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Finite-element time-domain solver for axisymmetric devices based on discrete exterior calculus and transformation optics

We present a new finite-element time-domain (FETD) solver for analysis of axisymmetric devices based on discrete exterior calculus (DEC) and transformation optics (TO) concepts. The proposed FETD solver decomposes the fields into TEϕ and TMϕ modes, which are expanded by using appropriate set of (vector or scalar) basis functions. Utilizing DEC, trigono-metric orthogonality, and a leap-frog time-integrator, we obtain energy-conserving fully discrete Maxwell's equations. We explore TO principles to map the original problem from a cylindrical system to an equivalent problem on a Cartesian mesh embedded on an effective (artificial) inhomogeneous medium with radial variation. The new FETD solver is illustrated for the efficient solution of a backward-wave oscillator (BWO) encompassing a slow-wave waveguide with sinusoidal corrugations.