Fourier Transform Analysis on Random Quasi-Phase-Matched Nonlinear Optical Interactions

Abstract

The Fourier transform method is adopted to analyze random quasi-phase matched (RQPM) nonlinear frequency conversion problems in polycrystalline materials. By treating the material as random signals of effective nonlinear coefficient (deff) along the beam path, fast Fourier transform (FFT) operations directly produce the generated field amplitude versus spatial frequency mismatch (Δk/2π), which relates to all the possible RQPM nonlinear interactions. Thus, the RQPM bandwidth is intuitive from the wavelength-dependent results. More importantly, the Fourier transform treatment greatly decreases the computational amount by orders compared with the traditional step-by-step integration method. The quantitative simulation of RQPM difference frequency generation (DFG) with three variable wavelengths is realized for the first time.

Study of broadband second harmonic generation based on random quasi-phase matching

“…Once the distribution of deff is determined, the terahertz field can be calculated either from step-to-step integration with Eq. ( 1) or based on the Fourier transform method [13]. In case of steady state, the dispersion of different frequencies can be ignored.…”