Theoretical analysis of general approach realizing phase matched second-harmonic generation in LiNbO_3 waveguides

摘要

Theoretical analysis on phase matched second-harmonic generation (SHG) in a more general manner is presented from the viewpoint of modulation of the nonlinear coefficient. The conventional quasi-phase matching (CQPM) is firstly analyzed, showing a noticeable result that the intensity of second-harmonic wave grows most rapidly at odd times of half Lc. i.e., Lc/2, 3Lc/2, 5Lc/2. etc., hut most slowly at even times of half Lc, i.e., 0. Lc, 2Lc, 3Lc. etc. Based on which, a new scheme to realize phase matched SHG by modulating the nonlinear coefficient using alternating "+", "0", "-", "0" every Lc/2 is proposed with the analytical expressions for conversion efficiency (η) and conversion bandwidth (Δ_(FWHM)) derived. Compared with CQPM, it is found that the same Δ_(FWHM) approximately 5.566/L, and at the same lime, a much more effective η can be achieved when ignoring partial waveguide in which the nonlinear coefficient is "0", however, when considering it there is a 3dB penalty for η. Furthermore, a much more general scheme to realize phase matched SHG is proposed, also using alternating "+", "0", "-", "0" but with variable duty cycle. We present the analytical expressions for η and Δ_(FWHM), with the result showing that Δ_(FWHM) keeps constant, i.e.. 5.566/L. In addition, the fabrication tolerances are discussed, and our proposed scheme exhibits a better performance.