagonal matrix D, so that the discrete fractional Fourier transform matrix can be expressed as:

[0030]

[0031] wherein represents the transpose matrix of U.

[0032] When the dimension n of the matrix is fixed, the discrete fractional Fourier transform matrix under any order can be expressed in the form of product of the base matrix U and the diagonal matrix D, wherein the base matrix U is fixed and can be implemented by using the reverse design method (which will be described below).

[0033] In step 102, the element matrix and the diagonal matrix can be respectively implemented by using the irregular micro-nano structure and the phase shifter array, so as to implement the fractional Fourier transform on the integrated photon chip. The irregular micro-nano structure is obtained by optimizing the position distribution of the semiconductor material in the micro-nano device structure based on the element matrix.

[0034] The irregular micro-nano structure can be obtained by using a reverse design method. The reverse design method is a micro-nano structure design method oriented by device function. At present, it is widely applied to design small-size micro-nano structures with specific functions, such as power dividers, polarization beam splitters, wavelength division multiplexers and the like, and has the advantages of small device size, simple design process and no need of professional optical background. The function of different devices is determined by the distribution of electromagnetic field, and the distribution of electromagnetic field is determined by the refractive index distribution of the actual physical structure. The reverse design uses an optimization method to continuously update the device topology to determine the refractive index distribution, solves the spatial electromagnetic field distribution under the current refractive index according to the Maxwell equations, evaluates the current optical performance of the device by using the solved electromagnetic field, and finally physically reaches the design of the micro-nano device structure capable of manipulating the ideal electromagnetic field distribution, i.e. having the expected device function after multiple rounds of iterative optimization.

[0035] Taking the element matrix as an example, first, the input and output in the structure are defined according to the result of the matrix, so as to obtain the ideal distribution of the optical field. The optimized structure includes two materials, silicon and silicon dioxide, and the refractive indexes of the two materials are different. The position distribution of the semiconductor material is determined by optimization, so that the irregular structure is generated. The output result of the finally optimized structure is equivalent to the result after the matrix transformation. In other words, the input and ideal optical field output in the micro-nano structure containing the semiconductor material can be defined based on the element matrix to obtain the electromagnetic field distribution satisfying the Maxwell equations, the position distribution of the semiconductor material is determined based on the ideal distribution of the optical field, so as to obtain the irregular micro-nano structure whose optical field output result is equivalent to the matrix transformation result. The position distribution of the semiconductor material is determined by optimization, including updating the gradient formula of different positions by using the adjoint method, neural network training, heuristic optimization method and the like.

[0036] Figure 2 It is a micro-nano structure diagram of the element matrix according to an embodiment of the application. As shown in Figure 2 , the element matrix with a size of 4x4 can be obtained by design, and the area is 6umx6umx0.22um, and the center wavelength is 1550nm. Similarly, the matrix can be designed by the same step or directly flipped U.

[0037] The diagonal matrix D changes with the order, and each value satisfies The form can be implemented by using a phase shifter array. Therefore, after designing the basic matrix U, only the numerical value of the diagonal matrix D needs to be changed to design the fractional Fourier transform matrix of any order. The final cascade system is shown in Figure 4 , that is, the fractional Fourier transform is realized by using a phase shifter array, the transpose of the basic matrix and the fractional Fourier transform cascade structure composed of the basic matrix.

[0038] Figure 3 is the optical implementation structure of the fractional Fourier transform according to the present application. The flow of Figure 3 : The control unit is used to control the voltage output of each channel of the programmable voltage source, the single-wavelength point light source with a stable output of 1550 nm in the laser source, the light source is divided into four paths and then modulates the intensity by using a Mach-Zehnder modulator (MZM), the MZM is controlled by the voltage of a direct current voltage source, which is used to convert the electrical signal into an optical signal and input into the subsequent cascade system, and the output of the direct current voltage source is controlled by the control unit. The modulated optical signal is sequentially input into the basic matrix , the phase shifter array and the basic matrix U realized by inverse design, and the output result is detected by using an optical power meter. The result is transmitted to the control unit after photoelectric conversion, which is used to compare the error between the actual output result and the target result. When the output signal is equal to the result of the signal after the FRFT transformation in mathematics, it represents that the cascade structure realizes the FRFT matrix.

[0039] As can be seen from the above embodiment, the fractional Fourier transform matrix is decomposed into a basic matrix and a diagonal matrix, the basic matrix and the diagonal matrix are respectively realized by using an irregular micro-nano structure and a phase shifter array, so that the fractional Fourier transform can be realized on an integrated photonic chip. The present application retains the super-high operation speed and energy efficiency of light and can be integrated into a photonic chip with extremely small area. The phase shifter array can be flexibly modulated into a fractional Fourier transform of any order, and has high reconfigurability.

[0040] Figure 4 is a schematic diagram of an optical implementation device of the fractional Fourier transform according to an embodiment of the present application. As shown in Figure 4 , the device for realizing the fractional Fourier transform comprises: a matrix decomposition unit 201, which decomposes the fractional Fourier transform matrix into a fixed basic matrix and a diagonal matrix product; a fractional Fourier transform unit 202, which realizes the basic matrix by using an irregular micro-nano structure and realizes the diagonal matrix by using a phase shifter array, so as to realize the fractional Fourier transform on an integrated photonic chip, wherein the irregular micro-nano structure is obtained based on the position distribution of the semiconductor material in the design area of the basic matrix.

[0041] The optical implementation device of the fractional Fourier transform of the application can realize the fractional Fourier transform on the integrated photonic chip by decomposing the fractional Fourier transform matrix into a primitive matrix and a diagonal matrix, and using the irregular micro-nano structure and the phase shifter array to realize the primitive matrix and the diagonal matrix, respectively.

[0042] In addition, in the present application, the description of the terms "embodiment", "the present embodiment", "further embodiment" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples without contradiction.

[0043] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. An optical implementation method for fractional Fourier transform, characterized in that, include: The fractional Fourier transform matrix is ​​decomposed into the form of a product of a fixed primitive matrix and a diagonal matrix; The primitive matrix is ​​realized using an irregular micro / nano structure, and the diagonal matrix is ​​realized using a phase shifter array, thereby realizing a fractional Fourier transform on an integrated photonic chip. The irregular micro / nano structure is a micro / nano structure obtained by designing the positional distribution of semiconductor materials in the region based on the primitive matrix. After designing the primitive matrix, the fractional Fourier transform matrix of arbitrary order is designed by changing the values ​​of the diagonal matrix. as well as A cascaded structure of fractional Fourier transform is formed by a phase shifter array, the transpose of the basic matrix, and the basic matrix itself, which is used to implement the fractional Fourier transform. The irregular micro / nano structure obtained by optimizing the positional distribution of semiconductor materials in the design region based on the primitive matrix includes: defining the input and ideal light field output in the micro / nano structure containing semiconductor materials based on the primitive matrix to obtain the electromagnetic field distribution that satisfies Maxwell's equations; optimizing the positional distribution of the semiconductor materials based on the ideal distribution of the light field to obtain the irregular micro / nano structure in which the light field output result is equivalent to the matrix transformation result; The form of decomposing a fractional Fourier transform matrix into a product of a fixed primitive matrix and a diagonal matrix includes: based on the principle of discrete fractional Fourier transform, using singular value decomposition (SVD) to decompose the fractional Fourier transform matrix into a product of a fixed primitive matrix and a diagonal matrix.

2. The method according to claim 1, characterized in that, Optimizing the location distribution of the semiconductor material based on the ideal distribution of the light field includes updating the gradient formula of the structure for different locations using methods including the adjoint method, neural network training, or heuristic training.

3. The method according to claim 1, characterized in that, The phase shifter includes a thermo-optical phase shifter, an electro-optical phase shifter, and a non-volatile phase change material.

4. The method according to claim 1, characterized in that, The semiconductor materials include silicon, silicon dioxide, and silicon nitride.

5. An optical device for realizing fractional Fourier transform, characterized in that, include: The matrix decomposition unit decomposes the fractional Fourier transform matrix into the form of a product of fixed primitive matrices and diagonal matrices. The form of decomposing the fractional Fourier transform matrix into the form of a product of fixed primitive matrices and diagonal matrices includes: based on the principle of discrete fractional Fourier transform, using singular value decomposition (SVD) to decompose the fractional Fourier transform matrix into the form of a product of fixed primitive matrices and diagonal matrices. The fractional Fourier transform unit utilizes an irregular micro / nano structure to realize the primitive matrix and a phase shifter array to realize the diagonal matrix, thereby achieving a fractional Fourier transform on an integrated photonic chip. The irregular micro / nano structure is obtained by designing the positional distribution of semiconductor materials in the region based on the primitive matrix. After designing the primitive matrix, the fractional Fourier transform matrix of arbitrary order is designed by changing the value of the diagonal matrix. A cascaded structure of fractional Fourier transform is formed by the phase shifter array, the transpose of the primitive matrix, and the primitive matrix to realize the fractional Fourier transform. The process of obtaining the irregular micro / nano structure by optimizing the positional distribution of semiconductor materials in the region based on the primitive matrix includes: defining the input and ideal light field output of the micro / nano structure containing semiconductor materials based on the primitive matrix to obtain an electromagnetic field distribution satisfying Maxwell's equations; optimizing the positional distribution of the semiconductor materials based on the ideal distribution of the light field to obtain the irregular micro / nano structure whose light field output result is equivalent to the matrix transformation result.

Images