Apparatus and method for obtaining the mode field diameter of an optical fiber

Abstract

The purpose of the present disclosure is to provide a device and a method capable of acquiring, from a near-field pattern, an MFD for more accurately estimating a connection loss of each spatial mode of an optical fiber containing a core capable of propagating a plurality of the spatial modes.　A mode-field diameter acquisition device according to the present disclosure acquires, from a near-field pattern, a mode-field diameter of each spatial mode of an optical fiber containing a core capable of propagating a plurality of the spatial modes, the device being characterized by using a near-field pattern of any spatial mode and a mathematical formula based on a variational expression of a propagation constant for said spatial mode and comprising a mode-field diameter acquisition unit that acquires the mode-field diameter of said spatial mode.

Description

Technical Field

[0001] The present disclosure relates to an apparatus and a method for obtaining a mode field diameter of an optical fiber.

Background Art

[0002] With the increase in large-capacity content such as videos and games and the spread of smartphones, the traffic volume in optical fiber networks has been increasing year by year. On the other hand, the transmission capacity of single-mode fibers currently used as transmission media is approaching its limit. As one of the technologies to cope with future traffic growth, spatial multiplexing transmission using multi-core fibers or multi-mode fibers has attracted attention. In a spatial multiplexing transmission system, a plurality of cores or a plurality of spatial modes are used as transmission channels, and it is important to grasp the transmission characteristics of each channel.

[0003] The transmission characteristics of an optical fiber are closely related to the electric field distribution of the guided mode. The mode field diameter (MFD) is a parameter representing the spread of the electric field of the fundamental mode (LP01 mode), and since the connection loss can be estimated from this, it is one of the important parameters for grasping the transmission characteristics of conventional single-mode fibers. In Non-Patent Document 1 and Non-Patent Document 2, it is disclosed that the connection loss for each spatial mode can be estimated by using the spot size at the beam waist when the electric field distribution of the higher-order mode is approximated by a higher-order Gaussian mode (Hermite-Gaussian or Laguerre-Gaussian) as the MFD. Therefore, the MFD is also an important parameter in an optical fiber having a core capable of propagating a plurality of spatial modes such as a few-mode fiber or a few-mode multi-core fiber.

[0004] When designing the refractive index distribution of an optical fiber, it is common practice to calculate the near-field pattern of the desired spatial mode using electromagnetic field analysis methods such as the finite element method, and then calculate the MFD from that value. Non-Patent Documents 1 and 2 disclose a method for calculating the MFD of higher-order modes from the near-field pattern, using the following definition formula, which is the same as that used to calculate the MFD of a conventional single-mode fiber.

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[0005] [Non-Patent Document 1] A. Nakamura et al., “Mathematical model for estimating splice loss in few-mode fibers from mode field diameter,” in Proceedings of the 6th International Symposium on Extremely Advanced Transmission Technologies, P-02, 2021. [Non-Patent Document 2] 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. [Non-Patent Document 3] A. Nakamura et al., “Mode field diameter definitions for few-mode fibers based on spot size of higher-order Gaussian mode,” IEEE Photonics Journal, vol. 12, no. 2, article number 7200609, 2020. [Non-Patent Document 4] Junichi Sagai, "Numerical Analysis Method of Electromagnetic Fields in Optical Waveguides," Morikita Publishing, 2015. [Overview of the project] [Problems that the invention aims to solve]

[0006] However, the field field distribution of spatial modes in multi-mode fibers and multi-mode multicore fibers does not actually match the exact higher-order Gaussian modes. As the difference between the actual field field distribution and the exact higher-order Gaussian modes becomes larger, the accuracy of the connection loss estimated using the MFD obtained by equation (1) deteriorates.

[0007] In other words, there was a problem in that it was unclear how to obtain MFD from near-field patterns to more accurately estimate connection losses in actual multi-mode fibers and multi-mode multicore fibers.

[0008] This disclosure is made in view of the above circumstances and aims to provide an apparatus and method for obtaining an MFD from a near-field pattern to more accurately estimate the connection loss of each spatial mode in an optical fiber having a core capable of propagating multiple spatial modes. [Means for solving the problem]

[0009] To achieve the above objective, the mode field diameter acquisition apparatus and acquisition method of this disclosure acquire the MFD from a near-field pattern using a mathematical formula based on the variational expression of the propagation constant derived from the wave equation.

[0010] Specifically, the mode field diameter acquisition device of this disclosure is A device for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, A mode field diameter acquisition unit that acquires the mode field diameter of an arbitrary spatial mode using the near-field pattern of that spatial mode and a mathematical formula based on the variational expression of the propagation constant for that spatial mode. It is characterized by having the following features.

[0011] The method for obtaining the mode field diameter in this disclosure is: A method for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, A procedure for obtaining the mode field diameter of an arbitrary spatial mode, using the near-field pattern of that spatial mode and a mathematical formula based on the variational expression of the propagation constant for that spatial mode. It is characterized by performing the following.

[0012] The mode field diameter acquisition device of this disclosure may further include a near-field pattern acquisition unit for acquiring the near-field pattern. The mode field diameter acquisition method of this disclosure may further include a near-field pattern acquisition procedure for acquiring the near-field pattern.

[0013] In the mode field diameter acquisition procedure described above, the mode field diameter acquisition unit may calculate the mode field diameter using equation (4) or equation (5).

[0014] In the mode field diameter acquisition procedure described above, the mode field diameter acquisition unit may calculate the connection loss using equation (7) or equation (6).

[0015] The program of the present disclosure is a program for realizing a computer as each functional unit provided in the mode field diameter acquisition device according to the present disclosure, and is a program for causing a computer to execute each procedure included in the mode field diameter acquisition method executed by the mode field diameter acquisition device according to the present disclosure.

[0016] Note that the above disclosures can be combined as much as possible.

Effect of the Invention

[0017] The present invention can provide a device and a method capable of obtaining the mode field diameter of each spatial mode of an optical fiber having a core in which a plurality of spatial modes can propagate from a near-field pattern.

Brief Description of the Drawings

[0018] [Figure 1] It is a diagram for explaining a configuration example of the mode field diameter acquisition device according to the present embodiment. [Figure 2] It is a process diagram for explaining the mode field diameter acquisition method of the present embodiment. [Figure 3] It is a diagram for explaining the relationship between the theoretical value and the estimated value of the connection loss.

Mode for Carrying Out the Invention

[0019] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Note that the present disclosure is not limited to the embodiments shown below. These examples are merely illustrative, and the present disclosure can be implemented in various modified and improved forms based on the knowledge of those skilled in the art. In the present specification and drawings, components having the same reference numerals indicate the same components.

[0020] (Embodiment) FIG. 1 is a diagram for explaining a configuration example of the mode field diameter acquisition device according to the present embodiment. The mode field diameter acquisition device 100 of the present embodiment is A device for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, A near-field pattern acquisition unit 10 acquires a near-field pattern of any spatial mode, A mode field diameter acquisition unit 11 acquires the mode field diameter of a spatial mode using the near-field pattern acquired by the near-field pattern acquisition unit 10 and a mathematical formula based on the variational expression of the propagation constant for the spatial mode. It is characterized by having the following features.

[0021] The near-field pattern acquisition unit 10 is, for example, an electromagnetic field analysis simulator that calculates the electromagnetic field distribution of an arbitrary spatial mode based on a given refractive index distribution, or an electric field distribution measurement device that measures a near-field pattern from test light output from the optical fiber under test.

[0022] The mode field diameter acquisition unit 11 acquires the mode field diameter of the spatial mode using the near-field pattern acquired by the near-field pattern acquisition unit 10 and a mathematical formula based on the variational expression of the propagation constant for the spatial mode. Details of acquiring the mode field diameter will be described later.

[0023] Figure 2 is a process diagram illustrating the method for obtaining the mode field diameter in this embodiment. A method for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, Near-field pattern acquisition procedure S1 for acquiring a near-field pattern of an arbitrary spatial mode, A mode field diameter acquisition procedure S2 is performed to acquire the mode field diameter of the spatial mode using the near-field pattern acquired in the near-field pattern acquisition procedure and a mathematical formula based on the variational expression of the propagation constant for the spatial mode. It is characterized by performing the following.

[0024] The following describes the calculation process performed by the mode field diameter acquisition unit 11 in the mode field diameter calculation procedure S2 to acquire the mode field diameter. Linear polarization modes (LP) with azimuthal and radial orders of ν and μ in the core of a cylindrical symmetric structure. νμ The electric field distribution ψ (mode) depends on the radial coordinates. νμ The following wave equation is satisfied (Non-Patent Document 4).

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[0025] However, k0 is the wavenumber in a vacuum, n is the refractive index distribution that depends on the radial coordinate, and β νμ is LP νμ The mode propagation constant, r, represents the radial coordinate. From this wave equation, the propagation constant β νμ The variational expression relating to can be expressed by the following equation (Non-Patent Document 4).

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[0026] From the second and third terms of this equation, LP νμ The mode MFD can be calculated using either equation (4) or equation (5) below.

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[0027] Equations (4) and (5) differ only in the presence or absence of the coefficient √(ν+2μ-1), but this is due to differences in the definition of MFD in multimode fibers, and essentially represent the same MFD.

[0028] Note that the MFD in equations (1) and (5) is a value corresponding to the spot size when the electric field distribution of the mode to be acquired is approximated by a Laguerre-Gaussian distribution, and in this case, the connection loss (dB) can be calculated by the following equation (6).

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[0029] Furthermore, when using the MFD in equation (4), the connection loss (dB) can be calculated using the following equation (7). The connection loss calculated using equations (4) and (6) is equal to the connection loss calculated using equations (5) and (6).

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[0030] Furthermore, the mode field diameter acquisition unit 11 can also be implemented using a computer and a program, and the program can be recorded on a recording medium or provided via a network.

[0031] (Examples) Numerical calculations were performed to confirm that equation (4) or (5) is more effective than equation (1) in estimating the connection loss of an optical fiber having a core capable of propagating multiple spatial modes. The optical fiber used in the numerical calculations (the optical fiber under test) was a step-type optical fiber with a core diameter of 21 μm and a relative refractive index difference of 0.45%.

[0032] Figure 3 illustrates the relationship between theoretical and estimated connection loss. Figures 3(a) to 3(d) show the results for LP01 mode, LP11 mode, LP21 mode, and LP02 mode, respectively. The horizontal axis represents the axial misalignment (μm) between the connected optical fibers. The vertical axis represents the connection loss (dB) on a logarithmic scale. The solid line represents the theoretical value of connection loss. The dashed line represents the connection loss estimated using the MFD calculated by equation (1) and equation (6). The dotted line represents the connection loss estimated using the MFD calculated by equation (5) and equation (6).

[0033] Figure 3 shows that for LP01 and LP02 modes, where the circumferential mode order is 0, the connection losses estimated from the MFDs in equations 1 and 5 both match the theoretical values. On the other hand, for LP11 and LP21 modes, where the circumferential mode order is not 0, the connection loss estimated from the MFD in equation (5) matches the theoretical value better than the connection loss estimated from the MFD in equation (1). From these results, it can be seen that the MFD obtained by this mode field diameter acquisition method is effective in estimating the connection loss of each spatial mode in optical fibers having a core capable of propagating multiple spatial modes. [Explanation of symbols]

[0034] 10: Near-field pattern acquisition unit 11: Mode field diameter acquisition unit 100: Mode field diameter acquisition device

Claims

1. A device for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, A mode field diameter acquisition unit that acquires the mode field diameter of an arbitrary spatial mode using the near-field pattern of that spatial mode and a mathematical formula based on the variational expression of the propagation constant for that spatial mode. A mode field diameter acquisition device characterized by comprising the following features.

2. The mode field diameter acquisition device according to claim 1, characterized in that the mode field diameter acquisition unit calculates the mode field diameter using the number C1. [Math C1] However, MFD is the mode field diameter, ν and μ are the mode orders in the azimuthal and radial directions of the spatial mode to be acquired, and ψ νμ LP depends on the radius coordinates νμ The electric field distribution of the mode; r represents the radial coordinate.

3. The mode field diameter acquisition device according to claim 1, characterized in that the mode field diameter acquisition unit calculates the mode field diameter using the number C2. [Math C2] However, MFD is the mode field diameter, ν and μ are the mode orders in the azimuthal and radial directions of the spatial mode to be acquired, and ψ νμ LP depends on the radius coordinates νμ The electric field distribution of the mode; r represents the radial coordinate.

4. The mode field diameter acquisition device according to claim 2, characterized in that the mode field diameter acquisition unit calculates the connection loss using the number C3. [Math C3] However, d represents the amount of axial misalignment.

5. The mode field diameter acquisition device according to claim 3, characterized in that the mode field diameter acquisition unit calculates the connection loss using the number C4. [Math C4] However, d represents the amount of axial misalignment.

6. The mode field diameter acquisition device according to claim 1, further comprising a near-field pattern acquisition unit for acquiring the aforementioned near-field pattern.

7. A method for obtaining the mode field diameter of each spatial mode of an optical fiber having a core capable of propagating multiple spatial modes from a near-field pattern, A procedure for obtaining the mode field diameter of an arbitrary spatial mode, using the near-field pattern of that spatial mode and a mathematical formula based on the variational expression of the propagation constant for that spatial mode. A method for acquiring mode field diameter, characterized by performing the following.

8. A program for realizing a computer as each functional unit in the mode field diameter acquisition device according to any one of claims 1 to 5.

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