Abstract

The eigenvalue equation is formulated for a general three-layered radially stratified metallic optical fiber waveguide and solved numerically using the zoom search method. The result is shown to be applicable to the common D-shaped fiber, which bears no similarity to a concentric stratum but may be converted as such through the Mobius conformal representation. The theoretical prediction agrees well with our experimental measurements, and the method should be proved valuable for optimizing metallic fiber design relationships.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Li, R. D. Birch, D. N. Payne, “High-Performance Composite Metal/Glass Fibre Polarisers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), Vol. 1, p. 137–140.
  2. L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.
  3. L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
    [CrossRef]
  4. S. C. Rashleigh, “Positive Permittivity Metal Cladding: its Effect on the Modes of Dielectric Optical Waveguides,” Appl. Opt. 15, 2804 (1976).
    [CrossRef] [PubMed]
  5. K. Thyagarajan, A. N. Kaul, S. I. Hosain, “Attenuation Characteristics of Single-Mode Metal-Clad Graded-Index Waveguides with a Dielectric Buffer: a Simple and Accurate Numerical Method,” Opt. Lett. 11, 479 (1986).
    [CrossRef] [PubMed]
  6. Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
    [CrossRef]
  7. H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
    [CrossRef]
  8. H. F. Mahlein, “Integrated Optical Polarizer,” Opt. Commun. 16, 420 (1976).
    [CrossRef]
  9. J. Ctyroky, J. Janta, J. Schrofel, “Thin-Film Polarizer for Optical Waveguides,” in Technical Digest, Tenth European Conference on Optical Communication, Stuttgart (1984), p.44–45.
  10. J. Ctyroky, H. J. Henning, “Thin Film Polariser for Ti:LiNbO3 Waveguides at λ = 1.3 μm,” Electron. Lett. 22, 756 (1986).
    [CrossRef]
  11. R. Shubert, J. H. Harris, “Optical Guided-Wave Focusing and Diffraction,” J. Opt. Soc. Am. 61, 154 (1971).
    [CrossRef]
  12. J. N. Polky, G. L. Mitchell, “Metal-Clad Planar Dielectric Waveguide for Integrated Optics,” J. Opt. Soc. Am. 64, 274 (1974).
    [CrossRef]
  13. Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
    [CrossRef]
  14. C. Y. H. Tsao, L. Li, D. N. Payne, “Propagation Characteristics of Guided Waves in Stratified Metallic Optical Waveguides,” Appl. Opt. 27, 1316 (1988).
    [CrossRef] [PubMed]
  15. C. Vassallo, “Rigorous Theory for Propagation in Optical Fibres with a Plane-Limited Cladding,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 333–335.
  16. S. J. Al-Bader, H. A. Jamid, “Comparison of Absorption Loss in Metal-Clad Optical Waveguides,” IEEE. Trans. Microwave Theory Tech. MTT-34, 310 (1986).
    [CrossRef]
  17. C. Y. H. Tsao, “Conformal Mapping for D-Shaped Fibres,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1986).
  18. W. R. Smythe, C. Yeh, “Formulas,” in American Institute of Physics Handbook, D. E.Gray Gray, Ed. (McGraw-Hill, New York, 1972), Sec. 5.
  19. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9.
  20. M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981), p. 225.
  21. M. Miyagi, S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared Transmission,” IEEE/OSA J. Lightwave Technol. LT-2, 116 (1984).
    [CrossRef]
  22. P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Vol. 2 (McGraw-Hill, New York, 1953), Chap. 10, p. 1175.
  23. R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1974), Appl. 2, p. 319.
  24. H. Kober, Dictionary of Conformal Representations (Dover, New York, 1952).
  25. C. Y. H. Tsao, “Vector Wave Equation in Curvilinear Coordinates and its Analytic Solution,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1985).
  26. J. P. Mason, “Cylindrical Bessel Functions for a Large Range of Complex Arguments,” Comput. Phys. Commun. 30, 1 (1983).
    [CrossRef]
  27. K. H. Burrel, “Algorithm 484. Evaluation of the Modified Bessel Function K0(z) and K1(z) for Complex Arguments,” Commun. ACM 17, 524 (1977).
    [CrossRef]
  28. D. J. Sookne, “Bessel Functions J and I of Complex Argument and Integer Order,” J. Natl. Bur. Stand. U.S.A. JNBBAU 77B (3 and 4) 73–214, pp. 111–114, 115–124, 125–132, and 133–136 (1973).

1988 (1)

1986 (4)

S. J. Al-Bader, H. A. Jamid, “Comparison of Absorption Loss in Metal-Clad Optical Waveguides,” IEEE. Trans. Microwave Theory Tech. MTT-34, 310 (1986).
[CrossRef]

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

K. Thyagarajan, A. N. Kaul, S. I. Hosain, “Attenuation Characteristics of Single-Mode Metal-Clad Graded-Index Waveguides with a Dielectric Buffer: a Simple and Accurate Numerical Method,” Opt. Lett. 11, 479 (1986).
[CrossRef] [PubMed]

J. Ctyroky, H. J. Henning, “Thin Film Polariser for Ti:LiNbO3 Waveguides at λ = 1.3 μm,” Electron. Lett. 22, 756 (1986).
[CrossRef]

1984 (1)

M. Miyagi, S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared Transmission,” IEEE/OSA J. Lightwave Technol. LT-2, 116 (1984).
[CrossRef]

1983 (1)

J. P. Mason, “Cylindrical Bessel Functions for a Large Range of Complex Arguments,” Comput. Phys. Commun. 30, 1 (1983).
[CrossRef]

1977 (1)

K. H. Burrel, “Algorithm 484. Evaluation of the Modified Bessel Function K0(z) and K1(z) for Complex Arguments,” Commun. ACM 17, 524 (1977).
[CrossRef]

1976 (2)

1975 (2)

H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
[CrossRef]

Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
[CrossRef]

1974 (1)

1973 (1)

D. J. Sookne, “Bessel Functions J and I of Complex Argument and Integer Order,” J. Natl. Bur. Stand. U.S.A. JNBBAU 77B (3 and 4) 73–214, pp. 111–114, 115–124, 125–132, and 133–136 (1973).

1972 (1)

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

1971 (1)

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981), p. 225.

Al-Bader, S. J.

S. J. Al-Bader, H. A. Jamid, “Comparison of Absorption Loss in Metal-Clad Optical Waveguides,” IEEE. Trans. Microwave Theory Tech. MTT-34, 310 (1986).
[CrossRef]

Birch, R. D.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

L. Li, R. D. Birch, D. N. Payne, “High-Performance Composite Metal/Glass Fibre Polarisers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), Vol. 1, p. 137–140.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.

Burrel, K. H.

K. H. Burrel, “Algorithm 484. Evaluation of the Modified Bessel Function K0(z) and K1(z) for Complex Arguments,” Commun. ACM 17, 524 (1977).
[CrossRef]

Chiba, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Churchill, R. V.

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1974), Appl. 2, p. 319.

Ctyroky, J.

J. Ctyroky, H. J. Henning, “Thin Film Polariser for Ti:LiNbO3 Waveguides at λ = 1.3 μm,” Electron. Lett. 22, 756 (1986).
[CrossRef]

J. Ctyroky, J. Janta, J. Schrofel, “Thin-Film Polarizer for Optical Waveguides,” in Technical Digest, Tenth European Conference on Optical Communication, Stuttgart (1984), p.44–45.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Vol. 2 (McGraw-Hill, New York, 1953), Chap. 10, p. 1175.

Furuya, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Hakuta, M.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Harris, J. H.

Hasumi, R.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Henning, H. J.

J. Ctyroky, H. J. Henning, “Thin Film Polariser for Ti:LiNbO3 Waveguides at λ = 1.3 μm,” Electron. Lett. 22, 756 (1986).
[CrossRef]

Hosain, S. I.

Jamid, H. A.

S. J. Al-Bader, H. A. Jamid, “Comparison of Absorption Loss in Metal-Clad Optical Waveguides,” IEEE. Trans. Microwave Theory Tech. MTT-34, 310 (1986).
[CrossRef]

Janta, J.

J. Ctyroky, J. Janta, J. Schrofel, “Thin-Film Polarizer for Optical Waveguides,” in Technical Digest, Tenth European Conference on Optical Communication, Stuttgart (1984), p.44–45.

Kamiya, T.

Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
[CrossRef]

Kaul, A. N.

Kawakami, S.

M. Miyagi, S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared Transmission,” IEEE/OSA J. Lightwave Technol. LT-2, 116 (1984).
[CrossRef]

Kober, H.

H. Kober, Dictionary of Conformal Representations (Dover, New York, 1952).

Li, L.

C. Y. H. Tsao, L. Li, D. N. Payne, “Propagation Characteristics of Guided Waves in Stratified Metallic Optical Waveguides,” Appl. Opt. 27, 1316 (1988).
[CrossRef] [PubMed]

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

L. Li, R. D. Birch, D. N. Payne, “High-Performance Composite Metal/Glass Fibre Polarisers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), Vol. 1, p. 137–140.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.

Mahlein, H. F.

H. F. Mahlein, “Integrated Optical Polarizer,” Opt. Commun. 16, 420 (1976).
[CrossRef]

H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
[CrossRef]

Mason, J. P.

J. P. Mason, “Cylindrical Bessel Functions for a Large Range of Complex Arguments,” Comput. Phys. Commun. 30, 1 (1983).
[CrossRef]

Mitchell, G. L.

Miyagi, M.

M. Miyagi, S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared Transmission,” IEEE/OSA J. Lightwave Technol. LT-2, 116 (1984).
[CrossRef]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Vol. 2 (McGraw-Hill, New York, 1953), Chap. 10, p. 1175.

Oberbacher, R.

H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
[CrossRef]

Payne, D. N.

C. Y. H. Tsao, L. Li, D. N. Payne, “Propagation Characteristics of Guided Waves in Stratified Metallic Optical Waveguides,” Appl. Opt. 27, 1316 (1988).
[CrossRef] [PubMed]

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

L. Li, R. D. Birch, D. N. Payne, “High-Performance Composite Metal/Glass Fibre Polarisers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), Vol. 1, p. 137–140.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.

Polky, J. N.

Rashleigh, S. C.

Rauscher, W.

H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
[CrossRef]

Schrofel, J.

J. Ctyroky, J. Janta, J. Schrofel, “Thin-Film Polarizer for Optical Waveguides,” in Technical Digest, Tenth European Conference on Optical Communication, Stuttgart (1984), p.44–45.

Shubert, R.

Smythe, W. R.

W. R. Smythe, C. Yeh, “Formulas,” in American Institute of Physics Handbook, D. E.Gray Gray, Ed. (McGraw-Hill, New York, 1972), Sec. 5.

Sookne, D. J.

D. J. Sookne, “Bessel Functions J and I of Complex Argument and Integer Order,” J. Natl. Bur. Stand. U.S.A. JNBBAU 77B (3 and 4) 73–214, pp. 111–114, 115–124, 125–132, and 133–136 (1973).

Suematsu, Y.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Thyagarajan, K.

Tsao, C. Y. H.

C. Y. H. Tsao, L. Li, D. N. Payne, “Propagation Characteristics of Guided Waves in Stratified Metallic Optical Waveguides,” Appl. Opt. 27, 1316 (1988).
[CrossRef] [PubMed]

C. Y. H. Tsao, “Vector Wave Equation in Curvilinear Coordinates and its Analytic Solution,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1985).

C. Y. H. Tsao, “Conformal Mapping for D-Shaped Fibres,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1986).

Vassallo, C.

C. Vassallo, “Rigorous Theory for Propagation in Optical Fibres with a Plane-Limited Cladding,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 333–335.

Wylangowski, G.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.

Yamamoto, Y.

Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
[CrossRef]

Yanai, H.

Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
[CrossRef]

Yeh, C.

W. R. Smythe, C. Yeh, “Formulas,” in American Institute of Physics Handbook, D. E.Gray Gray, Ed. (McGraw-Hill, New York, 1972), Sec. 5.

Appl. Opt. (2)

Appl. Phys. (1)

H. F. Mahlein, R. Oberbacher, W. Rauscher, “An Integrated Optical TE-TM Mode Splitter,” Appl. Phys. 7, 15 (1975).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291 (1972).
[CrossRef]

Commun. ACM (1)

K. H. Burrel, “Algorithm 484. Evaluation of the Modified Bessel Function K0(z) and K1(z) for Complex Arguments,” Commun. ACM 17, 524 (1977).
[CrossRef]

Comput. Phys. Commun. (1)

J. P. Mason, “Cylindrical Bessel Functions for a Large Range of Complex Arguments,” Comput. Phys. Commun. 30, 1 (1983).
[CrossRef]

Electron. Lett. (2)

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Broadband Metal/Glass Single-Mode Fibre Polarisers,” Electron. Lett. 22, 1020 (1986).
[CrossRef]

J. Ctyroky, H. J. Henning, “Thin Film Polariser for Ti:LiNbO3 Waveguides at λ = 1.3 μm,” Electron. Lett. 22, 756 (1986).
[CrossRef]

IEEE. J. Quantum Electron. (1)

Y. Yamamoto, T. Kamiya, H. Yanai, “Characteristics of Optical Guided Modes in Multilayer Metal/Clad Planar Optical Guide with Low-Index Dielectric Buffer Layer,” IEEE. J. Quantum Electron. QE-11, 729 (1975).
[CrossRef]

IEEE. Trans. Microwave Theory Tech. (1)

S. J. Al-Bader, H. A. Jamid, “Comparison of Absorption Loss in Metal-Clad Optical Waveguides,” IEEE. Trans. Microwave Theory Tech. MTT-34, 310 (1986).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

M. Miyagi, S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared Transmission,” IEEE/OSA J. Lightwave Technol. LT-2, 116 (1984).
[CrossRef]

J. Natl. Bur. Stand. U.S.A. JNBBAU 77B (3 and 4) 73–214 (1)

D. J. Sookne, “Bessel Functions J and I of Complex Argument and Integer Order,” J. Natl. Bur. Stand. U.S.A. JNBBAU 77B (3 and 4) 73–214, pp. 111–114, 115–124, 125–132, and 133–136 (1973).

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

H. F. Mahlein, “Integrated Optical Polarizer,” Opt. Commun. 16, 420 (1976).
[CrossRef]

Opt. Lett. (1)

Other (12)

L. Li, R. D. Birch, D. N. Payne, “High-Performance Composite Metal/Glass Fibre Polarisers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), Vol. 1, p. 137–140.

L. Li, G. Wylangowski, D. N. Payne, R. D. Birch, “Low-Cost Metal/Glass Fibre Polarisers Produced,” in Technical Digest, Fourth International Conference on Optical Fiber Sensors, Tokyo (1986), p. 163–166.

J. Ctyroky, J. Janta, J. Schrofel, “Thin-Film Polarizer for Optical Waveguides,” in Technical Digest, Tenth European Conference on Optical Communication, Stuttgart (1984), p.44–45.

C. Vassallo, “Rigorous Theory for Propagation in Optical Fibres with a Plane-Limited Cladding,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 333–335.

C. Y. H. Tsao, “Conformal Mapping for D-Shaped Fibres,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1986).

W. R. Smythe, C. Yeh, “Formulas,” in American Institute of Physics Handbook, D. E.Gray Gray, Ed. (McGraw-Hill, New York, 1972), Sec. 5.

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981), p. 225.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Vol. 2 (McGraw-Hill, New York, 1953), Chap. 10, p. 1175.

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1974), Appl. 2, p. 319.

H. Kober, Dictionary of Conformal Representations (Dover, New York, 1952).

C. Y. H. Tsao, “Vector Wave Equation in Curvilinear Coordinates and its Analytic Solution,” Internal Report, Optical Fibre Group, Electronics Department, U. Southampton (1985).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Typical three-layered radially stratified fiber.

Fig. 2
Fig. 2

(a) Fiber cross section of a typical D-shaped fiber. (b) The D-shaped fiber is modeled as having a circular core and an additional plane-limited metal cladding.

Fig. 3
Fig. 3

Two discrete circles on a z-plane with z = x + jy.

Fig. 4
Fig. 4

Two discrete circles on the z-plane are mapped to be two concentric ones on the ζ-plane, where ζ = ξ + .

Fig. 5
Fig. 5

Electric fields for the TE (broken lines) or TM (solid line) mode in a D-shaped fiber.

Fig. 6
Fig. 6

Equivalent index of the propagation constant for various modes.

Fig. 7
Fig. 7

Attenuations of various modes as a function of the core–metal separation d.

Fig. 8
Fig. 8

Waveguide performance in terms of propagation speed and attenuation as a function of the core radius A1 (n1 = 1.47, n2 = 1.46, d = 0.8 μm, λ = 0.83 μm, gallium).

Fig. 9
Fig. 9

Waveguide performance as a function of the relative refractive-index difference Δ = (n1n2)/n1,(n2 = 1.4585, d = 0.8 μ m, r1 = 1.5 μm, gallium at λ = 0.83 μm).

Equations (29)

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

e = ( Ψ / r ϕ - β Φ / ω r ) r 0 + ( - Ψ / r - β Φ / ω r ϕ ) ϕ 0 - ( k 2 n 2 - β 2 ) Φ z 0 / j ω ,
h = ( Φ / r ϕ + β Ψ / ω μ r ) r 0 + ( - Φ / r - β Ψ / ω μ r ϕ ) ϕ 0 + ( k 2 n 2 - β 2 ) Ψ z 0 / j ω μ .
[ Δ t + ( k 2 n i 2 - β 2 ) ] Ψ i = 0 ,
[ Δ t + ( k 2 n i 2 - β 2 ) ] Φ i = 0
Ψ 1 = A 1 J ν ( U 1 r / r 1 ) f ν ( ν ϕ ) ,
Ψ 2 = [ A 2 J ν ( U 2 r / r 1 ) + B 2 Y ν ( U 2 r / r 1 ) ] f ν ( ν ϕ ) ,
Ψ 3 = A 3 K ν ( W 3 r / r 2 ) f ν ( ν ϕ ) ,
e ϕ 1 = - A 1 ( U 1 / r 1 ) J ν ( U 1 r / r 1 ) ,
e ϕ 2 = - ( U 2 / r 1 ) [ A 2 J ν ( U 2 r / r 1 ) + B 2 Y ν ( U 2 r / r 1 ) ] ,
e ϕ 3 = - A 3 ( W 3 / r 2 ) K ν ( W 3 r / r 2 ) ,
h z 1 = - ( U 1 2 / r 1 2 j ω μ ) A 1 J ν ( U 1 r / r 1 ) ,
h z 2 = - ( U 2 2 / r 1 2 j ω μ ) [ A 2 J ν ( U 2 r / r 1 ) + B 2 Y ν ( U 2 r / r 1 ) ] ,
h z 3 = ( W 3 2 / r 2 2 j ω μ ) A 3 K ν ( W 3 r / r 2 ) .
[ J ν ( U 1 ) p ν / U 1 J ν ( U 1 ) - q ν / U 2 ] [ K ν ( W 3 ) p ν / W 3 K ν ( W 3 ) + r ν / a U 2 ] - ( 2 / π a U 2 2 ) 2 = 0 ,
[ J ν ( U 1 ) p ν / U 1 J ν ( U 1 ) - n 2 2 q ν / n 1 2 U 2 ] [ K ν ( W 3 ) p ν / W 3 K ν ( W 3 ) + n 2 2 r ν / n 3 2 a U 2 ] - ( 2 n 2 2 / π n 1 n 3 a U 2 2 ) 2 = 0.
p ν = - ( 2 / π ) [ I ν ( a W 2 ) K ν ( W 2 ) - I ν ( W 2 ) K ν ( a W 2 ) ] ,
q ν = j ( 2 / π ) { ν [ I ν ( a W 2 ) K ν ( W 2 ) - I ν ( W 2 ) K ν ( a W 2 ) ] / W 2 - [ I ν ( a W 2 ) K ν + 1 ( W 2 ) + I ν + 1 ( W 2 ) K ν ( W 2 ) ] } ,
r ν = j ( 2 / π ) { ν [ I ν ( a W 2 ) K ν ( W 2 ) - I ν ( W 2 ) K ν ( a W 2 ) ] / a W 2 + [ I ν ( W 2 ) K ν + 1 ( a W 2 ) + I ν + 1 ( a W 2 ) K ν ( W 2 ) ] } .
J ν ( U 1 ) / U 1 J ν ( U 1 ) - q ν / j W 2 p ν = 0 ,
J ν ( U 1 ) / U 1 J ν ( U 1 ) - n 2 2 q ν / n 1 2 j W 2 p ν = 0.
J ν ( U 1 ) / U 1 J ν ( U 1 ) + K ν ( W 3 ) / W 3 K ν ( W 3 ) = 0 ,
J ν ( U 1 ) / U 1 J ν ( U 1 ) + n 3 2 K ν ( W 3 ) / n 1 2 W 3 K ν ( W 3 ) = 0.
[ Δ t + ( k 2 n 2 - β 2 ) / ζ ( z ) 2 ] ( Ψ or Φ ) = 0.
x 1 · x 2 = R 1 2 ,
( R 1 + R 2 + d - x 1 ) · ( R 1 + R 2 + d - x 2 ) = R 2 2 .
x 1 = R 1 + d - R 1 2 + 2 R 1 d ,
x 2 = r 2 = R 1 + d + R 1 2 + 2 R 1 d ,
r 1 = R 1 ,
[ Δ t + ( 1 - x 1 / r 2 ) 2 ( k 2 n 2 - β 2 ) ] ( Ψ or Φ ) = 0.

Metrics