Processing device

Abstract

A processing device 10 obtains a propagation constant and a coupling coefficient of each eigenmode in a spatial division multiplexing optical fiber having N (N is an integer of 2 or more) eigenmodes. The processing device 10 comprises: a matrix K calculation unit 11 that obtains a propagation constant and an inter-core coupling coefficient of each core of an optical fiber in a linear state, and generates a matrix K having the propagation constants of the cores as diagonal terms and the inter-core coupling coefficients as off-diagonal terms; a propagation constant calculation unit 12 that generates, for each step width Δz of the optical fiber, a matrix B having the propagation constant of each eigenmode as diagonal terms by diagonalizing the matrix K using a matrix M composed of eigenvectors of the matrix K; and a coupling coefficient calculation unit 13 that generates a matrix C having the coupling coefficients between the eigenmodes as elements on the basis of the inner product of the matrix M and an inverse matrix M-1 of the matrix M at the next step width z + Δz. The processing device 10 is provided with a GDS14 calculation unit that obtains a group delay spread from the propagation constants of the eigenmodes obtained over the entire length of the optical fiber and the coupling coefficients between the eigenmodes.

Description

Processing equipment

[0001] The present disclosure relates to a processing device.

[0002] In recent years, optical transmission systems using multi-core optical fibers (MCFs) with multiple cores within the same optical fiber have been proposed as next-generation optical fibers for high-capacity communications. Among multi-core fibers, transmission systems using coupled multi-core optical fibers (C-MCFs) have attracted particular attention. C-MCFs tolerate mode coupling between cores and compensate for this coupling using Multiple-input Multiple-output (MIMO) signal processing techniques. C-MCFs can reduce the spacing between adjacent cores, enabling high core density. Furthermore, they can reduce the differential group delay between modes, thereby reducing the load of MIMO signal processing. Therefore, C-MCFs are considered promising optical fibers for long-distance, high-capacity transmission.

[0003] In transmission systems using C-MCF, large group delay spread (GDS) leads to an increased load on MIMO signal processing, so fiber design with low GDS characteristics is important, and a GDS simulation method is required.

[0004] Kunimasa Saitoh, Takeshi Fujisawa, and Takanori Sato,“Control of Group Delay Spread in Randomly-Coupled Multicore Fibers,”2020 Opto-Electronics and Communications Conference, 04-08 October 2020Taiji Sakamoto, Takayoshi Mori, Masaki Wada, Takashi Yamamoto, Fumihiko Yamamoto, and Kazuhide Nakajima,“Fiber Twisting- and Bending-Induced Adiabatic / Nonadiabatic Super-Mode Transition in Coupled Multicore Fiber,”JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 34, NO. 4, FEBRUARY 15, 2016, pp. 1228-1237

[0005] Non-Patent Document 1 shows that it is possible to simulate the GDS of C-MCF with any structure. However, because it uses the highly load-intensive two-dimensional finite element method (2d-FEM) and overlap integral calculation of the electric field distribution, it is not suitable for fiber design, which requires comprehensive calculation of the fiber structure.

[0006] Non-Patent Document 2 presents a GDS simulation that does not involve high-load processing, but it is applicable only when the number of cores is two, and there is a problem that it cannot perform calculations when there are three or more cores.

[0007] The present disclosure has been made in view of the above, and aims to determine the group delay spread in a coupled multi-core optical fiber having an arbitrary number of cores and an arbitrary number of modes using low-load calculation processing.

[0008] A processing device according to one aspect of the present disclosure is a processing device that calculates the propagation constant and coupling coefficient of each eigenmode over the entire length of a space division multiplexing optical fiber having a plurality of eigenmodes, and includes a matrix K calculation unit that calculates the propagation constant and inter-core coupling coefficient of each core of the optical fiber in a linear state and generates a matrix K in which the propagation constant of each core is a diagonal term and the inter-core coupling coefficient is a non-diagonal term; a propagation constant calculation unit that generates a matrix B in which the propagation constant of each eigenmode is a diagonal term by diagonalizing the matrix K using a matrix M in which each column is made up of an eigenvector of the matrix K for each infinitesimal width of the optical fiber; and a calculation unit that calculates an inverse matrix M of the matrix M and the matrix M at the next infinitesimal width. -1 The coupling coefficient calculation unit generates a matrix C having elements each representing a coupling coefficient between eigenmodes based on the inner product of

[0009] According to the present disclosure, it is possible to obtain the group delay spread in a coupled multi-core optical fiber with an arbitrary number of cores and an arbitrary number of modes using low-load calculation processing.

[0010] FIG. 1 is a diagram showing an example of the configuration of a processing device. FIG. 2 is a diagram showing an example of the hardware configuration of a processing device. FIG. 3 is a flowchart showing an example of the process flow for calculating a GDS. FIG. 4 is a flowchart showing an example of the process flow for calculating a matrix K. FIG. 5 is a flowchart showing an example of the process flow for calculating a propagation constant. FIG. 6 is a flowchart showing an example of the process flow for calculating a coupling coefficient. FIG. 7 is a flowchart showing an example of the process flow for calculating a GDS. FIG. 8 is a diagram showing an example of the calculation time for the conventional technology and the embodiment. FIG. 9 is a diagram showing an example of the calculation results of a GDS for the conventional technology and the embodiment.

[0011] [Configuration of Processing Apparatus] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0012] An example of the configuration of a processing device 10 according to this embodiment will be described with reference to Fig. 1. The processing device 10 shown in the figure is a device for calculating the propagation constants and coupling coefficients of each eigenmode, as well as the group delay spread (GDS), of a space division multiplexing optical fiber having N eigenmodes (N is an integer of 2 or more), and includes a matrix K calculation unit 11, a propagation constant calculation unit 12, a coupling coefficient calculation unit 13, and a GDS calculation unit 14.

[0013] The matrix K calculation unit 11 inputs the profile of each core and the core spacing, calculates the propagation constant and inter-core coupling coefficient of each core of the optical fiber in a linear state by one-dimensional finite element calculation of a single core, and generates a matrix K in which the propagation constant of each core is the diagonal term and the inter-core coupling coefficient is the off-diagonal term.

[0014] The propagation constant calculation unit 12 converts the diagonal terms of the matrix K into propagation constants in the curved waveguide for each step width, and generates a matrix B whose diagonal terms are the propagation constants of each eigenmode by diagonalizing the matrix K using a matrix M whose columns are made up of eigenvectors of the matrix K. The step width is a small increment of length used when calculating the propagation constants and coupling coefficients over the entire length of the optical fiber.

[0015] The coupling coefficient calculation unit 13 calculates the matrix M and the inverse matrix M of the matrix M at the next step size. -1 A matrix C having elements each representing a coupling coefficient between eigenmodes is generated based on the inner product of

[0016] The GDS calculation unit 14 calculates the GDS from the propagation constant of each eigenmode and the coupling coefficient between each eigenmode obtained over the entire length of the optical fiber.

[0017] The processing device 10 described above can be, for example, a general-purpose computer system including a central processing unit (CPU) 901, a memory 902, a storage 903, a communication device 904, an input device 905, and an output device 906, as shown in Fig. 2. In this computer system, the processing device 10 is realized by the CPU 901 executing a predetermined program loaded onto the memory 902. This program can be recorded on a computer-readable non-transitory recording medium such as a magnetic disk, an optical disk, or a semiconductor memory, or can be distributed via a network.

[0018] [Operation of Processing Device] Next, calculation of the propagation constant and coupling coefficient of each eigenmode in a space division multiplexing optical fiber, and calculation of the GDS will be described with reference to the flowchart in FIG.

[0019] In step S1, design parameters of the optical fiber are input to the processing device 10. Specifically, the profile of each core, such as the core radius a and the relative refractive index difference Δ, the core spacing Λ, the bending radius R, the bending angle θ, the step width Δz, the twist rate (twist amount per unit length) γ, and the total length L of the optical fiber are input to the processing device 10.

[0020] In step S2, the matrix K calculation unit 11 inputs the profile of each core and the core spacing, and calculates a matrix K for the cores in a linear state, with the propagation constants of each core on the diagonal terms and the inter-core coupling coefficients on the off-diagonal terms.

[0021] The processing device 10 performs the following calculations in steps S3 and S4 for each step width Δz from 0 to the total length L of the optical fiber.

[0022] In step S3, the propagation constant calculation unit 12 receives the matrix K and calculates the propagation constant β of the eigenmode i of the optical fiber. i Calculate the matrix B having the following diagonal terms:

[0023] In step S4, the coupling coefficient calculation unit 13 inputs a matrix M, each column of which is made up of eigencolumn vectors of the matrix K, and calculates the coupling coefficient c between the eigenmode i and the eigenmode j as the ij component. ij Calculate the matrix C with

[0024] By the processes of steps S3 and S4, the propagation constant β of the eigenmode i is calculated. i The matrix B has the following diagonal terms: ij The processing device 10 repeats the processes of steps S3 and S4 to obtain the propagation constant and the coupling coefficient over the entire length L of the optical fiber.

[0025] In step S5, the GDS calculation unit 14 inputs the propagation constant and coupling coefficient over the entire length L of the optical fiber and calculates the GDS.

[0026] [Calculation of Matrix K] Next, the processes of the matrix K calculation unit 11, the propagation constant calculation unit 12, the coupling coefficient calculation unit 13, and the GDS calculation unit 14 will be described.

[0027] First, an example of the processing flow of the matrix K calculation unit 11 will be described with reference to the flowchart of FIG.

[0028] In step S21, the matrix K calculation unit 11 receives the core radius a, the relative refractive index difference Δ, and the inter-core distance Λ.

[0029] In step S22, the matrix K calculation unit 11 performs a finite element calculation of a single core to calculate the linear core propagation constant β n Calculate.

[0030] In step S23, the matrix K calculation unit 11 calculates the linear core coupling coefficient κ ij Calculate the coupling coefficient between the linear cores κ ij is calculated using the following formula:

[0031]

[0032] Here, V is the V value of the core, and K is the modified Bessel function. U and W satisfy the following equation.

[0033]

[0034] where J is the Bessel function.

[0035] In step S24, the matrix K calculation unit 11 calculates the linear core propagation constant β as a diagonal term expressed by the following equation: i The off-diagonal terms are the coupling coefficients between the linear cores κ ij The output is a matrix K having the following formula:

[0036]

[0037] [Calculation of Propagation Constant] Next, an example of the flow of processing by the propagation constant calculation unit 12 will be described with reference to the flowchart of FIG.

[0038] In step S31, the propagation constant calculation unit 12 receives the matrix K as an input.

[0039] In step S32, the propagation constant calculation unit 12 calculates the propagation constant β of the diagonal terms of the matrix K, taking bending into consideration. i is converted using the following formula:

[0040]

[0041] Propagation constant β iThe matrix K after transformation is expressed as follows:

[0042]

[0043] In step S33, the propagation constant calculation unit 12 generates a matrix M in which each column is made up of an eigenvector of the matrix K, and diagonalizes the matrix K using the matrix M as shown in the following equation, thereby calculating the propagation constant β of each eigenmode: n Generate a matrix B with (upper ~) on the diagonal.

[0044]

[0045] In step S33, the propagation constant calculation unit 12 calculates the matrix M and the propagation constant β n (Outputs ~ above).

[0046] [Calculation of Coupling Coefficient] Next, an example of the processing flow of the coupling coefficient calculation unit 13 will be described with reference to the flowchart of FIG.

[0047] In step S41, the coupling coefficient calculation unit 13 receives the matrix M as an input.

[0048] In step S42, the coupling coefficient calculation unit 13 calculates the matrix M(z, θ) and the inverse matrix M of the matrix M at the next step size Δz as shown in the following equation. -1 From the inner product of (z+Δz, θ+Δθ) (where Δθ=γΔz), the coupling coefficient c between eigenmode i and eigenmode j is ij A matrix C having the elements:

[0049]

[0050] In step S43, the coupling coefficient calculation unit 13 calculates the coupling coefficient c ij Output.

[0051] [GDS Calculation] Next, an example of the processing flow of the GDS calculation unit 14 will be described with reference to the flowchart in Fig. 7. This processing is the same as that in Non-Patent Document 1.

[0052] In step S51, the GDS calculation unit 14 calculates the propagation constants B(z0), B(z1), ..., B(z n ) and coupling coefficients C(z0), B(z1), ..., C(z n).

[0053] In step S52, the GDS calculation unit 14 calculates the sum of the propagation constant B and the coupling coefficient C for each step to obtain the propagation matrix U for the entire length of the optical fiber.

[0054]

[0055] In step S53, the GDS calculation unit 14 calculates the group delay operator F(ω) using the following equation.

[0056]

[0057] In step S54, the GDS calculation unit 14 calculates the eigenvalues ​​of F to obtain the group delay τ of the eigenmode i. i You can see that.

[0058]

[0059] In step S55, the GDS calculation unit 14 calculates the standard deviation σ of the group delay. τ Ask for.

[0060]

[0061] The standard deviation of the group delay is the GDS.

[0062] In step S55, the GDS calculation unit 14 outputs the GDS.

[0063] [Implementation Results] Next, the implementation results of the conventional technology of Non-Patent Document 1 and this embodiment will be compared.

[0064] A comparison of calculation times will be described with reference to Fig. 8. Fig. 8 shows the calculation times for matrix K calculation, propagation constant calculation, and coupling coefficient calculation for the conventional technique and the embodiment. The calculation times in Fig. 8 are the calculation times when processing is performed on a computer equipped with an Intel (registered trademark) Xeon (registered trademark) Silver 4214R CPU and 32 GB of memory.

[0065] The matrix K calculation is performed using 2d-FEM in the conventional technology, while the embodiment uses 1d-FEM. It can be seen that the calculation time for the matrix K calculation is significantly reduced in the embodiment. For the propagation constant calculation, the conventional technology uses the calculation results of 2d-FEM, while the embodiment performs matrix diagonalization. The embodiment calculates the propagation constant, but the calculation time is short. For the coupling coefficient calculation, the conventional technology calculates the overlap integral, while the embodiment calculates the inner product of the matrix. It can be seen that the calculation time is reduced in the embodiment. The GDS calculation is the same as in the conventional technology and the embodiment, so it is not shown.

[0066] As such, it can be seen that the calculation time for matrix K calculation and coupling coefficient calculation is significantly reduced.

[0067] A comparison of calculation results will be described with reference to Figure 9. Figure 9 shows the calculation results of GDS for the conventional technology and the embodiment. The calculation results in Figure 9 show the GDS calculated for four core spacings (20, 25, 30, and 35 μm), with the core spacing on the horizontal axis and the GDS on the vertical axis. The calculation conditions other than the core spacing are as follows: number of cores: 4, core arrangement: square, core structure: step-type, fiber length: 1 km, core radius: 1 μm, relative refractive index difference: 0.35%, twist rate: 0.5π rad / m, torsional dispersion: 0.1π rad / m, and bend radius: 140 mm.

[0068] It can be seen from FIG. 9 that the embodiment provides calculation results equivalent to those of the prior art.

[0069] The processing device 10 of this embodiment has been extended to perform the same calculation process as in Non-Patent Document 2 with any number of core modes, thereby enabling GDS simulation to be performed with the same accuracy as in Non-Patent Document 1 with the same calculation load as in Non-Patent Document 2.

[0070] As described above, the processing device 10 of this embodiment calculates the propagation constants and coupling coefficients of each eigenmode over the entire length of a space division multiplexing optical fiber having a plurality of eigenmodes. The processing device 10 includes a matrix K calculation unit 11 that calculates the propagation constant and inter-core coupling coefficient of each core of the optical fiber in a straight state and generates a matrix K in which the propagation constants of each core are used as diagonal terms and the core coupling coefficients are used as off-diagonal terms, a propagation constant calculation unit 12 that calculates a matrix B in which the propagation constants of each eigenmode are used as diagonal terms by diagonalizing the matrix K using a matrix M whose columns are made up of eigenvectors of the matrix K for each step width Δz of the optical fiber, and a calculation unit 13 that calculates a matrix B in which the propagation constants of each eigenmode are used as diagonal terms by calculating a matrix M and an inverse matrix M of the matrix M at the step width z+Δz. -1 The processing device 10 includes a coupling coefficient calculation unit 13 that generates a matrix C whose elements are coupling coefficients between eigenmodes based on the inner product of . The processing device 10 includes a GDS 14 calculation unit that calculates the group delay spread from the propagation constant of each eigenmode calculated over the entire length of the optical fiber and the coupling coefficient between each eigenmode. This makes it possible to calculate the group delay spread in a coupled multi-core optical fiber with any number of cores and any number of modes using low-load calculation processing.

[0071] 10 Processing device 11 Matrix K calculation unit 12 Propagation constant calculation unit 13 Coupling coefficient calculation unit 14 GDS calculation unit

Claims

1. A processing device for calculating the propagation constants and coupling coefficients of each eigenmode over the entire length of a space division multiplexing optical fiber having multiple eigenmodes, comprising: a matrix K calculation unit that calculates the propagation constant and inter-core coupling coefficient of each core of the optical fiber in a straight state and generates a matrix K in which the propagation constants of each core are diagonal terms and the inter-core coupling coefficients are off-diagonal terms; a propagation constant calculation unit that, for each infinitesimal width of the optical fiber, diagonalizes the matrix K using a matrix M in which each column is made up of the eigenvectors of the matrix K to generate a matrix B in which the propagation constants of each eigenmode are diagonal terms; and a calculation unit that calculates the inverse matrix M of the matrix M and the matrix M at the next infinitesimal width. -1 a coupling coefficient calculation unit that generates a matrix C having elements each representing a coupling coefficient between eigenmodes based on an inner product of 2. A processing device according to claim 1, comprising a group delay spread calculation unit that calculates the group delay spread from the propagation constant of each eigenmode and the coupling coefficient between the eigenmodes calculated over the entire length of the optical fiber.

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