The theory of far-infrared generation by optical mixing of focused Gaussian beams is developed, taking into account the effects of diffraction, absorption, double refraction, and multiple and total reflections at the boundary surfaces. Results of numerical calculations are presented. It is shown that focusing of the pump beams appreciably enhances the far-infrared output despite the strong far-infrared diffraction. In a 1-cm-long crystal, the optimum focal-spot size is approximately equal to or smaller than the far-infrared wavelength for an output at frequency less than 100 ${\mathrm{cm}}^{-1\mathrm{}}$. Double refraction of the pump beams is relatively unimportant. Both far-infrared absorption and boundary reflections have major effects on the far-infrared output and its angular distribution. The former is often the factor which limits the output power. We show that a simple model treating the nonlinear polarization as a constant-$\frac{1}{e}$-radius Gaussian distribution of radiating dipoles is a good approximation to the problem. We also compare the results of our calculations with those for second-harmonic generation.

• Received 2 August 1976

DOI:https://doi.org/10.1103/PhysRevA.15.1143