Optical implementation method and device for fractional Fourier transform

Abstract

The invention provides an optical implementation method and device for fractional Fourier transform. The method comprises the following steps: decomposing a fractional Fourier transform matrix into a form of a product of a fixed primitive matrix and a diagonal matrix; the primitive matrix is realized by using an irregular micro-nano structure, the diagonal matrix is realized by using a phase shifter array, so that fractional order Fourier transform is realized on the integrated photonic chip, and the irregular micro-nano structure is a micro-nano structure obtained by designing position distribution of a semiconductor material in a region based on the primitive matrix. According to the optical implementation method and device for the fractional order Fourier transform, ultrahigh operation speed and energy efficiency on light are reserved, the optical implementation method and device can be integrated on a photon chip with a small area, fractional order Fourier transform of any order can be flexibly modulated through a phase shifter array, and high reconfigurability is achieved.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to an optical implementation method and device of fractional-order Fourier transform. Background Art

[0002] Fractional Fourier transform (FrFT) is a generalized extension of the traditional Fourier transform. It uses linear chirp basis functions to implement signal analysis in the time-frequency domain between the time domain and the frequency domain, providing additional degrees of freedom for signal transformation. Fractional Fourier transform can be implemented both electrically and optically. There are many bottlenecks in implementing fractional Fourier transform both electrically and optically.

[0003] To realize fractional Fourier transform electrically, the detected waveform needs to be quantized by an analog-to-digital converter. Due to physical limitations such as carrier migration rate, electronic analog-to-digital converters have rate and bandwidth bottlenecks, which limit the rate and bandwidth of fractional Fourier transform to a relatively low level. Secondly, complex signal processing tasks require huge storage space and computing resources, while the performance of electronic digital signal processors (DSPs) is limited, making it difficult to reduce the computational delay of fractional Fourier transforms, which are more complex than traditional FTs.

[0004] Although it is theoretically possible to simply implement fractional-order Fourier transform using existing spatial optical equipment, the system is too large and unstable to be used in practice. In addition, a certain system can only correspond to a specific order and is difficult to adjust flexibly according to demand. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides an optical implementation method and device of fractional-order Fourier transform, which retains the ultra-high optical computing speed and energy efficiency and can be integrated into a photonic chip with a very small area. Through a phase shifter array, it can be flexibly modulated into fractional-order Fourier transform of any order, thus having high reconfigurability.

[0006] Specifically, the present invention is achieved through the following technical solutions: In a first aspect, the present invention provides an optical implementation method of a fractional-order Fourier transform, the method comprising: decomposing a fractional-order Fourier transform matrix into the form of a product of a fixed primitive matrix and a diagonal matrix; using an irregular micro-nano structure to implement the primitive matrix, and using a phase shifter array to implement the diagonal matrix, thereby implementing a fractional-order 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 semiconductor materials in a region based on the primitive matrix.

[0007] Furthermore, the irregular micro-nano structure is obtained by optimizing the position distribution of semiconductor materials in the micro-nano device structure based on the primitive matrix, including: defining the input and ideal light field output in the micro-nano device structure containing semiconductor materials based on the primitive matrix to obtain an electromagnetic field distribution that satisfies Maxwell's equations, and determining the position distribution of the semiconductor material based on the actual electromagnetic field distribution, thereby obtaining the irregular micro-nano structure whose light field output result is equivalent to the matrix transformation result.

[0008] Furthermore, decomposing the fractional Fourier transform matrix into a form of product of a fixed primitive matrix and a diagonal matrix includes: based on the discrete fractional Fourier transform principle, using singular value decomposition SVD to decompose the fractional Fourier transform matrix into a form of product of a fixed primitive matrix and a diagonal matrix.

[0009] Further, optimizing and determining the position distribution of the semiconductor material based on the ideal distribution of the light field includes: updating the gradient formula of the structure for different positions using a method including an adjoint method, a neural network training or a heuristic training method.

[0010] Furthermore, the method further comprises: after designing the primitive matrix, designing a fractional Fourier transform matrix of any order by changing the value of the diagonal matrix.

[0011] Furthermore, the method also includes: forming a fractional-order Fourier transform cascade structure through a phase shifter array, a transpose of a primitive matrix and a primitive matrix to realize a fractional-order Fourier transform.

[0012] Furthermore, the method further includes: the phase shifter includes a thermo-optical phase shifter, an electro-optical phase shifter and a non-volatile phase change material.

[0013] Furthermore, the method further includes: the semiconductor material includes silicon, silicon dioxide and silicon nitride.

[0014] In a second aspect, the present invention provides an optical implementation device for fractional Fourier transform, the device comprising: a matrix decomposition unit, which decomposes the fractional Fourier transform matrix into the form of the product of a fixed primitive matrix and a diagonal matrix; a fractional Fourier transform unit, which uses an irregular micro-nano structure to implement the primitive matrix, and uses a phase shifter array to implement the diagonal matrix, thereby implementing 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 semiconductor materials in a region based on the primitive matrix.

[0015] The present invention decomposes the fractional-order Fourier transform matrix into a primitive matrix and a diagonal matrix, and respectively realizes the primitive matrix and the diagonal matrix using irregular micro-nano structures and phase shifter arrays, thereby realizing fractional-order Fourier transform on an integrated photonic chip. The present invention retains the ultra-high computing speed and energy efficiency of light and can be integrated into a photonic chip with a very small area. It can be flexibly modulated into any order of fractional-order Fourier transform through a phase shifter array, and has high reconfigurability. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 is a flow chart of a method for optically implementing fractional Fourier transform according to an embodiment of the present invention; Figure 2 is a micro-nano structure diagram of a primitive matrix according to an embodiment of the present invention; Figure 3 is a diagram of an optical implementation structure of a fractional-order Fourier transform according to the present invention; Figure 4 FIG. 4 is a schematic diagram of an optical device for implementing fractional Fourier transform according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Figure 1 FIG. 1 is a flow chart of a method for optically implementing fractional Fourier transform according to an embodiment of the present invention. Figure 1 , the method may include the following steps: Step 101: decomposing the fractional Fourier transform matrix into a product of a fixed primitive matrix and a diagonal matrix; Step 102: Use irregular micro-nano structures to realize the primitive matrix, and use phase shifter arrays to realize the diagonal matrix, so as to realize fractional Fourier transform on the integrated photonic chip, wherein the irregular micro-nano structures are micro-nano structures obtained by designing the position distribution of semiconductor materials in the region based on the primitive matrix.

[0020] Specifically, in this embodiment, it should be noted that before performing the method for realizing fractional Fourier transform according to an embodiment of the present invention, it is necessary to transform the traditional continuous fractional Fourier transform matrix into a discrete fractional Fourier transform matrix. For example, the traditional 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" published by Soo-Chang Pei et al. in Institute of Electrical and Electronics Engineers, where the matrix result is related to the dimension n and the transform order a (value range 0 to 4).

[0021] In step 101, the fractional Fourier transform matrix can be decomposed into the form of the product of a fixed primitive matrix and a diagonal matrix. Specifically, when the matrix dimension n is fixed, the fractional Fourier transform matrix can be decomposed into singular values ​​using singular value decomposition (SVD) based on the discrete fractional Fourier transform principle. Hermite eigenvectors that are orthogonal to each other The product form is:

[0022] Will Sort the columns to form the primitive matrix U, Form a diagonal matrix D, so the discrete fractional Fourier transform matrix can be expressed as:

[0023] in, Represents the transposed matrix of U.

[0024] When the dimension n of the matrix is ​​fixed, the discrete fractional Fourier transform matrix of any order can be expressed as the product of the primitive matrix U and the diagonal matrix D, where the primitive matrix U is fixed and can be implemented using the inverse design method (which will be described below).

[0025] In step 102, the irregular micro-nano structure and the phase shifter array can be used to realize the primitive matrix and the diagonal matrix respectively, so as to realize the fractional Fourier transform on the integrated photonic chip. The irregular micro-nano structure is a structure obtained by optimizing the position distribution of semiconductor materials in the micro-nano device structure based on the primitive matrix.

[0026] Inverse design methods can be used to obtain irregular micro-nano structures. Inverse design methods are a device function-oriented micro-nano structure design method. Currently, it is widely used to design small-sized micro-nano structures with specific functions, such as power dividers, polarization beam splitters, wavelength division multiplexers and other structures. It has the advantages of small device size, simple design process, and no professional basic optical knowledge background. The functions of different devices are determined by the distribution of electromagnetic fields, and the distribution of electromagnetic fields is determined by the refractive index distribution of the actual physical structure. Inverse design uses optimization methods 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 Maxwell's equations, and uses the solved electromagnetic field to evaluate the current optical performance of the device. After multiple rounds of iterative optimization, it finally physically achieves the design of a micro-nano device structure that can manipulate the ideal electromagnetic field distribution, that is, has the expected device function.

[0027] Taking the primitive matrix as an example, the input and output in the structure are first defined according to the result of the matrix, so as to obtain the ideal distribution of the light field. The optimized structure contains two materials, silicon and silicon dioxide, which have different refractive indices. The position distribution of the semiconductor material is determined by optimization, so an irregular structure will be generated. The output result of the optimized structure is equivalent to the result after the matrix transformation. In other words, the input and ideal light field output in the micro-nano structure containing semiconductor materials can be defined based on the primitive matrix to obtain the electromagnetic field distribution that satisfies Maxwell's equations. The position distribution of the semiconductor material is optimized based on the ideal distribution of the light field, so as to obtain an irregular micro-nano structure whose light field output result is equivalent to the result of the matrix transformation. Among them, determining the position distribution of the semiconductor material by optimization includes updating the gradient formula of the structure for different positions using adjoint methods, neural network training, heuristic optimization methods, etc.

[0028] Figure 2 FIG. 1 is a micro-nano structure diagram of a primitive matrix according to an embodiment of the present invention. Figure 2 As shown in the figure, the design can obtain a 4×4 element matrix with an area of ​​6um×6um×0.22um and a central wavelength of 1550nm. The same steps can be followed to design or the U can be directly flipped over to obtain the result.

[0029] As the order of the diagonal matrix D changes, the values ​​satisfy The form can be realized by using a phase shifter array. Therefore, after designing the primitive matrix U, it is only necessary to change the value of the diagonal matrix D to design the fractional Fourier transform matrix of any order. The resulting cascade system is as follows Figure 4 As shown, a fractional-order Fourier transform cascade structure is formed by a phase shifter array, a transposition of a primitive matrix and a primitive matrix to realize a fractional-order Fourier transform.

[0030] Figure 3 This is a diagram of the optical implementation structure of the fractional Fourier transform according to the present invention. Figure 3 The process is as follows: The control unit is used to control the voltage output of each channel of the programmable voltage source. The laser source stably outputs a single-wavelength point light source of 1550nm. The light source is divided into four paths and then modulated by Mach-Zehnder modulators (MZMs) to modulate the intensity. The MZM is controlled by the voltage of the DC voltage source and is used to convert electrical signals into optical signals and input them into the subsequent cascade system. The DC voltage source is controlled by the control unit to control the voltage output result. The modulated optical signal passes through the primitive matrix implemented by the inverse design in turn. , phase shifter array, and primitive matrix U, the output result is detected by an optical power meter, and the result is transmitted to the control unit after photoelectric conversion to compare the error between the actual output result and the target result. When the output signal is mathematically equal to the result of the signal after FRFT transformation, it means that the cascade structure has realized the FRFT matrix.

[0031] It can be seen from the above embodiments that the present invention can realize fractional-order Fourier transform on an integrated photonic chip by decomposing the fractional-order Fourier transform matrix into a primitive matrix and a diagonal matrix, respectively using irregular micro-nano structures and phase shifter arrays to realize the primitive matrix and the diagonal matrix. The present invention retains the ultra-high computing speed and energy efficiency of light and can be integrated into a photonic chip with a very small area. It can be flexibly modulated into any order of fractional-order Fourier transform through a phase shifter array, and is highly reconfigurable.

[0032] Figure 4 FIG. 1 is a schematic diagram of an optical implementation device of fractional Fourier transform according to an embodiment of the present invention. Figure 4 As shown, the device for realizing fractional-order Fourier transform includes: a matrix decomposition unit 201, which decomposes the fractional-order Fourier transform matrix into the form of the product of a fixed primitive matrix and a diagonal matrix; a fractional-order Fourier transform unit 202, which realizes the primitive matrix by using an irregular micro-nano structure, and realizes the diagonal matrix by using a phase shifter array, thereby realizing fractional-order 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 semiconductor materials in a region based on the primitive matrix.

[0033] The optical realization device of the fractional Fourier transform of the present invention decomposes the fractional Fourier transform matrix into a primitive matrix and a diagonal matrix, and respectively realizes the primitive matrix and the diagonal matrix using irregular micro-nano structures and phase shifter arrays, thereby realizing the fractional Fourier transform on an integrated photonic chip. The present invention retains the ultra-high computing speed and energy efficiency of light and can be integrated into a photonic chip with a very small area. It can be flexibly modulated into any order of fractional Fourier transform through a phase shifter array, and has high reconfigurability.

[0034] In addition, in the present invention, the description with reference to the terms "embodiment", "present embodiment", "another embodiment", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An optical implementation method of fractional Fourier transform, characterized in that: include: Decompose the fractional Fourier transform matrix into the product of a fixed primitive matrix and a diagonal matrix; The primitive matrix is ​​realized by using an irregular micro-nano structure, and the diagonal matrix is ​​realized by using a phase shifter array, so as to realize 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 semiconductor materials in a region based on the primitive matrix.

2. The method according to claim 1, characterized in that The irregular micro-nano structure is obtained by optimizing the position distribution of semiconductor materials in the design area based on the primitive matrix, including: The input and ideal light field output in a micro-nano structure containing semiconductor materials are defined based on the primitive matrix to obtain an electromagnetic field distribution that satisfies Maxwell's equations. The position distribution of the semiconductor material is optimized based on the ideal distribution of the light field, thereby obtaining the irregular micro-nano structure whose light field output result is equivalent to the matrix transformation result.

3. The method according to claim 2, characterized in that The fractional Fourier transform matrix is ​​decomposed into the product of a fixed primitive matrix and a diagonal matrix: Based on the discrete fractional Fourier transform principle, the fractional Fourier transform matrix is ​​decomposed into the product of a fixed primitive matrix and a diagonal matrix using singular value decomposition (SVD).

4. The method according to claim 2 or 3, characterized in that: Optimizing and determining the position distribution of the semiconductor material based on the ideal distribution of the light field includes: updating the gradient formula of the structure for different positions using a method including an adjoint method, a neural network training or a heuristic training method.

5. The method according to claim 4, characterized in that The method further comprises: After the primitive matrix is ​​designed, the fractional Fourier transform matrix of any order is designed by changing the values ​​of the diagonal matrix.

6. The method according to claim 5, characterized in that The method further comprises: A fractional-order Fourier transform cascade structure is formed by a phase shifter array, a transposition of a primitive matrix and a primitive matrix to realize a fractional-order Fourier transform.

7. The method according to claim 6, characterized in that The phase shifter includes a thermo-optical phase shifter, an electro-optical phase shifter and a non-volatile phase change material.

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

9. An optical implementation device for fractional Fourier transform, characterized in that: include: A matrix decomposition unit decomposes the fractional Fourier transform matrix into a product of a fixed primitive matrix and a diagonal matrix; The fractional-order Fourier transform unit utilizes an irregular micro-nano structure to realize the primitive matrix and utilizes a phase shifter array to realize the diagonal matrix, thereby realizing a fractional-order 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 semiconductor materials in a region based on the primitive matrix.

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