7 July 1998 Unified formalism for TE and TM beam propagators
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Abstract
The unification of transverse electric (TE) and transverse magnetic (TM) beam propagation algorithms is made possible through a transformation which converts the wave equation for TM fields in planar waveguides into a form identical to the corresponding TE wave equation. The transformation can be applied to any smoothly varying waveguide. This transformation can be made independently of any paraxial or other approximations. Thus, any TE propagation algorithm can also be applied immediately to TM fields without additional approximations. This includes the classical fast Fourier transform beam propagator, which has not previously been applied successfully to TM propagation. We also specifically develop a Finite Difference Beam Propagation Method that applies to both TE and TM propagation in 1D (planar) geometry. Previous implementations for the TM case involve an approximation that in certain circumstances leads to severe errors (including the totally unphysical occurrence of field amplification). This is the first TM propagator which exactly conserves power. We also investigate the role of the reference background wavenumber (or index) and clarify its role as it is dynamically adapted. The algorithms proposed are easily adaptable to wide-angle beam propagators and to modern transparent boundary conditions. The extension of these ideas to rapidly varying structures (such as Bragg gratings) is also briefly discussed.
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Leon Poladian, Leon Poladian, Francois J. Ladouceur, Francois J. Ladouceur, } "Unified formalism for TE and TM beam propagators", Proc. SPIE 3283, Physics and Simulation of Optoelectronic Devices VI, (7 July 1998); doi: 10.1117/12.316720; https://doi.org/10.1117/12.316720
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