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Applied Optics

Applied Optics


  • Vol. 24, Iss. 17 — Sep. 1, 1985
  • pp: 2809–2812

Modes of a planar waveguide with Fermi index profile

T. R. Chen and Z. L. Yang  »View Author Affiliations

Applied Optics, Vol. 24, Issue 17, pp. 2809-2812 (1985)

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The wave equation of a planar waveguide with Fermi refractive-index profile is treated theoretically. An analytical solution has been obtained in terms of hypergeometric functions. It has been shown that the dispersion equation can be expressed as an infinite series of functions of modal index which converges rapidly. Highly accurate results can be obtained by taking the zero-order approximation only.

© 1985 Optical Society of America

Original Manuscript: February 11, 1985
Published: September 1, 1985

T. R. Chen and Z. L. Yang, "Modes of a planar waveguide with Fermi index profile," Appl. Opt. 24, 2809-2812 (1985)

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  1. J. L. Jacket, “Variation in Waveguides Fabricated by Immersion of LiNbO3 in AgNO3 and TlNO3: The Role of Hydrogen,” Appl. Phys. Lett. 14, 508 (1982). [CrossRef]
  2. J. L. Jackel, “High-Δn Optical Waveguides in LiNB3: Thalium-Lithium Ion Exchange,” Appl Phys. Lett. 37, 739 (1980). [CrossRef]
  3. Y. X. Chen et al., “Characterization of LiNbO3 Waveguides Exchanged in TlNO3 Solution,” Appl. Phys. Lett. 40, 10 (1982). [CrossRef]
  4. J. L. Jackel et al., “Proton Exchange for High-Index Waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607 (1982). [CrossRef]
  5. E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 327 (1973). [CrossRef]
  6. D. Marcuse, “TE Modes of Graded-Index Slab Waveguides,” IEEE J. Quantum Electron. QE-9, 1000 (1973). [CrossRef]
  7. D. Marcuse, “Losses and Impulse Response in Parabolic Index Fibers With Square Cross Section,” Bell Syst. Tech. J. 53, 195 (1974).
  8. I. Savationova, E. Nadiakov, “Modes in Diffused Optical Waveguides (Parabolic and Gaussian Modes),” Appl. Phys. 8(3), 245 (1975). [CrossRef]
  9. P. K. Tien et al., “Optical Waveguide Modes in Single-Crystalline LiNbO3-LiTaO3 Solid-Solution Films,” Appl. Phys. Lett. 24, 503 (1974). [CrossRef]
  10. H. C. Dong, J. Q. Fan, “Fabrication of Glass Optical Waveguides by Tl2SO4 Ion Exchange,” in Digest of Second National Conference on Integrated Optics (Optical Society of China, 1983), p. 72.
  11. See, for example, Z. S. Wang, D. R. Gwo, Introduction to Special Functions (Science Publishing House, Beijing, 1985), Chap. 4, p. 178, in Chinese; A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 1.

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