It is well known that the conversion efficiency of the SHG in the Cerenkov
regime in a waveguide with a nonlinear substrate exhibits a very sharp peak
. Its position in a "pump wavelength-guide thickness" diagram follows a mod
ified dispersion relation. A particular material combination exactly determ
ines both the pump wavelength and the guide thickness. The existence of the
peak was also experimentally proved with relatively high normalised conver
sion efficiency of 210%/(cm W). However, in order to achieve such a high co
nversion efficiency, the required tolerance in the guide thickness should b
e smaller than 0.5 nm (the FWHM of the peak is approximately 0.8 nm). The a
llowed variations in refractive indices are also very low (< 10(-3)). The r
ecent theoretical study of the authors showed that an additional layer (idl
er) inserted into the waveguide facilitates more degrees of freedom which c
ould relax the conditions for reaching the efficiency peak. This paper pres
ents a detailed study of the behaviour of four-layer waveguide devices with
a nonlinear substrate which promise a less constrained way to reach the ef
ficiency peak.