Unification of TE and TM beam propagation algorithms

We present a formalism that unifies TE and TM beam propagation for both uniform and nonuniform structures. This implies that any TE propagation algorithm can also be applied to TM fields without further approximations, including the classical fast Fourier transform (FFT) beam propagator. In particular, we derive a paraxial TM propagator which correctly conserves power for uniform and nonuniform structures. We also clarify the role played by the reference background index when it is adjusted dynamically in adaptive propagators.