Method for determining cutoff wavelength of multicore optical fiber

Abstract

This method for determining a cutoff wavelength of a multicore optical fiber (MCF) determines, as the cutoff wavelength of the MCF, a wavelength at which, when the number of cores of the MCF is N, a decibel value ΔaMC [dB] of a ratio between power of all modes including a high-order mode in which light enters all cores of the MCF of a predetermined length and in a predetermined bent state and power of an operation mode is Δath / N [dB].

Description

Method for determining the cutoff wavelength of multicore optical fibers

[0001] This disclosure relates to a method for determining the cutoff wavelength of a multicore optical fiber. This application claims priority under Japanese application No. 2024-164061, filed on September 20, 2024, and incorporates all the provisions of the said Japanese application.

[0002] The cutoff wavelength is the wavelength above which unwanted higher-order modes are blocked, guaranteeing single-mode operation (or operation with a desired number of propagation modes). Non-patent document 1 discloses a method for measuring the cutoff wavelength of a single-mode optical fiber (SMF). The cutoff wavelength is measured using the transmission spectrum obtained when all modes are excited and all modes are received in the core.

[0003] Non-patent documents 2 and 3 disclose a method for measuring the cutoff wavelength of a multicore optical fiber (MCF) by simultaneously receiving light from all cores. This method allows for simpler measurement of the MCF cutoff wavelength compared to methods that measure the cutoff wavelength of each core individually.

[0004] ITU-T G. 650. 1(10 / 2020), “Definitions and test methods for linear, deterministic attributes of single-mode fiber and cable” M. Ohashi, “Simple Technique for Measuring Cut-Off Wavelength of Multi-Core Fiber (MCF) and Its Definition”, ACP Technical Digest, AF3A. 4R. Okuno, “Cutoff Wavelength Measurement of Two Core Multi-core Fiber”,2013 18th OptoElectronics and Communications Conference, MS1-3T. Nakanishi et al., “Reproducible Cutoff Wavelength Measurement Technique for Trench-assisted BIF,”, OptoElectron. Commun. Conf. (OECC), Kaohsiung, Taiwan, 2011, pp. 805-806

[0005] The method for determining the cutoff wavelength of an MCF according to this disclosure is a method for determining the cutoff wavelength of an MCF, wherein, given the number of cores of the MCF, Δa is the decibel value of the ratio of the power of all modes, including higher-order modes, incident on all cores of the MCF at a predetermined length and in a predetermined bending state, to the power of the operating mode. ＭＣ [dB] is Δa ｔｈ The wavelength at which the value is / N [dB] is determined as the cutoff wavelength of the MCF.

[0006] Figure 1 is a graph showing examples of Δa determined by the bending method and the multimode excitation method for an SMF with a cutoff wavelength of 1400 nm. Figure 2 shows the spectra of Δa(λ) for each core of the MCF according to the first embodiment. ＭＣ The spectrum of (λ), and NΔa ＭＣIt is a graph showing the spectrum of (λ). FIG. 3 shows the same data as FIG. 2, with the vertical axis on a logarithmic scale and Δa ｔｈ in the vicinity of (0.1 dB) enlarged and the horizontal axis in the vicinity of 1400 nm enlarged while remaining on a linear scale. FIG. 4 shows the spectra of Δa(λ) of each core of the MCF according to the second embodiment, Δa ＭＣ the spectrum of (λ), and the spectrum of NΔa ＭＣ (λ). FIG. 5 shows the same data as FIG. 4, with the vertical axis on a logarithmic scale and Δa ｔｈ in the vicinity of (0.1 dB) enlarged and the horizontal axis in the vicinity of 1400 nm enlarged while remaining on a linear scale. FIG. 6 shows the spectra of Δa(λ) of each core of the MCF according to the third embodiment, Δa ＭＣ the spectrum of (λ), and the spectrum of NΔa ＭＣ (λ). FIG. 7 shows the same data as FIG. 6, with the vertical axis on a logarithmic scale and Δa ｔｈ in the vicinity of (0.1 dB) enlarged and the horizontal axis in the vicinity of 1400 nm enlarged while remaining on a linear scale. FIG. 8 shows the spectra of Δa(λ) of each core of the MCF according to the fourth embodiment, Δa ＭＣ the spectrum of (λ), and the spectrum of NΔa ＭＣ (λ). FIG. 9 shows the same data as FIG. 8, with the vertical axis on a logarithmic scale and Δa ｔｈ in the vicinity of (0.1 dB) enlarged and the horizontal axis in the vicinity of 1400 nm enlarged while remaining on a linear scale.

[0007] In the MCF, it is necessary to measure the value of the longest cut-off wavelength among the individual cut-off wavelengths of all cores. In the methods described in Non-Patent Documents 2 and 3, due to the influence of cores having short cut-off wavelengths, a value shorter than the true value may be measured as the cut-off wavelength of the MCF. In this case, there is no guarantee that unnecessary higher-order modes will be blocked for wavelengths longer than the cut-off wavelength.

[0008] An object of the present disclosure is to provide a method for determining the cut-off wavelength of an MCF that can guarantee the blocking of unnecessary higher-order modes and is simple.

[0009] This disclosure provides a simple method for determining the cutoff wavelength of an MCF that can guarantee the blocking of unwanted higher-order modes.

[0010] First, the embodiments of this disclosure will be listed and described.

[0011] (1) A method for determining the cutoff wavelength of an MCF according to one aspect of the present disclosure is a method for determining the cutoff wavelength of an MCF, wherein, if the number of cores of the MCF is N, the decibel value Δa is the ratio of the power of all modes, including higher-order modes, incident on all cores of the MCF for a predetermined length and in a predetermined bending state, to the power of the operating mode. ＭＣ [dB] is Δa ｔｈ The wavelength at which the value is / N [dB] is determined as the cutoff wavelength of the MCF. In the method for determining the cutoff wavelength of the MCF, Δa ＭＣ [dB] is Δa ｔｈ The wavelength at which the cutoff frequency is / N [dB] is the upper limit or upper bound of the cutoff wavelength of the core with the longest individual cutoff wavelength among all cores. Since this wavelength is determined as the cutoff wavelength, it is possible to guarantee the blocking of unwanted higher-order modes. Since the cutoff wavelength of each core is not measured individually, the cutoff wavelength can be determined simply.

[0012] (2) In (1) above, the cutoff wavelength of the multicore optical fiber may be determined as the upper limit or upper bound of the cutoff wavelength of the core that has the longest individual cutoff wavelength.

[0013] (3) In (1) or (2) above, Δa ＭＣ [dB] is Δa ｔｈ The wavelength at which the value becomes [dB] may be determined as the lower limit or lower bound of the cutoff wavelength of the core with the longest individual cutoff wavelength among all the cores of the MCF. In this case, not only the upper limit or upper bound of the cutoff wavelength of the core with the longest individual cutoff wavelength can be determined, but also the lower limit or lower bound.

[0014] (4) In any of (1) to (3) above, Δa ｔｈ[dB] may be 0.1 dB. In this case, the cutoff wavelength as defined in Non-Patent Document 1 can be easily determined.

[0015] (5) In any of (1) to (4) above, the number of operating modes M ｏｐ And, the cutoff mode is several M ｃ The ratio ρ is When expressed as, Δa ｔｈ [dB] is, This is also acceptable. In this case, the cutoff wavelengths of multimode optical fibers, including ordinary single-mode optical fibers that do not maintain polarization, and polarization-maintaining optical fibers can be appropriately measured and calculated.

[0016] (6) In any of (1) to (5) above, the predetermined length may be 2 m, and the predetermined bending state may be a state in which a bend of 140 mm or more with a radius of 140 mm or more is applied for one full turn. In this case, the fiber cutoff wavelength specified in Non-Patent Document 1 can be easily determined.

[0017] (7) In any of (1) to (6) above, the predetermined length may be 22 m, and the predetermined bending state may be a state in which a bend of 20 m with a radius of 140 mm or more is applied, and a bend of 40 mm with a radius of 40 mm is applied to both ends of the bend with a radius of 140 mm or more for one full turn. In this case, the cable cutoff wavelength specified in Non-Patent Document 1 can be easily determined.

[0018] (8) In any of (1) to (7) above, Δa ＭＣ The noise contained in the [dB] measurement may be removed. In this case, accurate measurements can be performed with reduced noise influence.

[0019] (9) In the above (8), in the above process, Δa ＭＣ The measurement value in [dB] is fitted, and the formula obtained by the fitting is Δa ＭＣ It may be considered as [dB]. In this case, Δa ＭＣ Noise included in the [dB] measurement can be removed.

[0020] (10) In the above (9), the formula is, And here, N ｆ C and D are fitting variables, and N ｆ 1 ≤ N ｆ It may also be a real number satisfying ≤ N.

[0021] (11) In (9) above, the formula is Here, C and G may be fitting variables. In this case, the formula becomes simpler and the number of fitting variables decreases.

[0022] (12) In the above (9), the formula is, And here, the sequence {C ｎ}, and the sequence {D ｎ Each term in} is a fitting variable, and n may be a natural number from 1 to N. In this case, Δa of all cutoff modes for each of the N cores. ＭＣ Since the effect on (λ) is taken into consideration, a more accurate Δa ＭＣ (λ) fitting can be performed.

[0023] (13) In any of the above (9) to (12), in the above process, Δa ＭＣ The measurement values ​​in [dB] may be fitted using the least squares method.

[0024] [Details of Embodiments of the Disclosure] Specific examples of the method for determining the cutoff wavelength of a multicore optical fiber according to the Disclosure will be described below with reference to the drawings. The present invention is not limited to these examples, and is intended to include all modifications within the meaning and range equivalent to the claims, as indicated by the claims. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant descriptions are omitted.

[0025] Regarding methods for measuring the cutoff wavelength of SMF, Section 6.3 of Non-Patent Document 1 recommends a standard measurement method. The measurement method according to this embodiment extends the method described in Section 6.3 of Non-Patent Document 1 to provide a simple method for measuring the cutoff wavelength of MCF. For parts not detailed in this specification, refer to and apply or mutatis mutandis Section 6.3 of Non-Patent Document 1.

[0026] In general, with optical fibers used for long-distance transmission, if higher-order modes other than the fundamental mode (LP01 mode) are guided at the wavelength used for signal transmission (operating wavelength), signal quality degradation occurs due to interference between modes. For this reason, SMFs are used in which higher-order modes other than the fundamental mode are not guided at the operating wavelength in principle, i.e., they are cut off. Alternatively, SMFs are used in which the propagation loss of higher-order modes is sufficiently large at the operating wavelength to effectively cut them off. In Non-Patent Literature 1, the cutoff wavelength is defined as the longest wavelength at which the propagation loss of higher-order modes is sufficiently large to effectively prevent them from guiding, and is defined as "the wavelength at which the ratio of the total power including higher-order modes incident on the optical fiber to the power of the fundamental mode (LP01) is 0.1 dB."

[0027] In principle, the above standard measurement method can also be applied to MCFs where each core operates in single mode at the operating wavelength. The above definition of the cutoff wavelength in SMFs assumes that there is only one core in the optical fiber. In the case of MCFs, the cutoff wavelength of each core can be defined as "the wavelength at which the ratio of the total power including higher-order modes incident on the core under measurement to the power of the fundamental mode (LP01) is 0.1 dB."

[0028] To measure the cutoff wavelength of the first core (one core) of an MCF, first, light from a light source is input to the first end of the MCF so as to excite only the first core in all modes. Then, at the second end, only the light emitted from the first core, which has been excited in all modes, is received by a photodetector. This allows the cutoff wavelength of the first core of the MCF to be measured.

[0029] The MCF may be configured such that, at the first end, no light from the light source is input to cores other than the first core, and at the second end, light emitted from cores other than the first core can be ignored. Alternatively, the MCF may be configured such that light from the light source is input to cores other than the first core at the first end, and light is emitted from cores other than the first core at the second end. In a multi-core system, it is assumed that the crosstalk between higher-order modes is sufficiently small near the cutoff wavelength. In this case, the cutoff wavelength of the first core of the MCF can be approximately measured by either "inputting light to multiple cores, not just the first core, at the first end, and receiving only the light emitted from the first core at the second end," or "inputting light only to the first core at the first end, and receiving light emitted from multiple cores, including the first core, at the second end." In a multi-core system, if the crosstalk between higher-order modes is not sufficiently small near the cutoff wavelength, measurement errors may occur.

[0030] In either case, it is necessary to measure the cutoff wavelength of each core individually. If the core spacing of the MCF is narrow, when measuring the cutoff wavelength of each core individually, it is not possible to excite and receive all modes of all modes in only one core of the MCF; the modes of adjacent cores are also excited and received. In this way, the measurement accuracy of the cutoff wavelength is reduced because it is affected by the cutoff wavelength of cores other than the core being measured. This embodiment provides a method for easily determining the cutoff wavelength of an MCF without having to measure the cutoff wavelength of each core individually.

[0031] In recent years, research and development have been conducted on mode division multiplexing (MODD) technology, which uses higher-order modes other than the fundamental mode for signal transmission. Therefore, we investigated a method for determining the cutoff wavelength that can be applied to multimode cores for MODD multiplexing. At the operating wavelength, the low-order spatial modes used for optical transmission are called operating modes. At the operating wavelength, the lowest-order higher-order mode that should be effectively cut off is called the cutoff mode.

[0032] The ratio of the power of all modes, including higher-order modes, incident on the core to the power of the operating mode, expressed in decibels, is a predetermined value Δa. ｔｈThe cutoff wavelength can be defined as the wavelength at which the value becomes [dB]. In the definition of the SMF cutoff wavelength recommended in Non-Patent Document 1, the operating mode is only the basic mode (LP01), and Δa ｔｈ It is 0.1 dB. In other words, Δa ｔｈ [dB] is a parameter that defines the cutoff wavelength at a single core, and is a decibel value representing the ratio of the power of all modes, including higher-order modes, incident on the core to the power of the operating mode.

[0033] As a basis for considering methods for determining the cutoff wavelength of the MCF, we will organize and examine the mathematical formulas related to the definition of the cutoff wavelength of the SMF. The power of all modes, including higher-order modes, is P ｔｏｔ , Power of operating mode P ｏｐ The number of operating modes is M ｏｐ , the power of the cutoff mode P ｃ The number of cutoff modes is M ｃ P is the power incident on one mode. ０ , the loss in cutoff mode is α ｃ If we denote the power as [dB], the decibel value Δa(λ) [dB] of the ratio of the power of all modes, including higher-order modes, incident on the core to the power of the operating mode is expressed by equation (1). The number of operating modes M ｏｐ And, the cutoff mode is several M ｃ The ratio ρ is given by equation (2).

[0034] In SMF, there is only one operating mode, LP01 mode, so M ｏｐ It is 1. Since there are two cutoff modes due to the degeneration of the LP11 mode, M ｃ ρ is 2. Therefore, ρ is 2. Δa(λ) is Δa ｔｈ α when this is the case ｃ α ｃ，ｔｈ This can be expressed by equation (3). The cutoff wavelength is Δa(λ) ｔｈ The wavelength that results in, or α ｃ is α ｃ，ｔｈ This is the wavelength. Δa ｔｈ If it is 0.1 dB, then α ｃ，ｔｈThis is approximately 19.3 dB.

[0035] It is also possible that ρ is not 2. For example, even in an SMF, if the core shape is extremely non-circular and the LP11 mode is not degenerate, ρ will be 1. In the case of a multimode core with multiple operating modes, the value of ρ is almost always less than 2. As the number of operating modes increases, ρ may take a value of 1 or less. ρ is basically greater than 0 and usually takes a value of 2 or less. In this case, Δa ｔｈ You may leave it at 0.1 dB. The same Δa as when measuring the SMF cutoff wavelength. ｔｈ Using this as a reference, the cutoff wavelengths of MCFs with various types of cores can be measured.

[0036] However, if ρ is less than 2, Δa ｔｈ If we leave it at 0.1 dB, α ｃ，ｔｈ This becomes less than approximately 19.3 dB. Therefore, it is possible that the loss of the cutoff mode at the cutoff wavelength is not large enough (effectively, the cutoff wavelength is not sufficiently cut off). To avoid this, Δa ｔｈ [dB] may be expressed as in equation (4). This means that even if ρ is not 2, α ｃ，ｔｈ This can be reduced to approximately 19.3 dB.

[0037] Δa is the decibel value of the ratio between the power of all modes, including higher-order modes, incident on the entire core of the MCF, and the power of the operating mode. ＭＣ Let (λ) [dB]. Let N be a natural number greater than or equal to 2, and let n be a natural number from 1 to N. Let N be the number of cores in the MCF, and P be the number of the nth core. ｏｐ , P ｃ , α ｃ P ｏｐ，ｎ , P ｃ，ｎ , α ｃ，ｎ Then, Δa ＭＣ (λ) can be expressed by equation (5).

[0038] At this time, the sequence x ｎ Regarding this, as shown in equation (6), it is obvious that the mean value will be less than or equal to the maximum value. Using this, equation (7) holds true.

[0039] NΔa ＭＣ Consider NΔa. From Equation (5), NΔa ＭＣ can be expressed by Equation (8). Here, by utilizing the Taylor expansion of (1 + x) when x ≥ 0, it can be seen that Equation (9) holds. Ｎ Therefore, when Equation (9) is used in Equation (8), Equation (10) holds. Thus, when Equation (9) is used in Equation (8), Equation (10) holds.

[0040] For the sequence {x ｎ}, if x ｎ ≥ 0 for all n, as shown in Equation (11), it is obvious that the sum of the sequence {x ｎ} is not less than the maximum value of x ｎ . By using this, it can be seen that Equation (12) holds.

[0041] From Equation (7) and Equation (12), Equation (13) holds. In Equation (13), is equivalent to the ratio Δa ｃ of the power of all modes including the higher-order modes incident on the core with the smallest α ｍａｘ，ｃ (the longest cutoff wavelength) to the power of the operating mode. Therefore, the wavelength at which Δa ｍａｘ，ｃ (λ) becomes Δa ｔｈ is not less than the wavelength at which Δa [[ID=...]] (λ)がΔa ＭＣ (λ)がΔa ｔｈ となる波長以上であり、かつ、NΔa ＭＣ (λ)がΔa ｔｈ となる波長以下である。言い換えると、Δa ｍａｘ，ｃ (λ)がΔa ｔｈ となる波長は、Δa ＭＣ (λ)がΔa ｔｈ となる波長以上であり、かつ、Δa ＭＣ (λ)がΔa ｔｈ / Nとなる波長以下である。

[0042] ここで、Δa ＭＣLet's consider how to determine (λ). When determining Δa(λ) when measuring the cutoff wavelength of an SMF, it is difficult to individually measure the "power of all modes" and the "power of the operating mode" using only one specific wavelength. Therefore, first, light is incident on the first end of the SMF under incidence conditions that can equally excite all modes of the SMF. Specifically, a multimode optical fiber (MMF) is connected to the SMF to be measured and light is incident on it, or light is incident using an appropriate optical system with a large spot diameter and numerical aperture. Next, the transmission spectrum is measured in a measurement system that receives all the light emitted from the second end, and the component in the trend of the transmission spectrum that changes (rises) from long wavelength to short wavelength is determined as Δa(λ).

[0043] This method is disclosed in sections 6.3.1.3.2 and 6.3.1.3.3 of Non-Patent Document 1. Here, the so-called bending method is disclosed as method a), and the so-called multimode excitation method is disclosed as method b). In both the bending method and the multimode excitation method, at the first end of the SMF (sample) to be measured, which is of a predetermined length and in a predetermined bending state, light from a light source is input to excite the core in all modes, and at the second end, the power spectrum P1 (λ) of the light emitted from the all-mode excited core is measured.

[0044] In the bending method, the sample is bent at least once with a sufficiently small radius. Then, with the cutoff mode (LP11 mode in the case of an SMF) filtered near the cutoff wavelength, the power spectrum P2(λ) of the light emitted from the all-mode excited core at the second end is measured. In the multimode excitation method, the sample is replaced with a short MMF of less than 10 m, for example, about 1 to 2 m. Then, the power spectrum P3(λ) of the light emitted from the MMF is measured. The ratio of the output power from the sample to the reference power (P2(λ) or P3(λ)) is calculated in decibels using equation (14). Here, i is 2 in the bending method and 3 in the multimode excitation method.

[0045] Assuming that a(λ) is linear in the wavelength range longer than the cut-off wavelength, Δa(λ) can be expressed by Equation (15). A ｕ and B ｕ are obtained by fitting A + Bλ to Δa(λ) in an appropriate range in the wavelength range longer than the cut-off wavelength. In the bending method, A ｕ and B ｕ may both be set to 0.

[0046] When determining Δa ＭＣ (λ), light may be incident from the first end under an incident condition that can equally excite all modes of all cores of the MCF. Specifically, an MMF having a numerical aperture and core diameter sufficient to equally excite all modes of all cores of the MCF to be measured may be connected to the MCF to be measured, and light may be incident. Alternatively, light may be incident using an optical system having a numerical aperture and spot diameter sufficient to equally excite all modes of all cores of the MCF to be measured.

[0047] When determining Δa(λ), the bending method applied to the measurement of the SMF and the multimode excitation method may be applied by reference. For the MCF (sample) to be measured having a predetermined length and in a predetermined bending state, light from a light source is input at the first end of the SMF so as to equally excite all modes of all cores, and the power spectrum P ＭＣ，１ (λ) of the light emitted from all cores at the second end is measured. As an example, the predetermined length is 2 m, and the predetermined bending state is a state in which a bend with a radius of 140 mm or more is applied for one turn. As a second example, the predetermined length is 22 m, and the predetermined bending state is a state in which a bend with a radius of 140 mm or more is applied for 20 m, and bends with a radius of 40 mm are applied for one turn at both ends of the bend with a radius of 140 mm or more.

[0048] In the bending method, a bend with a sufficiently small radius is applied to the sample for one or more turns, and in a state where the cut-off mode is filtered near the cut-off wavelength, the power spectrum P of the light emitted from the core excited in all modes at the second end ＭＣ，２(λ) is measured. In the multimode excitation method, the sample is replaced with a short MMF, and the power spectrum P of the light emitted from the MMF is measured. ＭＣ，３ (λ) is measured. The length of the MMF is less than 10 m, for example, about 1 to 2 m. Next, the reference power (P) is measured. ＭＣ，２ (λ) or P ＭＣ，３ The ratio of the output power from the sample to (λ) is calculated in decibels using equation (16). Here, i is 2 in the bending method and 3 in the multimode excitation method.

[0049] Δa in the wavelength range longer than the cutoff wavelength ＭＣ Assuming that (λ) is a straight line, Δa ＭＣ (λ) can be shown by equation (17). A ＭＣ，ｕ and B ＭＣ，ｕ Δa is in an appropriate range of wavelengths longer than the cutoff wavelength. ＭＣ (λ) with A ＭＣ，ｕ +B ＭＣ，ｕ It is obtained by fitting λ. In the bending method, A ＭＣ，ｕ and B ＭＣ，ｕ Both can be set to 0.

[0050] Figure 1 is a graph showing examples of Δa determined by the bending method and the multimode excitation method for an SMF with a cutoff wavelength of 1400 nm. In the bending method, in the wavelength range significantly shorter than the cutoff wavelength, the determined Δa(λ) deviates from the theoretical value of Δa(λ) expressed in equation (1). Although not shown in the figure, in the multimode excitation method as well, further higher-order modes are guided at shorter wavelengths, resulting in a deviation from the theoretical value of Δa(λ) expressed in equation (1).

[0051] Therefore, the cutoff wavelength may be calculated using Δa(λ) determined near the cutoff wavelength. The deviation from the theoretical value and the use of the value determined near the cutoff wavelength are related to Δa ＭＣ The case of (λ) is similar. For example, Δa used in calculating the cutoff wavelength. ＭＣ The lower limit of the wavelength range of (λ) is Δa after excluding measurement noise. ＭＣIn the wavelength range where (λ) exceeds 0.1 dB and is less than or equal to the longest wavelength, Δa ＭＣ (λ) is greater than or equal to the longest wavelength at which it takes a maximum value, or Δa ＭＣ (λ) - Δa ＭＣ (λ + Δλ) may be greater than or equal to the longest wavelength at which it takes a maximum value. Here, Δλ is Δa ＭＣ (λ) is the wavelength step size when measured, or a multiple thereof, and may be, for example, 10 nm.

[0052] Here, Δa is in a format similar to that of Non-Patent Document 1. ＭＣ The method for determining Δa is described, ＭＣ If a value equivalent to Δa can be appropriately calculated from the measured values, then use a method other than those described above. ＭＣ You may calculate this.

[0053] As described above, in the methods described in Non-Patent Documents 2 and 3, the measured cutoff wavelength of the MCF may be shorter than the true value, so a margin must be taken into account for the measured cutoff wavelength. For example, if the measured cutoff wavelength is longer than a predetermined value such as 10 nm, 20 nm, or 30 nm, it is assumed that unwanted higher-order modes are blocked. Since the cutoff wavelength needs to be shortened by an extra amount due to the margin, the design center value must be a cutoff wavelength that is significantly shorter than the specification. This weakens the confinement of light to each core, increasing inter-core crosstalk and bending loss. Because the required margin is not certain, it cannot be guaranteed that the cutoff wavelength is below the desired value for all cores.

[0054] In contrast, the method for determining the cutoff wavelength of an MCF according to this embodiment is, where N is the number of cores in the MCF, the decibel value Δa is the ratio of the power of all modes, including higher-order modes, incident on all cores of an MCF of a predetermined length and a predetermined bending state, to the power of the operating mode. ＭＣ [dB] is Δa ｔｈ The wavelength at which the value is / N [dB] is determined as the cutoff wavelength of the MCF. Δa ＭＣ [dB] is Δa ｔｈThe wavelength at which / N [dB] is the upper limit or upper bound of the cutoff wavelength of the core with the longest individual cutoff wavelength among all cores. Since this wavelength is determined as the cutoff wavelength, it is possible to guarantee the blocking of unwanted higher-order modes. Since there is no need to take a margin, the above problems caused by taking a margin do not occur. Since the cutoff wavelength of each core is not measured individually, the cutoff wavelength can be determined simply. This determination method is Δa ＭＣ A step to measure [dB] and Δa ＭＣ [dB] is Δa ｔｈ This measurement and calculation method includes a step of calculating the wavelength at which the value becomes / N [dB].

[0055] In the method for determining the cutoff wavelength of the MCF according to this embodiment, Δa ＭＣ [dB] is Δa ｔｈ The wavelength at which the value is [dB] is determined as the lower limit or lower bound of the cutoff wavelength of the core with the longest individual cutoff wavelength among all the cores of the MCF. This allows us to determine not only the upper limit or upper bound of the cutoff wavelength of the core with the longest individual cutoff wavelength, but also the lower limit or lower bound.

[0056] (Example of simultaneous measurement in MCF) An example of measuring the cutoff wavelength of an MCF by simultaneous reception of light to all cores, that is, an example in which light is input to all cores of the MCF simultaneously and the cutoff wavelength of all cores is measured in one step, will be described. Figure 2 shows the spectrum of Δa(λ) of each core of the MCF according to the first embodiment, Δa ＭＣ The spectrum of (λ), and NΔa ＭＣ This is a graph showing the spectrum of (λ). In the first embodiment, N = 4. Δa ｔｈ The cutoff wavelengths at which the signal strength is 0.1 dB are 1400 nm for core 1, 1350 nm for core 2, 1300 nm for core 3, and 1250 nm for core 4. The cutoff wavelengths for cores 1 through 4 are different from each other. The Δa(λ) of core 1, which has the longest cutoff wavelength, is Δa ＭＣ (λ) or greater, NΔa ＭＣ It can be seen that it is less than or equal to (λ).

[0057] Figure 3 shows the same data as in Figure 2, but with the vertical axis on a logarithmic scale, representing Δa. ｔｈThis graph shows the area around (0.1 dB) magnified, and the area around 1400 nm magnified while keeping the horizontal axis a linear scale. The Δa(λ) of core 1, which has the longest cutoff wavelength, is Δa ＭＣ (λ) or greater, NΔa ＭＣ (λ) is less than or equal to NΔa ＭＣ It can be seen that it is slightly less than (λ). That is, Δa(λ) is Δa ｔｈ The wavelength at which the level becomes (0.1 dB) (= cutoff wavelength of core 1) is such that Δa(λ) is Δa ｔｈ The wavelength is greater than or equal to NΔa ＭＣ (λ) is Δa ｔｈ It is below the wavelength at which this occurs.

[0058] Figure 4 shows the Δa(λ) spectra of each core of the MCF according to the second embodiment. ＭＣ The spectrum of (λ), and NΔa ＭＣ This is a graph showing the spectrum of (λ). In the second embodiment, N = 4. Δa ｔｈ The cutoff wavelength at which the signal strength is 0.1 dB is 1400 nm for all four cores. The cutoff wavelengths of cores 1 through 4 are equal to each other. The Δa(λ) of all cores with the longest cutoff wavelength is Δa ＭＣ (λ) or greater, NΔa ＭＣ It can be seen that it is less than or equal to (λ).

[0059] Figure 5 is a graph of the same data as in Figure 4, but with the vertical axis set to a logarithmic scale and magnified around 0.1 dB, and the horizontal axis kept on a linear scale and magnified around 1400 nm. The Δa(λ) of all cores is Δa ＭＣ (λ) or greater, NΔa ＭＣ (λ) is less than or equal to Δa ＭＣ It can be seen that it overlaps with (λ).

[0060] Figure 6 shows the Δa(λ) spectra of each core of the MCF according to the third embodiment. ＭＣ The spectrum of (λ), and NΔa ＭＣ This is a graph showing the spectrum of (λ). In the third embodiment, N = 12. Δa ｔｈThe cutoff wavelength at which the signal strength is 0.1 dB is 1400 nm for core 1 and 1300 nm for cores 2 through 12. The cutoff wavelengths for cores 2 through 12 are equal to each other. The cutoff wavelength for core 1 is different from the cutoff wavelengths for cores 2 through 12.

[0061] The Δa(λ) of core 1, which has the longest cutoff wavelength, is Δa ＭＣ (λ) or greater, NΔa ＭＣ It can be seen that (λ) is less than or equal to Δa. That is, Δa(λ) is Δa ｔｈ The wavelength at which the level becomes (0.1 dB) (= cutoff wavelength of core 1) is such that Δa(λ) is Δa ｔｈ The wavelength is greater than or equal to NΔa ＭＣ (λ) is Δa ｔｈ It is below the wavelength at which this occurs.

[0062] Figure 7 shows the same data as in Figure 6, but with the vertical axis on a logarithmic scale, resulting in Δa ｔｈ This graph shows the area around (0.1 dB) magnified, and the area around 1400 nm magnified while keeping the horizontal axis a linear scale. The Δa(λ) of core 1, which has the longest cutoff wavelength, is Δa ＭＣ (λ) or greater, NΔa ＭＣ (λ) is less than or equal to NΔa ＭＣ It can be seen that it is slightly less than (λ). That is, Δa(λ) is Δa ｔｈ The wavelength at which (λ) (0.1 dB) is the cutoff wavelength of core 1 is when Δa(λ) is Δa ｔｈ The wavelength is greater than or equal to NΔa ＭＣ (λ) is Δa ｔｈ It is below the wavelength at which this occurs.

[0063] Figure 8 shows the Δa(λ) spectra of each core of the MCF according to the fourth embodiment. ＭＣ The spectrum of (λ), and NΔa ＭＣ This is a graph showing the spectrum of (λ). In the fourth embodiment, N = 12. Δa ｔｈ The cutoff wavelength at which the signal strength is 0.1 dB is 1400 nm for all 12 cores. The cutoff wavelengths of cores 1 through 12 are equal to each other. The Δa(λ) of all cores with the longest cutoff wavelength is Δa ＭＣ (λ) or greater, NΔa ＭＣIt can be seen that it is less than or equal to (λ).

[0064] Figure 9 shows the same data as in Figure 8, but with the vertical axis on a logarithmic scale, representing Δa. ｔｈ This graph shows the area around (0.1 dB) magnified, and the area around 1400 nm magnified while keeping the horizontal axis a linear scale. The Δa(λ) of all cores is Δa ＭＣ (λ) or greater, NΔa ＭＣ (λ) is less than or equal to Δa ＭＣ It can be seen that it overlaps with (λ). That is, Δa(λ) is Δa ｔｈ The wavelength at which the level becomes (0.1 dB) (= cutoff wavelength of core 1) is such that Δa(λ) is Δa ｔｈ The wavelength is greater than or equal to NΔa ＭＣ (λ) is Δa ｔｈ It is below the wavelength at which this occurs.

[0065] Here, graphs for the cases N=4 and N=12 are shown as the first to fourth embodiments. However, as is clear from the formulas, this method is applicable as long as N is an integer of 2 or greater. However, N may also satisfy formula (18). When only one core has a long cutoff wavelength, near that longest cutoff wavelength, the Δa on the wavelength axis is affected by the change in the cutoff mode loss on the wavelength axis. ＭＣ The change in (λ) is Δa ｔｈ This concludes the explanation. Therefore, using the method according to this embodiment, Δa ＭＣ (λ) is Δa ｔｈ The wavelength at which this occurs can be determined.

[0066] For clarity, here we have Δa ＭＣ The explanation was given using graphs based on the theoretical value of (λ) or the value determined by the multimode excitation method, but Δa determined by the bending method ＭＣ (λ) However, near the cutoff wavelength, Δa ＭＣ A waveform equivalent to the theoretical value of (λ) can be obtained. Therefore, the method of this embodiment yields Δa obtained by either the multimode excitation method or the bending method. ＭＣ It can also be applied to the calculated value of (λ). It is similar to the determination of Δa(λ) in SMF, and similar to the determination of Δa in MCF. ＭＣThe lower limit of the wavelength range in which the determination of (λ) can be considered valid is Δa in the wavelength range below the longest wavelength exceeding 0.1 dB. ＭＣ (λ) is greater than or equal to the longest wavelength at which it takes a maximum value, or Δa ＭＣ (λ) - Δa ＭＣ The wavelength may be greater than or equal to the longest wavelength at which (λ + Δλ) takes its maximum value.

[0067] Δa ＭＣ If (λ) can be measured with sufficient accuracy, then Δa ＭＣ Using the measured value of (λ) as is, Δa ｍａｘ，ｃ (λ) is Δa ｔｈ As the upper limit of the wavelength, Δa ＭＣ (λ) is Δa ｔｈ You may also measure the wavelength at which / N occurs. Δa ｍａｘ，ｃ (λ) is Δa ｔｈ As the lower limit of the wavelength, Δa ＭＣ (λ) is Δa ｔｈ You may also measure the wavelength at which the ratio becomes / N.

[0068] (Noise Reduction Processing) Measurement noise referred to as "humps," disclosed in Section 6.3.1.3.4 and Figures 9b and 10b of Non-Patent Document 1, may interfere with accurate measurements. In addition, measurement noise from the optical and electrical systems originating from either or both the measurement environment and the measurement system may contribute to Δa. ｔｈ and Δa ｔｈ It can be greater than / N and may interfere with accurate measurement. In such cases, Δa ＭＣ The measured value of (λ) is fitted, and the formula obtained by the fitting is Δa ＭＣ It is considered to be [dB]. That is, in the method for determining the cutoff wavelength of the MCF according to the embodiment, Δa ＭＣ This process removes noise from the measured value in [dB]. ＭＣ The measurement value in [dB] is fitted, and the formula obtained by the fitting is Δa ＭＣ It is considered to be [dB].

[0069] Δa is defined by any of the following equations: (19), (20), (21), and (22). ＭＣ，ｆ Fitting this using the least squares method, Δa ＭＣ，ｆΔa after the measurement noise has been removed. ＭＣ It can also be considered as (λ). This allows for accurate measurements with reduced influence from measurement noise.

[0070]

[0071] The lower limit of the wavelength range for fitting is, for example, Δa, after ignoring any noise present. ＭＣ In the wavelength range where (λ) exceeds 0.1 dB and is less than or equal to the longest wavelength, Δa ＭＣ (λ) is greater than or equal to the longest wavelength (first wavelength) at which it takes a maximum value, or Δa ＭＣ (λ) - Δa ＭＣ The wavelength may be greater than or equal to the longest wavelength (second wavelength) at which (λ + Δλ) takes its maximum value.

[0072] The upper limit of the wavelength range for fitting is, for example, Δa, after ignoring any noise present. ＭＣ The fourth wavelength may be less than or equal to the wavelength obtained by adding an appropriate value from 10 nm to 200 nm to the longest wavelength (third wavelength) in which (λ) exceeds 0.1 dB. For example, in Appendix I of Non-Patent Document 1, the wavelengths corresponding to the third and fourth wavelengths in Δa(λ) in the case of SMF are shown as "lower wavelength" and "upper wavelength" of the "upper wavelength region," respectively. It is exemplified that "upper wavelength" is the wavelength obtained by adding 150 nm to "lower wavelength." The fourth wavelength in this embodiment may also be the wavelength obtained by adding 150 nm to the third wavelength.

[0073] Regarding the calculation method for "upper waverating region" and "transition region" as defined in Appendix I of Non-Patent Document 1, Δa ＭＣ Fitting may be performed within the range of the "upper waverating region" and "transition region" which can be calculated by applying (λ) to the same method.

[0074] Equations (19) and (20) are equivalent, and the fitting variables for equations (19) and (20) are Nｆ , C, and D. Measured Δa ＭＣ (λ) with Δa ＭＣ，ｆ When fitting, N ｆ This can be fitted within the range of equation (23).

[0075] Here, 1 / N ｆ This can also be considered as the approximate ratio of the core with the longest cutoff wavelength and the cores with cutoff wavelengths sufficiently close to the longest cutoff wavelength among the N cores. This allows us to calculate a unique value rather than the range of possible cutoff wavelengths for the core with the longest cutoff wavelength.

[0076] D is an approximation of the cutoff wavelength of the core with the longest cutoff wavelength. Therefore, D may be calculated as a measured value of the cutoff wavelength of the core with the longest cutoff wavelength. To facilitate fitting convergence, a third wavelength may be set as the initial value of D. Equations (19) and (20) make it easy to set the initial value of D.

[0077] When fitting using equation (21), the formula becomes simpler and the number of fitting variables decreases. However, setting the initial values ​​of the fitting variables, especially the initial value of G, may become more difficult. The fitting variables in equation (21) are C and G, but they are equivalent to those in equations (19) and (20), only differing in expression.

[0078] Equations (19), (20), and (21) show the Δa of the cutoff mode of the core with the longest cutoff wavelength. ＭＣ This formula considers only the effect on (λ). In contrast, equation (22) shows the Δa of all cutoff modes for each of the N cores. ＭＣ This formula takes into account the effect on (λ). Therefore, if the fitting is successful, then Δa in equation (22) ＭＣ，ｆ Using this method will yield a more accurate Δa ＭＣ (λ) fitting can be performed.

[0079] The fitting variable in equation (22) is C for each of the following values ​​of n from 1 to N, where n is a natural number from 1 to N. ｎ and D ｎ In other words, the fitting variable is the sequence {C}. ｎ}, and the sequence {D ｎ These are the terms of}. Thus, since the number of fitting variables increases (2N), equations (19), (20), and (21) are more advantageous in terms of the ease with which the fitting converges.

[0080] When performing fitting using equation (22), as an example, in order to facilitate the convergence of the fitting, the initial values ​​of each element of the sequence {Dn} may be set to be greater than or equal to the first wavelength or greater than or equal to the second wavelength, and less than or equal to the third wavelength.

[0081] As a second example, the initial values ​​of each element of the sequence {Dn} may be set at equal intervals within the range from the first wavelength to the third wavelength, or they may be set in a regular pattern or randomly. If they are set at equal intervals, the minimum value of the elements of the sequence {Dn} may be the first wavelength, or it may be greater than the first wavelength.

[0082] As a third example, the initial values ​​of each element of the sequence {Dn} may be set at equal intervals within the range from the second wavelength to the third wavelength, or they may be set in a regular pattern, or they may be set randomly. If they are set at equal intervals, the minimum value of the elements of the sequence {Dn} may be the second wavelength, or it may be greater than the second wavelength. If they are set at equal intervals, the maximum value of the elements of the sequence {Dn} may be the third wavelength, or it may be less than the third wavelength.

[0083] As disclosed in Non-Patent Literature 4, "humps" can appear as noise caused by interference between the mode guiding the core and other modes. In this case, because it is a systematic error rather than measurement variation, the "humps" often do not disappear even after remeasurement. Even if the measurement noise including "humps" is smoothed out wavelength-averaged through fitting, the effect of "humps" may remain strong. Therefore, if "humps" are present, fitting may be performed excluding the wavelength band in which the "humps" appear. This makes it possible to perform fitting with reduced effect of "humps". As disclosed in Non-Patent Literature 4, the bending diameter of the optical fiber under measurement may be changed in the longitudinal direction. This can reduce the occurrence of "humps".

[0084] In the method for determining the cutoff wavelength of the MCF according to this embodiment, as a noise reduction process, Δa ＭＣ The process removes noise contained in the [dB] measurement, enabling accurate measurements with reduced noise influence. In the noise removal process, for example, Δa is calculated using the formulas from equations (19) to (22). ＭＣ The measurement value in [dB] is fitted, and the formula obtained by the fitting is Δa ＭＣ It is considered to be [dB]. This means that Δa ＭＣ Noise contained in the [dB] measurement can be removed. In the noise reduction process, fitting is performed, for example, by the least squares method.

[0085] While embodiments and modifications have been described above, this disclosure is not necessarily limited to the embodiments and modifications described herein, and various modifications are possible without departing from its essence. The above embodiments and modifications may be combined as appropriate.

Claims

1. A method for determining the cutoff wavelength of a multicore optical fiber, wherein, where N is the number of cores in the multicore optical fiber, Δa is the decibel value of the ratio of the power of all modes, including higher-order modes, incident on all cores of the multicore optical fiber of a predetermined length and in a predetermined bending state, to the power of the operating mode. ＭＣ [dB] is Δa ｔｈ A method for determining the cutoff wavelength of a multicore optical fiber, wherein the wavelength at which the value is / N [dB] is determined as the cutoff wavelength of the multicore optical fiber.

2. The method for determining the cutoff wavelength of a multicore optical fiber according to claim 1, wherein the cutoff wavelength of the multicore optical fiber is determined as the upper limit or upper bound of the cutoff wavelength of the core that has the longest individual cutoff wavelength.

3. Δa ＭＣ [dB] is Δa ｔｈ A method for determining the cutoff wavelength of a multicore optical fiber according to claim 1 or claim 2, wherein the wavelength at which the value becomes [dB] is determined as the lower limit or lower bound of the cutoff wavelength of the core with the longest individual cutoff wavelength among all the cores of the multicore optical fiber.

4. Δa ｔｈ A method for determining the cutoff wavelength of a multicore optical fiber according to any one of claims 1 to 3, wherein [dB] is 0.1 dB.

5. Number of operating modes (M) ｏｐ And, the cutoff mode is several M ｃ The ratio ρ is When expressed as, Δa ｔｈ [dB] is, The method for determining the cutoff wavelength of a multicore optical fiber according to any one of claims 1 to 4.

6. The method for determining the cutoff wavelength of a multicore optical fiber according to any one of claims 1 to 5, wherein the predetermined length is 2 m, and the predetermined bending state is a state in which a bend of 140 mm or more with a radius of 140 mm or more is applied for one full turn.

7. The method for determining the cutoff wavelength of a multicore optical fiber according to any one of claims 1 to 6, wherein the predetermined length is 22 m, and the predetermined bending state is a state in which a bend of 20 m with a radius of 140 mm or more is applied, and a bend of 40 mm with a radius of 40 mm is applied to each end of the bend with a radius of 140 mm or more for one full turn.

8. Δa ＭＣ The method for determining the cut-off wavelength of a multi-core optical fiber according to any one of claims 1 to 7, which performs a process of removing noise included in the measured value [dB].

9. In the above process, Δa ＭＣ The measurement value in [dB] is fitted, and the formula obtained by the fitting is Δa ＭＣ A method for determining the cutoff wavelength of a multicore optical fiber according to claim 8, wherein the cutoff wavelength is considered to be [dB].

10. The above formula is, And here, N ｆ C and D are fitting variables, and N ｆ 1 ≤ N ｆ A method for determining the cutoff wavelength of a multicore optical fiber according to claim 9, wherein the cutoff wavelength is a real number satisfying ≤ N.

11. The above formula is, A method for determining the cutoff wavelength of a multicore optical fiber according to claim 9, wherein C and G are fitting variables.

12. The above formula is, And here, the sequence {C ｎ }, and the sequence {D ｎ The method for determining the cutoff wavelength of a multicore optical fiber according to claim 9, wherein each term of} is a natural number from 1 to N.

13. In the above process, Δa ＭＣ A method for determining the cutoff wavelength of a multicore optical fiber according to any one of claims 9 to 12, wherein fitting is performed to the measured value of [dB] by the least squares method.

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