Abstract

A rigorous, much simplified, and accurate analysis of the modal field characteristics such as propagation constants, mode power confinement, delay and dispersion characteristics of a single-mode graded-index elliptical core fiber is presented applying a variational method and super-Gaussian approximation of the fundamental modal field. Normalized propagation constants, a fundamental parameter to evaluate other modal characteristics, obtained through this method showed a greater accuracy over the entire range of practical interest in comparison with other reported methods. The effects of various aspect ratios on these characteristics are analyzed. In addition, the effect of Kerr nonlinearity on these characteristics is investigated using the reported method, and a comparison is made with the linear results.

© 2009 Optical Society of America

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  1. C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235-3243 (1962).
    [CrossRef]
  2. F. Zhang and J. Y. Lit, “Polarization characteristics of double-clad elliptical fibers,” Appl. Opt. 29, 5336-5342 (1990).
    [CrossRef] [PubMed]
  3. R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 37-64.
  4. K. S. Chiang, “Finite element analysis of weakly guiding fibers with arbitrary index distribution,” J. Lightwave Technol. 4, 980-990 (1986).
    [CrossRef]
  5. C. Yeh, K. Ha, B. Dong, and W. P. Brown, “Single mode optical waveguides,” Appl. Opt. 18, 1490-1504 (1979).
    [CrossRef] [PubMed]
  6. A. B. Manenkov and A. G. Rozhnev, “Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods,” Opt. Quantum Electron. 30, 61-70(1998).
    [CrossRef]
  7. A. Kumar and R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: perturbation approach,” Opt. Quantum Electron. 16, 349-354 (1984).
    [CrossRef]
  8. S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
    [CrossRef]
  9. M. Karlsson and D. Anderson, “Super Gaussian approximation of the fundamental radial mode in nonlinear parabolic-index optical fibers,” J. Opt. Soc. Am. B 9, 1558-1562 (1992).
    [CrossRef]
  10. Z. Wang, J. Ju, and W. Jin, “Properties of elliptical core two-mode fiber,” Opt. Express 13, 4350-4357 (2005).
    [CrossRef] [PubMed]
  11. M. Eguchi and M. Koshiba, “Accurate finite element analyisis of dual-mode highly elliptical-core fibers,” J. Lightwave Technol. 12, 607-613 (1994).
    [CrossRef]
  12. M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
    [CrossRef]
  13. V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
    [CrossRef]
  14. R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 82-87.
  15. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, 1972).
  16. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
  17. J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics (Society for Industrial and Applied Mathematics, 1996).
    [CrossRef]
  18. R. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

2008

V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
[CrossRef]

2005

1998

A. B. Manenkov and A. G. Rozhnev, “Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods,” Opt. Quantum Electron. 30, 61-70(1998).
[CrossRef]

1996

M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
[CrossRef]

1994

M. Eguchi and M. Koshiba, “Accurate finite element analyisis of dual-mode highly elliptical-core fibers,” J. Lightwave Technol. 12, 607-613 (1994).
[CrossRef]

1992

1990

1986

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

1984

A. Kumar and R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: perturbation approach,” Opt. Quantum Electron. 16, 349-354 (1984).
[CrossRef]

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

1979

1962

C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235-3243 (1962).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, 1972).

Anderson, D.

Blake, J. N.

M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Brown, W. P.

Carrara, S. L. A.

M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
[CrossRef]

Chiang, K. S.

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

Dennis, J. E.

J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics (Society for Industrial and Applied Mathematics, 1996).
[CrossRef]

Dong, B.

Dyott, R. B.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 37-64.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 82-87.

Eguchi, M.

M. Eguchi and M. Koshiba, “Accurate finite element analyisis of dual-mode highly elliptical-core fibers,” J. Lightwave Technol. 12, 607-613 (1994).
[CrossRef]

Ghatak, A.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).

Ha, K.

Jin, W.

Ju, J.

Karlsson, M.

Khijwania, S. K.

V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
[CrossRef]

Koshiba, M.

M. Eguchi and M. Koshiba, “Accurate finite element analyisis of dual-mode highly elliptical-core fibers,” J. Lightwave Technol. 12, 607-613 (1994).
[CrossRef]

Kumar, A.

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

A. Kumar and R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: perturbation approach,” Opt. Quantum Electron. 16, 349-354 (1984).
[CrossRef]

Lit, J. Y.

Manenkov, A. B.

A. B. Manenkov and A. G. Rozhnev, “Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods,” Opt. Quantum Electron. 30, 61-70(1998).
[CrossRef]

Nair, V. M.

V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
[CrossRef]

Pacitti, M. C.

M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
[CrossRef]

Rozhnev, A. G.

A. B. Manenkov and A. G. Rozhnev, “Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods,” Opt. Quantum Electron. 30, 61-70(1998).
[CrossRef]

Sarkar, S.

V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
[CrossRef]

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

Schnabel, R. B.

J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics (Society for Industrial and Applied Mathematics, 1996).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, 1972).

Thyagarajan, K.

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).

Varshney, R. K.

A. Kumar and R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: perturbation approach,” Opt. Quantum Electron. 16, 349-354 (1984).
[CrossRef]

Wang, Z.

Yeh, C.

Zhang, F.

Appl. Opt.

IEEE Photon. Technol. Lett.

V. M. Nair, S. Sarkar, and S. K. Khijwania, “Scalar variational analysis of fundamental mode in single mode elliptical core fiber using super Gaussian approximation,” IEEE Photon. Technol. Lett. 20, 1381-1983 (2008).
[CrossRef]

J. Appl. Phys.

C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235-3243 (1962).
[CrossRef]

J. Lightwave Technol.

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

M. Eguchi and M. Koshiba, “Accurate finite element analyisis of dual-mode highly elliptical-core fibers,” J. Lightwave Technol. 12, 607-613 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of fundamental mode in single mode elliptical core fiber,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

M. C. Pacitti, J. N. Blake, and S. L. A. Carrara, “A simple model of dispersion in step-index elliptical core fiber,” Opt. Fiber Technol. 2, 201-206 (1996).
[CrossRef]

Opt. Quantum Electron.

A. B. Manenkov and A. G. Rozhnev, “Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods,” Opt. Quantum Electron. 30, 61-70(1998).
[CrossRef]

A. Kumar and R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: perturbation approach,” Opt. Quantum Electron. 16, 349-354 (1984).
[CrossRef]

Other

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 37-64.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995), pp. 82-87.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, 1972).

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).

J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics (Society for Industrial and Applied Mathematics, 1996).
[CrossRef]

R. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

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Figures (10)

Fig. 1
Fig. 1

Normalized dispersion curve ( P 2 V B ) for step-index ECF.

Fig. 2
Fig. 2

Normalized dispersion curve ( b V B ) for parabolic-index ECF.

Fig. 3
Fig. 3

Intensity along the semimajor axis for PIECF.

Fig. 4
Fig. 4

Intensity along the semiminor axis for PIECF.

Fig. 5
Fig. 5

Fractional core power for PIECF.

Fig. 6
Fig. 6

Normalized delay versus V b for PIECF.

Fig. 7
Fig. 7

Dispersion versus V b for PIECF.

Fig. 8
Fig. 8

Normalized dispersion curve ( b V B ) for PIECF.

Fig. 9
Fig. 9

Normalized intensity along the semimajor axis for PIECF.

Fig. 10
Fig. 10

Normalized intensity along the semiminor axis for PIECF.

Equations (13)

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n 2 ( x , y ) = n 1 2 { 1 2 δ [ ( x 2 a 2 ) + ( y 2 b 2 ) ] q / 2 } for     x 2 a 2 + y 2 b 2 1 = n 1 2 { 1 2 δ } = n 2 2 for     x 2 a 2 + y 2 b 2 1 ,
ψ ( ξ , η ) = 2 1 / 2 p p a b ρ 01 ρ 02 × 1 Γ ( 1 2 p ) exp ( { ( ξ ρ 01 ) 2 p + ( η ρ 02 ) 2 p } ) ,
β 2 = [ k 0 2 0 d ξ 0 d η n 2 ( ξ , η ) | ψ ( ξ , η ) | 2 1 a 2 0 d ξ 0 d η | ψ / ξ | 2 1 b 2 0 d ξ 0 d η | ψ / η | 2 ] [ 0 d ξ 0 d η | ψ ( ξ , η ) | 2 ] 1 ,
U 2 = ( V b 2 ( T 1 + T 2 ) + Ω 2 T 3 + T 4 ) / T 5 , P 2 = [ 1 ( U 2 / V b 2 ) ] ,
V b = k 0 b ( n 1 2 n 2 2 ) 1 / 2 ,
T 1 = 0 1 d ξ 0 1 ξ 2 d η ( ξ 2 + η 2 ) q / 2 | ψ ( ξ , η ) | 2 , T 2 = 0 1 d ξ 1 ξ 2 d η | ψ ( ξ , η ) | 2 + 1 d ξ 0 d η | ψ ( ξ , η ) | 2 , T 3 = 0 d ξ 0 d η | ψ ξ | 2 , T 4 = 0 d ξ 0 d η | ψ η | 2 , T 5 = 0 d ξ 0 d η | ψ ( ξ , η ) | 2 .
U 2 = V 2 + p 2 2 1 p × 1 Γ ( 1 / 2 p ) Γ ( 2 1 2 p ) [ Ω 2 ρ 01 2 + 1 ρ 02 2 ] 2 p 2 1 2 p V 2 ρ 01 × 1 Γ 2 ( 1 / 2 p ) 0 1 d ξ exp ( 2 ( ξ / ρ 01 ) 2 p ) γ ( 1 2 p , 2 ( 1 ξ 2 ρ 02 ) 2 p ) ,
U 2 = V 2 + p 2 2 1 p 1 Γ ( 1 / 2 p ) Γ ( 2 1 2 p ) [ Ω 2 ρ 01 2 + 1 ρ 02 2 ] + 2 p V 2 ρ 01 2 ρ 01 2 1 2 p 1 Γ 2 ( 1 / 2 p ) 0 1 d ξ exp ( 2 ( ξ / ρ 01 ) 2 p ) γ ( 3 2 p , 2 ( 1 ξ 2 ρ 02 ) 2 p ) + 2 p V 2 2 1 2 p ρ 01 1 Γ 2 ( 1 / 2 p ) 0 1 d ξ exp ( 2 ( ξ / ρ 01 ) 2 p ) ( ξ 2 1 ) γ ( 1 2 p , 2 ( 1 ξ 2 ρ 02 ) 2 p ) .
D ( V b ) = d ( V b P 2 ) d V b , G ( V b ) = V b d 2 ( V b P 2 ) d V b 2 .
1 a 2 2 ψ 2 ξ 2 + 1 b 2 2 ψ 2 η 2 + { k 0 2 ( n 2 ( ξ , η ) + n 2 n NL ψ 2 ) β 2 } ψ = 0 ,
V b 2 0 0 [ Q ( ξ , η ) + α ψ 2 ( ξ , η ) P 2 ] ψ 2 ( ξ , η ) d ξ d η Ω 2 0 0 | ψ ξ | 2 d ξ d η 0 0 | ψ η | 2 d ξ d η = 0 ,
Q ( ξ , η ) = n 2 ( ξ , η ) n 2 2 n 1 2 n 2 2 .
P 2 = 2 p 2 1 / 2 p ρ 01 Γ ( 1 / 2 p ) ) 0 1 d ξ ( 1 ξ 2 ) e 2 ( ξ / ρ 01 ) 2 p γ | ( 1 / 2 p , ( 2 1 ξ 2 ρ 02 ) 2 p ) | 2 p ρ 02 2 ρ 01 2 1 / 2 p Γ 2 ( 1 / 2 p ) ) 0 1 d ξ e 2 ( ξ / ρ 01 ) 2 p γ | ( 3 / 2 p , ( 2 1 ξ 2 ρ 02 ) 2 p ) | Ω 2 p 2 2 1 / 2 p Γ ( 2 1 / 2 p ) V b 2 ρ 01 2 Γ ( 1 / 2 p ) [ 1 ρ 01 2 1 ρ 02 2 ] + α p 2 Ω ρ 01 ρ 02 Γ 2 ( 1 / 2 p ) .

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