Fresnel phase matching for three-wave mixing in isotropic semiconductors

We deal with phase matching of three-wave mixing by total internal reflection in isotropic semiconductors. This technique makes use of the large relative phase lag between the three interacting waves at total internal reflection, as described by Augustin Fresnel. This is why we denote this technique as Fresnel phase matching. The theory of Fresnel phase matching is developed with a propagation matrix method: It allows us to describe the conditions (sample thickness, polarization, tuning angles, etc.) for phase matching, the influence of surface roughness, and the walk-off effects due to Goos-Hänchen shifts. Moreover, we show that nonresonant phase matching strongly alleviates the phase-matching tolerance while keeping good conversion yields. The potential of this technique is demonstrated by largely tunable mid-infrared generation (between 7 and 13 μm with a single sample) by use of difference-frequency mixing of two near-infrared sources. Excellent agreement between the presented theory and experiments is demonstrated both in GaAs and ZnSe samples.