An optical structure and method for matrix inversion

Abstract

This invention discloses an optical structure and method for matrix inversion. The optical path structure for matrix inversion consists of n interconnected and identical unit modules, one lens, and one phase grating. Each unit module consists of n-1 grating attenuators and two multimode fiber arrays. This invention employs the aforementioned optical structure and method for matrix inversion, which has the advantages of novelty, fewer optical components, and strong scalability. Only one phase grating is needed to realize the calculation of inverse matrices from 2×2 to N×N, showing broad application prospects in numerical analysis, optical computing, optical communication networks, and deep learning neural networks.

Description

Technical Field

[0001] This invention relates to the field of optical computing technology, and in particular to an optical structure and method for realizing matrix inversion. Background Technology

[0002] With globalization and rapid technological advancements, the amount of data requiring processing is increasing dramatically, leading to a surge in data processing models and algorithms. This, in turn, places ever-higher demands on computing power and power consumption. Currently, von Neumann architecture computers suffer from transmission bottlenecks, increased power consumption, and computing power limitations, making it increasingly difficult to meet the demands of the big data era. Therefore, improving computing speed while reducing power consumption is a pressing issue. For future computing systems, optical computing possesses inherent advantages: photons exhibit characteristics such as light-speed propagation, resistance to electromagnetic interference, and arbitrary superposition, giving optical computing inherent parallel computing capabilities. Consequently, it boasts extremely high processing speeds and is highly suitable for parallel computation.

[0003] Current research on optical matrix computation mainly focuses on multi-plane diffraction light conversion, on-chip micro-ring resonator arrays, and on-chip Mach-Zehnder interferometer networks. Kan Wu, Cesare Soci, and others from the University of Southampton proposed a scheme for implementing 3×3 matrix inversion over an optical fiber network, using optical fiber, nine 1×2 optical splitters, and nine optical fiber modulators. When the matrix dimension expands to N×N, N^2 1×2 optical splitters are required. Therefore, although this scheme can achieve matrix inversion, it requires many components, has a complex structure, high coupling loss, a large system size, and poor optical path scalability. Increasing the matrix dimension requires a large number of optical components, resulting in complex optical path structures and difficult debugging. The matrix inversion structure proposed in this invention is based on a phase grating, avoiding the extensive use of binary beam splitters. For any N-dimensional dimension, only a phase grating and a lens are needed to achieve multi-dimensional matrix inversion operations, making the system simpler, reducing the required optical components, and providing strong scalability, thus driving the development of optical computing architecture towards miniaturization and integration. Summary of the Invention

[0004] The purpose of this invention is to provide an optical structure and method for matrix inversion, which is novel, requires few optical components, has strong scalability, and can be implemented. Features of matrix inversion function.

[0005] To achieve the above objectives, the present invention provides an optical path structure for matrix inversion. The optical path structure for matrix inversion consists of n interconnected and identical unit modules, one lens, and one phase grating. Each unit module consists of n-1 grating attenuators and two multimode fiber arrays.

[0006] A method for implementing an optical path structure using matrix inversion, with the following specific steps:

[0007] S1, the n optical signals output from the multimode fiber array pass through... A uniformly split phase grating produces n sets of parallel beams output along different directions;

[0008] S2. The n sets of parallel light output by the phase grating are converged by the lens and coupled into the multimode fiber array;

[0009] S3. The optical signals in the multimode fiber array are attenuated by a specified factor by their respective grating attenuators and then sent to different modules to become one of the input signals.

[0010] S4. By sequentially changing the light intensity value of the input light signal I, we can obtain... The inverse of a matrix;

[0011] S5. The entire n×n matrix reverse optical path structure uses n unit modules that are exactly the same as those in steps S1-S4, and each unit module works in the same way.

[0012] Preferably, in step S4, when inputting the light intensity value, I is sequentially set... j for (j=1,2……n), other values ​​are zero, where, The total splitting efficiency of the phase grating; each module is obtained at different times. The signal value is the j-th column of the inverse matrix of matrix M.

[0013] Preferably, in step S5, the unit modules are connected using a fixed fiber optic channel.

[0014] Preferably, in step S5, the output of the optical signal of each unit module is one of the inputs of the optical signals of all unit modules.

[0015] Therefore, the optical structure and method for matrix inversion described above are novel, require fewer optical components, are highly scalable, and can be implemented. Features of matrix inversion function.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a structural diagram of a single node in an existing scheme;

[0018] Figure 2 This is a diagram showing the interconnections between nodes in an existing scheme;

[0019] Figure 3This is the optical path diagram for finding the inverse optical path of a 3×3 matrix in the all-optical mode of this scheme;

[0020] Figure 4 This is a structural diagram of a unit module for realizing the inverse optical path of an n×n matrix in the all-optical method of this scheme;

[0021] Figure 5 To obtain the overall structure diagram of the inverse optical path for the all-optical implementation of the n×n matrix in this scheme;

[0022] Figure 6 The process of incident light being split after passing through the phase grating S;

[0023] Figure 7 The process of parallel light incident from different directions being coupled into a multimode fiber array through lens L2;

[0024] Figure 8 This is the optical path diagram of a unit module for finding the inverse optical path of an n×n matrix in the all-optical implementation of this scheme;

[0025] Figure 9 To achieve the overall optical path diagram of the inverse optical path for the all-optical n×n matrix in this scheme.

[0026] Figure Labels

[0027] L, lens; S, phase grating; D ij 1. Adjustable fiber optic attenuator; F. Multimode fiber array. Detailed Implementation

[0028] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0030] The all-optical optical path for matrix inversion employs a hybrid interconnection structure of free-space light and fiber optics, utilizing a small number of optical components and a modular structure. Taking a 3×3 matrix inversion optical path as an example, in the scheme proposed by Kan Wu et al. at the University of Southampton, the system is divided into three interconnected nodes, each with the following structure: Figure 1 As shown, the light intensity is regulated by an optical attenuator D, and the splitting and recombining functions are achieved through three 2×2 optical couplers. The connection methods between different nodes are as follows: Figure 2 As shown. The optical path constructed using this scheme requires a large number of 2×2 optical couplers, making the system complex and difficult to expand. This invention improves upon this by using a phase grating and a lens to achieve the same function, as shown... Figure 3 As shown.

[0031] The optical path structure consists of three identical optical path modules, connected by optical fibers. In the upper module, light exits from the fiber array F, is split by a 1×3 phase grating, and then converges back into the fiber array F after passing through a lens L. It then passes through an optical attenuator. The overall splitting efficiency of the phase grating is 3×k. I1, I2, and I3 are signal input ports, and X1, X2, and X3 are signal output ports. The light intensities after being split by the grating and converged by the lens are X1, X2, and X3, respectively.

[0032] Therefore, we can obtain the following relationship:

[0033] (1)

[0034] (2)

[0035] (3)

[0036] By combining equations (1), (2), and (3), we can obtain the matrix equation:

[0037] (4)

[0038] Right now:

[0039] (5)

[0040] (6)

[0041] make , , , We can obtain X as the first column of the inverse matrix of matrix M, let , , We can obtain X as the second column of the inverse matrix of matrix M, and then let... , , We can obtain X as the third column of the inverse matrix of matrix M.

[0042] like Figure 5 As shown, from Matrix extension to The matrix optical path structure consists of n identical optical path modules, which are connected by optical fibers. The structure of a single module is as follows: Figure 4 As shown, the entire optical path consists of only a 1×n uniformly splitting phase grating S, a lens L, and an adjustable fiber optic attenuator D. ij Composed of (j=1, 2…n), where i represents the i-th module. The input n beams of light are incident through… After the uniform beam splitting grating S, each optical signal is split into n parallel beams of equal intensity but with different exit directions, thus we obtain n sets of parallel beams. Lens L2 converges each set of parallel beams and they enter different fibers in the multimode fiber array F, and then pass through optical attenuator D. i The light intensity is attenuated as required, and becomes one of the input signals of the other n-1 unit modules. The last output is used for monitoring.

[0043] Figure 6 This is the optical path diagram for a phase grating S to split incident light. A phase grating is a Fourier-type beam splitter that can divide a beam of incident monochromatic parallel light into one-dimensional or two-dimensional beam arrays with equal (or non-equal spacing), and has a non-equal spacing, periodically repeating structure. Here, we are using... A uniformly split phase grating divides an incident light beam into n parallel beams that exit in different directions. A stepped structure of varying depths can be periodically etched onto the surface of the phase grating beam splitter using photolithography. When a parallel incident laser beam passes through the phase grating, the periodic variation in grating thickness spatially modulates the phase of the incident monochromatic plane wave. After lens transformation, the beam is imaged at the back focal plane, forming periodically distributed light spots.

[0044] Figure 7 Lens L focuses the n parallel beams emitted from the phase grating S onto the focal plane, and then couples them into the multimode fiber array. Selecting a coupling lens for the multimode fiber requires that the numerical aperture (NA) of the lens and the numerical aperture of the fiber be close, so that the focal size of the light source matches the core size of the fiber, and the incident cone angle does not exceed the arcsine of the fiber's numerical aperture, in order to achieve high coupling efficiency.

[0045] Adjustable fiber optic attenuators reduce optical power through absorption, reflection, diffusion, scattering, deflection, diffraction, and dispersion of optical signals. In this invention, the adjustable fiber optic attenuator setting is determined by the matrix that needs to be inverted.

[0046] The optical path structure of an n×n matrix inverse, the optical signal processing process of a single unit module, such as... Figure 8 As shown, when an input optical signal is incident on the optical system, the beam is incident on the phase grating S. The phase grating S will split the incident parallel beam into n beams of parallel light emitted in different directions, such as... Figure 6 As shown, parallel light is converged onto the focal plane by lens L. Because the numerical aperture (NA) of the lens is close to that of the optical fiber, the focal size of the light source matches the core size of the optical fiber, and the incident cone angle does not exceed the arcsine of the optical fiber's numerical aperture, allowing the light to couple well into the multimode fiber. (See reference...) Figure 7 .

[0047] The optical signal transmitted in the optical fiber is attenuated by a specified factor by an adjustable optical fiber attenuator, and then becomes one of the input signals of n unit modules. This process is repeated until the system tends to stabilize.

[0048] The overall matrix is ​​used to find the inverse light path diagram as follows: Figure 9 As shown:

[0049] X i Let represent the light intensity of the optical signal in the fiber array L2 in the i-th module. Therefore, the following relationship exists in the first module:

[0050] (7)

[0051] k equals the total spectral efficiency of the grating divided by n.

[0052] Similarly, the following relationship can be obtained in the i-th module:

[0053] (8)

[0054] From equation (8), we can obtain the matrix equation:

[0055] (9)

[0056] Right now

[0057] (10)

[0058] Simplifying, we get:

[0059] (11)

[0060] Where E is the identity matrix.

[0061] Further Substituting this into equation (11), we get:

[0062] (12)

[0063] Therefore, firstly let , (i≠1) can be obtained Let be the first column of the inverse matrix M. And so on. The remaining values ​​are 0, which can be used to obtain the j-th column of the inverse matrix of matrix M.

[0064] In summary, the optical structure and method for matrix inversion described above are novel, require fewer optical components, are highly scalable, and can be implemented... Features of matrix inversion function.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An optical path structure for inverting an n×n matrix, characterized in that: The optical path structure for matrix inversion consists of n interconnected and identical unit modules, 1 lens, and 1 phase grating. Each unit module consists of n-1 grating attenuators, 1 front multimode fiber array, and 1 rear multimode fiber array. The specific steps for its implementation are as follows: S1, the n optical signals output from the front multimode fiber array pass through... The phase grating, which provides uniform beam splitting, produces n sets of parallel beams output along different directions; S2. The n sets of parallel light output by the phase grating are converged by the lens and coupled into the post-multimode fiber array; S3. The optical signals in the post-multimode fiber array are attenuated by a specified factor by their respective grating attenuators and sent to different modules to become one of the input signals. S4. By sequentially changing the light intensity value of the input light signal I, we can obtain... The inverse of a matrix; S5. The entire n×n matrix reverse optical path structure uses n unit modules that are exactly the same as those in steps S1-S4, and each unit module works in the same way.

2. The optical path structure for inverting an n×n matrix according to claim 1, characterized in that: In step S4, when inputting the light intensity value, I is sequentially set... j for (j=1,2……n), other values ​​are zero, where, The total splitting efficiency of the phase grating; each module is obtained at different times. The signal value is the j-th column of the inverse matrix of matrix M.

3. The optical path structure for inverting an n×n matrix according to claim 1, characterized in that: In step S5, the unit modules are connected using a fixed fiber optic channel.

4. The optical path structure for inverting an n×n matrix according to claim 1, characterized in that: In step S5, the output of the optical signal of each unit module is one of the inputs of the optical signals of all unit modules.

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