Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms

Third-order mixing of arbitrary beams of pump and second-harmonic light gives rise to a spatially periodic DC polarization whose noninversion symmetry and periodicity are correct for quasi-phase matching of the pump and second harmonic. Under appropriate conditions in certain materials, e.g., optical fibers, X⁽²⁾ forms in proportion to this DC polarization, resulting in a nonlinear hologram that can be used to recreate a second-harmonic image from a reference pump beam. Distributed feedforward and feedback reconstruction of plane waves by slab-shaped nonlinear holograms is analyzed, and expressions for the field profiles and conversion efficiencies are derived. In the DFB case at high fixed pump intensities, multistable states of conversion efficiency exist. The higher order states display catastrophes in their transverse amplitude distributions