= 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>.<Overview of Nonlinear Processes by Camacho Lab>[Sum and Difference Frequency Generation: quadratic field products and difference-frequency output]{ref}
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