Hole-assisted optical fiber and method for designing same

Abstract

A hole-assisted optical fiber (10) comprises a core (11) and a cladding (12) provided with a plurality of holes (13) around the core (11). The radius a of the core (11) and the radius Rin of an inscribed circle (15) inscribed in the plurality of holes (13) satisfy a relationship represented by FBD(Rin) ≤ a ≤ FCO(Rin) where FBD(Rin) is a first boundary at which the bending loss of the optical fiber 10 at a wavelength of 1675 nm or less becomes a bending loss specified in Recommendation ITU-T G.652 or G.654, and FCO(Rin) is a second boundary at which the cutoff wavelength of the optical fiber (10) becomes a predetermined wavelength in the range of 1260-1530 nm.

Description

Hole-assisted optical fiber and its design method

[0001] The present disclosure relates to a hole-assisted optical fiber and a method for designing the same.

[0002] Single-mode fiber with a zero-dispersion wavelength in the 1310 nm wavelength band is standardized as ITU-T Recommendation G.652 (International Telecommunication Union Telecommunication Standardization Sector recommendation G.652) and is the most widely used. This standardized single-mode fiber can be used for single-mode transmission in the wavelength band from 1260 nm to 1625 nm (i.e., O to L band) (see Non-Patent Document 1).

[0003] Generally, the bending loss of an optical fiber increases at longer wavelengths. On the other hand, it is known that a hole-assisted structure, in which holes are provided around the core, which is the main waveguide structure, is effective in reducing bending loss (see Non-Patent Document 2).

[0004] Recommendation ITU-T G.652, Characteristics of a single-mode optical fiber and cable, (2016). K. Nakajima et al., Single-mode Hole-assisted Fiber as a Bending Loss Insensitive Fiber, Opt. Fiber Technol., vol. 16, pp. 392-398, Dec. 2010.

[0005] The wavelength band of 1625 nm to 1675 nm, which is longer than the above-mentioned wavelength bands, is defined as the U band. However, no optical fiber design has been reported that takes into account the transmission characteristics of this U band.

[0006] The present disclosure has been proposed in view of the above-mentioned circumstances, and aims to provide a hole-assisted optical fiber that can achieve a broadband by reducing bending loss in the U band, and a design method thereof.

[0007] A hole-assisted optical fiber according to a first aspect of the present disclosure includes a core and a cladding having a plurality of holes provided around the core, and the radius a of the core and the radius R of an inscribed circle inscribed in the plurality of holes are ｉｎ The first boundary at which the bending loss of the optical fiber at wavelengths of 1675 nm or less becomes the bending loss specified in the ITU-T G.652 or G.654 recommendation is defined as F. ＢＤ (R ｉｎ ), and a second boundary where the cutoff wavelength of the optical fiber is a predetermined wavelength in the range of 1260 nm to 1530 nm is defined as F ＣＯ (R ｉｎ ) as F ＢＤ (R ｉｎ ) ≦ a ≦ F ＣＯ (R ｉｎ ) satisfies the relationship shown below.

[0008] A method according to a second aspect of the present disclosure is a method for designing a hole-assisted optical fiber comprising a core and a cladding having a plurality of air holes provided around the core, the method comprising: defining a radius of the core as a, defining a radius of an inscribed circle inscribed in the plurality of air holes as R, ｉｎ The first boundary F is a boundary at which the bending loss of the optical fiber at a wavelength of 1675 nm or less is equal to or less than the bending loss specified in the ITU-T G.652 or G.654 recommendation. ＢＤ (R ｉｎ ) and derive a second boundary F at which the cutoff wavelength of the optical fiber becomes a predetermined wavelength in the range of 1260 nm to 1530 nm. ＣＯ (R ｉｎ ) is derived, and the first boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (R ｉｎ ) is F ＢＤ (R ｉｎ ) ≦ a ≦ F ＣＯ (R ｉｎ ) satisfies the relationship shown below.

[0009] According to the present disclosure, it is possible to provide a hole-assisted optical fiber that can achieve a broader bandwidth by reducing bending loss in the U band, and a design method thereof.

[0010] FIG. 1 is a diagram illustrating an example of a cross section of an optical fiber according to an embodiment of the present disclosure. FIG. 2 is a diagram illustrating an example of an analysis result obtained by the finite element method. FIG. 3 is a diagram illustrating an example of an analysis result obtained by the finite element method. FIG. 4 is a table illustrating an example of coefficients of an approximation function. FIG. 5 is a table illustrating an example of coefficients of an approximation function. FIG. 6 is a table illustrating an example of coefficients of an approximation function. FIG. 7 is a diagram illustrating an example of an analysis result obtained by the finite element method. FIG. 8 is a table illustrating an example of coefficients of an approximation function. FIG. 9 is a table illustrating an example of coefficients of an approximation function.

[0011] Hereinafter, optical fibers according to embodiments of the present disclosure will be described with reference to the drawings. In the drawings, identical parts will be designated by the same reference numerals and their description will be omitted. In the following description, "cross section" refers to a cross section perpendicular to the longitudinal direction of the optical fiber. Furthermore, the "circumferential direction" is based on the center of the optical fiber.

[0012] The optical fiber according to this embodiment has a hole-assisted fiber (HAF) structure in which a plurality of holes are provided in the cladding surrounding the core. That is, the optical fiber according to this embodiment is a hole-assisted fiber (HAF), which is a type of photonic crystal fiber.

[0013] 1 is a diagram showing an example of a cross section of an optical fiber 10 according to this embodiment. As described above, the optical fiber 10 includes a core 11, which is a main optical waveguide structure, and a cladding 12 provided around the core 11. N (N = plural) holes 13 are provided in the cladding 12.

[0014] The core 11 is, for example, a step-index core. In this case, the core 11 has a refractive index n １ The core 11 has a circular cross section and its radius (core radius) is a. The cladding 12 has a refractive index n １ Lower refractive index n ２ Therefore, the relative refractive index difference Δ of the optical fiber 10 is (n １ ２ -n ２ ２ ) / (2n １ ２ ) (≒ (n １ -n２ ) / n １ )

[0015] The holes 13 are formed around the core 11 and extend parallel to the core 11. The holes 13 are arranged at equal intervals along the circumferential direction. Each hole 13 has a circular cross section and a diameter d. The holes 13 can be formed by drilling an optical fiber preform and drawing the preform in a molten state.

[0016] The centers of the holes 13 are located on the same circle 14 with the center of the core 11 as its center. Therefore, on the cross section of the optical fiber 10 illustrated in Fig. 1, an inscribed circle 15 inscribed in the circle of each hole 13 and a circumscribed circle 16 circumscribed in the circle of each hole 13 can be defined. The centers of the inscribed circle 15 and the circumscribed circle 16 coincide with the center of the core 11. The radius of the inscribed circle 15 (inscribed circle radius) is R ｉｎ and the radius of the circumscribing circle 16 (circumscribing circle radius) is R ｏｕｔ is.

[0017] The optical characteristics of the HAF structure according to this embodiment are determined by the above-mentioned core radius a, relative refractive index difference Δ, and inscribed circle radius R ｉｎ , and the hole occupancy rate S. The hole occupancy rate S is the proportion of N holes 13 to the region 17 between the inscribed circle 15 and the circumscribed circle 16 in a cross section perpendicular to the longitudinal direction of the optical fiber 10. The hole occupancy rate S is expressed by the following formula (1): In the formula (1), N is the number of the holes 13, d is the diameter of the above-mentioned holes 13, and R ｏｕｔ is the radius of the circumscribing circle 16, R ｉｎ is the radius of the inscribed circle 15.

[0018] The radius a of the core 11 and the radius R of the inscribed circle 15 ｉｎ satisfies the relationship shown in the following formula (2). Here, for convenience of explanation, F ＢＤ (R ｉｎ ) as the first boundary, F ＣＯ (R ｉｎ ) is called the second boundary. ｉｎ It can be approximated by a function such as a cubic function, which will be described later.

[0019] First boundary F ＢＤ (R ｉｎ ) is the radius a and radius R ｉｎ The first boundary F represents the boundary of the bending loss condition in the two-dimensional space (two-dimensional coordinates). ＢＤ (R ｉｎ ) is the radius a and radius R at which the bending loss of the optical fiber 10 at wavelengths of 1675 nm or less is the bending loss under the bending conditions specified in the ITU-T G.652 or G.654 recommendation. ｉｎ The bending loss is a so-called macrobending loss, and is a value that results in a loss (insertion loss) of 0.1 dB or less when light with a wavelength of 1625 nm is passed through the optical fiber 10.

[0020] Second boundary F ＣＯ (R ｉｎ ) is the radius a and radius R ｉｎ This shows the boundary of the cutoff wavelength condition in the two-dimensional space (two-dimensional coordinates). That is, the second boundary F ＣＯ (R ｉｎ ) is the cutoff wavelength λ of the optical fiber 10 ｃ The radius a and radius R are such that the wavelength is in the range of 1260 nm to 1530 nm. ｉｎ For example, the cutoff wavelength λ ｃ When the cutoff wavelength λ is set to 1260 nm, the optical fiber 10 satisfies the cutoff wavelength specification of ITU-T G.652. ｃ is set to 1260 nm, the optical fiber 10 satisfies the cutoff wavelength specification of ITU-T G.654.

[0021] First boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (R ｉｎ ) is calculated by the finite element method (FEM) using PML (perfectly matched layer) as the absorbing boundary condition, and the radius a and radius R ｉｎ The first boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (Rｉｎ ) can be approximated by, for example, a cubic function. In this case, the first boundary F ＢＤ (R ｉｎ ) is expressed by equation (5) using coefficients derived from equations (7) and (9) described later. Similarly, the second boundary F ＣＯ (R ｉｎ ) is expressed by the following equation (6) using coefficients derived from the following equations (8) and (10), for example.

[0022] 2 is a diagram showing an example of the analysis results by the finite element method. In this analysis, the relative refractive index difference Δ is set to 0.35%, the pore occupancy S is set to 0.2, and the cutoff wavelength λ ｃ was set to 1260 nm, and PML was set to 13 μm.

[0023] The solid line GB1 in Fig. 2 indicates the first boundary, i.e., the boundary of the bending loss condition. The dashed-dotted line GC1 in Fig. 2 indicates the second boundary, i.e., the boundary of the cutoff wavelength condition. The dashed line GL1 in Fig. 2 indicates the boundary of the leakage loss condition. The leakage loss condition is a confinement loss of 0.001 dB / km or less at a wavelength of 1675 nm.

[0024] The radius a and radius R shown in FIG. ｉｎ In the two-dimensional space, the region to the right of the solid line GB1 satisfies the bending loss condition. That is, the radius a and the radius R ｉｎ The bending loss of an optical fiber having the above formula is equal to or less than the bending loss under the bending conditions specified in the ITU-T G.652 or G.654 recommendation at a wavelength of 1675 nm or less.

[0025] Similarly, the region to the left of the dashed line GC1 satisfies the cutoff wavelength condition. ｉｎ An optical fiber having a cutoff wavelength λ ｃ It operates in a single mode for wavelengths above this.

[0026] The area to the right of the dashed line GL1 satisfies the leakage loss condition. ｉｎ The leakage loss of an optical fiber having this characteristic is 0.001 dB / km or less at a wavelength of 1675 nm. The boundary of the leakage loss condition indicated by the dashed line GL1 varies depending on, for example, the relative refractive index difference Δ.

[0027] 2, the area P between the solid line GB1 and the dashed line GC1 is shown by hatching. This area 17 satisfies all of the above conditions. That is, the radius a and the radius R in this area P ｉｎ By applying the combination of the bending loss (macrobending loss), cutoff wavelength λ ｃ It is possible to obtain (design) an optical fiber 10 that satisfies all of the conditions for the optical fiber 10a, 10b, 10c, 10d, 10e, 10f ...

[0028] According to this embodiment, the bending loss of the optical fiber in the long wavelength band such as the U band is reduced to the same level as or less than that of existing single mode optical fibers. In other words, by reducing the bending loss in the long wavelength band, it is possible to broaden the bandwidth of the optical fiber.

[0029] Like Fig. 2, Fig. 3 also shows an example of the analysis results obtained by the finite element method. The conditions assumed in the analysis of Fig. 3 are the same as those used in the analysis of the results shown in Fig. 2, except that the pore occupancy rate S was set to 0.5. As shown in Fig. 3, when the pore occupancy rate S changes from 0.2 to 0.5, the distribution of region 17 changes. For example, a comparison of Figs. 2 and 3 reveals that as the pore occupancy rate S increases, region 17 shifts in the direction of decreasing radius a.

[0030] In this way, even when the above three conditions are satisfied, the distribution of the region 17 changes depending on the change in the hole occupancy rate S. This is because the relative refractive index difference Δ or the cutoff wavelength λ ｃ The same is true when is changed.

[0031] Therefore, in this embodiment, the cutoff wavelength λ ｃ is set to a predetermined wavelength in the range from 1260 nm to 1530 nm, and the hole occupancy rate S and the relative refractive index difference Δ are changed. The boundary of the region 17, that is, the first boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (R ｉｎ ) are derived. As described above, the first boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (R ｉｎ) satisfies the relationship of formula (2). By deriving these approximate functions, the radius a and radius R that satisfy the above three conditions are obtained. ｉｎ Various combinations of

[0032] For example, the first boundary F indicated by the solid line GB1 in FIG. ＢＤ (R ｉｎ ) can be expressed by the following equation (3). Also, the cutoff wavelength λ ｃ The second boundary F indicated by the solid line GB1 when ＣＯ (R ｉｎ ) can be expressed by the following equation (4). Cutoff wavelength λ ｃ When the refractive index is 1260 nm, the relative refractive index difference Δ is 0.35%, and the hole occupancy S is 0.2, the radius a and radius R satisfying the condition of formula (2) using formulas (3) and (4) are ｉｎ Various combinations of these will satisfy the three conditions mentioned above.

[0033] Moreover, the cubic function shown in equation (3) can be expressed by the following equation (5) by generalizing each coefficient. Similarly, the cubic function shown in equation (4) can be expressed by the following equation (6) by generalizing each coefficient.

[0034] Coefficient A when the relative refractive index difference Δ is constant and the hole occupancy S is changed ｉ (i=1 to 4) can be approximated by a quartic function of the pore occupancy rate S shown in the following equation (7). Similarly, the coefficient B when the pore occupancy S is changed ｉ (i=1 to 4) can also be approximated by a quartic function of the pore occupancy rate S shown in the following equation (8). For example, the cutoff wavelength λ ｃ is 1260 nm, and the relative refractive index difference Δ is 0.35%, the coefficient C ｊｉ (j = 1 to 5, i = 1 to 4) and coefficient D ｊｉ (j=1 to 5, i=1 to 4) have the values ​​shown in Table 1 of FIG.

[0035] In this embodiment, the coefficient C ｊｉ is approximated by a fourth-order function of the relative refractive index difference Δ. ｊｉ is expressed by the following equation (9). Similarly, the coefficient D ｊｉ is also approximated by a fourth-order function of the relative refractive index difference Δ. ｊｉ is expressed by the following equation (10). Coefficient En ｊｉ (n=1 to 5, j=1 to 5, i=1 to 4) have the values ​​shown in Table 2 of FIG. 5, and the coefficient Fn ｊｉ (n=1 to 5, j=1 to 5, i=1 to 4) have the values ​​shown in Table 3 of FIG. 6. In this case, the optical fiber 10 satisfies the bending loss condition and the leakage loss condition. In addition, the optical fiber 10 has a cutoff wavelength λ ｃ In other words, the optical fiber 10 operates in a single mode at wavelengths of 1260 nm or greater.

[0036] In this way, the coefficient C for an arbitrary relative refractive index difference Δ ｊｉ , D ｊｉ Derive the coefficient C ｊｉ , D ｊｉ and coefficient A using an arbitrary pore occupancy rate S ｉ , B ｉ and find the radius R that satisfies the condition of Equation (2). ｉｎ and radius a can be selected (derived). In addition, the selected radius a and radius R ｉｎ The optical fiber 10 having the above radius satisfies the bending loss condition and the leakage loss condition. Furthermore, it also satisfies the cutoff wavelength condition imposed when deriving these radii. In other words, the optical fiber operates in a single mode at wavelengths equal to or greater than the cutoff wavelength in the cutoff wavelength condition.

[0037] 7 shows the cutoff wavelength λ when the relative refractive index difference Δ is 0.35% and the pore occupancy S is 0.2. ｃ The graph shows the change in the region P when the cutoff wavelength λ is changed to 1260 nm, 1460 nm, and 1530 nm. ｃ The second boundary F when ＣＯ (R ｉｎ The dashed dotted line GC2 is the cutoff wavelength λ ｃ The second boundary F when ＣＯ (R ｉｎ The dashed dotted line GC3 is the cutoff wavelength λ ｃ The second boundary F whenＣＯ (R ｉｎ ) As these lines show, the cutoff wavelength λ ｃ As the wavelength becomes longer, only the cutoff condition among the above three conditions is relaxed, and it can be seen that the region P expands in the direction in which the radius a of the core 11 increases.

[0038] Thus, the cutoff wavelength λ ｃ When the second boundary F ＣＯ (R ｉｎ ) changes. The second boundary F ＣＯ (R ｉｎ ) changes with coefficient B ｉ means the change in coefficient B ｉ The change in coefficient D ｊｉ means the change in coefficient D ｊｉ The change in coefficient Fn ｊｉ This means a change in

[0039] Table 4 in FIG. 8 shows the cutoff wavelength λ for an arbitrary relative refractive index difference Δ and an arbitrary pore occupancy S. ｃ Coefficient Fn when is 1460 nm ｊｉ On the other hand, the cutoff wavelength λ ｃ Even when the wavelength is 1460 nm, the first boundary F ＢＤ (R ｉｎ ) does not change. Therefore, the coefficient En ｊｉ For , the values ​​shown in Table 3 in Fig. 6 can be used. In this case, an optical fiber capable of single-mode operation at wavelengths of 1460 nm or more can be provided.

[0040] Table 5 in FIG. 9 shows the cutoff wavelength λ for an arbitrary relative refractive index difference Δ and an arbitrary pore occupancy S. ｃ Coefficient Fn when is 1530 nm ｊｉ On the other hand, the cutoff wavelength λ ｃ Even when the wavelength is 1460 nm, the first boundary F ＢＤ (R ｉｎ ) does not change. Therefore, the coefficient En ｊｉ For , the values ​​shown in Table 3 in Fig. 6 can be used. In this case, an optical fiber capable of single-mode operation at wavelengths of 1530 nm or more can be provided.

[0041] That is, the coefficient En ｊｉ(n=1 to 5, j=1 to 5, i=1 to 4) have the values ​​shown in Table 2, and the coefficient Fn ｊｉ (n=1 to 5, j=1 to 5, i=1 to 4) may have any one of the values ​​shown in Tables 3 to 5. In this case, the optical fiber 10 satisfies the above-mentioned bending loss condition and leakage loss condition, and has a cutoff wavelength λ ｃ The cutoff wavelength condition when is 1260 nm, 1460 nm or 1530 nm is also satisfied.

[0042] 10 Optical fiber 11 Core 12 Cladding 13 Hole a Core radius R ｉｎ Inscribed circle radius

Claims

1. A hole-assisted optical fiber comprising: a core; and a cladding having a plurality of holes provided around the core; wherein the radius a of the core and the radius R of an inscribed circle inscribed around the plurality of holes are ｉｎ is a first boundary at which the bending loss of the hole-assisted optical fiber at wavelengths of 1675 nm or less becomes the bending loss specified in the ITU-T G.652 or G.654 recommendation. ＢＤ (R ｉｎ ), and a second boundary at which the cutoff wavelength of the hole-assisted optical fiber is a predetermined wavelength in the range of 1260 nm to 1530 nm is defined as F ＣＯ (R ｉｎ ) and satisfying the relationship shown in the following formula (1):

2. The hole-assisted optical fiber according to claim 1, wherein, where Δ is the relative refractive index difference, N is the number of holes, and S is the occupancy rate of the holes in the region between the inscribed circle and a circumscribed circle circumscribing the plurality of holes, the first boundary is expressed by the following formula (2) using coefficients derived from the following formulas (4) and (6), and the second boundary is expressed by the following formula (3) using coefficients derived from the following formulas (5) and (7).

3. The coefficient En ｊｉ (n=1 to 5, j=1 to 5, i=1 to 4) have the values ​​shown in Table 1 below, and the coefficient Fn ｊｉ The hole-assisted optical fiber according to claim 2 , wherein (n=1 to 5, j=1 to 5, i=1 to 4) have values ​​shown in any one of Tables 2 to 4 below.

4. A method for designing a hole-assisted optical fiber having a core and a cladding in which a plurality of holes are provided around the core, wherein the radius of the core is a and the radius of an inscribed circle inscribed in the plurality of holes is R ｉｎ a first boundary F at which the bending loss of the hole-assisted optical fiber at a wavelength of 1675 nm or less becomes the bending loss specified in the ITU-T G.652 or G.654 recommendation; ＢＤ (R ｉｎ ) and derive an approximation function of the second boundary F at which the cutoff wavelength of the hole-assisted optical fiber falls within a predetermined range of 1260 nm to 1530 nm. ＣＯ (R ｉｎ ) is derived, and the first boundary F ＢＤ (R ｉｎ ) and the second boundary F ＣＯ (R ｉｎ ) satisfies the relationship of the following formula (8):

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