Geometrical representation of sum frequency generation and adiabatic frequency conversion

We present a geometrical representation of the process of sum frequency generation in the undepleted pump approximation, in analogy with the known optical Bloch equations. We use this analogy to propose a technique for achieving both high efficiency and large bandwidth in sum frequency conversion using the adiabatic inversion scheme. The process is analogous with rapid adiabatic passage in NMR, and adiabatic constraints are derived in this context. This adiabatic frequency conversion scheme is realized experimentally using an aperiodically poled potassium titanyl phosphate KTP device, where we achieved high efficiency signal-to-idler conversion over a bandwidth of 140 nm.