Propagation of Hermite–Gaussian beams in spatially curved optical waveguides having a parabolic refractive index profile

It is found that for a certain value of the parameter w, which characterizes the effective beam width, paraxial Hermite–Gaussian beams propagate along certain trajectories without changing their structure in a spatially curved waveguide having a parabolic refractive index profile. It is shown that in the case of a Gaussian intensity distribution at the entry to the waveguide and arbitrary w, the beam also propagates along a particular trajectory but the beam width varies periodically along the waveguide axis.