Radiative frequency mixing in propagating non-linear media

Abstract

A mode of frequency conversion in propagating non-linear media is presented which requires considerably less stringent phase-matching conditions than those in parametric mixing. This is due to the fact that the output frequencies are radiated at angles such that their phase constants along the direction of the `parent' waves exactly match the `generated' phase constants. This is true as long as the transverse dimensions of the interaction region are smaller than the radiated wavelength as, for example, in the difference frequency case. However, for the sum frequency radiation these dimensions are necessarily larger than the wavelength, owing to the diffraction-imposed limitations of focusing. In this case, the radiation is to be restricted to extremely small angles relative to the direction of the incident waves, thereby necessitating stricter phase matching. This requirement is of the same order of magnitude as that encountered in parametric mixing. The radiative mode of frequency conversion acts also as an `output coupler', and is particularly useful for ultra-microwave to optical frequencies, because of the enhanced radiation efficiency and directivity for a reasonable length of the non-linear medium.