Study of E-plane taper in a nonorthogonal coordinate system

A taper is a microwave component that ensures the continuity between two waveguides with different sizes. In this paper we take an interest in perfectly conducting E-plane taper: An E-plane discontinuity excited by the fundamental eigenmode TE01 generates the LSEn1 modes in input/output rectangular waveguides. The main purpose is to define the generalized scattering matrix that relates output LSE modes to input LSE modes. For that, Maxwell's equations are used in covariant form written in a nonorthogonal coordinate system fitted to the taper geometry. Covariant components of fields inside the taper fulfil a differential equation system with non-constant coefficients. This initial conditions problem requires the definition of independent input vectors. These vectors include the amplitudes of LSE modes generated by the discontinuity. The determination of output LSE modes relies upon the boundary conditions, the continuity equations of fields in waveguide-taper junctions and many numerical integrations with a fourth order Runge Kutta algorithm. Numerical stability is studied.