Abstract

A scalar variational analysis based on a Gaussian approximation of the fundamental mode of a double-clad elliptical fiber with a depressed inner cladding is studied. The polarization properties and graphic results are presented; they are given in terms of three parameters: the ratio of the major axis to the minor axis of the core, the ratio of the inner cladding major axis to the core major axis, and the difference between the core index and the inner cladding index. The variations of both the spot size and the field intensity with core ellipticity are examined. It is shown that high birefringence and dispersion-free orthogonal polarization modes can be obtained within the single-mode region and that the field intensity distribution may be more confined to the fiber center than in a single-clad elliptical fiber.

© 1990 Optical Society of America

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References

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  1. C. Yeh, “Elliptical Dielectric Waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
    [CrossRef]
  2. R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
    [CrossRef]
  3. S. C. Rashleigh, M. J. Marrone, “Polarization Holding in Elliptical-Core Birefringent Fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
    [CrossRef]
  4. V. Ramaswamy, W. G. French, R. D. Standley, “Polarization Characteristics of Noncircular Core Single-Mode Fibers,” Appl. Opt. 17, 3014–3017 (1978).
    [CrossRef] [PubMed]
  5. K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
    [CrossRef]
  6. T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
    [CrossRef]
  7. V. Ramaswamy, R. H. Stolen, M. D. Divine, W. Plieble, “Birefringence in Elliptically Clad Borosilicate Single-Mode Fibers,” Appl. Opt. 18, 4080–4084 (1979).
    [CrossRef] [PubMed]
  8. S. C. Rashleigh, M. J. Marrone, “Polarization-Holding in a High-Birefringence Fiber,” Electron. Lett. 18, 326–327 (1982).
    [CrossRef]
  9. T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
    [CrossRef]
  10. R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
    [CrossRef]
  11. R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
    [CrossRef]
  12. J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
    [CrossRef]
  13. S. C. Rashleigh, M. J. Marrone, “Temperature Dependence of Stress Birefringence in an Elliptically Clad Fiber,” Opt. Lett. 8, 127–129 (1983).
    [CrossRef] [PubMed]
  14. A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).
  15. A. Kumar, R. K. Varshney, K. Thyagarajan, “Birefringence Calculations in Elliptical-Core Optical Fibers,” Electron. Lett. 20, 112–113 (1984).
    [CrossRef]
  16. S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
    [CrossRef]
  17. R. B. Dyott, J. Bello, “Self-Locating Elliptically Cored Fiber with an Accessible Guiding Region,” Electron. Lett. 18, 980–981 (1982).
    [CrossRef]
  18. R. K. Varshney, R. Srivastava, R. V. Ramaswamy, “Characterization of Highly Elliptical Submicron Core Polarization Preserving Fibers: Theory and Experiment,” Appl. Opt. 27, 3114–3120 (1988).
    [CrossRef] [PubMed]
  19. R. K. Varshney, A. Kumar, “Effect of Depressed Inner Cladding on the Polarization Characteristics of Elliptical-Core Fibers,” Opt. Lett. 9, 522–525 (1984).
    [CrossRef] [PubMed]
  20. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  21. More than eight definitions have been proposed for spot size, and no agreement has been reached for a universally accepted one [E.-G. Neumann, Single-Mode Fibers (Springer-Verlag, New York, 1988), pp. 221–229.] The definition we used here is essentially that proposed by Snyder, “Understanding Mono-mode Optical Fibers,” Proc. IEEE 69, 6–12 (1981).
  22. R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

1988

1987

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).

1986

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

1985

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

1984

A. Kumar, R. K. Varshney, K. Thyagarajan, “Birefringence Calculations in Elliptical-Core Optical Fibers,” Electron. Lett. 20, 112–113 (1984).
[CrossRef]

S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
[CrossRef]

R. K. Varshney, A. Kumar, “Effect of Depressed Inner Cladding on the Polarization Characteristics of Elliptical-Core Fibers,” Opt. Lett. 9, 522–525 (1984).
[CrossRef] [PubMed]

R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
[CrossRef]

1983

1982

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

R. B. Dyott, J. Bello, “Self-Locating Elliptically Cored Fiber with an Accessible Guiding Region,” Electron. Lett. 18, 980–981 (1982).
[CrossRef]

S. C. Rashleigh, M. J. Marrone, “Polarization Holding in Elliptical-Core Birefringent Fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

S. C. Rashleigh, M. J. Marrone, “Polarization-Holding in a High-Birefringence Fiber,” Electron. Lett. 18, 326–327 (1982).
[CrossRef]

1981

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

1979

V. Ramaswamy, R. H. Stolen, M. D. Divine, W. Plieble, “Birefringence in Elliptically Clad Borosilicate Single-Mode Fibers,” Appl. Opt. 18, 4080–4084 (1979).
[CrossRef] [PubMed]

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

1978

1962

C. Yeh, “Elliptical Dielectric Waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
[CrossRef]

Akiyama, M.

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

Bello, J.

R. B. Dyott, J. Bello, “Self-Locating Elliptically Cored Fiber with an Accessible Guiding Region,” Electron. Lett. 18, 980–981 (1982).
[CrossRef]

Birch, R. D.

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

Chester, A. N.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).

Cozens, J. R.

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

Divine, M. D.

Dyott, R. B.

R. B. Dyott, J. Bello, “Self-Locating Elliptically Cored Fiber with an Accessible Guiding Region,” Electron. Lett. 18, 980–981 (1982).
[CrossRef]

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

French, W. G.

Horiguchi, M.

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

Hosaka, T.

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

Inada, K.

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

Kikuchi, Y.

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

Kitayama, K.

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

Kumar, A.

R. K. Varshney, A. Kumar, “Effect of Depressed Inner Cladding on the Polarization Characteristics of Elliptical-Core Fibers,” Opt. Lett. 9, 522–525 (1984).
[CrossRef] [PubMed]

S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
[CrossRef]

A. Kumar, R. K. Varshney, K. Thyagarajan, “Birefringence Calculations in Elliptical-Core Optical Fibers,” Electron. Lett. 20, 112–113 (1984).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Marrone, M. J.

S. C. Rashleigh, M. J. Marrone, “Temperature Dependence of Stress Birefringence in an Elliptically Clad Fiber,” Opt. Lett. 8, 127–129 (1983).
[CrossRef] [PubMed]

S. C. Rashleigh, M. J. Marrone, “Polarization Holding in Elliptical-Core Birefringent Fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

S. C. Rashleigh, M. J. Marrone, “Polarization-Holding in a High-Birefringence Fiber,” Electron. Lett. 18, 326–327 (1982).
[CrossRef]

Martellucci, S.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).

Morris, D. G.

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

Murayama, T.

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

Neumann, E.-G.

More than eight definitions have been proposed for spot size, and no agreement has been reached for a universally accepted one [E.-G. Neumann, Single-Mode Fibers (Springer-Verlag, New York, 1988), pp. 221–229.] The definition we used here is essentially that proposed by Snyder, “Understanding Mono-mode Optical Fibers,” Proc. IEEE 69, 6–12 (1981).

Nishimura, M.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Noda, J.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

Okamoto, K.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Oyamada, K.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Payne, D. N.

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

Pleibel, W.

R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
[CrossRef]

Plieble, W.

Ramaswamy, R. V.

Ramaswamy, V.

Rashleigh, S. C.

S. C. Rashleigh, M. J. Marrone, “Temperature Dependence of Stress Birefringence in an Elliptically Clad Fiber,” Opt. Lett. 8, 127–129 (1983).
[CrossRef] [PubMed]

S. C. Rashleigh, M. J. Marrone, “Polarization Holding in Elliptical-Core Birefringent Fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

S. C. Rashleigh, M. J. Marrone, “Polarization-Holding in a High-Birefringence Fiber,” Electron. Lett. 18, 326–327 (1982).
[CrossRef]

Sarkar, S.

S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
[CrossRef]

Sasaki, Y.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

Seikai, S.

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

Simpson, J. R.

R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Srivastava, R.

Standley, R. D.

Stolen, R. H.

R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
[CrossRef]

V. Ramaswamy, R. H. Stolen, M. D. Divine, W. Plieble, “Birefringence in Elliptically Clad Borosilicate Single-Mode Fibers,” Appl. Opt. 18, 4080–4084 (1979).
[CrossRef] [PubMed]

Sugawara, Y.

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

Tarbox, E. J.

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

Thyagarajan, K.

A. Kumar, R. K. Varshney, K. Thyagarajan, “Birefringence Calculations in Elliptical-Core Optical Fibers,” Electron. Lett. 20, 112–113 (1984).
[CrossRef]

S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
[CrossRef]

Uchida, N.

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

Varnham, M. P.

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

Varshney, R. K.

Verga Scheggi, A. M.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).

Yamauchi, R.

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

Yeh, C.

C. Yeh, “Elliptical Dielectric Waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
[CrossRef]

Yokota, H.

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

Appl. Opt.

Electron Lett.

R. D. Birch, M. P. Varnham, D. N. Payne, E. J. Tarbox, “Fabrication of Polarization-Maintaining Fibers Using Gas-Phase Etching,” Electron Lett. 18, 1036–1038 (1982).
[CrossRef]

Electron. Lett.

K. Kitayama, S. Seikai, N. Uchida, M. Akiyama, “Polarization-Maintaining Single-Mode Fiber With Azimuthally Inhomogeneous Index Profile,” Electron. Lett. 17, 419–420 (1981).
[CrossRef]

T. Okoshi, K. Oyamada, M. Nishimura, H. Yokota, “Side-Tunnel Fiber: An Approach to Polarization-Maintaining Optical Wave-Guiding Scheme,” Electron. Lett. 18, 824–826 (1982).
[CrossRef]

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of Polarization in Optical-Fiber Waveguides With Elliptical Cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

S. C. Rashleigh, M. J. Marrone, “Polarization-Holding in a High-Birefringence Fiber,” Electron. Lett. 18, 326–327 (1982).
[CrossRef]

T. Hosaka, Y. Sasaki, J. Noda, M. Horiguchi, “Low-Loss and Low-Crosstalk Polarization-Maintaining Optical Fibers,” Electron. Lett. 21, 920–921 (1985).
[CrossRef]

A. Kumar, R. K. Varshney, K. Thyagarajan, “Birefringence Calculations in Elliptical-Core Optical Fibers,” Electron. Lett. 20, 112–113 (1984).
[CrossRef]

R. B. Dyott, J. Bello, “Self-Locating Elliptically Cored Fiber with an Accessible Guiding Region,” Electron. Lett. 18, 980–981 (1982).
[CrossRef]

IEEE J. Quantum Electron.

S. C. Rashleigh, M. J. Marrone, “Polarization Holding in Elliptical-Core Birefringent Fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

R. H. Stolen, W. Pleibel, J. R. Simpson, “High-Birefringence Optical Fibers by Preform Deformation,” IEEE/OSA J. Lightwave Technol. LT-2, 639–641 (1984).
[CrossRef]

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” IEEE/OSA J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

J. Appl. Phys.

C. Yeh, “Elliptical Dielectric Waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
[CrossRef]

NATO ASI Series E: Appl. Sci.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical Fiber Sensors,” NATO ASI Series E: Appl. Sci. 132, 18–19 (1987).

Opt. Commun.

S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian Approximation of the Fundamental Mode in Single Mode Elliptic Core Fibers,” Opt. Commun. 49, 178–183 (1984).
[CrossRef]

Opt. Lett.

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

More than eight definitions have been proposed for spot size, and no agreement has been reached for a universally accepted one [E.-G. Neumann, Single-Mode Fibers (Springer-Verlag, New York, 1988), pp. 221–229.] The definition we used here is essentially that proposed by Snyder, “Understanding Mono-mode Optical Fibers,” Proc. IEEE 69, 6–12 (1981).

R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara, K. Inada, “Spot Sizes of Single-Mode Fibers with a Non-Circular Core,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (June 1983), 40–41.

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic diagram of a double-clad elliptical fiber with depressed inner cladding. (b) Refractive index distribution in the radial direction.

Fig. 2
Fig. 2

(a) Spot size Wx vs Vy for a1/b1 = 1.5 and 3.0. (b) Spot-size Wy vs Vy for a1/b1 = 1.5 and 3.0. Solid and dashed lines correspond to double-clad and single-clad elliptical fibers, respectively.

Fig. 3
Fig. 3

(a) Intensity distributions along the minor axis. (b) Intensity distributions along the major axis. Solid and dashed lines correspond to double-clad and single-clad elliptical fibers, respectively.

Fig. 4
Fig. 4

Comparison between the birefringences obtained by the eigenvalue method using Mathieu’s functions and the Gaussian approximation for a single-clad elliptical fiber.

Fig. 5
Fig. 5

Normalized birefringence B as a function of Vy for a1/b1 = 1.5, 2.0, 2.5, and 3.0. Solid and dashed lines correspond to double-clad elliptical fibers and single-clad fibers.

Fig. 6
Fig. 6

Normalized birefringence B as a function of Δ1 for a1/b1 = 1.5, 2.0, 2.5, and 3.0.

Fig. 7
Fig. 7

Normalized birefringence B as a function of Rx for a1/b1 = 1.5, 2.0, 2.5, and 3.0.

Fig. 8
Fig. 8

Modal dispersion as a function of Vy for a1/b1 = 1.5, 2.0, 2.5, and 3.0.

Fig. 9
Fig. 9

Modal dispersion as a function of Δ1 for a1/b1 = 1.5, 2.0, 2.5, and 3.0.

Fig. 10
Fig. 10

Modal dispersion as a function of Rx for a1/b1 = 1.5, 2.0, 2.5, and 3.0.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

n 2 ( ξ ) = n 0 2 [ 1 - 2 Δ 2 f ( ξ ) ] ,
f ( ξ ) = { 0 ξ < ξ 1 , α H ( ξ - ξ 1 ) , ξ 1 ξ < ξ 2 , H ( ξ - ξ 2 ) , ξ ξ 2 ,
H ( x ) = { 0 , x < 0 , 1 , x 0 , α = Δ 1 Δ 2 = n 0 2 - n 1 2 n 0 2 - n 2 2 ,
Δ 1 = n 0 2 - n 1 2 2 n 0 2 ,             Δ 2 = n 0 2 - n 2 2 2 n 0 2 .
R x = a 2 a 1 ,             R y = b 2 b 1 .
V x = k a 1 n 0 ( 2 Δ 2 ) 1 / 2 ,
V y = k b 1 n 0 ( 2 Δ 2 ) 1 / 2 .
E x = Ψ ( x , y ) exp [ i ( β + δ β x ) z ] ,
E y = Ψ ( x , y ) exp [ i ( β + δ β y ) z ] .
[ t 2 + k 2 n 2 ( x , y ) - β 2 ] Ψ ( x , y ) = 0 ,
δ β p = ρ p ( 2 Δ 2 ) 3 / 2 2 V p - - ( t · e t ) e t · t f ( x , y ) d x d y - - e t 2 d x d y , p = x , y ,
Ψ ( x , y ) = exp [ - 1 2 ( X 2 W x 2 + Y 2 W y 2 ) ] ,
β 2 = - - [ k 2 n 2 ( X , Y ) Ψ - ( Ψ X ) 2 - ( Ψ Y ) 2 ] d X d Y - - Ψ 2 d X d Y .
β W x = 0 , β W y = 0 ,
π V x 2 = W x W y - - X f X exp ( - X 2 W x 2 - Y 2 W y 2 ) d X d Y ,
π V y 2 = W y W x - - Y f Y exp ( - X 2 W x 2 - Y 2 W y 2 ) d X d Y .
X = Q x cosh ξ cos η ,
Y = Q y sinh ξ sin η ,
W y W x V x 2 + W x W y V y 2 = 2 0 Q x cosh ξ Q y sinh ξ f ξ exp [ - A ( ξ ) ] I 0 [ B ( ξ ) ] d ξ ,
W y W x V x 2 - W x W y V y 2 = 2 0 Q x cosh ξ Q y sinh ξ f ξ exp [ - A ( ξ ) ] I 1 [ B ( ξ ) ] d ξ ,
A ( ξ ) = W x 2 Q y 2 sinh 2 ξ + W y 2 Q x 2 cosh 2 ξ 2 W x 2 W y 2 , B ( ξ ) = W x 2 Q y 2 sinh 2 ξ - W y 2 Q x 2 cosh 2 ξ 2 W x 2 W y 2 .
f ξ = α δ ( ξ - ξ 1 ) + ( 1 - α ) δ ( ξ - ξ 2 )
W y W x V x 2 + W x W y V y 2 = 2 { α exp [ - A ( ξ 1 ) ] I 0 [ B ( ξ 1 ) ] + ( 1 - α ) R x R y exp [ - A ( ξ 2 ) ] I 0 [ B ( ξ 2 ) ] } ,
W y W x V x 2 - W x W y V y 2 = 2 { α exp [ - A ( ξ 1 ) ] I 1 [ B ( ξ 1 ) ] + ( 1 - α ) R x R y exp [ - A ( ξ 2 ) ] I 1 [ B ( ξ 2 ) ] } ,
A ( ξ 1 ) = W x 2 + W y 2 2 W x 2 W y 2 ,             B ( ξ 1 ) = W x 2 - W y 2 2 W x 2 W y 2 , A ( ξ 2 ) = W x 2 R y 2 + W y 2 R x 2 2 W x 2 W y 2 ,             B ( ξ 2 ) = W x 2 R y 2 - W y 2 R x 2 2 W x 2 W y 2 .
δ β x = - ( 2 Δ 2 ) 3 / 2 2 a 1 V x 3 W x 4 ,
δ β y = - ( 2 Δ 2 ) 3 / 2 2 b 1 V y 3 W y 4 .
B = δ β x - δ β y k = 2 n 0 Δ 2 2 V y 4 [ 1 W y 4 - 1 ( a 1 / b 1 ) 4 W x 4 ] .
Δ τ = 1 c d ( δ β x - δ β y ) d k = 2 n 0 Δ 2 2 c d d V y { 1 V y 3 [ 1 W y 4 - 1 ( a 1 / b 1 ) 4 W x 4 ] } .
S = Ψ 2 - - Ψ 2 d X d Y ,
S ¯ = A core S = exp [ - 1 2 ( X 2 W x 2 + Y 2 W y 2 ) ] W x W y ,

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