= Sum-frequency generation
{title2=$\omega_3=\omega_1+\omega_2$}
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A <nonlinear optics> process producing a field at the sum of two input <angular frequencies>. The driven <electric polarization> contains a term proportional to the product of the input <complex amplitudes>. With undepleted plane-wave inputs, integration along a crystal gives an output amplitude proportional to $L e^{i\Delta kL/2}\operatorname{sinc}(\Delta kL/2)$; the <sinc function> therefore determines the ideal length and <phase mismatch> dependence. A nonzero initial output field also interferes with this generated field.
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