Abstract

A segmented-cladding fiber consists of a uniform core of high refractive index and a cladding with regions of high and low refractive index alternating angularly. This type of fiber provides an effective approach for achieving widely extended single-mode operation with a large core size. We analyze the fiber in detail by the radial-effective-index method, which replaces the fiber with an effective circular fiber. The accuracy of the method is confirmed by comparison with results obtained from the finite-element method. By applying the transverse-matrix method to the effective fiber, the leakage losses of the first two modes of the fiber are calculated. These then form the basis for discussion of the single-mode operation of the fiber. The analysis elucidates not only the physics of the fiber, but also the dependence of the performance of the fiber on various fiber parameters. With illustrations, we demonstrate the possibility of designing an ultralarge-core, segmented-cladding fiber that is single moded over the entire S+C+L band. The fiber should be able to suppress nonlinear optical effects and therefore prove useful for broadband optical communication employing dense-wavelength-division multiplexing.

© 2004 Optical Society of America

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References

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  1. V. Rastogi and K. S. Chiang, “Propagation characteristics of a segmented cladding fiber,” Opt. Lett. 26, 491–493 (2001).
    [CrossRef]
  2. K. S. Chiang and V. Rastogi, “Ultra-large-core single-mode fiber for optical communications: the segmented cladding fiber,” in Optical Fiber Communication Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 620–621.
  3. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  4. T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000).
    [CrossRef]
  5. A. Ferrando, E. Silvestre, J. J. Miret, P. Andres, and M. V. Andres, “Full vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
    [CrossRef]
  6. K. S. Chiang, “Radial effective-index method for the analysis of optical fibers,” Appl. Opt. 26, 2969–2973 (1987).
    [CrossRef] [PubMed]
  7. K. S. Chiang, “Finite element analysis of weakly guiding fibers with arbitrary refractive-index distribution,” J. Lightwave Technol. LT-4, 980–990 (1986).
    [CrossRef]
  8. K. Thyagarajan, S. Diggavi, A. Taneja, and A. K. Ghatak, “Simple numerical technique for the analysis of cylindrically symmetric refractive-index profile optical fibers,” Appl. Opt. 30, 3877–3879 (1991).
    [CrossRef] [PubMed]
  9. K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
    [CrossRef]
  10. V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement loss in highly nonlinear optical fibers,” in Optical Fiber Communication Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 524–525.
  11. T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
    [CrossRef]
  12. L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
    [CrossRef]

2002 (1)

L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
[CrossRef]

2001 (2)

2000 (1)

1999 (1)

1997 (1)

1991 (1)

1987 (1)

1986 (1)

K. S. Chiang, “Finite element analysis of weakly guiding fibers with arbitrary refractive-index distribution,” J. Lightwave Technol. LT-4, 980–990 (1986).
[CrossRef]

1981 (1)

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

Andres, M. V.

Andres, P.

Bennett, P. J.

Birks, T. A.

Botten, L. C.

Broderick, N. G. R.

Chiang, K. S.

de Sterke, C. M.

Diggavi, S.

Ferrando, A.

Ghatak, A. K.

Issa, N. A.

L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
[CrossRef]

Knight, J. C.

McPhedran, R. C.

Miret, J. J.

Monro, T. M.

L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
[CrossRef]

T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000).
[CrossRef]

Morishita, K.

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

Poladian, L.

L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
[CrossRef]

Rastogi, V.

Richardson, D. J.

Russell, P. St. J.

Silvestre, E.

Steel, M. J.

Taneja, A.

Thyagarajan, K.

White, T. P.

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (1)

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[CrossRef]

J. Lightwave Technol. (1)

K. S. Chiang, “Finite element analysis of weakly guiding fibers with arbitrary refractive-index distribution,” J. Lightwave Technol. LT-4, 980–990 (1986).
[CrossRef]

Opt. Exp. (1)

L. Poladian, N. A. Issa, and T. M. Monro, “Fourier decomposition algorithm for leaky modes of fibers with arbitrary geometry,” Opt. Exp. 10, 449–454 (2002).
[CrossRef]

Opt. Lett. (5)

Other (2)

K. S. Chiang and V. Rastogi, “Ultra-large-core single-mode fiber for optical communications: the segmented cladding fiber,” in Optical Fiber Communication Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 620–621.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement loss in highly nonlinear optical fibers,” in Optical Fiber Communication Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 524–525.

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Figures (16)

Fig. 1
Fig. 1

Transverse cross section of a segmented-cladding fiber (SCF) with core radius a and cladding radius b. The refractive indices of the segments are n1 and n2, and 2θ1 and 2θ2 are the corresponding angular widths.

Fig. 2
Fig. 2

Refractive-index variation n(r, θ) of the segmented cladding in the angular direction at a given value of r.

Fig. 3
Fig. 3

Finite-element discretization of a quarter of the cross section of the SCF in Fig. 1.

Fig. 4
Fig. 4

Effective-index profile of the SCF with a=10 µm, b=30 µm, Δ=0.0035, N=8, and γ=0.5 at the wavelength 1.55 µm. The dashed horizontal lines mark the mode indices of the first few modes of the fiber.

Fig. 5
Fig. 5

Dispersion curves (solid curves) for the first two modes of the SCF. The dotted horizontal line shows the refractive index of the core and the dashed curve shows the effective cladding index. The fiber parameters are as for Fig. 4.

Fig. 6
Fig. 6

Intensity distributions of the fundamental mode of the SCF at the wavelengths 0.4 µm and 1.55 µm. The fiber parameters are as for Fig. 4.

Fig. 7
Fig. 7

Dependence of the leakage losses of the fundamental mode and the first higher-order mode of the coated SCF on the wavelength, showing an extended single-mode operation from 0.4 µm to 1.8 µm. The fiber parameters are as for Fig. 4.

Fig. 8
Fig. 8

Effective-index profiles of the coated SCF along with the mode indices of the first two modes for three different duty cycles: (a) γ=0.75, (b) γ=0.50, and (c) γ=0.20, showing three different positions of the mode indices in relation to the maximum cladding index. The other fiber parameters are as for Fig. 4.

Fig. 9
Fig. 9

Dependence of the leakage losses of the first two modes of the coated SCF on the wavelength for three different duty cycles, γ=0.25, 0.50, and 0.75. The other fiber parameters are as for Fig. 4.

Fig. 10
Fig. 10

Dependence of the leakage losses of the first two modes of the coated SCF on the wavelength for three different segment numbers, N=6, 8, and 10. The other fiber parameters are as for Fig. 4.

Fig. 11
Fig. 11

Dependence of the leakage losses of the first two modes of the coated SCF on the wavelength for three different values of relative index difference Δ=0.002, 0.0035, and 0.005. The other fiber parameters are as for Fig. 4.

Fig. 12
Fig. 12

Dependence of the leakage losses of the first two modes of the coated SCF on the wavelength for three different core radii, a=7.5 µm, 10 µm, and 15 µm. The other fiber parameters are as for Fig. 4.

Fig. 13
Fig. 13

Dependence of the leakage losses of the first two modes of the coated SCF on the core radius a at the wavelength 1.55 µm. The minimum leakage loss of the fundamental mode occurs at a specific core radius, denoted as the optimum core radius aopt. The other fiber parameters are as for Fig. 4.

Fig. 14
Fig. 14

Optimum core radius aopt of an SCF as a function of the duty cycle γ for N=4 and 8 at the wavelength 1.55 µm for b=30 µm and b=62.5 µm (assuming Δ=0.0035).

Fig. 15
Fig. 15

Dependence of the leakage losses of the first two modes of the coated SCF using an optimum core radius aopt on the duty cycle γ for four combinations of segment number N and cladding radius b (assuming λ=1.55 µm and Δ=0.0035).

Fig. 16
Fig. 16

Leakage loss curves of the SCF with a core radius as large as 17 µm (assuming Δ=0.0035, b=62.5 µm, N=8, and γ=0.6), showing effective single-mode operation in the entire S+C+L band.

Tables (1)

Tables Icon

Table 1 Comparison of Mode Indices for the Segmented-Cladding Fiber Calculated by the Radial-Effective-Index Method (REIM) and the Finite-Element Method (FEM) at Varying Wavelengthsa

Equations (12)

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2ϕr2+1r ϕr+1r2 2ϕθ2+k2[n2(r, θ)-neff2]ϕ=0,
ϕ(r, θ)=ϕr(r)ϕrθ(r, θ).
ϕrθ d2ϕrdr2+ϕrθr dϕrdr+ϕrr2 2ϕrθθ2
+k2[n2(r, θ)-neff2]ϕrϕrθ=0.
2ϕrθθ2+k2[n2(r, θ)-neffr2(r)]r2ϕrθ=0.
d2ϕrdr2+1r dϕrdr+k2n˜effr2(r)-l2k2r2-neff2ϕr=0,
n˜effr2(r)=neffr2(r)+l2k2r2l=0, 1, 2,.
neffr2(r)=n2(r)-l2k2r2.
2ϕrθ(ri, θ)θ2+k2[n2(ri, θ)-neffr2(ri)]ri2ϕrθ(ri, θ)=0.
u˜ tan u˜=w˜ tanhw˜ θ2θ1
cosh2w˜ θ2θ1cos 2u˜+w˜2-u˜22u˜w˜ sinh2w˜ θ2θ1sin 2u˜
=cos 2πN

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