Čerenkov Waveguide SHG: a Less Critical Way to Reach the Efficiency Peak

It is well known that the conversion efficiency of the SHG in the Čerenkov regime in a waveguide with a nonlinear substrate exhibits a very sharp peak. Its position in a "pump wavelength-guide thickness" diagram follows a modified dispersion relation. A particular material combination exactly determines both the pump wavelength and the guide thickness. The existence of the peak was also experimentally proved with relatively high normalised conversion efficiency of 210%/(cm W). However, in order to achieve such a high conversion efficiency, the required tolerance in the guide thickness should be smaller than 0.5 nm (the FWHM of the peak is approximately 0.8 nm). The allowed variations in refractive indices are also very low (<10$\text{}^{-3}$). The recent theoretical study of the authors showed that an additional layer (idler) inserted into the waveguide facilitates more degrees of freedom which could relax the conditions for reaching the efficiency peak. This paper presents a detailed study of the behaviour of four-layer waveguide devices with a nonlinear substrate which promise a less constrained way to reach the efficiency peak.