Abstract

Computations are made of the mode parameter in a cylindrical dielectric waveguide whose permittivity is a function of the radius. The mode parameter, whose sign determines whether a mode is HE or EH, is computed as a function of the propagation constant and the values of the permittivities on each side of a cylindrical boundary in the waveguide. Fields in the waveguide are then computed as a function of the mode parameter. The expressions for the fields are valid when variations in the permittivity are large or when the permittivity is not continuous. The approach is demonstrated by computations of the mode parameter in two waveguides: one whose permittivity has a discontinuity at the interface between core and cladding and one whose permittivity is continuous everywhere. The characteristics of the propagation modes that arise from each case are described and compared with those of a cylindrical dielectric waveguide whose permittivity is constant in the core region and in the cladding region.

© 1999 Optical Society of America

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  1. D. Hondros, “Über elektromagnetische Drahtwellen,” Ann. Phys. Ser. 4 30, 905–950 (1909).
    [CrossRef]
  2. S. E. Miller, “Light propagation in generalized lens-like media,” Bell Syst. Tech. J. 44, 2017–2064 (1965).
    [CrossRef]
  3. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
    [CrossRef]
  4. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14.
  5. C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part I: Formulation, solution for quadratic inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 11–15 (1969).
    [CrossRef]
  6. C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part II: Asymptotic solution for general weak inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 250–253 (1969).
    [CrossRef]
  7. M. Hashimoto, “Asymptotic eigenvalues of vector waves in an inhomogeneous circular waveguide,” Opt. Commun. 34, 43–45 (1980).
    [CrossRef]
  8. M. Hashimoto, “Asymptotic vector modes of inhomogeneous circular waveguides,” Radio Sci. 17, 3–9 (1982).
    [CrossRef]
  9. H. Ikuno, “Vectorial wave analysis of graded-index fibers,” Radio Sci. 17, 37–42 (1982).
    [CrossRef]
  10. T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
    [CrossRef]
  11. A. W. Snyder, W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
    [CrossRef]
  12. J. A. Sader, “Integral equation analysis for first order vector correction of arbitrary profiles,” IEEE J. Quantum Electron. 27, 2159–2169 (1991).
    [CrossRef]
  13. Y. Miyazaki, “Vector wave analysis of dispersion in gradient fibers,” Arch. Elektr. Übertrag. 29, 205–211 (1975).
  14. H. J. Heyke, M. H. Kuhn, “Dispersion characteristics of general gradient fibers,” Arch. Elektr. Übertrag. 27, 235–238 (1973).
  15. C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
    [CrossRef]
  16. I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
    [CrossRef]
  17. H. Ikuno, “Vectorial wave analysis of a dual shape core optical fiber with a parabolic centre core,” IEE Proc. J. 137, 163–170 (1990).
  18. H. Kirchhoff, “Wave propagation along radially inhomogeneous glass fibers,” Arch. Elektr. Übertrag. 27, 13–18 (1973).
  19. J. G. Dil, H. Blok, “Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide,” Opto-Electron. 5, 415–428 (1973).
    [CrossRef]
  20. M. O. Vassell, “Calculation of propagating modes in a graded-index optical fibre,” Opto-Electron. 6, 271–286 (1974).
    [CrossRef]
  21. G. L. Yip, S. Nemoto, “The relations between scalar modes in a lenslike medium and vector modes in a self-focusing optical fiber,” IEEE Trans. Microwave Theory Tech. MTT-23, 260–263 (1975).
    [CrossRef]
  22. P. J. B. Clarricoats, K. B. Chan, “Electromagnetic-wave propagation along radially inhomogeneous dielectric cylinders,” Electron. Lett. 6, 694–695 (1970).
    [CrossRef]
  23. C. Yeh, G. Lindgren, “Computing the propagation characteristics of radially stratified fibers: an efficient method,” Appl. Opt. 16, 483–493 (1977).
    [CrossRef] [PubMed]
  24. E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibers: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
    [CrossRef]
  25. T. Tanaka, Y. Suematsu, “An exact analysis of cylindrical fiber with index distribution by matrix method and its application to focusing fiber,” Trans. IECE Japan E59, 1–11 (1976).
  26. H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).
  27. A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (1)

1996 (1)

I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
[CrossRef]

1993 (1)

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

1991 (1)

J. A. Sader, “Integral equation analysis for first order vector correction of arbitrary profiles,” IEEE J. Quantum Electron. 27, 2159–2169 (1991).
[CrossRef]

1990 (1)

H. Ikuno, “Vectorial wave analysis of a dual shape core optical fiber with a parabolic centre core,” IEE Proc. J. 137, 163–170 (1990).

1987 (1)

A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

1982 (2)

M. Hashimoto, “Asymptotic vector modes of inhomogeneous circular waveguides,” Radio Sci. 17, 3–9 (1982).
[CrossRef]

H. Ikuno, “Vectorial wave analysis of graded-index fibers,” Radio Sci. 17, 37–42 (1982).
[CrossRef]

1980 (1)

M. Hashimoto, “Asymptotic eigenvalues of vector waves in an inhomogeneous circular waveguide,” Opt. Commun. 34, 43–45 (1980).
[CrossRef]

1978 (1)

1977 (2)

C. Yeh, G. Lindgren, “Computing the propagation characteristics of radially stratified fibers: an efficient method,” Appl. Opt. 16, 483–493 (1977).
[CrossRef] [PubMed]

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibers: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[CrossRef]

1976 (1)

T. Tanaka, Y. Suematsu, “An exact analysis of cylindrical fiber with index distribution by matrix method and its application to focusing fiber,” Trans. IECE Japan E59, 1–11 (1976).

1975 (3)

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).

G. L. Yip, S. Nemoto, “The relations between scalar modes in a lenslike medium and vector modes in a self-focusing optical fiber,” IEEE Trans. Microwave Theory Tech. MTT-23, 260–263 (1975).
[CrossRef]

Y. Miyazaki, “Vector wave analysis of dispersion in gradient fibers,” Arch. Elektr. Übertrag. 29, 205–211 (1975).

1974 (2)

M. O. Vassell, “Calculation of propagating modes in a graded-index optical fibre,” Opto-Electron. 6, 271–286 (1974).
[CrossRef]

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[CrossRef]

1973 (3)

H. J. Heyke, M. H. Kuhn, “Dispersion characteristics of general gradient fibers,” Arch. Elektr. Übertrag. 27, 235–238 (1973).

H. Kirchhoff, “Wave propagation along radially inhomogeneous glass fibers,” Arch. Elektr. Übertrag. 27, 13–18 (1973).

J. G. Dil, H. Blok, “Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide,” Opto-Electron. 5, 415–428 (1973).
[CrossRef]

1970 (1)

P. J. B. Clarricoats, K. B. Chan, “Electromagnetic-wave propagation along radially inhomogeneous dielectric cylinders,” Electron. Lett. 6, 694–695 (1970).
[CrossRef]

1969 (2)

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part I: Formulation, solution for quadratic inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 11–15 (1969).
[CrossRef]

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part II: Asymptotic solution for general weak inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 250–253 (1969).
[CrossRef]

1965 (2)

1961 (1)

1909 (1)

D. Hondros, “Über elektromagnetische Drahtwellen,” Ann. Phys. Ser. 4 30, 905–950 (1909).
[CrossRef]

Benech, P.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).

Bianciardi, E.

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibers: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[CrossRef]

Blok, H.

J. G. Dil, H. Blok, “Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide,” Opto-Electron. 5, 415–428 (1973).
[CrossRef]

Capobianco, A.

I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
[CrossRef]

Chan, K. B.

P. J. B. Clarricoats, K. B. Chan, “Electromagnetic-wave propagation along radially inhomogeneous dielectric cylinders,” Electron. Lett. 6, 694–695 (1970).
[CrossRef]

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Clarricoats, P. J. B.

P. J. B. Clarricoats, K. B. Chan, “Electromagnetic-wave propagation along radially inhomogeneous dielectric cylinders,” Electron. Lett. 6, 694–695 (1970).
[CrossRef]

Dil, J. G.

J. G. Dil, H. Blok, “Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide,” Opto-Electron. 5, 415–428 (1973).
[CrossRef]

Ding, H.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).

Gerard, P.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).

Ghatak, A. J.

A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

Hashimoto, M.

M. Hashimoto, “Asymptotic vector modes of inhomogeneous circular waveguides,” Radio Sci. 17, 3–9 (1982).
[CrossRef]

M. Hashimoto, “Asymptotic eigenvalues of vector waves in an inhomogeneous circular waveguide,” Opt. Commun. 34, 43–45 (1980).
[CrossRef]

Heyke, H. J.

H. J. Heyke, M. H. Kuhn, “Dispersion characteristics of general gradient fibers,” Arch. Elektr. Übertrag. 27, 235–238 (1973).

Hondros, D.

D. Hondros, “Über elektromagnetische Drahtwellen,” Ann. Phys. Ser. 4 30, 905–950 (1909).
[CrossRef]

Huang, W. P.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Ikuno, H.

H. Ikuno, “Vectorial wave analysis of a dual shape core optical fiber with a parabolic centre core,” IEE Proc. J. 137, 163–170 (1990).

H. Ikuno, “Vectorial wave analysis of graded-index fibers,” Radio Sci. 17, 37–42 (1982).
[CrossRef]

Kirchhoff, H.

H. Kirchhoff, “Wave propagation along radially inhomogeneous glass fibers,” Arch. Elektr. Übertrag. 27, 13–18 (1973).

Kogelnik, H.

Kuhn, M. H.

H. J. Heyke, M. H. Kuhn, “Dispersion characteristics of general gradient fibers,” Arch. Elektr. Übertrag. 27, 235–238 (1973).

Kurtz, C. N.

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part I: Formulation, solution for quadratic inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 11–15 (1969).
[CrossRef]

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part II: Asymptotic solution for general weak inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 250–253 (1969).
[CrossRef]

Lahart, M. J.

Lindgren, G.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14.

Mansour, I.

I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
[CrossRef]

Miller, S. E.

S. E. Miller, “Light propagation in generalized lens-like media,” Bell Syst. Tech. J. 44, 2017–2064 (1965).
[CrossRef]

Miyazaki, Y.

Y. Miyazaki, “Vector wave analysis of dispersion in gradient fibers,” Arch. Elektr. Übertrag. 29, 205–211 (1975).

Nemoto, S.

G. L. Yip, S. Nemoto, “The relations between scalar modes in a lenslike medium and vector modes in a self-focusing optical fiber,” IEEE Trans. Microwave Theory Tech. MTT-23, 260–263 (1975).
[CrossRef]

Okamoto, K.

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[CrossRef]

Rizzoli, V.

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibers: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[CrossRef]

Rosa, C.

I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
[CrossRef]

Sader, J. A.

J. A. Sader, “Integral equation analysis for first order vector correction of arbitrary profiles,” IEEE J. Quantum Electron. 27, 2159–2169 (1991).
[CrossRef]

Shenoy, M. R.

A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

Snitzer, E.

Snyder, A. W.

A. W. Snyder, W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14.

Streifer, W.

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part II: Asymptotic solution for general weak inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 250–253 (1969).
[CrossRef]

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part I: Formulation, solution for quadratic inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 11–15 (1969).
[CrossRef]

Suematsu, Y.

T. Tanaka, Y. Suematsu, “An exact analysis of cylindrical fiber with index distribution by matrix method and its application to focusing fiber,” Trans. IECE Japan E59, 1–11 (1976).

Tanaka, T.

T. Tanaka, Y. Suematsu, “An exact analysis of cylindrical fiber with index distribution by matrix method and its application to focusing fiber,” Trans. IECE Japan E59, 1–11 (1976).

Thyagarajan, K.

A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

Vassell, M. O.

M. O. Vassell, “Calculation of propagating modes in a graded-index optical fibre,” Opto-Electron. 6, 271–286 (1974).
[CrossRef]

Xu, C. L.

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

Yeh, C.

Yip, G. L.

G. L. Yip, S. Nemoto, “The relations between scalar modes in a lenslike medium and vector modes in a self-focusing optical fiber,” IEEE Trans. Microwave Theory Tech. MTT-23, 260–263 (1975).
[CrossRef]

Young, W. R.

Ann. Phys. Ser. 4 (1)

D. Hondros, “Über elektromagnetische Drahtwellen,” Ann. Phys. Ser. 4 30, 905–950 (1909).
[CrossRef]

Appl. Opt. (2)

Arch. Elektr. Übertrag. (3)

H. Kirchhoff, “Wave propagation along radially inhomogeneous glass fibers,” Arch. Elektr. Übertrag. 27, 13–18 (1973).

Y. Miyazaki, “Vector wave analysis of dispersion in gradient fibers,” Arch. Elektr. Übertrag. 29, 205–211 (1975).

H. J. Heyke, M. H. Kuhn, “Dispersion characteristics of general gradient fibers,” Arch. Elektr. Übertrag. 27, 235–238 (1973).

Bell Syst. Tech. J. (1)

S. E. Miller, “Light propagation in generalized lens-like media,” Bell Syst. Tech. J. 44, 2017–2064 (1965).
[CrossRef]

Electron. Lett. (1)

P. J. B. Clarricoats, K. B. Chan, “Electromagnetic-wave propagation along radially inhomogeneous dielectric cylinders,” Electron. Lett. 6, 694–695 (1970).
[CrossRef]

IEE Proc. J. (1)

H. Ikuno, “Vectorial wave analysis of a dual shape core optical fiber with a parabolic centre core,” IEE Proc. J. 137, 163–170 (1990).

IEEE J. Quantum Electron. (2)

J. A. Sader, “Integral equation analysis for first order vector correction of arbitrary profiles,” IEEE J. Quantum Electron. 27, 2159–2169 (1991).
[CrossRef]

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless dielectric waveguides,” IEEE J. Quantum Electron. JQE-31, 411–416 (1975).

IEEE Trans. Microwave Theory Tech. (4)

G. L. Yip, S. Nemoto, “The relations between scalar modes in a lenslike medium and vector modes in a self-focusing optical fiber,” IEEE Trans. Microwave Theory Tech. MTT-23, 260–263 (1975).
[CrossRef]

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[CrossRef]

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part I: Formulation, solution for quadratic inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 11–15 (1969).
[CrossRef]

C. N. Kurtz, W. Streifer, “Guided waves in inhomogeneous focusing media. Part II: Asymptotic solution for general weak inhomogeneity,” IEEE Trans. Microwave Theory Tech. MTT-17, 250–253 (1969).
[CrossRef]

J. Lightwave Technol. (3)

C. L. Xu, W. P. Huang, S. K. Chaudhuri, “Efficient and accurate vector mode calculations by beam propagation method,” J. Lightwave Technol. 11, 1209–1215 (1993).
[CrossRef]

I. Mansour, A. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996).
[CrossRef]

A. J. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical analysis of planar optical waveguides using matrix approach,” J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

M. Hashimoto, “Asymptotic eigenvalues of vector waves in an inhomogeneous circular waveguide,” Opt. Commun. 34, 43–45 (1980).
[CrossRef]

Opt. Quantum Electron. (1)

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibers: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[CrossRef]

Opto-Electron. (2)

J. G. Dil, H. Blok, “Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide,” Opto-Electron. 5, 415–428 (1973).
[CrossRef]

M. O. Vassell, “Calculation of propagating modes in a graded-index optical fibre,” Opto-Electron. 6, 271–286 (1974).
[CrossRef]

Radio Sci. (2)

M. Hashimoto, “Asymptotic vector modes of inhomogeneous circular waveguides,” Radio Sci. 17, 3–9 (1982).
[CrossRef]

H. Ikuno, “Vectorial wave analysis of graded-index fibers,” Radio Sci. 17, 37–42 (1982).
[CrossRef]

Trans. IECE Japan (1)

T. Tanaka, Y. Suematsu, “An exact analysis of cylindrical fiber with index distribution by matrix method and its application to focusing fiber,” Trans. IECE Japan E59, 1–11 (1976).

Other (1)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 14.

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