JP7435981B2 - Mode field diameter measuring device and measuring method - Google Patents

Description

The present disclosure relates to a technique for measuring transmission characteristics in a spatial multiplexing system.

With the increase in large-capacity content such as videos and games and the spread of smartphones, the amount of traffic on optical fiber networks is increasing year by year. On the other hand, the single mode fiber currently used as a transmission medium is approaching its transmission capacity limit. Spatial multiplexing transmission using multi-core fibers and multi-mode fibers is attracting attention as a technology to cope with future traffic increases. Spatial multiplexing transmission systems use multiple cores and multiple waveguide modes as transmission channels, and it is important to understand the transmission characteristics of each channel.

The transmission characteristics of optical fibers are closely related to the electric field distribution of the waveguide mode. The mode field diameter is a parameter that represents the spread of the electric field of the fundamental mode (LP01 mode), and it is possible to estimate splice loss, chromatic dispersion, backscattered light capture rate, etc. It is one of the important parameters in understanding the characteristics.

The variable aperture method (VA method) is known as a method for measuring the mode field diameter in a single mode fiber. The VA method is a method of measuring the output light intensity from an optical fiber under test through a variable aperture. However, the method for measuring the mode field diameter for higher-order modes has not been clarified. Additionally, since the VA method performs measurements on the assumption that the core center of the measurement target is located at the center of the optical fiber, the core of the measurement target is not necessarily located at the center of the optical fiber, unlike multi-core fibers. It is not clear how this applies in this case.

A. Nakamura et al. , “Effective mode field diameter for LP11 mode and its measurement technique,” IEEE Photonics Technology Letters, vol. 28, no. 22, pp. 2553-2556, 2016. M. Ohashi et al. , “Prediction of modal dispersion of high-order mode from wavelength dependence of the mode field radius,” OECC2019, WP4-C10 , 2019. A. Nakamura et al. , “Reduction of modal evolution flux in 2-LP mode optical time domain reflectometry,” Optics Express, vol. 25, no. 17, pp. 20727-20736, 2017. N. Hanzawa et al. , “Three-mode PLC-type multi/demultiplexer for mode-division multiplexing transmission,” ECOC2013, Tu1. B. 3, 2013. Y. Tottori et al. , “Multi functionality demonstration for multi core fiber fan-in/fan-out devices using free space optics,” OFC2014, Th2A. 44, 2014. A. Nakamura et al. , “Mode field diameter definitions for fewer mode fibers based on spot size of higher-order Gaussian mode,” IEEE Photonics J our own, vol. 12, no. 2, 7200609, 2020. J. D. LOVE, C. D. HUSSEY, “Variational approximations for higher-ordermodes of weakly-guiding fibers” Optical and Quantum Electronics 16 (1984) 41-48, 1984.

The present invention has been made in view of the above circumstances, and it is an object of the present invention to provide a mode field diameter measuring device and a measuring method that can measure the mode field diameter of any channel in a spatial multiplexing transmission system.

In order to achieve the above object, the mode field diameter measuring device and measuring method of the present disclosure selectively inject test light in a mode to be measured into a core to be measured of an optical fiber under test having a plurality of transmission channels, The mode field diameter is measured using a variable aperture (VA) method.

Specifically, the mode field diameter measuring device according to the present disclosure includes:
a test light input section that selectively inputs test light into the core of the optical fiber to be measured in a mode to be measured;
The center of the opening is arranged on the central axis of the other end of the optical fiber, the opening angle with respect to the central axis of the other end is variable, and the output light from the other end passing through the opening is a light intensity measurement unit that measures light intensity;
The test is performed using the mode orders in the azimuthal direction and the radial direction of the mode incident as the test light at the test light incidence section, and the dependence of the light intensity measured by the light intensity measurement section on the aperture angle. A mode field diameter calculating section that calculates a mode field diameter of a mode incident as light.

Specifically, the mode field diameter measuring method according to the present disclosure includes:
a test light injection procedure for selectively injecting test light into a core of a measurement target in an optical fiber in a measurement target mode;
The output light from the other end passing through the opening is changed while changing the aperture angle with respect to the central axis of the other end of the opening, which is installed so that the center is on the central axis of the other end of the optical fiber. a light intensity measurement procedure for measuring light intensity;
The test is performed using the azimuthal and radial mode orders of the mode incident as the test light in the test light input procedure and the dependence of the light intensity on the aperture angle measured in the light intensity measurement procedure. A mode field diameter calculation procedure for calculating a mode field diameter of a mode incident as light is performed.

The present invention can provide a mode field diameter measuring device and a measuring method that can measure the mode field diameter of any channel in a spatial multiplexing transmission system.

An example of the procedure of the mode field diameter measurement method is shown. An example of a schematic configuration of a mode field diameter measuring device is shown. It is a figure explaining the calculation result of mode field diameter. It is a figure explaining the calculation result of mode field diameter. It is a figure explaining the relative error of the calculation result of a mode field diameter. It is a figure explaining the relative error of the calculation result of a mode field diameter. FIG. 3 is a diagram illustrating conditions for the mode field diameter calculation result to satisfy desired accuracy. FIG. 3 is a diagram illustrating conditions for the mode field diameter calculation result to satisfy desired accuracy.

Embodiments of the present disclosure will be described in detail below with reference to the drawings. Note that the present disclosure is not limited to the embodiments shown below. These implementation examples are merely illustrative, and the present disclosure can be implemented with various changes and improvements based on the knowledge of those skilled in the art. Note that components with the same reference numerals in this specification and the drawings indicate the same components.

ただし、ＭＦＤはモードフィールド径、νおよびμは試験光として入射したモードの方位角方向および半径方向のモード次数、θは被試験光ファイバ１０の中心軸からの可変開口１４の開口角、Ｐ_νμ（θ）は可変開口１４の開口角がθの場合における光強度、θ_ｍａｘは最大の開口角を表す。 (Embodiment)
FIG. 1 is a process diagram illustrating the mode field diameter measuring method of this embodiment.
The mode field diameter measuring method of this embodiment is as follows:
A mode field diameter measurement method for measuring the mode field diameter of an optical fiber under test having multiple cores and multiple modes as multiple transmission channels using a variable aperture (VA) method, the method comprising:
a test light input procedure S1 of selectively injecting test light into the core of the measurement target in the optical fiber under test in the mode of the measurement target;
Output light from the other end of the optical fiber to be tested passes through the opening while changing an aperture angle with respect to the central axis of the other end of the opening, which is installed so that its center is on the central axis of the other end of the optical fiber under test. a light intensity measurement step S2 of measuring the light intensity of
The mode order in the azimuth direction and the radial direction of the mode incident as the test light in the test light input procedure S1, the dependence of the light intensity on the aperture angle measured in the light intensity measurement procedure S2, and the following equation (1 ) and a mode field diameter calculation step S3 of calculating the mode field diameter of the mode incident as the test light using
It is characterized by doing the following.

Here, MFD is the mode field diameter, ν and μ are the mode orders in the azimuthal and radial directions of the mode incident as the test light, θ is the aperture angle of the variable aperture 14 from the central axis of the optical fiber 10 under test, P _νμ (θ) represents the light intensity when the aperture angle of the variable aperture 14 is θ, and θ _max represents the maximum aperture angle.

In the test light incidence procedure S1,
a generation step (S1a) of generating test light having a desired wavelength;
a mode conversion step (S1b) of converting the test light generated in the generation step into a mode to be measured;
an input step (S1c) in which the test light converted into the mode to be measured in the mode conversion step is inputted from one end of the optical fiber under test to the core to be measured;
I do.

In the light intensity measurement procedure S2,
The light intensity of the test light outputted from the other end of the optical fiber to be tested passing through the opening of the variable aperture is measured. At this time, by measuring the light intensity while changing the aperture angle of the aperture, a change in light intensity with respect to the aperture angle is obtained.

In mode field diameter calculation step S3,
The mode is determined using the azimuthal and radial mode orders of the mode to be measured that entered the optical fiber under test in the test light input procedure S1, and the change in light intensity with respect to the aperture angle measured in the light intensity measurement procedure S2. Calculate the field diameter.
Details of calculating the mode field diameter will be described later.

FIG. 2 is a diagram illustrating a configuration example of a mode field diameter device that performs the mode field diameter measuring method according to the present embodiment.
The mode field diameter measuring device 100 of this embodiment includes:
A mode field diameter measuring device that measures the mode field diameter of an optical fiber under test 10 having multiple cores and multiple modes as multiple transmission channels using a variable aperture (VA) method, comprising:
a test light incidence section 100A that selectively injects test light into the core of the measurement target in the optical fiber under test 10 in the mode of the measurement target;
a light intensity measurement unit 100B that measures the light intensity of the output light from the test light output end 10b passing through the opening 14a of the variable aperture 14;
The test light is incident as test light using the mode order in the azimuth direction and radial direction of the mode that is incident as test light at test light input section 100A, and the dependence of the light intensity on aperture angle θ measured by light intensity measurement section 100B. a mode field diameter calculation unit 100C that calculates the mode field diameter of the mode;
It is characterized by having the following.

The test light incidence section 100A performs a test light incidence procedure S1.
Specifically, the test light incidence section 100A includes a light source 11, a mode exciter 12, and an input/output device 13. Continuous light output from the light source 11 is converted into a mode to be measured by a mode exciter 12. The mode exciter 12 is a mode multiplexer/demultiplexer including a directional coupler configured with a plane light wave circuit as described in Non-Patent Document 4, for example. The continuous light converted into the mode to be measured by the mode exciter 12 is input from the test light input end 10a of the optical fiber under test 10 to the core to be measured via the input/output device 13. The input/output device 13 is a fan-in fan-out device configured with a spatial optical system as described in Non-Patent Document 5, for example.

The light intensity measurement unit 100B performs a light intensity measurement procedure S2.
Specifically, the light intensity measurement section 100B includes a variable aperture 14 having an aperture 14a, an optical lens 15, a light receiver 16, and a control section 17. The test light output from the test light output end 10b of the optical fiber under test 10 passes through the aperture 14a of the variable aperture 14, is focused by the optical lens 15, and is photoelectrically converted by the light receiver 16. At this time, the aperture angle θ of the aperture 14a is changed according to a signal from the control section 17. Note that in order to align the center axis of the optical fiber under test 10 with the center of the opening 14a of the variable aperture 14, it is desirable to install a centering device at the test light output end 10b of the optical fiber under test 10.

In addition, when the optical fiber under test 10 is a multi-core fiber (MCF: Multi-Core Fiber) having a plurality of cores, the mode field diameter obtained by this measurement method and measuring device is based on the test light in the optical fiber under test 10. Since it depends on the distance z between the output end 10b and the variable aperture 14, the distance z needs to be appropriately set according to the desired measurement accuracy. This point will be discussed later.

The mode field diameter calculation unit 100C performs a mode field diameter calculation procedure S3.
Specifically, the mode field diameter calculation section 100C includes an A/D (analog/digital) converter 18 and a signal processing section 19. A signal related to light intensity output from the light receiver 16 is converted into digital data by an A/D (analog/digital) converter 18. The signal processing unit 19 obtains the light intensity for the aperture angle θ of the aperture 14 a of the variable aperture 14 based on the signal regarding the aperture angle θ from the control unit 17 and the digital data converted by the converter 18 . Further, the signal processing unit 19 performs arithmetic processing to calculate the mode field diameter using the light intensity with respect to the aperture angle θ and the mode order in the azimuth direction and the radial direction of the mode incident as the test light.

ただし、θおよびφはそれぞれ、発散角および被試験光ファイバ１０の断面における方位角を表す。Ｅ_ｆνμ（θ，φ）は遠視野における電界分布、Ψ_νμ（φ）は方位角方向の変数、Ｆ_νμ（θ）は半径方向の電界分布を表す。なお、θは、後述する式（４）を使用することで、開口角と見なせる。 The calculation process for calculating the mode field diameter performed by the mode field diameter calculation unit 100C in the mode field diameter calculation procedure S3 will be described below. The electric field distribution in the far field of a linearly polarized light mode (LP _νμ mode) with orders ν and μ in the azimuthal direction and the radial direction, respectively, is expressed by the following equation.

However, θ and φ represent the divergence angle and the azimuth angle in the cross section of the optical fiber 10 under test, respectively. E _fνμ (θ, φ) represents the electric field distribution in the far field, Ψ _νμ (φ) represents the variable in the azimuthal direction, and F _νμ (θ) represents the electric field distribution in the radial direction. Note that θ can be regarded as the aperture angle by using equation (4) described later.

ただし、ｋは真空中での波数を表す。
式（３）の両辺を開口角αで微分すると、以下の式が得られる。

At this time, the light intensity passing through the variable aperture 14 having the aperture angle α can be described by the following equation.

However, k represents the wave number in vacuum.
By differentiating both sides of equation (3) with respect to the aperture angle α, the following equation is obtained.

From Equation (2), F _νμ is a function having the divergence angle as an argument, so α in F _νμ (α) on the right side of Equation (4) represents the divergence angle. On the other hand, α in P _νμ (α) on the left side of equation (4) represents the aperture angle. Therefore, equation (4) expresses the radial electric field distribution F _νμ (α) at the divergence angle α as the light intensity P _νμ after passing through the variable aperture 14 with the aperture angle α having the same angular magnitude as the divergence angle α. This means that it can be expressed as (α).

On the other hand, according to Non-Patent Document 6, the mode field diameter of the LP _νμ mode can be expressed by the following equation (5) using the radial electric field distribution in the far field and where θ is the divergence angle.

ただし、θ_ｍａｘは最大の開口角である。
式（６）では、θを発散角ではなく開口角として扱うことができ、可変開口１４を用いて測定した光強度Ｐ_νμ（θ）からモードフィールド径を算出することができる。 By applying equation (4) in which α is replaced with θ to equation (5), the equation for calculating the mode field diameter can be rewritten as the following equation.

However, θ _max is the maximum aperture angle.
In equation (6), θ can be treated as an aperture angle rather than a divergence angle, and the mode field diameter can be calculated from the light intensity P _νμ (θ) measured using the variable aperture 14.

ただし、Ｅ_ｎνμはＬＰνμモードの近視野における半径方向の電界分布を、ｗ_νμはＬＰνμモードの近視野におけるモードフィールド半径（スポットサイズ）を、ｒは被試験光ファイバ１０の断面における半径方向の座標を表す。ｄは被試験光ファイバ１０の中心と測定対象のコアの中心との間の距離を表す。 As an example, consider an optical fiber under test 10 in which four LP modes can propagate. Here, the radial electric field distribution in the near field of the LP01, LP11, LP21, and LP02 modes is approximated by the following equation using a Gaussian function (see, for example, Non-Patent Document 7).

Here, E _nνμ is the radial electric field distribution in the near field of the LPνμ mode, w _νμ is the mode field radius (spot size) in the near field of the LPνμ mode, and r is the radial coordinate in the cross section of the optical fiber 10 under test. represents. d represents the distance between the center of the optical fiber 10 under test and the center of the core to be measured.

ただし、Ｒは遠視野における半径方向の座標を表す。ｚは被試験光ファイバ１０の試験光出力端１０ｂと可変開口１４間の距離を表す。 At this time, the radial electric field distribution in the far field is expressed by the following equation.

However, R represents the coordinate in the radial direction in the far field. z represents the distance between the test light output end 10b of the optical fiber under test 10 and the variable aperture 14.

ただし、λは試験光の波長を表す。 W _νμ (z) is a spot size at a point (far field) a distance z away from the test light output end 10b of the optical fiber 10 under test, and is expressed by the following formula.

However, λ represents the wavelength of the test light.

Here, from Equations (3), Equations (6), and Equations (11) to (15), when the center of the core to be measured is located at the center of the optical fiber 10 under test (when d=0), each The mode field diameter of the mode can be expressed by the following formula.

As shown in equations (16) to (19), it can be seen that the mode field diameter of each mode changes depending on the distance z between the test light output end 10b of the optical fiber under test 10 and the variable aperture 14. Here, when z >> (πw ² _νμ /λ) ² is satisfied, from equation (15), it can be approximated as w _νμ =zλ/πw _νμ , and each mode shown in equations (16) to (19) The mode field diameter converges to the MFD' _νμ of the MFD' _νμ shown in equations (20) to (23), where ν and μ are the same as itself.

FIGS. 3 and 4 are diagrams illustrating the relationship between the calculation results of the mode field diameter w _νμ (z) and the distance z in the cases of d=0 and d=20, respectively. 3 and 4 show calculation results for LP01 mode, LP11 mode, LP21 mode, and LP02 mode. Here, the mode field diameter was calculated using equation (3), equation (6), and equations (11) to (15). Further, the mode field diameter 2w _νμ in the near field of each mode was set to 10 μm.

From FIGS. 3 and 4, in both cases of d=0 and d=20, the mode field diameter obtained in the region where the distance z between the test light output end 10b of the optical fiber under test 10 and the variable aperture 14 is small is It can be seen that the mode field diameter changes greatly and as the distance z increases, the obtained mode field diameter converges to a constant value. Note that if the electric field distribution of the mode to be measured is an ideal Gaussian function, the converging mode field diameter will be a value slightly larger than the true value.

FIGS. 5 and 6 are diagrams illustrating the relationship between the relative error of the obtained mode field diameter with respect to the converging mode field diameter in the cases of d=0 and d=20, respectively. The relative error was defined by equation (24).

It can be seen from FIGS. 5 and 6 that the smaller the distance z is, the larger the relative error is for any mode. Further, in the case of d=0 shown in FIG. 5, the measurement results of each mode are displayed almost overlapping, so the distance dependence of the relative error hardly depends on the mode of the measurement target. On the other hand, in the case of d=20 shown in FIG. 6, it can be seen that the lower-order mode tends to have a larger relative error.

FIG. 7 illustrates the relationship between the distance d between the center of the optical fiber 10 under test and the center of the core to be measured, and the minimum distance z that makes the relative error expressed by equation (24) 1% or less. This is a diagram. The horizontal axis is the distance d between the center of the optical fiber 10 under test and the center of the core to be measured, and the vertical axis is the distance z normalized by the test wavelength and mode field radius. From FIG. 7, it can be seen that as the distance d between the center of the optical fiber 10 under test and the center of the core to be measured increases, the minimum distance z that makes the relative error 1% or less increases. Furthermore, it can be seen that the minimum distance z that makes the relative error with respect to the LP01 mode 1% or less is the largest.

また、ｄが１０μｍより小さい場合、以下の式で近似することができる。

つまり、可変開口１４を設置する位置を、式（２５）および（２６）を満たす距離ｚより大きくすることで、各モードに対するモードフィールド径を十分な精度で測定することが可能となる。 FIG. 8 is a diagram showing an excerpt of the calculation results for the LP01 mode in FIG. The minimum distance z that makes the relative error to the distance d between the center of the optical fiber 10 under test and the center of the core to be measured 1% or less can be approximated by the following formula when d is larger than 10 μm. can.

Moreover, when d is smaller than 10 μm, it can be approximated by the following formula.

That is, by setting the position where the variable aperture 14 is installed to be larger than the distance z that satisfies equations (25) and (26), it becomes possible to measure the mode field diameter for each mode with sufficient accuracy.

As explained above, test light is selectively input in the mode to be measured into the core of the optical fiber under test having multiple transmission channels, and the mode field diameter is determined using the variable aperture (VA) method. By measuring, it is possible to provide a mode field diameter measuring device and a measuring method that can measure the mode field diameter of any channel in a spatial multiplexing transmission system. As a result, by applying Non-Patent Document 1 to Non-Patent Document 3 to the mode field diameter of the higher-order mode measured by the present invention, the splice loss, chromatic dispersion, and chromatic dispersion of any mode in any core of the spatial multiplexing transmission system, It becomes possible to obtain the backscattered light capture rate, etc.

Furthermore, as explained above, the VA method is performed by installing a variable aperture at a position away from the other end of the optical fiber by a distance z or more determined according to the distance d between the center of the optical fiber and the center of the core to be measured. As a result, it is possible to provide a mode field diameter measuring device and a measuring method that can accurately measure the mode field diameter of any core in a multicore fiber.

Although the above description uses a multi-mode and multi-core optical fiber as a plurality of channels, the present invention can be similarly applied to multi-core fibers (MCFs) and multi-mode fibers. Specifically, in the case of a multi-core fiber, the effects of the present invention can be obtained even if the test light incidence section 100A measures only one mode in the test light incidence procedure S1. Further, in the case of a multimode fiber, the present invention can be applied with the distance d between the center of the optical fiber 10 under test and the center of the core to be measured being 0. Further, even if the optical fiber is a single-core and single-mode optical fiber, the present invention can be applied in the same manner, assuming that there is only one mode to be measured and the distance d is 0.

Note that the signal processing section 19 can also be realized by a computer and a program, and the program can be recorded on a recording medium or provided through a network.

The mode field diameter measuring device and measuring method according to the present disclosure can be applied to the information and communication industry.

10: Optical fiber under test 10a: Test light input end 10b: Test light output end 11: Light source 12: Mode exciter 13: Input/output device 14: Variable aperture 14a: Aperture 15: Optical lens 16: Light receiver 17: Control Section 18: A/D converter 19: Signal processing section 100: Mode field diameter measuring device 100A: Test light incident section 100B: Light intensity measuring section 100C: Mode field diameter calculating section

Claims (5)

a test light input section that selectively inputs test light into the core of the optical fiber to be measured in a mode to be measured;
The center of the opening is arranged on the central axis of the other end of the optical fiber, the opening angle with respect to the central axis of the other end is variable, and the output light from the other end passing through the opening is a light intensity measurement unit that measures light intensity;
The test is performed using the mode orders in the azimuthal direction and the radial direction of the mode incident as the test light at the test light incidence section, and the dependence of the light intensity measured by the light intensity measurement section on the aperture angle. a mode field diameter calculation unit that calculates a mode field diameter of a mode incident as light;
A mode field diameter measuring device comprising: The optical fiber has a plurality of cores,
The light intensity measuring section includes:
The mode field diameter, which changes depending on the distance between the other end and the variable aperture, can be considered to have converged to a predetermined value using the distance between the center of the optical fiber and the center of the core to be measured. Calculating the distance between the other end and the variable opening,
2. The variable opening is installed at a position away from the other end by at least the calculated distance and such that the center of the opening is on the central axis of the other end. mode field diameter measuring device. 3. The mode field diameter measuring device according to claim 2, wherein the light intensity measuring unit calculates the distance between the other end and the variable aperture using a number C1.

Here, z is the distance between the other end and the variable aperture, λ is the wavelength of the test light, d is the distance between the center of the optical fiber and the center of the core to be measured, and w ₀₁ is the near field of the LP ₀₁ mode. represents the mode field radius at . 4. The mode field diameter measuring device according to claim 1, wherein the mode field diameter calculating section calculates the mode field diameter using a number C2.

Here, MFD is the mode field diameter, ν and μ are the mode orders in the azimuthal and radial directions of the mode incident as the test light, θ is the aperture angle of the variable aperture from the central axis of the optical fiber, and P _νμ ( θ) represents the light intensity measured when the aperture angle of the variable aperture is θ, and θ _max represents the maximum aperture angle. a test light injection procedure for selectively injecting test light into a core of a measurement target in an optical fiber in a measurement target mode;
The output light from the other end passing through the opening is changed while changing the aperture angle with respect to the central axis of the other end of the opening, which is installed so that the center is on the central axis of the other end of the optical fiber. a light intensity measurement procedure for measuring light intensity;
The test is performed using the azimuthal and radial mode orders of the mode incident as the test light in the test light input procedure and the dependence of the light intensity on the aperture angle measured in the light intensity measurement procedure. A mode field diameter calculation procedure for calculating the mode field diameter of a mode incident as light;
A mode field diameter measuring method characterized by performing the following.

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