Real matrix evaluation of leaky and absorbing planar waveguides

Abstract

A simple method for obtaining propagation characteristics of optical waveguides of arbitrary refractive-index profile is presented. The method involves dividing the inhomogeneous profile into a suitable number of homogeneous layers of equal/unequal thicknesses and choosing real field equations appropriately to construct a real matrix eigenvalue equation, which may be readily solved. When the waveguide becomes leaky or absorbing, the propagation constant β and the eigenvalue equation become complex. However, the matrices still can be made real except for layers of complex indices. If one now writes the eigenvalue equation as F(β) = 0, a plot of 1/|F|2 gives Lorentzians peaked at a real part of β and having an HWHM equal to the imaginary part of β. The procedure is extremely simple for simple structures. One can use a computer which does not have the facility to handle complex numbers. Also, this method requires much shorter computer time compared with other methods. Owing to the general approach and simplicity, the method should find application in a variety of waveguiding problems.