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

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 (
d
_eff
) along the beam path, fast Fourier transform (FFT) operations directly produce the generated field amplitude versus spatial frequency mismatch (Δ
k
/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.