Circular Fourier analysis of full Maxwell equations for arbitrarily shaped dielectric waveguides-application to gain factors of semiconductor laser waveguides

A new method is proposed to derive the vectorial modes of dielectric waveguides made of an arbitrarily shaped core embedded in a homogeneous cladding. The method is based upon rigorous circular Fourier expansions for the field components and the permittivity profile. The method should be restricted to cores which are not elongated too much (in the case of rectangular cores, the ratio of sides should be between 1/4 and 4/1). The convergence properties and the accuracy are analyzed. Some results about the gain factors of optical semiconductor laser waveguides are presented for rectangular and trapezoidal cores.>