Abstract

Light propagation in graded-index optical fibers is described by two WKB methods, a classical formulation and the Langer-McKelvey approach. Explicit errors in these methods are evaluated for a fiber profile of near-parabolic shape and for one far from parabolic shape by comparing the methods with the results of evanescent wave theory that involve asymptotic error estimates. The most accurate formulation in general is the classical method, but in special cases the Langer—McKelvey approach is slightly more accurate. One example shows an inaccuracy of —672.5 to —672.1 psec/km in modal group delay for the latter method when the maximum intermodal group delay difference is 2.84 nsec/km.

© 1981 Optical Society of America

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  1. D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563–1578 (1973).
  2. K. Petermann, "The mode attenuation in general graded core multimode fibers," Arch. Elektronik Übertragungstech. 29, 345–348 (1975).
  3. J. J. Ramskov Hansen and E. Nicolaisen, "Propagation in graded index fibers: comparison between experiment and three theories," Appl. Opt. 17, 2831–2835 (1978).
  4. R. E. Langer, "On the asymptotic solutions of ordinary differential equations with reference to the Stoke’s phenomenon about a singular point," Tran. Am. Math. Soc. 37, 397–416 (1935).
  5. R. W. McKelvey, "Solution about a singular point of a linear differential equation involving a large parameter," Trans. Am. Math. Soc. 91, 410–424 (1959).
  6. W. Streifer and C. N. Curtz, "Scalar analysis of radially inhomogeneous media," J. Opt. Soc. Am. 57, 779–786 (1967).
  7. R. Olshansky, "Multiple-α index profiles," Appl. Opt. 18,683–689 (1979).
  8. S. Choudhary and L. B. Felsen, "Guided modes in graded index optical fibers," J. Opt. Soc. Am. 67, 1192–1196 (1977).
  9. R. C. Tobey, PL-1-Formac Interpreter User's Reference Manual, IBM 1967/69, 360 D-0.3.3004 (IBM Corp., unpublished).
  10. G. Jacobsen and J. J. Ramskov Hansen, "Propagation constants and group delays of guided modes in graded index fibers: a comparison of three theories," Appl. Opt. 18, 2837–2842 (1979).
  11. G. Jacobsen, "Evanescent-wave and nonlinear transformation analysis of graded-index fibers," J. Opt. Soc. Am. 70, 1338–1344 (1980).
  12. D. Shanks, "Nonlinear transforms of divergent and slowly convergent sequences," J. Math. Phys. 34, 1–42 (1955).
  13. G. Jacobsen and F. Ramskov Hansen, "Behavior of transients in propagation constant series of evanescent wave theory," Radio Sci. 16, 519–524 (1981).
  14. G. Jacobsen and J. J. Ramskov Hansen, "Detailed error estimates for a first order WKB calculation method," Electron. Lett. 16, 540–541 (1980).
  15. K. Oyamada and T. Okoshi, "High-accuracy WKB analysis of α-power graded-core fibers," IEEE Trans. Microwave Tech. MTT-28, 839–845 (1980).
  16. R. Olshansky, "Effect of the cladding on pulse broadening in graded-index optical waveguides," Appl. Opt. 16, 2171–2174 (1977).
  17. R. Olshansky and D. B. Keck, "Pulse broadening in graded index optical fibers," Appl. Opt. 15, 483–491 (1976).
  18. J. Arnold, "Inhomogeneous dielectric waveguides: a uniform asymptotic theory," J. Phys. A. Math. Nucl. Gen. 13, 347–360 (1980).

1981 (1)

G. Jacobsen and F. Ramskov Hansen, "Behavior of transients in propagation constant series of evanescent wave theory," Radio Sci. 16, 519–524 (1981).

1980 (4)

G. Jacobsen and J. J. Ramskov Hansen, "Detailed error estimates for a first order WKB calculation method," Electron. Lett. 16, 540–541 (1980).

K. Oyamada and T. Okoshi, "High-accuracy WKB analysis of α-power graded-core fibers," IEEE Trans. Microwave Tech. MTT-28, 839–845 (1980).

J. Arnold, "Inhomogeneous dielectric waveguides: a uniform asymptotic theory," J. Phys. A. Math. Nucl. Gen. 13, 347–360 (1980).

G. Jacobsen, "Evanescent-wave and nonlinear transformation analysis of graded-index fibers," J. Opt. Soc. Am. 70, 1338–1344 (1980).

1979 (2)

1978 (1)

1977 (2)

1976 (1)

1975 (1)

K. Petermann, "The mode attenuation in general graded core multimode fibers," Arch. Elektronik Übertragungstech. 29, 345–348 (1975).

1973 (1)

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563–1578 (1973).

1967 (1)

1959 (1)

R. W. McKelvey, "Solution about a singular point of a linear differential equation involving a large parameter," Trans. Am. Math. Soc. 91, 410–424 (1959).

1955 (1)

D. Shanks, "Nonlinear transforms of divergent and slowly convergent sequences," J. Math. Phys. 34, 1–42 (1955).

1935 (1)

R. E. Langer, "On the asymptotic solutions of ordinary differential equations with reference to the Stoke’s phenomenon about a singular point," Tran. Am. Math. Soc. 37, 397–416 (1935).

Arnold, J.

J. Arnold, "Inhomogeneous dielectric waveguides: a uniform asymptotic theory," J. Phys. A. Math. Nucl. Gen. 13, 347–360 (1980).

Choudhary, S.

Curtz, C. N.

Felsen, L. B.

Gloge, D.

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563–1578 (1973).

Hansen, F. Ramskov

G. Jacobsen and F. Ramskov Hansen, "Behavior of transients in propagation constant series of evanescent wave theory," Radio Sci. 16, 519–524 (1981).

Hansen, J. J. Ramskov

Jacobsen, G.

G. Jacobsen and F. Ramskov Hansen, "Behavior of transients in propagation constant series of evanescent wave theory," Radio Sci. 16, 519–524 (1981).

G. Jacobsen and J. J. Ramskov Hansen, "Detailed error estimates for a first order WKB calculation method," Electron. Lett. 16, 540–541 (1980).

G. Jacobsen, "Evanescent-wave and nonlinear transformation analysis of graded-index fibers," J. Opt. Soc. Am. 70, 1338–1344 (1980).

G. Jacobsen and J. J. Ramskov Hansen, "Propagation constants and group delays of guided modes in graded index fibers: a comparison of three theories," Appl. Opt. 18, 2837–2842 (1979).

Keck, D. B.

Langer, R. E.

R. E. Langer, "On the asymptotic solutions of ordinary differential equations with reference to the Stoke’s phenomenon about a singular point," Tran. Am. Math. Soc. 37, 397–416 (1935).

Marcatili, E. A. J.

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563–1578 (1973).

McKelvey, R. W.

R. W. McKelvey, "Solution about a singular point of a linear differential equation involving a large parameter," Trans. Am. Math. Soc. 91, 410–424 (1959).

Nicolaisen, E.

Okoshi, T.

K. Oyamada and T. Okoshi, "High-accuracy WKB analysis of α-power graded-core fibers," IEEE Trans. Microwave Tech. MTT-28, 839–845 (1980).

Olshansky, R.

Oyamada, K.

K. Oyamada and T. Okoshi, "High-accuracy WKB analysis of α-power graded-core fibers," IEEE Trans. Microwave Tech. MTT-28, 839–845 (1980).

Petermann, K.

K. Petermann, "The mode attenuation in general graded core multimode fibers," Arch. Elektronik Übertragungstech. 29, 345–348 (1975).

Shanks, D.

D. Shanks, "Nonlinear transforms of divergent and slowly convergent sequences," J. Math. Phys. 34, 1–42 (1955).

Streifer, W.

Tobey, R. C.

R. C. Tobey, PL-1-Formac Interpreter User's Reference Manual, IBM 1967/69, 360 D-0.3.3004 (IBM Corp., unpublished).

Appl. Opt. (5)

Arch. Elektronik Übertragungstech. (1)

K. Petermann, "The mode attenuation in general graded core multimode fibers," Arch. Elektronik Übertragungstech. 29, 345–348 (1975).

Bell. Syst. Tech. J. (1)

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563–1578 (1973).

Electron. Lett. (1)

G. Jacobsen and J. J. Ramskov Hansen, "Detailed error estimates for a first order WKB calculation method," Electron. Lett. 16, 540–541 (1980).

IEEE Trans. Microwave Tech. (1)

K. Oyamada and T. Okoshi, "High-accuracy WKB analysis of α-power graded-core fibers," IEEE Trans. Microwave Tech. MTT-28, 839–845 (1980).

J. Math. Phys. (1)

D. Shanks, "Nonlinear transforms of divergent and slowly convergent sequences," J. Math. Phys. 34, 1–42 (1955).

J. Opt. Soc. Am. (3)

J. Phys. A. Math. Nucl. Gen. (1)

J. Arnold, "Inhomogeneous dielectric waveguides: a uniform asymptotic theory," J. Phys. A. Math. Nucl. Gen. 13, 347–360 (1980).

Radio Sci. (1)

G. Jacobsen and F. Ramskov Hansen, "Behavior of transients in propagation constant series of evanescent wave theory," Radio Sci. 16, 519–524 (1981).

Tran. Am. Math. Soc. (1)

R. E. Langer, "On the asymptotic solutions of ordinary differential equations with reference to the Stoke’s phenomenon about a singular point," Tran. Am. Math. Soc. 37, 397–416 (1935).

Trans. Am. Math. Soc. (1)

R. W. McKelvey, "Solution about a singular point of a linear differential equation involving a large parameter," Trans. Am. Math. Soc. 91, 410–424 (1959).

Other (1)

R. C. Tobey, PL-1-Formac Interpreter User's Reference Manual, IBM 1967/69, 360 D-0.3.3004 (IBM Corp., unpublished).

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