Fractional photon model of three-photon mixing in the non-linear interaction process

Abstract

In this paper, a fractional photon model is proposed by considering the photon-exchange interaction in the reverse process of the non-linear three-photon mixing interaction. The phase matching condition for various types of uniaxial crystals can be simplified and classified by this model with the consideration of the unequal fractional photon-exchange of the two generated waves in the reverse manner. This also leads to the explanation of observing the phase mismatch and output bandwidth of the resonant and non-resonant waves in a cavity. Finally, a quantitative approach to this model, with experimental results, is also demonstrated.