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)