Metal-clad graded-index planar optical waveguides: accurate perturbation analysis

Abstract

We present a perturbation analysis of propagation constants and attenuation coefficients of TE and TM modes in a metal-clad linear index planar optical waveguide. The imaginary part N″ of the complex modal index N= N′ + iN″ is given by N″ = ( ∂N′ / ∂∈′), where ∈=∈′ + i∈″ is the complex dielectric constant of the metal cladding and ∂ N′ / ∂∈′ is obtained by numerical differentiation of the solution of the real eigenvalue equation. The cumbersome solution of a complex transcendental equation is thus completely eliminated. The results are in good agreement with those obtained by solving the eigenvalue equation in the complex plane. By taking the metal-clad linear planar waveguide as a preselected waveguide, we can use our RWKB method to solve metal-clad planar waveguides with parabolic, exponential, gaussian and complementary error function index profiles.