Mode-dependent loss calculation device and mode-dependent loss calculation method for multimode fiber

Abstract

To recover a time axis before multiplexing for restoring the time axis of each impulse response to the time axis before multiplexing, in order to calculate a mode dependence loss of a multi-mode fiber even when each impulse response has peaks that are dispersed on the time axis, or even when a delay amount required for multiplexing on the time axis is not measured in advance.SOLUTION: In the present disclosure, in canceling the same delay amount given to each of a plurality of impulse responses, each of the plurality of impulse responses is shifted by the same time amount that "can be different" from the same delay amount. However, it is possible to calculate a mode dependence loss of a multi-mode fiber F, based on maximum and minimum singular values of a spectral transfer matrix, "independently" of a difference between the same delay amount and the same time amount.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to techniques for calculating mode-dependent loss in multimode fibers. [Background technology]

[0002] Coupled multicore fibers and few-mode fibers (collectively referred to as multimode fibers) are promising optical fibers for realizing future high-capacity optical communications. In space division multiplexing (SDM) transmission systems using multimode fibers, multiple-input multiple-output (MIMO) signal processing is used on the transmission side to restore the transmitted signal.

[0003] In SDM transmission systems using MIMO signal processing, the mode dependent loss (MDL) of multimode fiber is a factor limiting the transmission capacity. To ensure the quality of SDM transmission systems, a technique for calculating the mode dependent loss of multimode fiber is required. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] T. Arakawa et al,. “Simultaneous mode-by-mode impulse response measurement of multi-mode optical systems based on linear optical sampling”, Optics Express, Vol. 27, No. 9, 12070. [Non-patent document 2] S. Rommel et al., “Few-mode fiber, splice and SDM component characterization by spatially-diverse optical vector network analysis”, Optics Express, Vol. 25, No. 19, 22347. Summary of the Invention [Problem to be solved by the invention]

[0005] First, a general prior art will be described. Each impulse response between each input mode and each output mode of a multimode fiber is measured one by one. The time axes of each impulse response are aligned on the same time axis, and each impulse response is calculated as a matrix element of an impulse response matrix. Each impulse response is frequency converted into a spectral transfer function, and each spectral transfer function is calculated as a matrix element of the spectral transfer matrix. Since the singular values ​​of the spectral transfer matrix correspond to the loss of each mode, the mode-dependent loss of the multimode fiber is calculated based on the maximum and minimum singular values ​​of the spectral transfer matrix.

[0006] However, in general conventional techniques, each impulse response is measured one by one, which requires a large number of multimode fiber output signal receivers. Even if there is only one multimode fiber output signal receiver, it is necessary to switch the path by a switch or manually to measure each impulse response in order, which takes a long time to measure each impulse response.

[0007] Next, Non-Patent Documents 1 and 2 will be described. In particular, the differences from general prior art will be described. The impulse responses between each input mode and each output mode of a multimode fiber are multiplexed on the time axis and measured collectively. The time axis of each impulse response is restored to the time axis before multiplexing, and each impulse response is calculated as each matrix element of an impulse response matrix.

[0008] That is, in Non-Patent Documents 1 and 2, each impulse response is multiplexed on the time axis and measured collectively, so only one output signal receiving device for the multimode fiber is required, and the measurement time for each impulse response is short. However, in Non-Patent Documents 1 and 2, in order to restore the time axis of each impulse response to the time axis before multiplexing, the amount of delay given to each impulse response needs to be accurately understood and then eliminated, and the following method is adopted.

[0009] In Non-Patent Document 1, the amount of delay given to each impulse response is accurately determined by maximizing the cross-correlation between each impulse response, whereas in Non-Patent Document 2, the amount of delay given to each impulse response is accurately determined by measuring the amount of delay of an input signal multiplexer and an output signal multiplexer of a multimode fiber.

[0010] Therefore, in Non-Patent Document 1, there is no need to take the time and effort beforehand to measure the delay amounts of the input signal multiplexer and the output signal multiplexer of the multimode fiber. However, Non-Patent Document 1 can be applied when each impulse response has a clear peak on the time axis, such as in a weakly coupled multimode fiber, but cannot be applied when each impulse response has a peak that spreads on the time axis, such as in a coupled multimode fiber.

[0011] On the other hand, Non-Patent Document 2 can be applied when each impulse response has a clear peak on the time axis, as in the case of a weakly coupled multimode fiber, and can also be applied when each impulse response has a peak that spreads on the time axis, as in the case of a coupled multimode fiber. However, Non-Patent Document 2 requires prior work to measure the delay amounts of the input signal multiplexer and output signal multiplexer of the multimode fiber.

[0012] Therefore, in order to solve the above-mentioned problems, an object of the present disclosure is to restore the time axis of each impulse response to the time axis before multiplexing in order to calculate the mode-dependent loss of a multimode fiber, even when each impulse response has a peak that spreads on the time axis, and even when the delay amount required for multiplexing on the time axis is not measured in advance. [Means for solving the problem]

[0013] To solve the above problem, when canceling the same delay amount imparted to each of the multiple impulse responses, each of the multiple impulse responses is shifted by the same amount of time that may be different from the same delay amount. However, the mode-dependent loss of a multimode fiber can be calculated based on the maximum and minimum singular values ​​of the spectral transfer matrix without depending on the difference between the same delay amount and the same amount of time.

[0014] Specifically, the present disclosure provides an impulse response acquisition unit that multiplexes and collectively acquires impulse responses between input modes and output modes of a multimode fiber on a time axis; an impulse response matrix calculation unit that restores the time axis of each impulse response to the time axis before multiplexing, and calculates each impulse response as a matrix element of an impulse response matrix, with each input mode as a column or a row, and each output mode as a row or a column; a spectral transfer matrix calculation unit that frequency-converts each impulse response into a spectral transfer function, and calculates each spectral transfer function as a matrix element of a spectral transfer matrix, with each input mode as a column or a row, and each output mode as a row or a column; and a maximum singular value and a minimum singular value of the spectral transfer matrix. and a mode-dependent loss calculation unit that calculates the mode-dependent loss of the multimode fiber based on a minimum value of the spectral transfer matrix, wherein the impulse response matrix calculation unit, in order to cancel the same delay amount imparted to a plurality of impulse responses among all of the impulse responses, shifts the plurality of impulse responses by the same amount of time that may be different from the same amount of delay, and the mode-dependent loss calculation unit calculates the mode-dependent loss of the multimode fiber based on the maximum and minimum values ​​of the singular values ​​of the spectral transfer matrix, without depending on the amount of difference between the same amount of delay and the same amount of time.

[0015] The present disclosure also provides an impulse response acquisition procedure for multiplexing impulse responses between input modes and output modes of a multimode fiber on a time axis and collectively acquiring them; an impulse response matrix calculation procedure for restoring the time axis of each impulse response to the time axis before multiplexing, setting each input mode as a column or a row, each output mode as a row or a column, and calculating each impulse response as a matrix element of an impulse response matrix; a spectral transfer matrix calculation procedure for frequency-converting each impulse response into a spectral transfer function, setting each input mode as a column or a row, each output mode as a row or a column, and calculating each spectral transfer function as a matrix element of a spectral transfer matrix; and a spectral transfer matrix calculation procedure for calculating a maximum value and a minimum value of singular values ​​of the spectral transfer matrix. and a mode-dependent loss calculation procedure for calculating a mode-dependent loss of the multimode fiber based on a spectral transfer matrix, wherein the impulse response matrix calculation procedure shifts each of the plurality of impulse responses by a same amount of time that may be different from the same amount of delay in order to eliminate the same amount of delay imparted to each of the plurality of impulse responses among all of the impulse responses, and the mode-dependent loss calculation procedure calculates the mode-dependent loss of the multimode fiber based on a maximum value and a minimum value of singular values ​​of the spectral transfer matrix, without depending on an amount of difference between the same amount of delay and the same amount of time.

[0016] According to these configurations, the mode dependent loss of a multimode fiber can be accurately calculated simply by roughly restoring the time axis of each impulse response to the time axis before multiplexing.

[0017] The present disclosure also provides a mode dependent loss calculation device for a multimode fiber, wherein the impulse response matrix calculation unit, when arranging the impulse responses multiplexed on the time axis as matrix elements of the impulse response matrix, prevents the impulse responses included in different columns or rows of the impulse response matrix from overlapping on the time axis.

[0018] The present disclosure also provides a method for calculating a mode dependent loss of a multimode fiber, wherein the impulse response matrix calculation procedure is such that, when the impulse responses multiplexed on a time axis are arranged as matrix elements of the impulse response matrix, the impulse responses included in different columns or rows of the impulse response matrix are not superimposed on the time axis.

[0019] According to these configurations, the amount of time shift of each impulse response is not estimated to be far from the length of the extension line, so that the time axis of each impulse response can be roughly restored to the time axis before multiplexing, and the mode-dependent loss of the multimode fiber can be accurately calculated.

[0020] The present disclosure also provides a mode-dependent loss calculation device for a multimode fiber, wherein the impulse response matrix calculation unit shifts each of the plurality of impulse responses by the same amount of time estimated from the length of a delay line that imparts the same amount of delay.

[0021] The present disclosure also provides a method for calculating mode-dependent loss of a multimode fiber, wherein the impulse response matrix calculation step shifts each of the plurality of impulse responses by the same amount of time estimated from the length of a delay line that imparts the same amount of delay.

[0022] According to these configurations, by estimating the amount of time shift of each impulse response based on the length of the extension line, it is possible to roughly restore the time axis of each impulse response to the time axis before multiplexing, and then accurately calculate the mode-dependent loss of the multimode fiber. [Effects of the Invention]

[0023] In this way, in order to calculate the mode-dependent loss of a multimode fiber, the present disclosure can restore the time axis of each impulse response to the time axis before multiplexing, even when each impulse response has a peak that spreads on the time axis, or even when the delay amount required for multiplexing on the time axis is not measured in advance. [Brief explanation of the drawings]

[0024] [Figure 1] FIG. 1 is a diagram illustrating a configuration of a mode-dependent loss calculation system according to the present disclosure. [Figure 2] FIG. 10 is a diagram illustrating a procedure for a mode-dependent loss calculation process according to the present disclosure. [Figure 3] FIG. 10 is a diagram showing impulse responses multiplexed on the time axis of the present disclosure. [Figure 4] FIG. 1 is a diagram illustrating a recovery process of the time axis of each impulse response according to the prior art. [Figure 5] FIG. 1 is a diagram illustrating a recovery process of the time axis of each impulse response according to the prior art. [Figure 6] FIG. 10 is a diagram illustrating the preservation of singular values ​​with respect to the application of delay amounts according to the present disclosure. [Figure 7] FIG. 10 is a diagram illustrating a process for recovering the time axis of each impulse response according to the present disclosure. [Figure 8] 10A and 10B are diagrams illustrating a process for restoring the time axis of each impulse response in a comparative example. [Figure 9] FIG. 10 is a diagram illustrating a process for recovering the time axis of each impulse response according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0025]

[0023] The following embodiments of the present disclosure will be described with reference to the accompanying drawings. The embodiments described below are examples of implementation of the present disclosure, and the present disclosure is not limited to the following embodiments.

[0026] (Configuration of the mode-dependent loss calculation system disclosed herein) The configuration of the mode-dependent loss calculation system of the present disclosure is shown in Figure 1. The procedure for the mode-dependent loss calculation process of the present disclosure is shown in Figure 2. Each impulse response multiplexed on the time axis of the present disclosure is shown in Figure 3. The mode-dependent loss calculation system S includes a test light generating device 1, an input signal multiplexing device 2, an output signal multiplexing device 3, a reference light generating device 4, an output signal receiving device 5, and a mode-dependent loss calculation device 6. The mode-dependent loss calculation device 6 can be realized by installing the mode-dependent loss calculation program of Figure 2 on a computer. The mode-dependent loss calculation program of Figure 2 can be recorded on a recording medium or provided via a network.

[0027] The multimode fiber F has cores F1 and F2. The test light generating device 1 is disposed on the input side of the multimode fiber F and generates test pulse light at a repetition frequency f using a pulse light source 11. The reference light generating device 4 is disposed on the output side of the multimode fiber F and generates reference pulse light at a repetition frequency f-Δf using a pulse light source 41.

[0028] As in the first stage of Fig. 3, the input signal multiplexer 2 uses a demultiplexer 21, a delay line 22, and a polarizing beam splitter 23 to impart a delay amount τ3 to the y-polarized output relative to the x-polarized output. As in the second stage of Fig. 3, the input signal multiplexer 2 uses a demultiplexer 24 and a delay line 25 to impart a delay amount τ2 to the input to core F2 relative to the input to core F1.

[0029] The multimode fiber F generates mode coupling between each input mode and each output mode. Hereinafter, "1x" denotes an input or output mode in which an x-polarized wave propagates through the core F1, "1y" denotes an input or output mode in which a y-polarized wave propagates through the core F1, "2x" denotes an input or output mode in which an x-polarized wave propagates through the core F2, and "2y" denotes an input or output mode in which a y-polarized wave propagates through the core F2. Furthermore, "α'β'←αβ" (α, α'=1, 2, β, β'=x, y) denotes mode coupling between the input mode "αβ" and the output mode "α'β'".

[0030] 3, the output signal multiplexer 3 applies a delay τ1 to the output of core F2 compared to the output of core F1 using a delay line 31 and a multiplexer 32. The output signal receiving device 5 separates and extracts the x-polarized output using a polarizing beam splitter 51, a demultiplexer 52, an optical hybrid unit 53x, an optical detection unit 54x, and an A / D conversion unit 55. The output signal receiving device 5 separates and extracts the y-polarized output using a polarizing beam splitter 51, a demultiplexer 52, an optical hybrid unit 53y, an optical detection unit 54y, and an A / D conversion unit 55.

[0031] In the fourth row of Fig. 3, the impulse responses α'β'←αβ between the input mode αβ and the output mode α'β' can be multiplexed on the time axis and acquired collectively as follows: Here, each impulse response α'β'←αβ has a peak that spreads on the time axis. Delay amount added to impulse response 1x←1x, 1y←1x=0 Delay amount added to impulse response 2x←1x, 2y←1x = τ1 Delay amount given to impulse response 1x←2x, 1y←2x = τ2 Delay amount given to impulse response 2x←2x, 2y←2x=τ2+τ1 Delay amount added to impulse response 1x←1y, 1y←1y=τ3 Delay amount added to impulse response 2x←1y, 2y←1y = τ3 + τ1 Delay amount added to impulse response 1x←2y, 1y←2y=τ3+τ2 Delay amount added to impulse response 2x←2y, 2y←2y=τ3+τ2+τ1

[0032] The mode-dependent loss calculation device 6 executes the mode-dependent loss calculation process shown in Fig. 2. First, the time axis restoration process of each impulse response in the conventional technology will be described. Next, the time axis restoration process of each impulse response in the present disclosure will be described. In particular, the differences from the conventional technology will be described.

[0033] (Prior art time axis recovery process for each impulse response) 4 and 5 show the time axis recovery process of each impulse response in the prior art. The impulse response acquisition unit 61 multiplexes the impulse responses between each input mode and each output mode of the multimode fiber F on the time axis and acquires them all at once (step S1).

[0034] The impulse response matrix calculation unit 62 restores the time axis of each impulse response to the time axis before multiplexing, and calculates each impulse response as each matrix element of the impulse response matrix, with each input mode as each column and each output mode as each row (step S2). Here, in order to eliminate the same delay amount imparted to each of multiple impulse responses among all the individual impulse responses, the impulse response matrix calculation unit 62 shifts each of the multiple impulse responses by the same amount of time equal to the same delay amount (which can be measured by the methods of Non-Patent Documents 1 and 2).

[0035] In Figure 4, impulse responses 2x←1x and 2y←1x are shifted by a time amount τ1 equal to the delay τ1 and are included in time window W1 along with impulse responses 1x←1x and 1y←1x. Impulse responses 2x←2x and 2y←2x are shifted by a time amount τ1 equal to the delay τ1 and are included in time window W2 along with impulse responses 1x←2x and 1y←2x. Impulse responses 2x←1y and 2y←1y are shifted by a time amount τ1 equal to the delay τ1 and are included in time window W3 along with impulse responses 1x←1y and 1y←1y. Impulse responses 2x←2y and 2y←2y are shifted by a time amount τ1 equal to the delay τ1 and are included in time window W4 along with impulse responses 1x←2y and 1y←2y.

[0036] 5, the impulse responses 1x←2x, 1y←2x, 2x←2x, and 2y←2x included in time window W2 are shifted by a time amount τ2 equal to the delay τ2, and are included in time window W1 together with the impulse responses 1x←1x, 1y←1x, 2x←1x, and 2y←1x. The impulse responses 1x←2y, 1y←2y, 2x←2y, and 2y←2y included in time window W4 are shifted by a time amount τ2 equal to the delay τ2, and are included in time window W3 together with the impulse responses 1x←1y, 1y←1y, 2x←1y, and 2y←1y.

[0037] 5, the impulse responses 1x←1y, 1y←1y, 2x←1y, 2y←1y, 1x←2y, 1y←2y, 2x←2y, and 2y←2y included in time window W3 are shifted by a time amount τ3 equal to the delay τ3, and are included in time window W1 together with impulse responses 1x←1x, 1y←1x, 2x←1x, 2y←1x, 1x←2x, 1y←2x, 2x←2x, and 2y←2x. In this way, the time axis of each impulse response is restored.

[0038] The spectral transfer matrix calculation unit 63 frequency-converts each impulse response into a spectral transfer function, and calculates each spectral transfer function as each matrix element of the spectral transfer matrix, with each input mode as each column and each output mode as each row (step S3).

[0039] The mode-dependent loss calculation unit 64 calculates the mode-dependent loss of the multimode fiber F based on the maximum and minimum singular values ​​of the spectral transfer matrix (step S4). Here, the mode-dependent loss calculation unit 64 calculates the spectral transfer matrix H as shown in the second side of Equation 1, calculates the singular values ​​λ1 to λ4 of the spectral transfer matrix H as shown in the third side of Equation 1 (P and Q are arrangement matrices of singular value vectors), and calculates the mode-dependent loss of the multimode fiber F as MDL=λ max 2 / λ min 2 Calculate as follows (λ max , λ min are the maximum and minimum values ​​of λ1 to λ4.

number

[0040] (Time axis recovery process of each impulse response according to the present disclosure) The preservation of singular values ​​with respect to the addition of delay amounts according to the present disclosure is shown in Fig. 6. In the upper and lower left columns of Fig. 6, the delay amount τ is not added by the delay line D to any of the input and output modes among the input modes 1x, 1y, 2x, and 2y and the output modes 1x, 1y, 2x, and 2y.

[0041] In the upper right column of Fig. 6, among the input modes 1x, 1y, 2x, 2y and the output modes 1x, 1y, 2x, 2y, a delay amount τ due to the delay line D is applied only to the output mode 1x. The spectral transfer matrix H' taking into consideration both the multimode fiber F and the delay line D is expressed as in Equation 2. Here, the spectral transfer matrix H' in Equation 2 has e in only the first row compared to the spectral transfer matrix H in Equation 1. -jωτ (ω is each frequency.)

number

[0042] That is, the spectral transfer matrix H' in Equation 2 is e -jωτ and 1 (the absolute values ​​of both are equal to 1) are multiplied from the left side. Therefore, the singular values ​​λ1 to λ4 of the spectral transfer matrix H' in Formula 2 are equal to the singular values ​​λ1 to λ4 of the spectral transfer matrix H in Formula 1. However, the arrangement matrix P' of the singular value vectors in Formula 2 is different from the arrangement matrix P of the singular value vectors in Formula 1. The mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 2 is equal to the mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 1.

[0043] In the lower right column of Fig. 6, among the input modes 1x, 1y, 2x, 2y and the output modes 1x, 1y, 2x, 2y, a delay amount τ due to the delay line D is applied only to the input mode 1x. The spectral transfer matrix H' taking into consideration both the multimode fiber F and the delay line D is expressed as in Equation 3. Here, the spectral transfer matrix H' in Equation 3 has e in only the first column compared to the spectral transfer matrix H in Equation 1. -jωτ (ω is each frequency.)

number

[0044] That is, the spectral transfer matrix H' in Equation 3 is e -jωτ and 1 (the absolute values ​​of both are equal to 1) are multiplied from the right side. Therefore, the singular values ​​λ1 to λ4 of the spectral transfer matrix H' in Formula 3 are equal to the singular values ​​λ1 to λ4 of the spectral transfer matrix H in Formula 1. However, the arrangement matrix Q' of the singular value vectors in Formula 3 is different from the arrangement matrix Q of the singular value vectors in Formula 1. The mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 3 is equal to the mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 1.

[0045] 7 and 9 show the process of restoring the time axis of each impulse response according to the present disclosure. The impulse response acquisition unit 61 multiplexes the impulse responses between each input mode and each output mode of the multimode fiber F on the time axis and acquires them all at once (step S1).

[0046] The impulse response matrix calculation unit 62 restores the time axis of each impulse response to the time axis before multiplexing, and calculates each impulse response as a matrix element of an impulse response matrix, with each input mode as a column and each output mode as a row (step S2). Here, to eliminate the same delay amount imparted to multiple impulse responses among all the impulse responses, the impulse response matrix calculation unit 62 shifts each of the multiple impulse responses by the same amount of time, which may differ from the same delay amount (measurement is not required in the methods of Non-Patent Documents 1 and 2) (step S2-1). For example, the impulse response matrix calculation unit 62 shifts each of the multiple impulse responses by the same amount of time estimated from the length of a delay line imparting the same delay amount.

[0047] In Figure 7, impulse responses 2x←1x and 2y←1x are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in time window W1 along with impulse responses 1x←1x and 1y←1x. Impulse responses 2x←2x and 2y←2x are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in time window W2 along with impulse responses 1x←2x and 1y←2x. Impulse responses 2x←1y and 2y←1y are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in time window W3 along with impulse responses 1x←1y and 1y←1y. Impulse responses 2x←2y and 2y←2y are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in time window W4 along with impulse responses 1x←2y and 1y←2y.

[0048] 9, the impulse responses 1x←2x, 1y←2x, 2x←2x, and 2y←2x included in time window W2 are shifted by a time amount τ2', which is different from the delay amount τ2, and are included in time window W1 together with the impulse responses 1x←1x, 1y←1x, 2x←1x, and 2y←1x. The impulse responses 1x←2y, 1y←2y, 2x←2y, and 2y←2y included in time window W4 are shifted by a time amount τ2', which is different from the delay amount τ2, and are included in time window W3 together with the impulse responses 1x←1y, 1y←1y, 2x←1y, and 2y←1y.

[0049] 9, the impulse responses 1x←1y, 1y←1y, 2x←1y, 2y←1y, 1x←2y, 1y←2y, 2x←2y, and 2y←2y included in time window W3 are shifted by a time amount τ3', which is different from the delay amount τ3, and are included in time window W1 together with impulse responses 1x←1x, 1y←1x, 2x←1x, 2y←1x, 1x←2x, 1y←2x, 2x←2x, and 2y←2x. In this way, the time axis of each impulse response is restored.

[0050] However, when arranging each impulse response multiplexed on the time axis as each matrix element of the impulse response matrix, the impulse response matrix calculation unit 62 does not superimpose each impulse response included in a different column of the impulse response matrix on the time axis (step S2-2).

[0051] FIG. 8 shows the process of restoring the time axis of each impulse response in the comparative example. In FIG. 8, impulse responses 2x←1x and 2y←1x are shifted by a time amount τ1' that is different from the delay amount τ1, and unlike impulse responses 1x←1x and 1y←1x, they are not included in the time window W1. Impulse responses 2x←2x and 2y←2x are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in the time window W1 together with impulse responses 1x←1x and 1y←1x. Impulse responses 2x←1y and 2y←1y are shifted by a time amount τ1' that is different from the delay amount τ1, and are not included in the time window W3 together with impulse responses 1x←1y and 1y←1y. Impulse responses 2x←2y and 2y←2y are shifted by a time amount τ1' that is different from the delay amount τ1, and are included in the time window W3 together with impulse responses 1x←1y and 1y←1y. Then, even if the shifts of time amounts τ2' and τ3' are performed, the time axis of each impulse response is not restored.

[0052] The spectral transfer matrix calculation unit 63 frequency-converts each impulse response into a spectral transfer function, and calculates each spectral transfer function as each matrix element of the spectral transfer matrix, with each input mode as each column and each output mode as each row (step S3).

[0053] The mode-dependent loss calculation unit 64 calculates the mode-dependent loss of the multimode fiber F based on the maximum and minimum singular values ​​of the spectral transfer matrix (step S4). Here, the mode-dependent loss calculation unit 64 calculates the mode-dependent loss of the multimode fiber F based on the maximum and minimum singular values ​​of the spectral transfer matrix, without depending on the difference between the same delay amount and the same time amount (step S4-1).

[0054] That is, the mode-dependent loss calculation unit 64 calculates the spectral transfer matrix H′ as shown in the second side of Equation 4, calculates the singular values ​​λ1 to λ4 of the spectral transfer matrix H′ as shown in the third side of Equation 4 (P′ and Q′ are arrangement matrices of singular value vectors), and calculates the mode-dependent loss of the multimode fiber F as MDL=λ max 2 / λ min 2 Calculate as follows (λ max , λ min are the maximum and minimum values ​​of λ1 to λ4.) The diagonal elements of the diagonal matrix on the second side of Equation 4 will be explained below.

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[0055] In FIG. 7, the delay amount τ1' (≠τ1) is eliminated only for the output modes 2x and 2y among the input modes 1x, 1y, 2x, and 2y and the output modes 1x, 1y, 2x, and 2y, but the delay amount τ1-τ1' (≠0) is maintained. Therefore, the spectral transfer matrix H' of Equation 4 is obtained by subtracting e from the spectral transfer matrix H of Equation 1. -jω(τ1-τ1’) and 1 (the absolute value of both is equal to 1) are multiplied from the left.

[0056] In the second stage of Fig. 9, the delay amount τ2' (≠τ2) is eliminated only for the input modes 2x and 2y among the input modes 1x, 1y, 2x, and 2y and the output modes 1x, 1y, 2x, and 2y, but the delay amount τ2-τ2' (≠0) is maintained. Therefore, the spectral transfer matrix H' of Equation 4 is obtained by subtracting e from the spectral transfer matrix H of Equation 1. -jω(τ2-τ2’)and 1 (the absolute value of both is equal to 1) are multiplied from the right.

[0057] In the third row of Fig. 9, the delay amount τ3' (≠τ3) is eliminated only for the input modes 1y and 2y among the input modes 1x, 1y, 2x, and 2y and the output modes 1x, 1y, 2x, and 2y, but the delay amount τ3-τ3' (≠0) is maintained. Therefore, the spectral transfer matrix H' of Equation 4 is obtained by subtracting e from the spectral transfer matrix H of Equation 1. -jω(τ3-τ3’) and 1 (the absolute value of both is equal to 1) are multiplied from the right.

[0058] Therefore, the singular values ​​λ1 to λ4 of the spectral transfer matrix H' in Formula 4 are equal to the singular values ​​λ1 to λ4 of the spectral transfer matrix H in Formula 1. However, the arrangement matrices P' and Q' of the singular value vectors in Formula 4 are different from the arrangement matrices P and Q of the singular value vectors in Formula 1. The mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 4 is equal to the mode dependent loss MDL of the multimode fiber F based on the singular values ​​λ1 to λ4 of Formula 1.

[0059] In this way, when restoring the time axis of each impulse response to the time axis before multiplexing in order to calculate the mode-dependent loss of the multimode fiber F, the time axis before multiplexing can be restored even when each impulse response has a peak that spreads on the time axis (see Figures 3, 4, 7, and 8) and even when the delay amount required for multiplexing on the time axis is not measured in advance.

[0060] In other words, the mode dependent loss of the multimode fiber F can be accurately calculated simply by roughly restoring the time axis of each impulse response to the time axis before multiplexing.

[0061] Then, by not estimating the time amount of the shift of each impulse response so far as the length of the extension line, the time axis of each impulse response can be roughly restored to the time axis before multiplexing, and the mode-dependent loss of the multimode fiber F can be accurately calculated.

[0062] Furthermore, by estimating the amount of time shift of each impulse response based on the length of the extension line, the time axis of each impulse response can be roughly restored to the time axis before multiplexing, and the mode-dependent loss of the multimode fiber F can be accurately calculated. [Industrial Applicability]

[0063] The multimode fiber mode dependent loss calculation device and mode dependent loss calculation method of the present disclosure can calculate the mode dependent loss of a multimode fiber in an SDM transmission system or the like that uses a multimode fiber and MIMO signal processing. [Explanation of symbols]

[0064] S: Mode-dependent loss calculation system F: Multimode fiber F1, F2: Core W1, W2, W3, W4: Time windows D: Delay line 1: Test light generating device 2: Input signal multiplexer 3: Output signal multiplexer 4:Reference light generation device 5: Output signal receiving device 6: Mode-dependent loss calculation device 11: Pulsed light source 21: Duplexer 22: Delay line 23: Polarizing beam splitter 24: Duplexer 25: Delay line 31: Delay line 32: Multiplexer 41: Pulsed light source 51: Polarizing beam splitter 52: Duplexer 53x, 53y: Optical hybrid section 54x, 54y: Light detection unit 55: A / D conversion section 61: Impulse response acquisition unit 62: Impulse response matrix calculation unit 63: Spectral transfer matrix calculation unit 64: Mode dependent loss calculation section

Claims

1. an impulse response acquisition unit that multiplexes impulse responses between each input mode and each output mode of the multimode fiber on a time axis and acquires them all at once; an impulse response matrix calculation unit that restores a time axis of each of the impulse responses to a time axis before multiplexing, sets each of the input modes as columns or rows, sets each of the output modes as rows or columns, and calculates each of the impulse responses as matrix elements of an impulse response matrix; a spectral transfer matrix calculation unit that converts the impulse responses into spectral transfer functions by frequency conversion, defines the input modes as columns or rows, defines the output modes as rows or columns, and calculates the spectral transfer functions as matrix elements of a spectral transfer matrix; a mode-dependent loss calculation unit that calculates a mode-dependent loss of the multimode fiber based on the maximum and minimum singular values ​​of the spectral transfer matrix; A mode-dependent loss calculation apparatus for a multimode fiber, comprising: the impulse response matrix calculation unit, when canceling the delay amounts assigned to each of the plurality of impulse responses among all the impulse responses, shifts each of the plurality of impulse responses by a time amount that may be different from the delay amount, includes each of the plurality of impulse responses in a predetermined time window set on a time axis, which corresponds to each column or each row of the impulse response matrix, and arranges the each of the impulse responses multiplexed on the time axis as each matrix element of the impulse response matrix, and when arranging the each of the impulse responses multiplexed on the time axis as each matrix element of the impulse response matrix, does not include each of the impulse responses included in a different column or row of the impulse response matrix in the time window; the mode-dependent loss calculation unit calculates the mode-dependent loss of the multimode fiber based on the maximum and minimum singular values ​​of the spectral transfer matrix obtained by singular value decomposition, without depending on the difference between the delay amount and the time amount. A multimode fiber mode-dependent loss calculation device comprising:

2. 2. The multimode fiber mode dependent loss calculation device according to claim 1, wherein the impulse response matrix calculation unit shifts each of the plurality of impulse responses by the time amount estimated from the length of a delay line that imparts the delay amount.

3. an impulse response acquisition procedure for multiplexing impulse responses between each input mode and each output mode of the multimode fiber on a time axis and acquiring them all at once; an impulse response matrix calculation step of recovering the time axis of each of the impulse responses to the time axis before multiplexing, setting each of the input modes as each column or each row, setting each of the output modes as each row or each column, and calculating each of the impulse responses as each matrix element of an impulse response matrix; a spectral transfer matrix calculation step of frequency-transforming each of the impulse responses into a spectral transfer function, and calculating each of the spectral transfer functions as matrix elements of a spectral transfer matrix, with each of the input modes being columns or rows, and each of the output modes being rows or columns; a mode-dependent loss calculation step of calculating a mode-dependent loss of the multimode fiber based on the maximum and minimum singular values ​​of the spectral transfer matrix; 1. A method for calculating mode dependent loss in a multimode fiber comprising, in order: the impulse response matrix calculation step, when canceling delay amounts assigned to each of a plurality of impulse responses among all the impulse responses, shifts each of the plurality of impulse responses by a time amount that may be different from the delay amount, includes each of the plurality of impulse responses in a predetermined time window set on a time axis, which corresponds to each column or each row of the impulse response matrix, and arranges the impulse responses multiplexed on the time axis as each matrix element of the impulse response matrix, and when arranging the impulse responses multiplexed on the time axis as each matrix element of the impulse response matrix, does not include each of the impulse responses included in a different column or row of the impulse response matrix in the time window; the mode-dependent loss calculation step calculates the mode-dependent loss of the multimode fiber based on the maximum and minimum singular values ​​of the spectral transfer matrix obtained by singular value decomposition, without depending on the difference between the delay amount and the time amount. A method for calculating mode-dependent loss of a multimode fiber, comprising:

4. 4. The method for calculating mode-dependent loss of a multimode fiber according to claim 3, wherein the step of calculating the impulse response matrix includes shifting each of the plurality of impulse responses by the time amount estimated from the length of a delay line that imparts the delay amount.

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