Vectorial finite—element formalism for electromagnetic waveguiding structures with loss and/or gain

Abstract

AbstractTo carry out a vectorial wave analysis of the eigenmode in an electromagnetic wave‐guiding structure with loss or gain, an efficient vector finite‐element expression is derived based on the finite‐element method in terms of the transverse magnetic field component. Since the eigenvalue of the final matrix equation corresponds to the propagation constant, it is possible to obtain the propagation constant for a given frequency. Hence, it is possible to avoid inefficient iterative calculations on a complex plane which have been used in a conventional method in which the frequency is used as an eigenvalue. Also, the present method can be applied to a dispersive medium in which the medium constant is dependent on frequency and to a structure containing a conductive material in which the loss tangent varies in proportion to the inverse of frequency. From these properties, the present method is believed to be a practical numerical method for the vectorial analysis of guided wave structures containing loss or gain. To confirm the validity of the method, some analytical results are presented for a rectangular waveguide loaded with a lossy dielectric material. Convergence of the solution is checked and the result is compared with the exact solution. Next, as a more interesting example, guided mode analyses are performed for buried heterostructure semiconductor lasers and lossy coupled dielectric waveguides and the results obtained are discussed.