ABSTRACT
In analysing linear optical waveguides supporting only one or two modes, the scalar or weak-guidance approximation may be applied by solving the scalar Helmholtz wave equation instead of the curl-curl equation. The numerical computation of the propagation of vectorial waves in a 3D nonlinear waveguide structure for several hundred steps is daunting and perhaps a supercomputer is needed to perform such an analysis. The accurate analytical approach to the stability analysis of nonlinear modes is almost intractable in the case of quasi-3D structures. As the nonlinear region is rather large compared with the size of the field pattern at high power, the self-focussing can take place at different areas of the nonlinear region. The computation of nonlinear waveguide problems is much more expensive than that of their linear counterparts. Under the weak-guidance approximation, the discontinuity of the field can be reasonably ignored.
