Linear solutions to metamaterial volume hologram design using a variational approach

Multiplex volume holograms are conventionally constructed by the repeated exposure of a photosensitive medium to a sequence of external fields, each field typically being the superposition of a reference wave that reconstructs the hologram and the other being a desired signal wave. Because there are no sources of radiation internal to the hologram, the pattern of material modulation is limited to the solutions to Helmholtz's equation in the medium. If the three-dimensional structure of the medium could be engineered at each point rather than limited to the patterns produced by standing waves, more versatile structures may result that can overcome the typical limitations to hologram dynamic range imposed by sequentially superimposing holograms. Metamaterial structures and other synthetic electromagnetic materials offer the possibility of achieving high medium contrast engineered at the subwavelength scale. By posing the multiplex volume holography problem as a linear medium design problem, we explore the potential improvements that such engineered synthetic media may provide over conventional multiplex volume holograms.