Patent Publication Number: US-11022523-B2

Title: Mode-dependent loss measurement method and measurement device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application of PCT/JP2016/088146 claiming the benefit of priority of the Japanese Patent Application No. 2016-042209 filed on Mar. 4, 2016, the entire contents of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a Mode-Dependent Loss (hereinafter referred to as “MDL”) measurement method and a MDL measurement device for measuring MDL in a transmission medium applied to a mode division multiplex transmission system, and relates to an optical fiber that can be applied to the transmission medium for mode division multiplexing. 
     BACKGROUND ART 
     Non Patent Document 1 discloses that when Multi-Input/Multi-Output (hereinafter referred to as “MIMO”) processing is performed in a mode division multiplex transmission system, transmission capacity during mode division multiplex transmission by a MIMO configuration decreases due to MDL of a transmission medium, and discloses an expression for calculating the MDL from a transfer matrix. 
     Non Patent Document 2 discloses results of analyzing MDL of a mode division multiplex transmission system in which a coupled Multi-Core Optical Fiber (hereinafter referred to as “MCF”) is applied as a transmission medium, by using the expression disclosed in the above Non Patent Document 1 by MIMO processing. The analyzed MDL of the coupled MCF varies for each graph, but the MDL is approximately 0.06 dB/km 1/2  to 0.14 dB/km 1/2 . 
     CITATION LIST 
     Non Patent Literature 
     
         
         Non Patent Document 1: P. J. Winzer and G J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express, vol. 19, no. 17, pp. 16680-16696, August 2011. 
         Non Patent Document 2: S. Randel, C. Schmidt, R. Ryf, R. J. Essiambre, and P. J. Winzer, “MIMO-based signal processing for mode-multiplexed transmission,” in IEEE Photonics Society Summer Topical Meeting Series, 2012, pp. 181-182, paper MC 4.1. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     As a result of examining the conventional technique, the inventor has found the following problems. That is, according to the above-described conventional technique, analysis by MIMO processing is necessary for measuring MDL, so that it is necessary to perform coherent detection of a plurality of, (number of spatial modes)×(number of polarization modes), signals, to predict a transfer matrix of a transmission line including time delay and wavelength dependency, and to perform singular value decomposition of the transfer matrix. For that reason, it has been necessary to perform complicated measurement and calculation, during MDL evaluation for an optical fiber for mode division multiplexing. 
       FIG. 1A  is a diagram illustrating a schematic configuration of a general MDL measurement device in an optical fiber applied to a transmission medium for mode division multiplex transmission, and a MDL measurement device  100  illustrated in  FIG. 1A  includes: a transmission system  20  disposed on an input end  10   a  (first end) side of an optical fiber  10  as a measurement target; a reception system  30  disposed on an output end  10   b  (second end) side of an optical fiber  10 ; and a control device  40  configured to control the transmission system  20  via a transmission system control line (Including a data line)  25  and control the reception system  30  via a reception system control line (including a data line)  35 . The control device  40  includes a calculation means  50  for calculating MDL of the optical fiber  10  by using observation data obtained from the reception system  30 . 
     As illustrated in  FIG. 2A , as an example, a transmission system  20 A in a conventional MDL measurement device corresponding to the transmission system  20  in  FIG. 1A , includes a Spatial-Division-Multiplexing (hereinafter referred to as “SDM”) multiplexer  21 , and N (≥2) In-phase/Quadrature (IQ) modulators  22 . The N IQ modulators  22  are provided respectively to N (≥2) spatial channels # 1  to #N in the optical fiber  10 , and are controlled via control line (# 1  to #N)  25  by the control device  40 . The SDM multiplexer  21  inputs multiplexed light of modulated light from the N IQ modulators  22 , from the input end  10   a  of the optical fiber  10  to the optical fiber  10 . 
     Meanwhile, as illustrated in  FIG. 2B , as an example, a reception system  30 A in the conventional MDL measurement device corresponding to the reception system  30  in  FIG. 1A , includes an SDM splitter  31 , and N coherent receivers  32  (coherent receivers # 1  to #N) provided respectively to the spatial channels # 1  to #N in the optical fiber  10 . Light outputted from the output end  10   b  of the optical fiber  10  is split into light beams of the respective spatial channels by the SDM splitter  31 , and complex amplitude information of light received by a corresponding coherent receiver  32  is measured. The control device  40  takes in the complex amplitude information of each of the spatial channels # 1  to #N via control line  35 , and the calculation means  50  calculates the MDL in the optical fiber  10 . 
     Specifically, as illustrated in  FIG. 3 , a conventional MDL measurement method performs: multiplexing and outputting of the modulated light for the number of spatial channels (step ST 310 ); acquisition of the complex amplitude information for the number of spatial channels (step ST 320 ); generation of an estimation matrix of a transfer matrix T relating to the complex amplitude (step ST 330 ); and determination of a value of the MDL (step ST 340 ), and main operation of the method will be described below. 
     In step ST 310 , in the transmission system  20 A, the IQ modulators  22  individually generate (modulate with a known pilot signal) the modulated light for each of the N spatial channels # 1  to #N, and the multiplexed light multiplexed by the SDM multiplexer  21  is inputted from the input end  10   a  to the optical fiber  10 . In step ST 320 , the light outputted from the output end  10   b  of the optical fiber  10  is split by the SDM splitter  31 , complex amplitude information of the light is acquired by the coherent receivers  32  provided respectively to the spatial channels # 1  to #N, and the acquired complex amplitude information is sent to the control device  40  via the control line  35 . In step ST 330 , the calculation means  50  of the control device  40  uses the known pilot signal and the complex amplitude information of the light propagating through the optical fiber  10  as the measurement target, to calculate the estimation matrix of the transfer matrix T relating to the complex amplitude. Here, calculation of the estimation matrix is performed by various methods such as Zero-Forcing estimation, least squares estimation, minimum norm solution, general/linear minimum mean square error estimation, maximum likelihood estimation, maximum ratio combining, subspace method, and compressed sensing. In step ST 340 , the calculation means  50  performs singular decomposition of the calculated estimation matrix, and determines a ratio between the maximum value and the minimum value of squares of singular values, as an estimated value of the MDL. 
     The present invention has been made to solve the above-described problem (necessity of performing complicated measurement and calculation), and it is an object of the present invention to provide a MDL measurement method and a MDL measurement device including a structure for enabling measurement of MDL of an optical fiber applied as a transmission line to a mode division multiplex transmission system without increasing a processing load, and an optical fiber applicable to the transmission medium for mode division multiplexing. 
     Solution to Problem 
     To solve the above-described problem, a MDL (mode-dependent loss) measurement method according to a present embodiment measures MDL of an optical fiber as a measurement target, the optical fiber having a first end and a second end opposite to the first end and enabling optical transmission in N (≥2) spatial modes between which a large mutual crosstalk occurs. Specifically, the MDL measurement method executes generation of a transfer matrix relating to transmission loss in the optical fiber from the first end to the second end, and determination of a linear value of MDL per unit fiber length. The transfer matrix is obtained by repeating, for each of the N spatial modes while changing the target spatial mode, light-input operation and intensity measurement operation, the light-input operation inputting light of a predetermined intensity, from the first end of the optical fiber, to an arbitrary target spatial mode, the intensity measurement operation measuring intensity of light of each of the N spatial modes including the target spatial mode, the light being outputted from the second end of the optical fiber in response to light-input to the target spatial mode. The linear value of the MDL per unit fiber length is given by a ratio obtained by dividing the maximum value of matrix elements constituting the transfer matrix by the minimum value of the matrix elements, or a ratio obtained by dividing the maximum value of eigenvalues or singular values of the transfer matrix by the minimum value of the eigenvalues or the singular values. Further, a decibel value [dB/(unit fiber length) 1/2 ] of the MDL per unit fiber length may be determined by multiplying a common logarithm of the linear value by ten. 
     Advantageous Effects of Invention 
     According to the present embodiment, the MDL of the transmission medium, that is, the transmission loss difference between the spatial modes can be measured without coherent detection or calculation of a MIMO coefficient in mode division multiplex transmission. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a diagram illustrating a schematic configuration of a general MDL measurement device in an optical fiber for mode division multiplex transmission. 
         FIG. 1B  is a diagram illustrating a cross-sectional structure of a coupled MCF. 
         FIG. 2A  is a diagram illustrating a schematic configuration of a transmission system in a conventional MDL measurement device. 
         FIG. 2B  is a diagram illustrating a schematic configuration of a reception system in the conventional MDL measurement device. 
         FIG. 3  is a flowchart for explaining a conventional MDL measurement method. 
         FIG. 4A  is a diagram illustrating an example of a schematic configuration of a transmission system applicable to a MDL measurement device according to a present embodiment. 
         FIG. 4B  is a diagram illustrating another example of the schematic configuration of the transmission system applicable to the MDL measurement device according to the present embodiment. 
         FIG. 5A  is a diagram illustrating an example of a schematic configuration of a reception system applicable to the MDL measurement device according to the present embodiment. 
         FIG. 5B  is a diagram illustrating another example of the schematic configuration of the reception system applicable to the MDL measurement device according to the present embodiment. 
         FIG. 6  is a flowchart for explaining a MDL measurement method according to the present embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Description of Embodiments of the Present Invention 
     First, contents of embodiments of the present invention will be individually listed and described. 
     (1) A mode-dependent loss measurement method (MDL measurement method) according to a present embodiment enables measurement of MDL of a transmission medium, that is, measurement of transmission loss difference between spatial modes, without coherent detection or calculation of a MIMO coefficient in mode division multiplex transmission. As its one aspect, the MDL measurement method measures MDL of an optical fiber as a measurement target, the optical fiber having a first end and a second end opposite to the first end and enabling optical transmission in N (≥2) spatial modes between which a large mutual crosstalk occurs. The MDL measurement method is particularly suitable for measurement of an optical fiber in which crosstalk is −10 dB or more in a fiber length during measurement, and also suitable for an optical fiber having a power coupling coefficient between spatial modes of 0.1 [km −1 ] or more. Specifically, the MDL measurement method executes generation of a transfer matrix relating to transmission loss in the optical fiber from the first end to the second end, and determination of a linear value of MDL per unit fiber length. The transfer matrix is obtained by repeating, for each of the N spatial modes while changing the target spatial mode, light-input operation and intensity measurement operation, the light-input operation inputting light of a predetermined intensity, from the first end of the optical fiber, to an arbitrary target spatial mode, the intensity measurement operation measuring intensity of light of each of the N spatial modes including the target spatial mode, the light being outputted from the second end of the optical fiber in response to light-input to the target spatial mode. The linear value of the MDL per unit fiber length is given by a ratio obtained by dividing the maximum value of matrix elements constituting the transfer matrix by the minimum value of the matrix elements, or a ratio obtained by dividing the maximum value of eigenvalues or singular values of the transfer matrix by the minimum value of the eigenvalues or the singular values. Further, a decibel value [dB/(unit fiber length) 1/2 ] of the MDL per unit fiber length may be determined by multiplying a common logarithm of the linear value by ten. 
     The mode-dependent loss measurement device (MDL measurement device) according to the present embodiment includes a transmission system, a reception system, and a control device configured to control the transmission system and the reception system. The transmission system inputs the light of the predetermined intensity, from the first end of the optical fiber, to any of the N spatial modes. The reception system measures the intensity of the light of each of the N spatial modes, the light being outputted from the second end of the optical fiber. The control device controls the transmission system to input the light of the predetermined intensity, from the first end of the optical fiber, to the arbitrary target spatial mode, and controls the reception system to measure the intensity of the light of each of the N spatial modes including the target spatial mode, the light being outputted from the second end of the optical fiber in response to the light-input to the target spatial mode. In addition, the control device executes generation of the transfer matrix relating to the transmission loss in the optical fiber from the first end to the second end, and determination of the linear value of the MDL per unit fiber length, as described above. The control device may further determine the decibel value [dB/(unit fiber length) 1/2 ] of the MDL per unit fiber length from the linear value. 
     (2) As one aspect of the present embodiment, in a case where random coupling occurs between the spatial modes and the MDL [dB/(km) 1/2 ] accumulates, the light-input operation by the transmission system preferably includes operation of inputting light of an intensity P i  [mW], from the first end of an optical fiber having a fiber length L i [unit fiber length], to an i-th (i=1, 2, . . . , N) spatial mode as the target spatial mode out of the N spatial modes. In addition, the intensity measurement operation by the reception system preferably includes operation of measuring the intensity of light of each of N spatial modes in which light intensity of an j-th (j=1, 2, . . . , N) spatial mode is represented by P ji  [mW], the light being outputted from the second end of the optical fiber in response to light-input to the i-th spatial mode. The control device controls the transmission system and the reception system to repeat the light-input operation and the intensity measurement operation for each of the N spatial modes while changing the target spatial mode, to generate a transfer matrix relating to transmission loss represented by the expression (1) as follows: 
     
       
         
           
             
               
                 
                   
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     (3) In MDL measurement without a cutback as described above, influence of variation in connection loss at the first end appears in the light intensity P ji  [mW] of the j-th spatial mode measured in response to the light-input to the i-th spatial mode. Therefore, as one aspect of the present embodiment, a configuration can be applied that eliminates the influence of variation in connection loss in the MDL measurement, by the cutback. Specifically, in the light-input operation by the transmission system, the light of the intensity P i  [mW] is inputted, from the first end of the optical fiber having the fiber length L i  [unit fiber length], to the i-th spatial mode as the target spatial mode out of the N spatial modes. The intensity measurement operation by the reception system includes first operation of measuring the intensity before the cutback, and second operation of measuring the intensity after the cutback. In the first operation, the intensity is measured of the light of each of the N spatial modes in which the light intensity of the j-th spatial mode is represented by P ji  [mW], the light being outputted from the second end of the optical fiber in response to the light-input to the i-th spatial mode. In the second operation, first, a cutback part is prepared having the first end and a cutback length L i ′ (&lt;L i ) [unit fiber length], obtained by cutting the optical fiber at a position of 1 [m] to 50 [m] from the first end while leaving the first end. Then, in response to the light-input to the i-th spatial mode, light intensity P i ′ [mW] is measured of the i-th spatial mode outputted from a third end opposite to the first end of the cutback part. The control device controls the transmission system and the reception system to repeat the light-input operation and the intensity measurement operation for each of the N spatial modes while changing the target spatial mode, to generate a transfer matrix relating to transmission loss represented by the expression (2) as follows: 
     
       
         
           
             
               
                 
                   
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     (4) The optical fiber according to the present embodiment enables an increase in transmission capacity in mode division multiplexing transmission of a MIMO configuration. As its one aspect, in the optical fiber, the MDL measured by the above-described MDL measurement method is sufficiently suppressed in a wavelength range of 1530 nm to 1565 nm or a wavelength range of 1460 nm to 1625 nm. Specifically, in the above wavelength range, the MDL is 0.02 dB/km 1/2  or less, or an average value of the MDL is 0.01 dB/km 1/2  or less. 
     (5) As one aspect of the present embodiment, the above optical fiber is preferably a coupled MCF (multi-core optical fiber). Specifically, as optical properties of the coupled MCF, a mode coupling coefficient is preferably 1 [m −1 ] to 100 [m −1 ] at a wavelength of 1550 nm. In the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm, the transmission loss at all mode excitation is preferably 0.20 dB/km or less, 0.18 dB/km or less, 0.16 dB/km or less, or 0.15 dB/km or less. A mode average of chromatic dispersion is preferably 16 ps/(nm·km) or more. With respect to light with a wavelength of 1550 nm of all spatial modes, bending loss is preferably 0.2 dB or less when the optical fiber is wound one turn around a mandrel having a diameter of 30 mm. With respect to the light with the wavelength of 1550 nm of all the spatial modes, bending loss at a diameter of 20 mm is preferably 20 dB/m or less. With respect to the light with the wavelength of 1550 nm of all the spatial modes, bending loss is preferably 0.5 dB or less when the optical fiber is wound 100 turns around a mandrel having a radius of 30 mm. Under external stress application, an effective area A eff  of a spatial mode localized in each core is preferably 75 μm 2  to 180 μm 2  in all the spatial modes. 
     (6) As one aspect of the present embodiment, the optical fiber preferably has an average value of 10 ps/km 1/2  or less, 1 ps/km 1/2  or less, or 0.1 ps/km 1/2  or less, when the maximum value of inter-mode differential group delay (DGD) is measured at each wavelength over the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm. 
     (7) As one aspect of the present embodiment, the same number of spatial modes as the number of cores included in the optical fiber are set as propagation modes in descending order of effective refractive indexes. In this case, when the fiber length of the optical fiber is 22 m, in a wavelength range of 1530 nm or more, transmission loss of a spatial mode having the highest effective refractive index out of spatial modes excluding the propagation modes, is preferably greater than the transmission loss of each of the propagation modes by 19.3 dB or more, regardless of a bending state of the optical fiber. 
     (8) As one aspect of the present embodiment, the optical fiber includes a coupled MCF including a plurality of cores, a common optical cladding covering all of the plurality of cores, and a physical cladding covering the common optical cladding. 
     As described above, each aspect listed in the “Description of Embodiments of the Present invention” can be applied to all remaining aspects, or to all combinations of the remaining aspects. 
     Details of Embodiments of the Present Invention 
     Hereinafter, a detailed structure of the MDL measurement method, the MDL measurement device, and the optical fiber according to the present embodiment will be described in detail with reference to the accompanying drawings. The present invention is not limited to the exemplifications, and it is intended that all modifications are included indicated by the claims, and within a scope and meaning equivalent to the claims. In the description of the drawings, the same elements will be denoted by the same reference signs, without redundant description. 
     First, a state of light transmission of an optical fiber for mode division multiplexing as the measurement target in the present embodiment will be described below. 
     When an input complex amplitude of N (≥2) spatial channels (corresponding to N spatial modes) to the optical fiber is a column vector |x&gt; having NM elements including M (≥2) series (time series and wavelength series), an output complex amplitude of the N spatial channels from the optical fiber is a column vector |y&gt;, a transfer function of a transmission line including M pieces of time series or wavelength series information is a transfer matrix T of N rows and NM columns, and noise is n, the state of light transmission in the optical fiber can be modeled as the expression (3) as follows:
 
| y     =T|x     +n   (3)
 
The spatial mode in the optical fiber as the measurement target also includes a polarization mode. In a case where the measurement target is a MCF, the spatial mode may be a spatial mode as a core mode of each core, or a spatial mode as an eigenmode of when a whole of a plurality of cores has a waveguide structure (super mode).
 
     At this time, calculation of signal restoration by MIMO processing is calculated by the expression (4) as follows:
 
| x     ≅H|y         (4).
 
However, if at least T is not a square matrix, T does not have an inverse matrix, so that a matrix corresponding to H is calculated by using Singular Value Decomposition (SVD) or the like (see Non Patent Document 2).
 
     A transfer matrix T of an actual optical fiber cannot be measured directly, so that the transfer matrix T is estimated from |x&gt; and |y&gt;. However, the above expression (3) can be thought of as N simultaneous expressions including (N×NM) variables in the transfer matrix T, so that the number of expressions is insufficient and the solution cannot be uniquely determined. For that reason, by using various methods (such as zero-forcing estimation, least squares estimation, minimum norm solution, general/linear minimum mean square error estimation, maximum likelihood estimation, maximum ratio combining, subspace method, and compressed sensing), a plausible solution (estimation matrix) is estimated as the transfer matrix T. Such calculation is not easy, and detection including phase information of light is necessary by using coherent receivers for the N spatial channels. 
     MDL (transmission loss difference between MIMO transmission channels) of the optical fiber as the measurement target is obtained by singular value decomposition of the transfer matrix T predicted by MIMO processing into a form of the expression (5) below, and a ratio between the maximum value and the minimum value of the squares of the singular values is obtained as an estimated value of the MDL (see Non Patent Document 2). (This value is a linear value, which is usually represented in a decibel value by multiplying a common logarithm of the linear value by ten. If the transfer matrix T is not a predicted matrix but a true value, by singular value decomposition of the transfer matrix T into the form of the expression (5) below, the ratio between the maximum value and the minimum value of the squares of the singular values can be defined as the MDL.). In the expression (5) as follows:
 
 T=U∧V*   (5),
 
the matrices U and V* are unitary matrices of N rows and N columns, and NM rows and NM columns, respectively, and ∧ is a matrix of N rows and NM columns in which a diagonal matrix of N rows and N columns whose diagonal components are singular values is included in the first part (a part including a matrix element (1, 1)) and the remaining matrix elements are zero.
 
     As described above, a complicated model is necessary to consider the transfer matrix of the complex amplitude signal. Therefore, in the present embodiment, considering only the transmission loss of the optical fiber as a transmission medium of a measurement target, a simpler model is adopted. 
     That is, when powers of input and output of the N spatial channels of the optical fiber as the measurement target are column vectors |P in &gt; and |P out &gt;, respectively, and a transfer matrix of N rows and N columns including only transmission loss information in the optical fiber is α, the model can be represented by the expression (6) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     At this time, the transfer matrix α is considered to be an ensemble average of TT*. However, the matrix T′ is an adjoint matrix of the matrix T. When &lt;x&gt; represents an ensemble average of x, from the above equation (5), the transfer matrix α is given by the expression (7) as follows:
 
α=   TT*     =     U∧V*V∧*U*     =U     ∧∧*     U*   (7)
 
In the expression (7), &lt;∧∧*&gt; is a diagonal matrix whose diagonal components are ensemble averages of respective squares of absolute values of individual singular values. For that reason, a ratio obtained by dividing the maximum value of the diagonal elements of &lt;∧∧*&gt; by the minimum value corresponds to the linear value of the MDL. The above expression (7) corresponds to an expression of eigenvalue decomposition of the transfer matrix α, so that a matrix of N rows and N columns whose as diagonal elements are eigenvalues of the transfer matrix α is &lt;∧∧*&gt;. The transfer matrix α can be easily measured by the MDL measurement method of the present embodiment described above. However, if there is a measurement error, eigenvalue decomposition may not be possible. In such a case, if singular value decomposition is performed, although an error is included, &lt;∧∧*&gt; can be obtained by the expression (8) as follows:
 
α= U     ∧∧*     W*   (8).
 
Here, W* is a unitary matrix of N rows and N columns different from U.
 
     If it is difficult to perform singular value decomposition, a ratio obtained by dividing the maximum value of elements of &lt;∧∧*&gt; by the minimum value may be determined as the MDL. 
     In the following, a configuration will be described of the MDL measurement device according to the present embodiment that enables the MDL measurement described above, with reference to  FIGS. 1A, 4A to 4B, and 5A to 5B . 
     A basic configuration of the MDL measurement device according to the present embodiment is similar to that of a general MDL measurement device  100  illustrated in  FIG. 1A . That is, as illustrated in  FIG. 1A , the MDL measurement device according to the present embodiment also includes a transmission system  20 , a reception system  30 , and a control device  40  including a calculation means  50 . The control device  40  and the transmission system  20  are connected to each other via a transmission system control line (including a data line)  25 , and the control device  40  and the reception system  30  are connected to each other via a reception system control line (including a data line)  35 . 
     As an example, as illustrated in  FIG. 4A , a transmission system  20 B in the MDL measurement device according to the present embodiment, which corresponds to the transmission system  20  in  FIG. 1A , includes an SDM multiplexer  21 , a 1×N optical switch  23 , and a light source  24 . ON/OFF of the light source  24  is controlled by the control device  40  via the control line  25 . The control device  40  controls, via the control line  25 , the 1×N optical switch  23  to select a spatial mode as a target of light-input out of the N spatial modes (spatial channels) # 1  to #N propagating in an optical fiber  10 . In the transmission system  20 B, light of the i-th spatial mode selected by the 1×N optical switch  23  is inputted from an input end (first end)  10   a  via the SDM multiplexer  21  to the optical fiber  10 . 
     As another example, as illustrated in  FIG. 4B , a transmission system  20 C in the MDL measurement device according to the present embodiment, which corresponds to the transmission system  20  in  FIG. 1A , includes an alignment device  26 , a single core optical fiber (hereinafter referred to as “SCF”)  27 , and the light source  24 . The alignment device  26  optically connects a specific core whose end face is positioned on the input end  10   a  of the optical fiber  10  as the measurement target, and the core of the SCF  27  to each other. The light source  24  is controlled from the control device  40  via the control line  25 , and light outputted from the light source  24  is input into the core of the optical fiber  10  connected by the alignment device  26  via the SCF  27 . 
     Meanwhile, as an example, as illustrated in  FIG. 5A , a reception system  30 B in the MDL measurement device according to the present embodiment, which corresponds to the reception system  30  in  FIG. 1A , includes an SDM splitter  31 , and N power meters  33  (power meters # 1  to #N) provided to correspond respectively to the N spatial modes # 1  to #N propagating in the optical fiber  10 . The SDM splitter  31  splits light outputted from an output end (second end)  10   b  of the optical fiber  10  into light beams of the N spatial modes # 1  to #N, and each of the N power meters  33  measures light intensity of a corresponding spatial mode. The control device  40  takes in light intensity information of each of the spatial modes # 1  to #N from corresponding one of the N power meters  33  via the control line  35 . 
     As another example, as illustrated in  FIG. 5B , a reception system  30 C in the MDL measurement device according to the present embodiment, which corresponds to the reception system  30  in  FIG. 1A , includes an alignment device  34 , an SCF  36 , and a power meter  37 . The alignment device  34  optically connects a core positioned on the output end  10   b  of the optical fiber  10 , and the core of the SCF  36  to each other, and sequentially guides, to the SCF  36 , the light beams of the N spatial modes # 1  to #N propagating in the optical fiber  10 . The power meter  37  measures light intensity of each of the spatial modes reached via the SCF  36 , and sequentially transmits measured light intensity information to the control device  40  via the control line  35 . 
       FIG. 6  is a flowchart for explaining the MDL measurement method according to the present embodiment. That is, the MDL measurement method according to the present embodiment executes identification of an unmeasured spatial mode (step ST 610 ), measured light output to the identified spatial mode (step ST 620 ), acquisition of a loss coefficient of all the spatial modes (step ST 630 ), for all the spatial modes (step ST 640 ). When steps ST 610  to ST 630  are completed for all the spatial modes, generation of the transfer matrix α relating to transmission loss of the optical fiber  10  (step ST 650 ), and determination of a value of the MDL (step ST 660 ) are executed. In the following description,  FIG. 1A  is appropriately referenced. 
     In step ST 610 , in the transmission system  20 B or  20 C, an unmeasured i-th (i=1, 2, . . . , N) spatial mode is identified out of the N spatial modes # 1  to #N of the optical fiber  10  as the measurement target. In step ST 620 , as the light-input operation, the transmission system  20 B or  20 C inputs the light of the intensity P i , from the input end (first end)  10   a  of the optical fiber  10  having the fiber length L i  [unit fiber length], to the i-th spatial mode. 
     In step ST 630 , in a case where random coupling between the spatial modes # 1  to #N occurs and the MDL [dB/(km) 1/2 ] accumulates, as the intensity measurement operation, the reception system  30 B or  30 C measures intensity of the light of each of the N spatial modes # 1  to #N in which the light intensity of the j-th (j=1, 2, . . . , N) spatial mode is represented by P ji  [mW], the light being outputted from the output end (second end)  10   b  of the optical fiber  10  in response to the light-input to the i-th spatial mode. When the light-input operation and the intensity measurement operation are completed for all the spatial modes # 1  to #N (step ST 640 ), in step ST 650 , the calculation means  50  of the control device  40  generates the transfer matrix α given by the above expression (1). In step ST 660 , the calculation means  50  of the control device  40  determines, as a linear value of the mode-dependent loss per unit fiber length, a ratio obtained by dividing the maximum value of matrix elements constituting the transfer matrix α by the minimum value of the matrix elements, or a ratio obtained by dividing the maximum value of eigenvalues or singular values of the transfer matrix α by the minimum value of the eigenvalues or the singular values, and determines the decibel value of the MDL [dB/(unit fiber length) 1/2 ] by multiplying the common logarithm of the obtained linear value by ten. 
     In the MDL measurement without a cutback as described above, influence of variation in connection loss at the input end  10   a  appears in the light intensity P ji  [mW] of the j-th spatial mode measured in response to the light-input to the i-th spatial mode. In this case, a configuration is preferable that eliminates the influence of variation in connection loss in the MDL measurement, by the cutback. Specifically, in the light-input operation in step ST 620 , the light of the intensity P i  is inputted, from the input end  10   a  of the optical fiber  10  having the fiber length L i  [unit fiber length], to the i-th spatial mode. In the intensity measurement operation in step ST 630 , the first operation of measuring the intensity before the cutback, and the second operation of measuring the intensity after the cutback are performed. That is, in the first operation, the intensity is measured of the light of each of the N spatial modes in which the light intensity of the j-th spatial mode is represented by P ji  [mW], the light being outputted from the output end  10   b  in response to the light-input to the i-th spatial mode. In the second operation, first, the cutback part is obtained having the input end  10   a  and the cutback length L i ′ (&lt;L i ) [unit fiber length], obtained by cutting the optical fiber  10  at the position of 1 [m] to 50 [m] from the input end  10   a  while leaving the input end (first end)  10   a . In the second operation, in response to the light-input operation to the i-th spatial mode, the light intensity P i ′ [mW] is measured of the i-th spatial mode outputted from the output end (third end)  10   c  opposite to the input end  10   a  of the obtained cutback part. When a combination of the first operation of the light-input operation and the intensity measurement operation, and a combination of the second operation of the light-input operation and the intensity measurement operation are completed for all the spatial modes # 1  to #N (step ST 640 ), in step ST 650 , the calculation means  50  of the control device  40  generates the transfer matrix α given by the above expression (2). In step ST 660 , the calculation means  50  of the control device  40  determines, as a linear value of the mode-dependent loss per unit fiber length, a ratio obtained by dividing the maximum value of matrix elements constituting the transfer matrix α by the minimum value of the matrix elements, or a ratio obtained by dividing the maximum value of eigenvalues or singular values of the transfer matrix α by the minimum value of the eigenvalues or the singular values, and determines the decibel value of the MDL [dB/(unit fiber length) 1/2 ] by multiplying the common logarithm of the obtained linear value by ten. 
     According to the above Non Patent Document 2, the MDL in an optical fiber for mode division multiplex transmission in which crosstalk (hereinafter referred to as “XT”) between the spatial modes is large that has been reported so far, that is, the MDL in a coupled MCF varies for each graph, but is approximately 0.06 dB/km 1/2  to 0.14 dB/km 1/2 . According to the above Non Patent Document 1, it is known that when the MDL is large, the transmission capacity degrades during the mode division multiplex transmission in the MIMO configuration. 
     From the above, as in the embodiment, in the optical fiber  10  capable of optical transmission in the spatial mode in which XT is large, the MDL measured by the MDL measurement method according to the present embodiment is preferably 0.02 dB/km 1/2  or less in the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm that are suitable for long distance transmission. In this case, it is possible to maximize the capacity of a long distance transmission system using, as a transmission line, the optical fiber for mode division multiplex transmission in which XT between spatial modes is large. Further, the MDL of the optical fiber  10  is preferably 0.01 dB/km 1/2  or less, further, 0.005 dB/km 1/2  or less, further 0.002 dB/km 1/2  or less, and further preferably 0.001 dB/km 1/2  or less. 
     The average value of the MDL in the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm is 0.01 dB/km 1/2  or less, preferably 0.005 dB/km 1/2  or less, more preferably 0.002 dB/km 1/2  or less, and further preferably 0.001 dB/km 1/2  or less. In order for the optical fiber  10  to have optical properties suitable for long distance transmission, the mode coupling coefficient is preferably 1 [m −1 ] to 100 [m −1 ] at the wavelength of 1550 nm. From a viewpoint of reducing noise caused by optical amplification, from a viewpoint of widening an amplifier interval, or from a viewpoint of extending a transmission distance in a non-relay (no amplifier in a transmission line) transmission system, the transmission loss at all mode excitation is preferably 0.020 dB/km or less, more preferably 0.018 dB/km or less, further 0.16 dB/km or less, and further preferably 0.15 dB/km or less in the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm. To suppress nonlinear noise, the mode average of chromatic dispersion is preferably 16 ps/(nm·km) or more. Further, from a viewpoint of nonlinear noise suppression, or from a viewpoint of suppressing macro loss and microbending loss increase due to excessive effective area expansion, under external stress application, the effective area A eff  of the spatial mode localized in each core is preferably 75 μm 2  to 180 μm 2  in all the spatial modes. From a viewpoint of suppression of loss increase due to bending of the optical fiber in a repeater or a station building, with respect to the light with the wavelength of 1550 nm of all the spatial modes, the bending loss is preferably 0.2 dB or less when the optical fiber is wound one turn around the mandrel having the diameter of 30 mm. With respect to the light with the wavelength of 1550 nm of all the spatial modes, bending loss at a diameter of 20 mm is preferably 20 dB/m or less. With respect to the light with the wavelength of 1550 nm of all the spatial modes, bending loss is preferably 0.5 dB or less when the optical fiber is wound 100 turns around a mandrel having a radius of 30 mm. 
     From a viewpoint of reducing a calculation load of MIMO processing, the optical fiber  10  preferably has an average value of 10 ps/km 1/2  or less, 1 ps/km 1/2  or less, or 0.1 ps/km 1/2  or less, when the maximum value of the inter-mode DGD is measured at each wavelength over the wavelength range of 1530 nm to 1565 nm or the wavelength range of 1460 nm to 1625 nm. 
     The same number of spatial modes as the number of cores included in the optical fiber are set as propagation modes in descending order of effective refractive indexes. In this case, when the fiber length of the optical fiber is 22 m, in a wavelength range of 1530 nm or more, transmission loss of a spatial mode having the highest effective refractive index out of spatial modes excluding the propagation modes, is preferably greater than the transmission loss of each of the propagation modes by 19.3 dB or more, regardless of a bending state of the optical fiber. 
     From a viewpoint of manufacturing efficiency improvement, as illustrated in  FIG. 1B , the optical fiber  10  includes a coupled MCF including a plurality of cores  11 , a common optical cladding  12   a  covering all of the plurality of cores  11 , and a physical cladding  12   b  covering the common optical cladding  12   a . Here, the optical cladding  12   a  is a part of a cladding  12  contributing to optical transmission, and the physical cladding  12   b  is a part of the cladding  12  not contributing to optical transmission. From a viewpoint of consistency with a conventional cabling technology, a cladding diameter of the optical fiber  10  is desirably 124 μm to 126 μm. In addition, from the viewpoint of consistency with the conventional cabling technology, a covering diameter of the optical fiber  10  is desirably 240 μm to 260 μm. 
     REFERENCE SIGNS LIST 
       10  . . . Optical fiber (measurement target);  20 ,  20 B,  20 C . . . Transmission system;  25  . . . Transmission system control line;  30 ,  30 B,  30 C . . . Reception system;  35  . . . Reception system control line (including data line);  40  . . . Control device;  50  . . . Calculation means; and  100  . . . MDL measurement device.