Difference-frequency generation

Difference-frequency generation produces a wave at the positive difference ${\omega }_i={\omega }_p-{\omega }_s$ of two incident angular frequencies, through a second-order nonlinear optical susceptibility. The product of two oscillating electric fields contains both sum and difference frequencies, and the corresponding polarization density drives the generated wave.

For plane waves in a uniform medium, coherent buildup is favored by ${\mathbf{k}}_p={\mathbf{k}}_s+{\mathbf{k}}_i$, the relevant phase matching condition. Two shorter-wavelength inputs can thereby generate longer-wavelength infrared radiation. Collecting the output after removing both incident frequencies distinguishes frequency generation from scattered pump light.^[ref]