Abstract

In 1976 Marcuse developed an equivalent index model to predict the effects of bending in waveguides, and predicted deformation of the spatial modes in bent optical fibers. Perturbative approaches have been previously applied and tested to predict the behavior of single- and few-moded-fibers. However, much more significant mode deformation has been predicted for large-mode-area fibers than for single- or few-moded-fibers. In this paper, the spatial profiles of modes deformed by bending in large-mode-area fibers are measured for the first time. A finite difference method employing the equivalent index model is used to calculate the modes of the helical fiber, which show an offset that is twice as large as that predicted for single-mode fiber, and mode compression that is five times greater. These calculated results are compared to the experimental data, yielding significantly better agreement than previous perturbative approaches.

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References

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  1. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25(7), 442–444 (2000).
    [CrossRef] [PubMed]
  2. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976).
    [CrossRef]
  3. Z. W. Bao, M. Miyagi, and S. Kawakami, “Measurements of field deformations caused by bends in a single-mode optical fiber,” Appl. Opt. 22(23), 3678–3680 (1983).
    [CrossRef] [PubMed]
  4. I. Verrier and J. P. Goure, “Effects of bending on multimode step-index fibers,” Opt. Lett. 15(1), 15–17 (1990).
    [CrossRef] [PubMed]
  5. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006).
    [CrossRef] [PubMed]
  6. J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
    [CrossRef]
  7. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of bend-induced nonlinearities in large-mode area fibers,” Opt. Lett. 32, 2562–2564 (2007).
  8. P. Wang, L. J. Cooper, J. K. Sahu, and W. A. Clarkson, “Efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser,” Opt. Lett. 31, 226–228 (2006).
  9. D. Marcuse, “Radiation loss of a helically deformed optical fiber,” J. Opt. Soc. Am. 66, 1025–1031 (1976).
  10. W. P. Huang, ed., Method for Modeling and Simulation of Guided-wave Optoelectronic Devices (EMW Publishing, 1995.)
  11. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations and the Schrödinger Equation (Wiley, 2001).
  12. S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15(23), 15402–15409 (2007).
    [CrossRef] [PubMed]
  13. S. J. Garth, “Modes on a bent optical waveguide,” in IEE Proc. J. Optoelectron. 134, 221–229 (1987).

2007

2006

2003

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

2000

1990

1987

S. J. Garth, “Modes on a bent optical waveguide,” in IEE Proc. J. Optoelectron. 134, 221–229 (1987).

1983

1976

Baggett, J. C.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Bao, Z. W.

Clarkson, W. A.

Cooper, L. J.

Feder, K.

Finazzi, V.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Fini, J. M.

Furusawa, K.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Garth, S. J.

S. J. Garth, “Modes on a bent optical waveguide,” in IEE Proc. J. Optoelectron. 134, 221–229 (1987).

Goldberg, L.

Goure, J. P.

Headley, C.

Kawakami, S.

Kliner, D. A. V.

Koplow, J. P.

Marcuse, D.

Miyagi, M.

Monro, T. M.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Nicholson, J. W.

Richardson, D. J.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Sahu, J. K.

Verrier, I.

Wang, P.

Westbrook, P. S.

Wielandy, S.

Yablon, A. D.

Appl. Opt.

in IEE Proc. J. Optoelectron.

S. J. Garth, “Modes on a bent optical waveguide,” in IEE Proc. J. Optoelectron. 134, 221–229 (1987).

J. Opt. Soc. Am.

Opt. Commun.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, “Understanding bending losses in holey optical fibers,” Opt. Commun. 227(4-6), 317–335 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Other

W. P. Huang, ed., Method for Modeling and Simulation of Guided-wave Optoelectronic Devices (EMW Publishing, 1995.)

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations and the Schrödinger Equation (Wiley, 2001).

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Figures (6)

Fig. 1
Fig. 1

Calculated spatial profiles of the first four fiber modes. The dashed white lines mark the edges of the fiber core and the white dots mark the centers of the cores. The fibers are bent toward the bottom of the figure.

Fig. 2
Fig. 2

Measured intensity profile at the cleaved end of a helical-core fiber.

Fig. 3
Fig. 3

Model prediction of the LP01 mode of the bent fiber. The white line marks the edge of the fiber core and the white dot marks the center of the core.

Fig. 4
Fig. 4

Composite model prediction containing the LP 01 , LP 11 sin , LP 11 cos and LP 21 sin modes of the fiber. The white line marks the edge of the fiber core and the white dot marks the center of the core.

Fig. 5
Fig. 5

Intensity line-outs along the direction of the bend for a 4.5-µm 0.095-NA single-mode fiber bent at a 4.5-mm radius: prediction using Garth’s model (red line); finite difference calculation using Marcuse’s equivalent index model (blue line); and data measured by Bao et al. [3] (black dots). The gray shaded areas indicate the cladding cladding region, while white indicates the core.

Fig. 6
Fig. 6

Intensity line-outs along the direction of the bend for the large-mode-area helical-core fiber used in the experiment: prediction using Garth’s model (red line); finite difference calculation using Marcuse’s equivalent index model (blue line); and measured data (black dots) from Fig. 2. The gray shaded areas indicate the cladding region, while white indicates the core.

Tables (3)

Tables Icon

Table 1 Modal power distribution and relative phase difference required to maximize overlap between calculated modes and measured data

Tables Icon

Table 2 Beam offset, beam full-width at half maximum (FWHM), and mode overlap of Garth’s perturbative model, Marcuse’s equivalent index model, and Bao’s experimental data

Tables Icon

Table 3 Beam offset, second-moment beam width, and mode overlap of Garth’s perturbative model, Marcuse’s equivalent index model, and measured data

Equations (3)

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n eff 2 (x,y,z)= n 2 (x,y)( 1+ 2x R(z) )
R B = Q sin 2 θ Q tan 2 θ = P 2 4 π 2 Q ,
nrmsd= i=1 n ( I data,i I model,i ) 2 /n max( I data )min( I data ) .

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