EQUIPMENT AND METHODS FOR EVALUATING THE CHARACTERISTICS OF SPATIAL MULTIPLEX OPTICAL TRANSMISSION LINES

Abstract

A backscattered light intensity measurement unit is presented that acquires a combination of backscattered light intensities of individual transmittable spatial channels of an optical fiber obtained when test light, for the respective transmittable spatial channels of the optical fiber, is incident on the optical fiber, and a transfer matrix calculation unit that calculates a transfer matrix for each section of the optical fiber in order from a side closer to an incident end of the test light, in which characteristics in a section of the optical fiber are evaluated by using the transfer matrix.

Description

TECHNICAL FIELD

The present disclosure relates to a technique of evaluating characteristics of a spatial multiplex optical transmission line.

BACKGROUND ART

As a technique for expanding a signal transmission capacity per optical fiber, there is a spatial multiplex optical transmission technique using a multi-core optical fiber or a multi-mode optical fiber. In spatial multiplex optical transmission, signals are spatially multiplexed in a plurality of spatial channels (cores or modes) in one optical fiber to increase transmission capacity. However, it is known that crosstalk of signal light or an optical loss difference between spatial channels lead to deterioration in signal quality or complication of a signal restoration process. Thus, in order to ensure desired transmission performance in a spatial multiplex optical transmission line, it is desirable that evaluation of characteristics such as crosstalk and an optical loss can be measured in a distributed manner in a longitudinal direction of an optical fiber.

As a technique capable of measuring a distribution of the crosstalk or an optical loss of a spatial multiplex optical transmission line, there is a method using optical time-domain reflectometry (Non Patent Literature 1). However, since the conventional optical time-domain reflection measurement method is based on the premise that mode coupling or an optical loss is uniform in a longitudinal direction of an optical fiber, local variation of the mode coupling or the optical loss in a transmission line causes a problem of impossibility of accurate evaluation.

CITATION LIST

Non Patent Literature

• Non Patent Literature 1: F. Liu, G. Hu, C. Song, W. Chen, C. Chen, and J. Chen, “Simultaneous measurement of mode dependent loss and mode coupling in few mode fibers by analyzing the Rayleigh backscattering amplitudes, “Applied Optics, Vol. 57, No. 30, pp. 8894-8902, 2018.

SUMMARY OF INVENTION

Technical Problem

The present disclosure has been made in view of the above circumstances, and an object of the present disclosure is to provide a method capable of performing distribution measurement of evaluation of characteristics for each spatial channel in a longitudinal direction in a spatial multiplex optical transmission line in which mode coupling or an optical loss changes in the longitudinal direction.

Solution to Problem

The present disclosure solves the above problem by calculating a transfer matrix representing evaluation of characteristics, such as crosstalk and an optical loss, for each minute distance section by using a backscattered light intensity distribution waveform of a plurality of spatial channels obtained by light reflection measurement means such as an OTDR.

According to the present disclosure, characteristics such as crosstalk and optical loss can be evaluated even in a spatial multiplex optical transmission line in which mode coupling between spatial channels or an optical loss is non-uniform.

According to the present disclosure, there is provided an apparatus including:

• • a backscattered light intensity measurement unit that acquires a combination of backscattered light intensities of individual transmittable spatial channels of an optical fiber obtained when test light, for the individual transmittable spatial channels of the optical fiber, is incident on the optical fiber; and
  • a transfer matrix calculation unit that calculates a transfer matrix for each section of the optical fiber in order from a side closer to an incident end of the test light, in which
  • characteristics in a section of the optical fiber are evaluated by using the transfer matrix.

According to the present disclosure, there is provided a method including the following sequence of steps:

• • a backscattered light intensity distribution measurement step of acquiring a combination of backscattered light intensities of individual transmittable spatial channels of an optical fiber obtained when test light, for the individual transmittable spatial channels of the optical fiber, is incident on the optical fiber;
  • a transfer matrix calculation step of calculating a transfer matrix for each section of the optical fiber in order from a side closer to an incident end of the test light; and
  • an evaluation step of evaluating characteristics in a section of the optical fiber by using the transfer matrix.

Advantageous Effects of Invention

According to the present disclosure, it is possible to obtain evaluation of characteristics such as crosstalk and an optical loss even in a spatial multiplex optical transmission line in which mode coupling between spatial channels or an optical loss is non-uniform.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a flowchart illustrating a flow of measurement in an embodiment of the present disclosure.

FIG. 2 is a block diagram illustrating an example of an apparatus configuration used in the embodiment of the present disclosure.

DESCRIPTION OF EMBODIMENTS

Hereinafter, an embodiment of the present disclosure will be described in detail with reference to the drawings. The present disclosure is not limited to the embodiment described below. Such an embodiment is merely an example, and the present disclosure can be carried out in forms with various modifications and improvements based on the knowledge of those skilled in the art. Constituents having the same reference signs in the present specification and the drawings indicate the same constituents.

(Optical Time-Domain Reflectometry)

In optical time-domain reflectometry (hereinafter, OTDR), pulsed test light is incident on a spatial channel to obtain a backscattered light intensity distribution waveform for a spatial channel. By changing a combination of a spatial channel on which the test light is incident and a spatial channel for detecting backscattered light, M² backscattered light intensity distribution waveforms can be obtained in a fiber having the number of spatial channels M. Assuming that a mode coupling coefficient and an optical loss coefficient for each spatial channel are uniform in a fiber longitudinal direction, the backscattered light intensities p_bs,i(z) and p_bs,j(z) detected from i-th and j-th spatial channels, in a case where the test light is incident on the i-th spatial channel, are expressed by the following equations, respectively.

$\begin{array}{cc}\left[\mathrm{Math}.1\right]& \\ p_{\mathrm{bs},i}\left(z\right)=\frac{p_0}{2}S\frac{v_g\tau }{2}{e}^{-2\mathrm{az}}\left(1+e^{-4h_{i,j}z}+\frac{K-{\mathrm{Ke}}^{-4h_{i,j}z}}{2}\right)& \left(1\right)\end{array}$ $\begin{array}{cc}\left[\mathrm{Math}.2\right]& \\ p_{\mathrm{bs},i}\left(z\right)=\frac{p_0}{2}S\frac{v_g\tau }{2}{e}^{-2\mathrm{az}}\left(1+e^{-4h_{i,j}z}+\frac{K+{\mathrm{Ke}}^{-2h_{i,j}z}+{\mathrm{Ke}}^{-4h_{i,j}z}}{2}\right)& \left(2\right)\end{array}$

Here, z is a distance from the test light incident end, p₀ is incident light power, a is an optical loss coefficient, v_g is a light group velocity, τ is a pulse width of the test light, and S and K are constants. h_i,j is a mode coupling coefficient between the i-th and j-th spatial channels, and is obtained from a slope of mode coupling efficiency η_i,j(z) obtained from the following equation with respect to the distance z.

$\begin{array}{cc}\left[\mathrm{Math}.3\right]& \\ {\eta }_{i,j}\left(z\right)=\frac{p_{\mathrm{bs},j}}{p_{\mathrm{bs},i}}\cong 2h_{i,j}z+K& \left(3\right)\end{array}$

The crosstalk XT_i,j(z) between the i-th and j-th spatial channels at the distance z is obtained from the following equation by using Equation (3).

[Math. 4]

XT _i,j(z)=tan h(h_i,jz)  (4)

The optical loss coefficient α of the i-th spatial channel is obtained from the distance dependence of p_bs,i by assigning h_i,j to Equation (1).

(Outline of Present Disclosure)

The present disclosure solves the above problem by calculating a transfer matrix, representing crosstalk and an optical loss, for each minute distance section by using a backscattered light intensity distribution waveform of a plurality of spatial channels obtained by light reflection measurement means such as OTDR. The transfer matrix T(z_k-1, z_k) in the distance section z_k-1≤z<z_k (where k is a natural number) is obtained from the simultaneous equation of the following equation. Here, z₀ is in the vicinity of the test light incident end, and it is assumed that mode coupling and an optical loss at 0≤z<z₀ are negligible.

[Math. 5]

P _out(z_k)=T(z₀,z₁) . . . T(z_k-2,z_k-1)P_out(z₀)T(z_k-1,z_k)T(z_k-2,z_k-1) . . . T(z₀,z₁)  (5)

Here, P_out(z_k) is a matrix of the backscattered light intensity obtained with respect to the distance z_k point, and the (i,j) component (where i and j are natural numbers.) of the matrix P_out(z_k) represents the backscattered light intensity detected from the i-th spatial channel when the test light is incident on the j-th spatial channel. The (i,i) component of the matrix T(z_k-1, z_k) represents the optical loss of the i-th spatial channel in the section z_k-1≤z<z_k, and the (i,j) component (where i≠j) represents the mode coupling between the i-th spatial channel and the j-th spatial channel. T(z₀, z₁) . . . T(z_k-2, z_k-1) T(z_k-1, z_k) and T(z_k-1, z_k) T(z_k-2, z_k-1) . . . T(z₀, z₁) multiplied from the left and right of P_out(z₀) on the right side, respectively, are products of k matrices each. That is, in the case of k=1 and k=2, Equation (5) is as follows.

(In case of k=1)

[Math. 6]

P _out(z₁)=T(z₀,z₁)P_out(z₀)T(z₀,z₁)  (6)

[Math. 7]

P _out(z₂)=T(z₀,z₁)T(z₁,z₂)P_out(z₀)T(z₁,z₂)T(z₀,z₁)  (7)

T(z₀, z₁) satisfying Equation (6) is first obtained, T(z₀, z₁) is then assigned to Equation (7) to obtain T(z₁, z₂), and thereafter, T(z₂, z₃), T(z₃, z₄), . . . are sequentially obtained from Equation (5) for each case of k=3, 4, . . . , and thus T(z_k-1, z_k) can be obtained for any k. By using T(z_k-1, z_k), the transfer matrix T(z_a, z_b) in a section z_a≤z<z_b (where a and b are non-negative integers) is obtained from the following equation.

[Math. 8]

T(z_a,z_b)=T(z_b-1,z_b)T(z_b-2,z_b-1) . . . T(z_a+1,z_a+2)T(z_a,z_a+1)  (8)

The crosstalk XT_i,j(z_a, z_b) from the j-th spatial channel to the i-th spatial channel in the section z_a≤z<z_b is obtained from the following equation by using the (i, j) component η_i,j(z_a, z_b) that is a non-diagonal component of T(z_a, z_b)

$\begin{array}{cc}\left[\mathrm{Math}.9\right]& \\ {\mathrm{XT}}_{i,j}\left(z_a,z_b\right)=-10\log \frac{{\eta }_{i,j}\left(z_a,z_b\right)}{{\eta }_{i,i}\left(z_a,z_b\right)}\left[\mathrm{dB}\right]& \left(9\right)\end{array}$

The average crosstalk XT_i(z_a, z_b) to the i-th spatial channel in the same distance section is obtained from the following equation.

$\begin{array}{cc}\left[\mathrm{Math}.10\right]& \\ {\mathrm{XT}}_i\left(z_a,z_b\right)=-10\log \frac{{\sum }_{j\ne i}{\eta }_{i,j}\left(z_a,z_b\right)}{{\eta }_{i,i}\left(z_a,z_b\right)}\left[\mathrm{dB}\right]& \left(10\right)\end{array}$

The optical loss L_i(z_a, z_b) of the i-th spatial channel in the same distance section is obtained from the following equation by using the diagonal component of T(z_a, z_b).

[Math. 11]

L _i(z_a,z_b)=−10 log η_i,i(z_a,z_b)[dB]  (11)

From the above description, the matrix T(z_a, z_b) is obtained by using Equations (5) to (8), and the (i,j) component η_i,j(z_a, z_b) of T(z_a, z_b) is assigned to Equations (9) to (11), and thus the crosstalk and the optical loss in a section z_a≤z<z_b are obtained. The matrix calculation in the present disclosure is calculation for power (non-negative real number) instead of field (complex number), and elements of each matrix in the present disclosure are non-negative real numbers.

An embodiment of the present disclosure will be described with reference to the accompanying drawings. Here, as an example, a case where OTDR is used as light reflection measurement means and a two-mode single-core optical fiber is used as a measurement target optical fiber will be described. The present disclosure is not limited thereto, and other means such as optical frequency-domain reflectometry may be used as light reflection measurement means, and a multimode optical fiber or a multicore optical fiber may be used as a measurement target optical fiber. When a multicore optical fiber is used as a measurement target optical fiber, the following mode selection means may be replaced with a fan-in/fan-out device or the like.

FIG. 1 is a flowchart illustrating an example of an embodiment of a characteristic evaluation method according to the present disclosure. The characteristic evaluation method according to the present disclosure sequentially includes a backscattered light intensity distribution measurement step S10, a transfer matrix calculation step S20, and a crosstalk and optical loss calculation step S30. In the present embodiment, first, in the backscattered light intensity distribution measurement step S10, a backscattered light intensity distribution waveform in a certain propagation mode is obtained by using the light reflection measurement means.

FIG. 2 is an example of an apparatus configuration used in the present embodiment. A characteristic evaluation apparatus 91 of the present embodiment includes a pulsed light source 11, circulators 12 and 13, mode selection means 14, light receivers 15 and 16, an A/D converter 17, and an arithmetic processing device 18. These configurations function as a backscattered light intensity measurement unit. The arithmetic processing device 18 functions as a transfer matrix calculation unit, a crosstalk calculation unit, and an optical loss calculation unit. In the configuration in FIG. 2, except for a measurement target optical fiber 92, optical fibers are single-mode single-core optical fibers.

The pulsed light source 11 is used as a light source, and pulsed test light is incident on the measurement target optical fiber 92 in a propagation mode by the mode selection means 14. The light receivers 15 and 16 are connected to ports corresponding to the respective propagation modes of the mode selection means, and the backscattered light intensities in the plurality of propagation modes are individually converted into electrical signals by the light receivers. In this case, backscattered light received after the time t has elapsed from incidence of the test light corresponds to backscattered light from a distance z=ct/2 (where c is the group velocity of light in the measurement target optical fiber 92) from the incident end. The backscattered light intensity signal converted into the electrical signal is converted into a digital signal by the A/D converter 17 and transferred to the arithmetic processing device 18.

(Backscattered Light Intensity Distribution Measurement Step S10)

For the measurement target optical fiber 92 having the number of spatial channels M, the characteristic evaluation apparatus 91 selects a spatial channel j to which the test light is incident and a spatial channel i for measuring a backscattered light intensity (step S11). Here, i, j, and M are natural numbers.

Next, the characteristic evaluation apparatus 91 makes the test light to be incident on an i-th spatial channel, and measures the backscattered light intensity of a j-th spatial channel as a function of the distance z (S12).

The characteristic evaluation apparatus 91 determines whether backscattered light intensities have been measured for all (i,j) combinations of 1≤i≤M and 1≤j≤M (S13) and repeatedly performs steps S11 and S12 until the backscattered light intensities for all (i,j) combinations are measured.

Consequently, the characteristic evaluation apparatus 91 acquires a combination of backscattered light intensities of individual transmittable spatial channels of the measurement target optical fiber 92 obtained when pieces of test light, for the individual transmittable spatial channels of the measurement target optical fiber 92, are incident on the measurement target optical fiber 92.

As described above, in the present embodiment, a combination of a propagation mode of the test light and a propagation mode of the backscattered light is changed. In a case where a two-mode single-core optical fiber is used as the measurement target optical fiber 92, a total of four types of backscattered light intensity distribution waveforms including two modes of test light and two modes of backscattered light are obtained. Consequently, the backscattered light intensity of the i-th spatial channel obtained by making the test light incident on the j-th spatial channel can be detected. In the present embodiment, an example in which a two-mode single-core optical fiber is used as the measurement target optical fiber 92 is described, but M² backscattered light intensity distribution waveforms are obtained in a case where the number of spatial channels of the measurement target optical fiber 92 is M.

(Transfer Matrix Calculation Step S20)

Next, in the transfer matrix calculation step S20 illustrated in FIG. 1, the arithmetic processing device 18 obtains a transfer matrix distribution in the longitudinal direction of the measurement target optical fiber 92 by using the backscattered light intensity distribution waveform measured in the backscattered light intensity distribution measurement step S10.

In this step, first, the transfer matrix T(z₀, z₁) in the section z₀≤z<z₁ is obtained. Here, z₀ is in the vicinity of the test light incident end, and it is assumed that mode coupling and an optical loss at 0≤z<z₀ are negligible. A matrix P_out(z₀) of the backscattered light intensity observed with respect to z=z₀ is expressed as the following equation.

[Math. 12]

P _out(z₀)=BP_in  (12)

Here, the matrix B is a matrix representing a capture rate in each propagation mode in the backscattering process, and each component of P_out(z₀) and B is defined as follows.

$\begin{array}{cc}\left[\mathrm{Math}.13\right]& \\ P_{\mathrm{out}}\left(z_0\right)\equiv \left(\begin{array}{cc}{p}_{1,1}\left(z_0\right)& p_{1,2}\left(z_0\right)\\ p_{2,1}\left(z_0\right)& p_{2,2}\left(z_0\right)\end{array}\right)& \left(13\right)\end{array}$ $\begin{array}{cc}\left[\mathrm{Math}.14\right]& \\ B\equiv \left(\begin{array}{cc}{b}_{1,1}& b_{1,2}\\ b_{2,1}& b_{2,2}\end{array}\right)& \left(14\right)\end{array}$

Here, p_i,j(z₀) is a backscattered light intensity in the mode i observed with respect to z=z₀ in a case where the test light is incident in the mode j, and b_i,j is a ratio of the intensity at which propagation light in the mode j is backscattered in the mode i. When normalization is performed such that Pin becomes an identity matrix, Equation (12) is expressed as the following equation.

[Math. 15]

P _out(z₀)=B  (15)

On the other hand, a matrix P_out(z₁) of the backscattered light intensity observed with respect to z=z₁ is expressed as the following equation.

[Math. 16]

P _out(z₁)=T(z₀,z₁)BT(z₀,z₁)  (16)

Equation (15) is assigned to Equation (16), and the relationship of Equation (6) is obtained with respect to P_out (z₀) and P_out(z₁). T(z₀, z₁) is obtained by solving Equation (6) as simultaneous equations having each component of T(z₀, z₁) as a variable (step S22). Next, the transfer matrix T(z₁, z₂) in the section z₁≤z<z₂ is obtained (steps S23, S24, and S22). A matrix P_out(z₂) of the backscattered light intensity observed with respect to z=z₂ is expressed as the following equation.

[Math. 17]

P _out(z₂)=T(z₀,z₁)T(z₁,z₃)BT(z₁,z₂)T(z₀,z₁)  (17)

Equation (15) is assigned to Equation (17), and the relationship of Equation (7) is obtained with respect to P_out(z₀) and P_out(z₂). T(z₁, z₂) is obtained by assigning each component of T(z₀, z₁) obtained from the simultaneous equation (6) to Equation (7) and solving Equation (7) as simultaneous equations having each component of T(z₁, z₂) as a variable (step S25).

Thereafter, T(z₂, z₃), T(z₃, z₄), . . . are sequentially obtained from Equation (5) for each case of k=3, 4, . . . , Next, the transfer matrix T(z_a, z_b), in the distance section z_a≤z<z_b (where a and b are non-negative integers;) for obtaining crosstalk and an optical loss, is obtained by using Equation (8).

(Crosstalk and Optical Loss Calculation Step S30)

Finally, in the crosstalk and optical loss calculation step S30 illustrated in FIG. 1, the arithmetic processing device 18 assigns the (i,j) component η_i,j(z_a, z_b) of T(z_a, z_b) to the Equations (9) to (11) to obtain the crosstalk and the optical loss at z_a≤z<z_b (S31).

In the present embodiment, the case where the measurement target optical fiber 92 is a two-mode fiber is described, but the present disclosure is not limited thereto, and an optical fiber having the number of spatial channels M (where M is an integer of 2 or more) may be used. The number of spatial channels M makes simultaneous equations (5) to (7) be solved with respect to M² variables, so that it becomes difficult to directly obtain a solution as the number of spatial channels increases. However, for example, a value close to the solution may be searched numerically according to the following method, and the obtained value may be used as each approximated component of T(z_k-1, z_k). Hereinafter, two types of methods for searching an approximate solution of each component of T(z_k-1, z_k) from the simultaneous equation (5) will be described. Hereinafter, for the sake of simplification, the components η_1,1(z_k-1, z_k), . . . , η_i,j(z_k-1, z_k), . . . , and η_M,M(z_k-1, z_k) of T(z_k-1, z_k) will be abbreviated to η_1,1, . . . , η_i,j, . . . , and η_M,M.

(First Approximate Solution Search Method)

A function c(η_1,1, . . . , η_i,j, . . . , η_M,M) is defined as the following equation.

$\begin{array}{cc}\left[\mathrm{Math}.18\right]& \\ c\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)=\sum _{i=1}^M\sum _{j=1}^M{\left[q_{i,j}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)-p_{i,j}\left(z_k\right)\right]}^2& \left(18\right)\end{array}$

Here, q_i,j(η_1,1, . . . , η_i,j, . . . , η_M,M) is the (i, j) component of the right side of Equation (5), and p_i,j(z_k) is the (i,j) component of the matrix P_out(z_k). Since c(η_1,1, . . . , η_i,j, . . . , η_M,M) is a function that takes a value of 0 or more and becomes 0 when η_1,1, . . . , η_i,j, . . . , and η_M,M satisfy the simultaneous equation (5), an approximate solution of the simultaneous equation (5) is obtained from a condition for minimizing c(η_1,1, . . . , η_i,j, . . . , η_M,M).

Regarding η_1,1, . . . , η_i,j, . . . , and η_M,M that minimizes c(η_1,1, . . . , η_i,j, . . . , η_M,M), initial values are given to η_1,1, . . . , η_i,j, . . . , η_M,M, and c(η_1,1, . . . , η_i,j, . . . , η_M,M) is repeatedly calculated by changing by minute amounts Δη_1,1, . . . , η_i,j, . . . , and Δη_M,M, respectively, and η_1,1, . . . , η_i,j, . . . , η_M,M when c(η_1,1, . . . , η_i,j, . . . , η_M,M) converges to a value close to 0 is taken as an approximate solution. Δη_i,j in this case is obtained from the following equation.

$\begin{array}{cc}\left[\mathrm{Math}.19\right]& \\ {\mathrm{\Delta \eta }}_{i,j}=-d\sum _{k=1}^M\sum _{l=1}^M\frac{\partial c\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}{\partial q_{k,l}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}\frac{\partial q_{k,l}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}{\partial {\eta }_{i,j}}& \left(19\right)\end{array}$

Here, d is a constant. Equation (19) means that η_i,j is changed in the reverse direction of a gradient of c(η_1,1, . . . , η_i,j, . . . , η_M,M). Since the gradient of c(η_1,1, . . . , η_i,j, . . . , η_M,M) is 0 when c(η_1,1, . . . , η_i,j, . . . , η_M,M) takes the minimum value, an approximate solution of η_1,1, . . . , η_i,j, . . . , and η_M,M satisfying the simultaneous equation (5) can be obtained by changing η_1,1, . . . , η_i,j, . . . , and η_M,M by minute amounts in the reverse direction of the gradient of c(η_1,1, . . . , η_i,j, . . . , η_M,M).

(Second Approximate Solution Search Method)

A function f(η_1,1, . . . , η_i,j, . . . , η_M,M) is defined as the following equation.

$\begin{array}{cc}\left[\mathrm{Math}.20\right]& \\ f\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)=\sum _{i=1}^M\sum _{j=1}^M\left[q_{i,j}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)-p_{i,j}\left(z_k\right)\right]& \left(20\right)\end{array}$

Since f(η_1,1, . . . , η_i,j, . . . , η_M,M) is 0 when η_1,1, . . . , η_i,j, . . . , and η_M,M satisfy the simultaneous equation (5), an approximate solution of the simultaneous equation (5) is obtained from a condition that f(η_1,1, . . . , η_i,j, . . . , η_M,M) takes a value close to 0.

Regarding η_1,1, . . . , η_i,j, . . . , η_M,M satisfying f(η_1,1, . . . , η_i,j, . . . , η_M,M)=0, initial values are given to η_1,1, . . . , η_i,j, . . . , η_M,M, and f(η_1,1, . . . , η_i,j, . . . , η_M,M) is repeatedly calculated by changing by minute amounts Δη_1,1, . . . , Δη_i,j, . . . , and Δη_M,M, respectively, and η_1,1, . . . , η_i,j, . . . , and η_M,M when f(η_1,1, . . . , η_i,j, . . . , η_M,M) converges to a value close to 0 is taken as an approximate solution. Δη_i,j in this case is obtained from the following equation.

$\begin{array}{cc}\left[\mathrm{Math}.21\right]& \\ {\mathrm{\Delta \eta }}_{i,j}=-\frac{f\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}{{\sum }_{k=1}^M{\sum }_{l=1}^M\frac{\partial f\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}{\partial q_{k,l}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}\frac{\partial q_{k,l}\left({\eta }_{1,1},\dots ,{\eta }_{i,j},\dots ,{\eta }_{M,M}\right)}{\partial {\eta }_{i,j}}}& \left(21\right)\end{array}$

Equation (21) means that η_i,j is changed toward the η_i,j coordinate at the intersection of the tangent of f(η_1,1, . . . , η_i,j, . . . , η_M,M) and the η_i,j axis. In this case, since f(η_1,1+Δη_1,1, . . . , η_i,j+Δη_i,j, . . . , η_M,M+Δη_M,M) takes a value closer to 0 than f(η_1,1, . . . , η_i,j, . . . , η_M,M), by changing η_1,1, . . . , η_i,j, . . . , and η_M,M by minute amounts Δη_1,1, . . . , Δη_i,j, . . . , Δη_M,M until making f(η_1,1+Δη_1,1, . . . , η_i,j+Δη_i,j, . . . , η_M,M+Δη_M,M) converge to a value close to 0, an approximate solution of η_1,1, . . . , η_i,j, . . . , and η_M,M satisfying the simultaneous equation (5) can be obtained.

Effects of Present Disclosure

According to the present disclosure, it is possible to obtain evaluation of characteristics such as crosstalk and an optical loss even in a spatial multiplex optical transmission line in which mode coupling between spatial channels or an optical loss is non-uniform. In particular, since there are a large number of connection points and fiber bending depending on a laying environment in an actual transmission line, it is assumed that the characteristics change locally and temporally with transmission line laying work or maintenance operation work. In the related art, it is difficult to accurately evaluate characteristics since a backscattered light intensity fluctuates after a point where mode coupling locally changes due to a connection point or bending of an optical fiber, but in the present disclosure, evaluation of characteristics such as crosstalk and an optical loss including the influence of a connection point or fiber bending can be measured in a distributed manner, and thus there is an advantage over the related art from the viewpoint of usefulness in an actual transmission line environment.

INDUSTRIAL APPLICABILITY

The present disclosure can be applied to information and communication industries.

REFERENCE SIGNS LIST

• 11 PULSED LIGHT SOURCE
• 12, 13 CIRCULATOR
• 14 MODE SELECTION MEANS
• 15, 16 LIGHT RECEIVER
• 17 A/D CONVERTER
• 18 ARITHMETIC PROCESSING DEVICE
• 91 CHARACTERISTIC EVALUATION APPARATUS
• 92 MEASUREMENT TARGET OPTICAL FIBER

Claims

1. An apparatus comprising: a backscattered light intensity measurement unit that acquires a combination of backscattered light intensities of individual transmittable spatial channels of an optical fiber obtained when test light, for the individual transmittable spatial channels of the optical fiber, is incident on the optical fiber; anda transfer matrix calculation unit that calculates a transfer matrix for each section of the optical fiber in order from a side closer to an incident end of the test light, whereincharacteristics in a section of the optical fiber are evaluated by using the transfer matrix.

2. The apparatus according to claim 1, wherein the backscattered light intensity measurement unit measures, as a function Pout(z) of a distance z, a matrix of a backscattered light intensity obtained using light incident on a j-th spatial channel, for transmission through the optical fiber by using spatial multiplexing, and detected from an i-th spatial channel, as an (i,j) component, andthe transfer matrix calculation unitobtains T(zk-1, zk) (where k is a natural number) satisfying Equation (C1) for each case of k=1 to b by using the Pout(z), andcalculates a transfer matrix T(za, zb) in a section za≤z<zb (where a and b are non-negative integers) by using Equation (C2). [Math. C1]Pout(zk)=T(z0,z1) . . . T(zk-2,zk-1)T(zk-1,zk)Pout(z0)T(zk-1,zk)T(zk-2,zk-1) . . . T(z0,z1)  (C1)[Math. C2]T(za,zb)=T(zb-1,zb)T(zb-2,zb-1) . . . T(za+1,za+2)T(za,za+1)  (C2)

3. The apparatus according to claim 2, wherein the transfer matrix calculation unitcalculates a square error of the right side with respect to the left side of Equation (C1) as a function c(η1,1, . . . , ηi,j, . . . , ηM,M) having matrix components η1,1, . . . , ηi,j, . . . , and ηM,M (where ηi,j is the (i,j) component of T(zk-1, zk)) of T(zk-1, zk) as variables, andgives initial values to η1,1, . . . , ηi,j, . . . , and ηM,M changes values of η1,1, . . . , ηi,j, . . . , and ηM,M in a reverse direction of a gradient of c(η1,1, . . . , ηi,j, . . . , ηM,M), and calculates the T(za, zb) by using η1,1, . . . , ηi,j, . . . , and ηM,M when a value of c(η1,1, . . . , ηi,j, . . . , ηM,M converges.

4. The apparatus according to claim 2, wherein the transfer matrix calculation unitcalculates a difference between the left side and the right side of Equation (C1) as a function f(η1,1, . . . , ηi,j, . . . , ηM,M) having matrix components η1,1, . . . , ηi,j, . . . , and ηM,M (where ηi,j is the (i,j) component of T(zk-1, zk)) of T(zk-1, zk) as variables,gives initial values to η1,1, . . . , ηi,j, . . . , and ηM,M, changes values of η1,1, . . . , ηi,j, . . . , and ηM,M to approach an η1,1 coordinate . . . , an ηi,j coordinate, . . . , and an ηM,M coordinate of intersections of a tangent of f(η1,1, . . . , ηi,j, . . . , ηM,M) and an η1,1 axis, β, an ηi,j axis . . . , and an ηM,M axis, respectively, andcalculates the T(za, zb) by using η1,1, . . . , ηi,j, . . . , and ηM,M when a value of f(η1,1, . . . , ηi,j, . . . , ηM,M) converges.

5. The apparatus according to claim 2, further comprising: a crosstalk calculation unit that calculates crosstalk in the section za≤z<zb by using a non-diagonal component of the T(za, zb).

6. The apparatus according to claim 2, further comprising: an optical loss calculation unit that calculates an optical loss in the section za≤z<zb by using a diagonal component of the T(za, zb).

7. A method comprising the following sequence of steps: a backscattered light intensity distribution measurement step of acquiring a combination of backscattered light intensities of individual transmittable spatial channels of an optical fiber obtained when test light, for the individual transmittable spatial channels of the optical fiber, is incident on the optical fiber;a transfer matrix calculation step of calculating a transfer matrix for each section of the optical fiber in order from a side closer to an incident end of the test light; andan evaluation step of evaluating characteristics in a section of the optical fiber by using the transfer matrix.