High Efficiency Third-Harmonic Generation in a Medium with Quadratic Susceptibility Due to Cubic-like Nonlinearity Caused by Cascaded Second-Harmonic Generation

Abstract

Third-harmonic generation (THG) is of interest for its various applications. We propose using the cascaded second-harmonic generation (SHG) to implement the frequency conversion process, which is similar to that occurring in a medium with cubic susceptibility. Physically, the process is based on consecutive generation of the second-harmonic and the sum frequency in the same crystal with quadratic susceptibility at large phase mismatching between the fundamental wave and the second-harmonic wave. In this case, at phase matching between the fundamental wave and the third-harmonic wave, THG occurs with high efficiency. To demonstrate such a possibility theoretically, we apply the multi-scale method to a set of Schrödinger equations, describing a three-wave interaction with the frequencies ω,2ω and 3ω in a medium with quadratic susceptibility, to derive modified equations describing the frequency tripling process. These equations are solved without using the fundamental wave energy non-depletion approximation. A THG efficiency equal to 94.5% is predicted theoretically. The analytical solution is confirmed by computer simulation results. We study how various factors, such as the incident pulse intensity, phase mismatching between interacting waves, group velocity mismatching of the pulses, and second-order dispersion of the wave packets influence the THG process.