JP7624653B2 - Optical characteristic measuring method and optical characteristic measuring device - Google Patents

Description

The present invention relates to a method for evaluating the characteristics of coupled multicore fibers used in optical communications, etc., and to a method and device for measuring the mode field diameter, relative refractive index difference, and chromatic dispersion.

With the spread of a wide variety of Internet services, the amount of traffic flowing through a single optical fiber is increasing rapidly year by year. However, the transmission capacity that can be transmitted through an optical fiber is limited, and it is predicted that the single-mode fiber (SMF), which is currently in widespread use, will not be able to handle the increase in traffic in the future. To overcome this situation, spatial multiplexing transmission systems using optical fiber with multiple cores (hereinafter referred to as multicore fiber) are being considered.

In recent years, in order to achieve both high-density spatial multiplexing and reduced group delay time difference between propagation modes, multicore fibers in which the modes between cores are randomly coupled by random bending and twisting in the longitudinal direction of the optical fiber (hereinafter referred to as coupled multicore fibers) have attracted attention. As with general-purpose single-mode fibers, the mode field diameter, relative refractive index difference, and chromatic dispersion are important optical properties of coupled multicore fibers. To develop and commercialize coupled multicore fiber technology, a technique that can easily evaluate these optical properties is required.

Non-Patent Document 1 discloses a method for measuring the mode field diameter, relative refractive index difference, and chromatic dispersion in an SMF using bidirectional OTDR (Optical Time Domain Reflectometry). This method is widely used as a technique for evaluating the optical characteristics of an SMF because it can easily measure the optical characteristics of an optical fiber from one end non-destructively.

A. Rossaro et al. , “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” Journal of Lightwave Technology, vol. 7, no. 3, pp. 475-483, 2001. M. Ohashi et al. , “Longitudinal fiber parameter measurements of multi-core fiber using OTDR,” Optics Express, vol. 22, no. 24, pp. 30137-30147, 2014. M. Ohashi et al. , “OTDR technology for measuring crosstalk and fiber parameters in multi-core fibers,” Proc. IEEE 6th International Conference on Photonics, 2016. S. Kobayashi et al. , “Characteristics of optical fibers in infrared wavelength region,” Review of the Electrical Communication Laboratories, vol. 26, no. 3-4, pp. 453-467, 1978. K. Nakajima et al. , “Chromatic dispersion distribution measurement along a single-mode optical fiber,” Journal of Lightwave Technology, vol. 15, no. 7, pp. 1905-1101, 1997.

For example, Non-Patent Document 2 discloses a method for measuring the mode field diameter, relative refractive index difference, and chromatic dispersion in a coupled multicore fiber using a bidirectional OTDR method. In this method, the mode field diameter, relative refractive index difference, and chromatic dispersion are obtained by assuming that the crosstalk between the cores is negligibly small.

However, the method of Non-Patent Document 2 can only be applied to coupled multicore fibers in which the inter-core coupling is negligible, and there is a problem in that it is not possible to measure the mode field diameter, relative refractive index difference, and chromatic dispersion of coupled multicore fibers in which the inter-core coupling cannot be ignored.

In order to solve the above problems, the present invention aims to provide an optical characteristic measuring method and an optical characteristic measuring device that can measure the mode field diameter, relative refractive index difference, and chromatic dispersion of a coupled multicore fiber using a bidirectional OTDR, regardless of the magnitude of the inter-core coupling.

To achieve the above object, the optical characteristic measurement method and optical characteristic measurement device disclosed herein use an optical fiber transmission line in which two single-core fibers, each having different optical characteristics and known optical characteristics, and a coupled multi-core fiber, the optical characteristics of which are unknown, are connected in series. The unknown optical characteristics of the coupled multi-core fiber are calculated using the backscattered light intensity distributions acquired at one end and the other end of the optical fiber transmission line and the known optical characteristics.

Specifically, the optical property measuring method according to the present disclosure includes:
1. A method for measuring optical characteristics of a coupled multi-core fiber, comprising the steps of:
forming an optical fiber transmission line by connecting in series a first single-core fiber and a second single-core fiber, the first single-core fiber and the second single-core fiber having different mode field diameters and relative refractive index differences and the mode field diameters and the relative refractive index differences being known, and connecting one core of the coupled multi-core fiber in series to an unconnected end of the second single-core fiber;
inputting a first test optical pulse from one end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the first test light pulse with respect to distance from the one end;
inputting a second test optical pulse from the other end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the second test light pulse with respect to distance from the one end;
calculating an arithmetic mean intensity of the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse, the backscattered light intensity being displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in a longitudinal direction of the coupled multi-core fiber;
calculating at least one of a mode field diameter, a relative refractive index difference, and a chromatic dispersion of the coupled multicore fiber from the three arithmetic mean intensities, mode field diameters of the first single-core fiber and the second single-core fiber, and relative refractive index differences of the first single-core fiber and the second single-core fiber;
Do the following.

Specifically, the optical property measuring device according to the present disclosure includes:
a test optical pulse generator for generating a test optical pulse;
an input/output unit that inputs a first test light pulse to one end of an optical fiber transmission line and outputs backscattered light due to the first test light pulse, and inputs a second test light pulse to the other end of the optical fiber transmission line and outputs backscattered light due to the second test light pulse, the input/output unit being configured to input a first test light pulse to one end of the optical fiber transmission line and output backscattered light due to the second test light pulse, the first test light pulse being different from the second test light pulse in mode field diameter and relative refractive index difference, the mode field diameter and relative refractive index difference being known, and a coupled multicore fiber having one of its cores connected in series to the second single-core fiber;
a measuring device that measures a distribution of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse output by the input/output device with respect to a distance from the one end;
a calculator that calculates an arithmetic mean intensity of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse, displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in the longitudinal direction of the coupled multicore fiber, and calculates at least one of a mode field diameter, a relative refractive index difference, and a chromatic dispersion of the coupled multicore fiber from the three arithmetic mean intensities, each of the mode field diameters of the first single-core fiber and the second single-core fiber, and each of the relative refractive index differences of the first single-core fiber and the second single-core fiber;
Equipped with.

ただし、ｚ_hは前記一端から前記中間点までの距離、ｚ_１は前記一端から前記第１シングルコアファイバの任意の１点までの距離、ｚ_２は前記一端から前記第２シングルコアファイバの任意の１点までの距離であり、
Ｉ（ｚ_h）は前記中間点に関しての相加平均強度、Ｉ（ｚ_１）は前記第１シングルコアファイバの任意の１点に関しての相加平均強度、Ｉ（ｚ_２）は前記第２シングルコアファイバの任意の１点に関しての相加平均強度であり、
λは波長であり、
ｗ（λ、ｚ_h）は前記中間点に関してのモードフィールド径、ｗ（λ、ｚ_１）は前記第１シングルコアファイバの任意の１点に関してのモードフィールド径、ｗ（λ、ｚ_２）は前記第２シングルコアファイバの任意の１点に関してのモードフィールド径である。 For example, in the optical characteristic measuring method and the optical characteristic measuring apparatus according to the present disclosure,
The mode field diameter of the coupled multi-core fiber may be calculated using the formula C1.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is the mode field diameter with respect to the midpoint, w(λ, z ₁ ) is the mode field diameter with respect to any point of the first single-core fiber, and w(λ, z ₂ ) is the mode field diameter with respect to any point of the second single-core fiber.

ただし、ｚ_hは前記一端から前記中間点までの距離、ｚ_１は前記一端から前記第１シングルコアファイバの任意の１点までの距離、ｚ_２は前記一端から前記第２シングルコアファイバの任意の１点までの距離であり、
Ｉ（ｚ_h）は前記中間点に関しての相加平均強度、Ｉ（ｚ_１）は前記第１シングルコアファイバの任意の１点に関しての相加平均強度、Ｉ（ｚ_２）は前記第２シングルコアファイバの任意の１点に関しての相加平均強度であり、
Δ（ｚ_h）は前記中間点に関しての比屈折率差、Δ（ｚ_１）は前記第１シングルコアファイバの任意の１点に関しての比屈折率差、Δ（ｚ_２）は前記第２シングルコアファイバの任意の１点に関しての比屈折率差であり、
ｋは定数である。 For example, in the optical characteristic measuring method and the optical characteristic measuring apparatus according to the present disclosure,
The relative refractive index difference of the coupled multi-core fiber may be calculated using Equation C2.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant.

ただし、ｚ_hは前記一端から前記中間点までの距離、ｚ_１は前記一端から前記第１シングルコアファイバの任意の１点までの距離、ｚ_２は前記一端から前記第２シングルコアファイバの任意の１点までの距離であり、
Ｉ（ｚ_h）は前記中間点に関しての相加平均強度、Ｉ（ｚ_１）は前記第１シングルコアファイバの任意の１点に関しての相加平均強度、Ｉ（ｚ_２）は前記第２シングルコアファイバの任意の１点に関しての相加平均強度であり、
λは波長であり、
ｗ（λ、ｚ_h）は前記中間点に関してのモードフィールド径、ｗ（λ、ｚ_１）は前記第１シングルコアファイバの任意の１点に関してのモードフィールド径、ｗ（λ、ｚ_２）は前記第２シングルコアファイバの任意の１点に関してのモードフィールド径であり、
Δ（ｚ_h）は前記中間点に関しての比屈折率差、Δ（ｚ_１）は前記第１シングルコアファイバの任意の１点に関しての比屈折率差、Δ（ｚ_２）は前記第２シングルコアファイバの任意の１点に関しての比屈折率差であり、
ｋは定数である。 For example, in the optical characteristic measuring method and the optical characteristic measuring apparatus according to the present disclosure,
When calculating the chromatic dispersion of the coupled multicore fiber,
Calculating a mode field diameter of the coupled multicore fiber using Equation C3;
Calculating the relative refractive index difference of the coupled multicore fiber using Equation C4;
calculating material dispersion from the relative refractive index difference of the coupled multicore fiber;
calculating a wavelength dependency of a mode field diameter of the coupled multicore fiber from mode field diameters of the coupled multicore fiber acquired for a plurality of wavelengths λ;
calculating waveguide dispersion from the wavelength dependence;
The chromatic dispersion may be calculated by adding the material dispersion and the waveguide dispersion.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is a mode field diameter with respect to the midpoint, w(λ, z ₁ ) is a mode field diameter with respect to any one point of the first single-core fiber, and w(λ, z ₂ ) is a mode field diameter with respect to any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant.

The optical characteristic measurement method and optical characteristic measurement device disclosed herein use the backscattered light intensity distribution and known optical characteristics acquired at each end of an optical fiber transmission line in which two single-core fibers with different and known optical characteristics and a coupled multi-core fiber with unknown optical characteristics are connected in series, and can measure the mode field diameter, relative refractive index difference, and chromatic dispersion of the coupled multi-core fiber by bidirectional OTDR regardless of the magnitude of inter-core coupling.

The above inventions can be combined as much as possible.

According to the present disclosure, it is possible to provide an optical characteristic measuring method and an optical characteristic measuring device that can measure the mode field diameter, relative refractive index difference, and chromatic dispersion of a coupled multicore fiber using a bidirectional OTDR, regardless of the magnitude of the inter-core coupling.

1 shows an example of a schematic configuration of an optical characteristic measuring device according to the present invention. 1 shows an example of a schematic configuration of an optical characteristic measuring device according to the present invention. 1 shows an example of a schematic configuration of an optical characteristic measuring device according to the present invention. 1 shows an example of a procedure for the optical property measuring method according to the present invention. 1 shows an example of a procedure for the optical property measuring method according to the present invention. 1A to 1C are diagrams illustrating an optical characteristic measuring method according to the present invention. 1A to 1C are diagrams illustrating an optical characteristic measuring method according to the present invention.

The following describes in detail the embodiments of the present disclosure with reference to the drawings. Note that the present invention is not limited to the embodiments shown below. These implementation examples are merely illustrative, and the present disclosure can be implemented in various forms with various modifications and improvements based on the knowledge of those skilled in the art. Note that components with the same reference numerals in this specification and drawings are mutually identical.

(Embodiment 1)
FIG. 1 shows an example of a schematic configuration of an optical characteristic measuring apparatus according to this embodiment.
The optical property measuring apparatus according to the present disclosure comprises:
a test optical pulse generator 11 for generating a test optical pulse;
an input/output unit 12 that inputs a first test light pulse to one end A of an optical fiber transmission line 10 and outputs backscattered light due to the first test light pulse, and inputs a second test light pulse to the other end B of the optical fiber transmission line 10 and outputs backscattered light due to the second test light pulse; the input/output unit 12 inputs a first test light pulse to one end A of the optical fiber transmission line 10 and outputs backscattered light due to the second test light pulse, the input/output unit 12 comprising a first single-core fiber 10-1 and a second single-core fiber 10-2 that are connected in series and have different mode field diameters and relative refractive index differences and that are known from each other, and a coupled multi-core fiber 10-3 that has one of its cores connected in series to the second single-core fiber 10-2;
a measuring device 13 for measuring the distribution of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse outputted from the input/output device 12 with respect to the distance from the one end A;
and a calculator 14 that calculates an arithmetic mean intensity of the intensity of the backscattered light due to the first test light pulse and the intensity of the backscattered light due to the second test light pulse, displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber 10-1, an arbitrary point on the second single-core fiber 10-2, and a midpoint in the longitudinal direction of the coupled multi-core fiber 10-3, and calculates at least one of the mode field diameter, the relative refractive index difference, and the chromatic dispersion of the coupled multi-core fiber 10-3 from the three arithmetic mean intensities, the mode field diameters of the first single-core fiber 10-1 and the second single-core fiber 10-2, and the relative refractive index differences of the first single-core fiber 10-1 and the second single-core fiber 10-2.

An example of the configuration of the optical property measuring device according to this embodiment will be specifically described with reference to Figures 2 and 3.

An example of the test optical pulse generator 11 is shown in Figure 2. The test optical pulse generator 11 includes a light source 11-1, an optical intensity modulator 11-2, and a pulse generator 11-3.

Light source 11-1 outputs continuous light of the wavelength to be used as test light.

The pulse generator 11-3 sends a pulse signal to the optical intensity modulator 11-2. The pulse generator 11-3 may also output a trigger signal to the measuring instrument 13 to determine the timing to start measuring the backscattered light intensity distribution.

The optical intensity modulator 11-2 pulses the continuous light output from the light source 11-1 according to a signal from the pulse generator 11-3 to generate a test optical pulse. The optical intensity modulator 11-2 may be, for example, an acousto-optic modulator equipped with an acousto-optic switch that pulse-drives an acousto-optic element.

The input/output device 12 includes, for example, an optical circulator. The optical circulator controls the propagation direction of the light.

An example of the measuring device 13 is shown in Figure 3. The measuring device 13 includes a photoreceiver 13-1, an A/D (analog/digital) converter 13-2, and a signal processing unit 13-3.

The optical receiver 13-1 is connected to the input/output device 12 via a single-core fiber, and receives the backscattered light generated within the optical transmission path 10 via the input/output device 12.

The A/D converter 13-2 converts the electrical signal from the photoreceiver 13-1 into digital data. The A/D converter 13-2 inputs the digital data to the signal processing unit 13-3.

The signal processing unit 13-3 obtains the intensity distribution of the backscattered light from the input digital data.

The calculator 14 performs a calculation process to calculate the mode field diameter, the relative refractive index difference, and the chromatic dispersion from the distribution of the backscattered light intensity acquired by the signal processor 13-3. Details of this calculation process will be explained in step S07 below.

The signal processing unit 13-3 and the calculator 14 can also be realized by a computer and a program, and the program can be recorded on a recording medium or provided via a network.

An example of the procedure of the optical characteristic measuring method according to this embodiment is shown in FIG. 4 and FIG.
The optical characteristic measuring method according to the present embodiment includes the steps of:
An optical characteristic measuring method for measuring optical characteristics of a coupled multi-core fiber 10-3, comprising the steps of:
A first single-core fiber 10-1 and a second single-core fiber 10-2, which have different mode field diameters and relative refractive index differences and are known, are connected in series, and one core of a coupled multi-core fiber 10-3 is connected in series to an unconnected end of the second single-core fiber 10-2, thereby forming an optical fiber transmission line 10 (step S00);
A first test optical pulse is input from one end A of the optical fiber transmission line 10 (step S01);
Measuring a distribution of backscattered light intensity by a first test light pulse with respect to a distance from one end A (steps S02 and S03);
A second test optical pulse is input from the other end B of the optical fiber transmission line 10 (step S04);
Measuring a distribution of backscattered light intensity by the second test light pulse with respect to distance from the one end A (steps S05 and S06);
Calculating an arithmetic mean intensity of the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse, which are displayed on a logarithmic scale, for each of an arbitrary point of the first single-core fiber 10-1, an arbitrary point of the second single-core fiber 10-2, and a midpoint in the longitudinal direction of the coupled multi-core fiber 10-3 (substep S07-1);
At least one of the mode field diameter, the relative refractive index difference, and the chromatic dispersion of the coupled multicore fiber 10-3 is calculated from the three arithmetic mean intensities, the mode field diameters of the first single-core fiber 10-1 and the second single-core fiber 10-2, and the relative refractive index differences of the first single-core fiber 10-1 and the second single-core fiber 10-2 (substeps S07-2 to S07-7).
Steps S00 to S07 will be described in detail below.

(Step S00)
As shown in FIG. 1, a first single-core fiber 10-1 and a second single-core fiber 10-2, which have different mode field diameters and relative refractive index differences and whose mode field diameters and relative refractive index differences are known, are connected in series, and one core of a coupled multi-core fiber 10-3 is connected in series to the unconnected end of the second single-core fiber 10-2 to form an optical fiber transmission line 10.

(Step S01)
As described above, the test optical pulse generator 11 converts the continuous light output from the light source 11-1 into a test optical pulse, and inputs the first test optical pulse from one end A of the optical fiber transmission line 10 via the input/output unit 12.

(Step S02)
The measuring instrument 13 receives the backscattered light generated in the optical fiber transmission line 10 by the first test light pulse input in step S01 via the input/output unit 12 connected to one end A, as described above.

(Step S03)
The measuring instrument 13 measures the distribution of the intensity of the backscattered light due to the first test light pulse received in step S02 with respect to the distance from one end A of the optical fiber transmission line 10.

(Step S04)
As described above, the test optical pulse generator 11 converts the continuous light output from the light source 11-1 into a test optical pulse, and inputs the second test optical pulse from the other end B of the optical fiber transmission line 10 via the input/output unit 12.

(Step S05)
The measuring instrument 13 receives the backscattered light generated in the optical fiber transmission line 10 by the second test light pulse input in step S04 via the input/output unit 12 connected to the other end B, as described above.

(Step S06)
The measuring instrument 13 measures the distribution of the intensity of the backscattered light due to the second test light pulse received in step S05 with respect to the distance from the one end A of the optical fiber transmission line 10.

In addition, steps S04 to S06 may be performed first to measure the distribution of backscattered light intensity due to the second test light pulse, and then steps S01 to S03 may be performed to measure the distribution of backscattered light intensity due to the first test light pulse.

(Step S07)
In steps S03 and S06, the calculator 14 calculates the mode field diameter, the relative refractive index difference, and the chromatic dispersion of the coupled multi-core fiber by using the distribution of the backscattered light intensity by the first test light pulse and the distribution of the backscattered light intensity by the second test light pulse measured by the signal processor 13-3. This step may further include sub-steps S07-1 to S07-7 shown in Fig. 5. Sub-steps S07-1 to S07-7 will be described below.

(Substep S07-1)
In steps S03 and S06, the calculator 14 extracts the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse at the midpoint in the longitudinal direction of the coupled multicore fiber 10-3 from the distribution of the backscattered light intensity due to the first test light pulse and the distribution of the backscattered light intensity due to the second test light pulse measured by the signal processing unit 13-3, and displays them on a logarithmic scale. The backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse displayed on the logarithmic scale are added and divided by 2 to obtain an arithmetic mean intensity. Similarly, the arithmetic mean intensity is obtained for each of an arbitrary point of the first single-core fiber 10-1 and an arbitrary point of the second single-core fiber 10-2.

The arithmetic mean intensity calculated directly from the measured backscattered light intensity can be expressed by a formula if the formula for the distribution of the backscattered light intensity is known. A formula expressing the arithmetic mean intensity will be described by taking a coupled multicore fiber having two cores as an example. Here, the distance from one end A of the optical fiber transmission line 10 is represented by z. The coupled multicore fiber has two cores, which are referred to as core 1 and core 2, respectively. The properties of the loss coefficient α, Rayleigh scattering coefficient _αs, and backscattered light capture rate B of core 1 and core 2 with respect to the distance z are equal, and the power coupling coefficient h can be considered to be uniform in the longitudinal direction. The power coupling coefficient h is a parameter representing the magnitude of inter-core coupling. Here, the description will be given assuming that the second single-core fiber 10-2 is connected in series to the core 1, but the same applies to the case of the core 2.

In step S01, the intensity of a first test optical pulse input from one end A of the optical fiber transmission line 10 is set to _P0 . In step S04, the intensity of a second test optical pulse input from the other end B of the optical fiber transmission line 10 is set to _P1 .

なお、Ｐ_ｂｓ１（ｚ）は光ファイバ伝送路１０の一端Ａから第１の試験光パルスを入力した際の後方散乱光の強度分布を表す。Ｌ_０は第１シングルコアファイバ１０－１及び第２シングルコアファイバ１０－２の合計の長さを表す。Ｌは結合型マルチコアファイバ１０－３の長さを表す。 In the above setting, the distribution of the backscattered light intensity due to the first test light pulse in the core 1 obtained in step S03 can be expressed by the following equation 1.

Here, P _bs1 (z) represents the intensity distribution of the backscattered light when the first test light pulse is input from one end A of the optical fiber transmission line 10. L ₀ represents the total length of the first single-core fiber 10-1 and the second single-core fiber 10-2. L represents the length of the coupled multi-core fiber 10-3.

なお、Ｐ_ｂｓ２（ｚ）は光ファイバ伝送路１０の他端Ｂから第２の試験光パルスによる試験光パルスを入力した際の後方散乱光の強度分布を表す。数１および数２では、損失係数αが距離ｚによらないとしている。 The backscattered light intensity distribution due to the second test light pulse in the core 1 obtained in step S06 can be expressed by Equation 2.

Here, P _bs2 (z) represents the intensity distribution of the backscattered light when the second test light pulse is input from the other end B of the optical fiber transmission line 10. In Equation 1 and Equation 2, it is assumed that the loss coefficient α does not depend on the distance z.

The arithmetic mean intensity I(z) can be expressed by Equation 3 using Equations 1 and 2.

If the term having the power coupling coefficient h of the arithmetic mean intensity I(z) in Equation 3 is M(z), I(z) can be expressed using M(z) as in Equation 3a, and M(z) can be expressed as in Equation 3b. Note that in Equation 3a, I(z) is expressed by one equation for the entire range of 0≦z≦L ₀ +L.

Two OTDR waveforms acquired by bidirectional OTDR and their arithmetic mean intensity are shown in FIG. 7. In FIG. 7, the length of the first single-core fiber 10-1 is L ₁ , the length of the second single-core fiber 10-2 is L ₂ , and L ₀ = L ₁ + L _2. As shown in FIG. 7, the arithmetic mean intensity I(z) has a constant value independent of the distance z in the ranges of 0≦z≦L ₁ and L ₁ ≦z≦L _0. In FIG. 7, α _s (z) and B(z) of the first single-core fiber 10-1 and the second single-core fiber 10-2 are constants independent of the distance z. On the other hand, in the range of L ₀ ≦z≦L ₀ +L, the arithmetic mean intensity I(z) has a value according to the distance z. By using the arithmetic mean intensity I(z _h ) at z _h = L ₀ + L/2 within the range L ₀ ≦z≦L ₀ + L, it becomes possible to calculate the mode field diameter and the relative refractive index difference with high accuracy, as will be described later.

よって、各コアの損失係数αが一様でない場合には、相加平均強度は数５のように表すことができる。

従って、相加平均強度Ｉ（ｚ）は、数３ａ及び３ｂ又は数５及び３ｂで表現することができる。 In the above, the case where the loss coefficient α of each core of the optical fiber transmission line 10 is uniform has been shown. However, when the loss coefficient α of each core is not uniform, the loss coefficient α can be expressed by Equation 4.

Therefore, when the loss factor α of each core is not uniform, the arithmetic mean strength can be expressed as in Equation 5.

Therefore, the arithmetic mean intensity I(z) can be expressed by Equations 3a and 3b or Equations 5 and 3b.

なお、ｚ_ｈは一端Ａから結合型マルチコアファイバ１０－３の長手方向における中間点までの距離、ｚ_１は一端Ａから第１シングルコアファイバ１０－１の任意の１点までの距離、ｚ_２は一端Ａから第２シングルコアファイバ１０－２の任意の１点までの距離であり、
Ｉ（ｚ_ｈ）は結合型マルチコアファイバ１０－３の長手方向における中間点に関しての相加平均強度、Ｉ（ｚ_１）は第１シングルコアファイバ１０－１の任意の１点に関しての相加平均強度、Ｉ（ｚ_２）は第２シングルコアファイバ１０－２の任意の１点に関しての相加平均強度であり、
λは波長であり、
ｗ（λ、ｚ_ｈ）は結合型マルチコアファイバ１０－３の長手方向における中間点に関してのモードフィールド径、ｗ（λ、ｚ_１）は第１シングルコアファイバ１０－１の任意の１点に関してのモードフィールド径、ｗ（λ、ｚ_２）は第２シングルコアファイバ１０－２の任意の１点に関してのモードフィールド径である。 (Substep S07-2)
The three arithmetic mean intensities obtained in sub-step S07-1, the mode field diameter of the first single-core fiber 10-1, and the mode field diameter of the second single-core fiber 10-2 are used in equation 7 (see non-patent document 3) to calculate the mode field diameter of the coupled multi-core fiber 10-3.

Here, _zh is the distance from one end A to the midpoint in the longitudinal direction of the coupled multicore fiber 10-3, _z1 is the distance from one end A to an arbitrary point on the first single-core fiber 10-1, and _z2 is the distance from one end A to an arbitrary point on the second single-core fiber 10-2.
I(z _h ) is the arithmetic mean intensity for the midpoint in the longitudinal direction of the coupled multicore fiber 10-3, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber 10-1, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber 10-2,
λ is the wavelength,
w(λ, z _h ) is the mode field diameter at the midpoint in the longitudinal direction of the coupled multicore fiber 10-3, w(λ, z ₁ ) is the mode field diameter at any point in the first single-core fiber 10-1, and w(λ, z ₂ ) is the mode field diameter at any point in the second single-core fiber 10-2.

なお、Δ（ｚ_ｈ）は結合型マルチコアファイバ１０－３の長手方向における中間点に関しての比屈折率差、Δ（ｚ_１）は第１シングルコアファイバ１０－１の任意の１点に関しての比屈折率差、Δ（ｚ_２）は第２シングルコアファイバ１０－２の任意の１点に関しての比屈折率差である。また、ｋは結合型マルチコアファイバ１０－３のコアに添加される材料に依存する定数であり、例えば、コアへの添加材料がＧｅＯ_２の場合は０．６２である。 (Substep S07-3)
The three arithmetic mean intensities obtained in sub-step S07-1, the relative refractive index difference of the first single-core fiber 10-1, and the relative refractive index difference of the second single-core fiber 10-2 are used in equation 8 (see non-patent document 3) to calculate the relative refractive index difference of the coupled multi-core fiber 10-3.

Here, Δ(z _h ) is the relative refractive index difference at the midpoint in the longitudinal direction of the coupled multicore fiber 10-3, Δ(z ₁ ) is the relative refractive index difference at an arbitrary point of the first single-core fiber 10-1, and Δ(z ₂ ) is the relative refractive index difference at an arbitrary point of the second single-core fiber 10-2. Also, k is a constant depending on the material doped to the core of the coupled multicore fiber 10-3, and is 0.62 when the doped material to the core is GeO ₂ , for example.

By using the arithmetic mean intensity I(z _h ) of the midpoint in the longitudinal direction of the coupled multicore fiber 10-3 in Equation 7 and Equation 8, the accuracy of calculation of the mode field diameter and the relative refractive index difference is improved regardless of the magnitude of the inter-core coupling. In order to accurately calculate the mode field diameter and the relative refractive index difference regardless of the magnitude of the inter-core coupling, it is necessary that the difference in the arithmetic mean intensity, that is, I(z _h )-I(z ₁ ) and I(z ₂ )-I(z ₁ ) in Equation 7 and Equation 8, does not include a term having the power coupling coefficient h (Non-Patent Document 3). And, by using the arithmetic mean intensity I(z _h ) of the midpoint in the longitudinal direction of the coupled multicore fiber 10-3 obtained in sub-step S07-1, the term having the power coupling coefficient h can be deleted from I(z _h )-I(z ₁ ) regardless of the magnitude of the power coupling coefficient h. As described above, _z1 is the distance from one end A to an arbitrary point on the first single-core fiber 10-1, and _z2 is the distance from one end A to an arbitrary point on the second single-core fiber 10-2, each satisfying 0≦z≦ _L0 .

Below, we will explain why the difference in arithmetic mean intensity does not include a term with the power coupling coefficient h when the arithmetic mean intensity at the midpoint in the longitudinal direction of the coupled multicore fiber 10-3 is used.

The term having the power combining coefficient h of the arithmetic mean intensity is written as M(z) in Equation 3b, so that the term having the power combining coefficient h in the difference of the arithmetic mean intensity I(z), e.g., I(z)-I(z ₁ ), is expressed as the difference of M(z), e.g., M(z)-M(z ₁ ).

数６のＭ（ｚ_ｈ）は、数３ｂの０≦ｚ≦Ｌ_０におけるＭ（ｚ）と一致する。これより、Ｍ（ｚ_ｈ）－Ｍ（ｚ_１）は０となり、Ｉ（ｚ_ｈ）－Ｉ（ｚ_１）には電力結合係数ｈを有する項は含まれない。 As shown in Equation 3b, M(z) is constant regardless of the distance z when 0≦z≦ _L0 . Therefore, for _z1 and _z2 that satisfy 0≦z≦ _L0 , M( _z2 )-M( _z1 ) is 0, and I( _z2 )-I( _z1 ) does not include a term having the power coupling coefficient h. On the other hand, when _L0 ≦z≦ _L0 +L, M(z) is a function of the distance z. Here, Equation 6 shows the case where _zh = _L0 +L/2, which is the midpoint in the longitudinal direction of the coupled multi-core fiber 10-3, is substituted for M(z).

M(z _h ) in Expression 6 is equal to M(z) in Expression 3b where 0≦z≦L _0. As a result, M(z _h )−M(z ₁ ) is 0, and I(z _h )−I(z ₁ ) does not include a term having the power combining coefficient h.

Therefore, by using the arithmetic mean intensity of the midpoint in the longitudinal direction of the coupled multicore fiber 10-3, any one point of the first single-core fiber 10-1, and any one point of the second single-core fiber 10-2, it is possible to delete the term having the power coupling coefficient h from the difference in arithmetic mean intensity, i.e., I(z _h )-I(z ₁ ) and I(z ₂ )-I(z ₁ ) in Equations 7 and 8, regardless of the magnitude of the power coupling coefficient h, and it becomes possible to accurately calculate the mode field diameter and the relative refractive index difference using Equations 7 and 8.

数９のＡ_ｉおよびＢ_ｉはファイバ材料に依存する定数であり、結合型マルチコアファイバ１０－３の比屈折率差から決定できる。例えば、Ａ_ｉを求める場合には、図６に示すように、非特許文献４に記載されている、ドーパント量が特定の値であるコアの比屈折率差に対応する定数（Ａ_ａ）と、純石英の比屈折率差に対応する定数（Ａ_ｂ）との間で線形補間を行ってもよい。そして、その結果得られた直線を比屈折率差Δを変数とする一次関数Ａ_ｉ（Δ）として求め、Ａ_ｉ（Δ）のΔに数８で得た比屈折率差Δ（ｚ_ｈ）を代入することにより所望の定数（Ａ_ｉ）を求めてもよい。Ｂ_ｉを求める場合も同様にしてもよい。 (Substep S07-4)
The refractive index wavelength dependence of the core of the coupled multicore fiber 10-3 is calculated using the relative refractive index difference Δ(z _h ) calculated in sub-step S07-3 and Equation 9 (see Non-Patent Document 4) which represents the Sellmeier dispersion relation describing the wavelength dependence of the refractive index n.

A _i and B _i in Equation 9 are constants that depend on the fiber material and can be determined from the relative refractive index difference of the coupled multicore fiber 10-3. For example, when A _i is obtained, as shown in FIG. 6, linear interpolation may be performed between a constant (A _a ) corresponding to the relative refractive index difference of a core having a specific dopant amount and a constant (A _b ) corresponding to the relative refractive index difference of pure quartz, as described in Non-Patent Document 4. Then, the straight line obtained as a result may be obtained as a linear function A _i (Δ) with the relative refractive index difference Δ as a variable, and the desired constant (A _i ) may be obtained by substituting the relative refractive index difference Δ(z _h ) obtained in Equation 8 for Δ of A i ₍ Δ). The same procedure may be used when obtaining B _i .

The wavelength dependence of the refractive index of the core calculated by Equation 9 is used in Equation 10 (see Non-Patent Document 3) to determine the material dispersion _Dm , where c represents the speed of light.

(Substep S07-5)
Steps S01 to S06 are repeated multiple times while changing the wavelength of the test light pulse, the distribution of backscattered light intensity for multiple wavelengths is measured, and the mode field diameter of the coupled multicore fiber 10-3 for multiple wavelengths is calculated by sub-steps S07-1 and S07-2.

ここで、３波長以上のモードフィールド径の測定結果から、係数ａ、ｂ、ｃを決定することにより、結合型マルチコアファイバ１０－３のモードフィールド径の波長依存性を算出することが望ましい。 The wavelength dependence of the mode field diameter of the coupled multicore fiber 10-3 is calculated using the mode field diameter of the coupled multicore fiber 10-3 at multiple wavelengths and equation 11 (see non-patent document 5), which represents an approximation formula expressing the wavelength dependence of the mode field radius.

Here, it is desirable to calculate the wavelength dependency of the mode field diameter of the coupled multi-core fiber 10-3 by determining the coefficients a, b, and c from the measurement results of the mode field diameters of three or more wavelengths.

なお、Ｄ_ｗは導波路分散を、ｃは光速を、ｎはコアの屈折率を表す。また、数１１のｗ（λ、ｚ_ｈ）を数１２のｗに代入することにより、導波路分散Ｄ_ｗは数１３で表すこともできる。

(Substep S07-6)
The wavelength dependence of the mode field diameter of the coupled multicore fiber 10-3 calculated in sub-step S07-5 is used in Equation 12 (see Non-Patent Document 3), which is an approximation of the waveguide dispersion, to calculate the waveguide dispersion.

Here, _Dw is the waveguide dispersion, c is the speed of light, and n is the refractive index of the core. By substituting w(λ, _zh ) in equation (11) for w in equation (12), the waveguide dispersion _Dw can also be expressed by equation (13).

(Substep S07-7)
As shown in Equation 14, the chromatic dispersion is calculated by adding the material dispersion Dm calculated in substep S07-4 and the waveguide dispersion _Dw calculated in substep S07-6.

As described above, the optical characteristic measurement method and optical characteristic measurement device disclosed herein use the backscattered light intensity distribution and the known optical characteristics acquired at each end of an optical fiber transmission line in which two single-core fibers with different optical characteristics and known optical characteristics are connected in series with a coupled multi-core fiber with unknown optical characteristics, and can measure the mode field diameter, relative refractive index difference, and chromatic dispersion of the coupled multi-core fiber by bidirectional OTDR, regardless of the magnitude of the inter-core coupling.

The optical property measuring method and optical property measuring device disclosed herein can be applied to the information and communications industry.

10: Optical fiber transmission line 10-1: First single-core fiber 10-2: Second single-core fiber 10-3: Coupled multi-core fiber 11: Test optical pulse generator 11-1: Light source 11-2: Optical intensity modulator 11-3: Pulse generator 12: Input/output device 13: Measuring device 13-1: Photoreceiver 13-2: A/D converter 13-3: Signal processing unit 14: Arithmetic unit 101: Optical characteristic measuring device

Claims (6)

1. An optical characteristic measuring method for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising the steps of :
forming an optical fiber transmission line by connecting in series a first single-core fiber and a second single-core fiber, the first single-core fiber and the second single-core fiber having different mode field diameters and relative refractive index differences and the mode field diameters and the relative refractive index differences being known, and connecting in series one core of the coupled multi-core fiber to an unconnected end of the second single-core fiber;
inputting a first test optical pulse from one end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the first test light pulse with respect to distance from the one end;
inputting a second test optical pulse from the other end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the second test light pulse with respect to distance from the one end;
calculating an arithmetic mean intensity of the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse, the backscattered light intensity being displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in a longitudinal direction of the coupled multi-core fiber;
calculating a mode field diameter of the coupled multicore fiber from the three arithmetic mean intensities and the mode field diameters of the first single-core fiber and the second single-core fiber using a formula C1;
A method for measuring optical properties.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is the mode field diameter with respect to the midpoint, w(λ, z ₁ ) is the mode field diameter with respect to any point of the first single-core fiber, and w(λ, z ₂ ) is the mode field diameter with respect to any point of the second single-core fiber. 1. An optical characteristic measuring method for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising the steps of :
forming an optical fiber transmission line by connecting in series a first single-core fiber and a second single-core fiber, the first single-core fiber and the second single-core fiber having different mode field diameters and relative refractive index differences and the mode field diameters and the relative refractive index differences being known, and connecting one core of the coupled multi-core fiber in series to an unconnected end of the second single-core fiber;
inputting a first test optical pulse from one end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the first test light pulse with respect to distance from the one end;
inputting a second test optical pulse from the other end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the second test light pulse with respect to distance from the one end;
calculating an arithmetic mean intensity of the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse, the backscattered light intensity being displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in a longitudinal direction of the coupled multi-core fiber;
calculating a relative refractive index difference of the coupled multicore fiber from the three arithmetic average intensities and the respective relative refractive index differences of the first single-core fiber and the second single-core fiber using a formula C2;
A method for measuring optical properties.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant. 1. An optical characteristic measuring method for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising the steps of :
forming an optical fiber transmission line by connecting in series a first single-core fiber and a second single-core fiber, the first single-core fiber and the second single-core fiber having different mode field diameters and relative refractive index differences and the mode field diameters and the relative refractive index differences being known, and connecting in series one core of the coupled multi-core fiber to an unconnected end of the second single-core fiber;
inputting a first test optical pulse from one end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the first test light pulse with respect to distance from the one end;
inputting a second test optical pulse from the other end of the optical fiber transmission line;
measuring a distribution of backscattered light intensity due to the second test light pulse with respect to distance from the one end;
calculating an arithmetic mean intensity of the backscattered light intensity due to the first test light pulse and the backscattered light intensity due to the second test light pulse, the backscattered light intensity being displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in a longitudinal direction of the coupled multi-core fiber;
calculating a mode field diameter of the coupled multicore fiber from the three arithmetic mean intensities and the mode field diameters of the first single-core fiber and the second single-core fiber using a formula C3;
calculating a relative refractive index difference of the coupled multicore fiber from the three arithmetic average intensities and the respective relative refractive index differences of the first single-core fiber and the second single-core fiber using Equation C4;
calculating material dispersion from the relative refractive index difference of the coupled multicore fiber;
calculating a wavelength dependency of a mode field diameter of the coupled multicore fiber from mode field diameters of the coupled multicore fiber acquired for a plurality of wavelengths λ;
calculating waveguide dispersion from the wavelength dependence;
calculating the chromatic dispersion of the coupled multicore fiber by adding the material dispersion and the waveguide dispersion;
A method for measuring optical properties.

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is a mode field diameter with respect to the midpoint, w(λ, z ₁ ) is a mode field diameter with respect to any one point of the first single-core fiber, and w(λ, z ₂ ) is a mode field diameter with respect to any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant. An optical characteristic measuring apparatus for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising:
a test optical pulse generator for generating a test optical pulse;
an input/output unit that inputs a first test optical pulse to one end of an optical fiber transmission line and outputs backscattered light due to the first test optical pulse, and inputs a second test optical pulse to the other end of the optical fiber transmission line and outputs backscattered light due to the second test optical pulse, the input/output unit being configured to input a first test optical pulse to one end of the optical fiber transmission line and output backscattered light due to the second test optical pulse, the first test optical pulse being configured to input a second test optical pulse to the other end of the optical fiber transmission line, the second test optical pulse being configured to output backscattered light due to the second test optical pulse;
a measuring device that measures a distribution of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse output by the input/output device with respect to a distance from the one end;
a calculator that calculates an arithmetic mean intensity of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse, which are displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in the longitudinal direction of the coupled multi-core fiber, and calculates a mode field diameter of the coupled multi-core fiber from the three arithmetic mean intensities and each of the mode field diameters of the first single-core fiber and the second single-core fiber using a formula C5;
An optical characteristic measuring apparatus comprising:

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is the mode field diameter with respect to the midpoint, w(λ, z ₁ ) is the mode field diameter with respect to any point of the first single-core fiber, and w(λ, z ₂ ) is the mode field diameter with respect to any point of the second single-core fiber. An optical characteristic measuring apparatus for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising:
a test optical pulse generator for generating a test optical pulse;
an input/output unit that inputs a first test optical pulse to one end of an optical fiber transmission line and outputs backscattered light due to the first test optical pulse, and inputs a second test optical pulse to the other end of the optical fiber transmission line and outputs backscattered light due to the second test optical pulse, the input/output unit being configured to input a first test optical pulse to one end of the optical fiber transmission line and output backscattered light due to the second test optical pulse, the first test optical pulse being configured to input a second test optical pulse to the other end of the optical fiber transmission line, the second test optical pulse being configured to output backscattered light due to the second test optical pulse;
a measuring device that measures a distribution of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse output by the input/output device with respect to a distance from the one end;
a calculator that calculates an arithmetic mean intensity of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse, which are displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in the longitudinal direction of the coupled multi-core fiber, and calculates a relative refractive index difference of the coupled multi-core fiber from the three arithmetic mean intensities and each of the relative refractive index differences of the first single-core fiber and the second single-core fiber using equation C6;
An optical characteristic measuring apparatus comprising:

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant. An optical characteristic measuring apparatus for measuring optical characteristics of a coupled multicore fiber without measuring the magnitude of inter-core coupling, comprising:
a test optical pulse generator for generating a test optical pulse;
an input/output unit that inputs a first test optical pulse to one end of an optical fiber transmission line and outputs backscattered light due to the first test optical pulse, and inputs a second test optical pulse to the other end of the optical fiber transmission line and outputs backscattered light due to the second test optical pulse, the input/output unit being configured to input a first test optical pulse to one end of the optical fiber transmission line and output backscattered light due to the second test optical pulse, the first test optical pulse being configured to input a second test optical pulse to the other end of the optical fiber transmission line, the second test optical pulse being configured to output backscattered light due to the second test optical pulse;
a measuring device that measures a distribution of the intensity of backscattered light due to the first test light pulse and the intensity of backscattered light due to the second test light pulse output by the input/output device with respect to a distance from the one end;
calculating an arithmetic mean intensity of the intensities of backscattered light due to the first test light pulse and the backscattered light due to the second test light pulse, the intensities being displayed on a logarithmic scale, for each of an arbitrary point on the first single-core fiber, an arbitrary point on the second single-core fiber, and a midpoint in the longitudinal direction of the coupled multi-core fiber;
calculating a mode field diameter of the coupled multicore fiber from the three arithmetic mean intensities and the mode field diameters of the first single-core fiber and the second single-core fiber using Equation C7;
calculating a relative refractive index difference of the coupled multicore fiber from the three arithmetic average intensities and the respective relative refractive index differences of the first single-core fiber and the second single-core fiber using Equation C8;
calculating material dispersion from the relative refractive index difference of the coupled multicore fiber;
calculating a wavelength dependency of a mode field diameter of the coupled multi-core fiber from the mode field diameters of the coupled multi-core fiber acquired for a plurality of wavelengths λ;
Calculating the waveguide dispersion from the wavelength dependence;
a calculator for calculating the chromatic dispersion of the coupled multi-core fiber by adding the material dispersion and the waveguide dispersion;
An optical characteristic measuring apparatus comprising:

where _zh is the distance from the one end to the midpoint, _z1 is the distance from the one end to any one point of the first single-core fiber, and _z2 is the distance from the one end to any one point of the second single-core fiber;
I(z _h ) is the arithmetic mean intensity for the midpoint, I(z ₁ ) is the arithmetic mean intensity for any one point of the first single-core fiber, and I(z ₂ ) is the arithmetic mean intensity for any one point of the second single-core fiber;
λ is the wavelength,
w(λ, z _h ) is a mode field diameter with respect to the midpoint, w(λ, z ₁ ) is a mode field diameter with respect to any one point of the first single-core fiber, and w(λ, z ₂ ) is a mode field diameter with respect to any one point of the second single-core fiber;
Δ(z _h ) is the relative refractive index difference with respect to the midpoint, Δ(z ₁ ) is the relative refractive index difference with respect to any one point of the first single-core fiber, and Δ(z ₂ ) is the relative refractive index difference with respect to any one point of the second single-core fiber;
k is a constant.

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