  A photon with a modulated wavefront can produce a quantum communication
channel in a larger Hilbert space. For example, higher dimensional quantum key
distribution (HD-QKD) can encode information in the transverse linear momentum
(LM) or orbital angular momentum (OAM) modes of a photon. This is markedly
different than using the intrinsic polarization of a photon. HD-QKD has
advantages for free space QKD since it can increase the communication
channel\~Os tolerance to bit error rate (BER) while maintaining or increasing
the channels bandwidth. We describe an efficient numerical simulation of the
propagation photon with an arbitrary complex wavefront in a material with an
isotropic but inhomogeneous index of refraction. We simulate the waveform
propagation of an optical vortex in a volume holographic element in the
paraxial approximation using an operator splitting method. We use this code to
analyze an OAM volume-holographic sorter. Furthermore, there are analogue
models of the evolution of a wavefront in the curved spacetime environs of the
Earth that can be constructed using an optical medium with a given index of
refraction. This can lead to a work-bench realization of a satellite HD-QKD
system.
