The Lanczos–Fourier series expansion is employed to analyze the guided-mode field in an asymmetrical slab waveguide, the core of which has an anisotropic and inhomogeneous dielectric permittivity. A system of linear homogeneous equations is derived by the collocation technique with consideration of the wave equation and the appropriate boundary conditions at the interfaces between the core and cladding media. The propagation constants are found from a determinant equation that ensures the existence of a nontrivial solution of the system. Numerical results are presented for several cases of dielectric permittivity, including the constant, parabolic, linear, and anisotropic cases. This approach is found to converge reasonably fast, and Richardson’s extrapolation technique is applied to accelerate the convergence further. The approach can be easily generalized from the scalar to the vector equation, and, as an example, we consider the guided modes of a circular fiber.
© 2002 Optical Society of America
Original Manuscript: March 28, 2002
Revised Manuscript: May 31, 2002
Manuscript Accepted: May 31, 2002
Published: November 1, 2002
Panagiota A. Koukoutsaki, Ioannis G. Tigelis, and Alexander B. Manenkov, "Guided-mode analysis by the Lanczos–Fourier expansion," J. Opt. Soc. Am. A 19, 2293-2300 (2002)