Creating a terrahertz wave source through nonlinear sum frequency generation in a microwave pumped ferroelectric crystal

This paper explores theoretically a model for sum-frequency generation in ferroelectric crystals which, being resonant in the far infrared, will also respond to microwave frequencies (a view that is substantiated in this paper). The essential idea is that the summing of the frequency components of microwave radiation incident on the ferroelectric brought about by sum-frequency generation will produce waves in the terahertz region. The response of ferroelectric crystals in their interaction with microwaves of frequencies in the range 200 to 300 GHz makes this a viable proposal, together with the fact that the nonlinear processes generated in ferroelectrics tend to be stronger that in conventional dielectrics. Landau-Devonshire theory has been used to calculate nonlinear susceptibility coefficients. Here susceptibility coefficients for sum-frequency generation are given and it is shown how the slowly varying amplitude (SVA) approximation together with a susceptibility coefficient can be used to solve the wave equation, and this describes the propagation of the generated waves in the crystal. Conditions on the length through which the waves travel that optimize the phase matching are a useful result of this analysis.