Small nonlinear particles in waveguides and resonators

A theoretical analysis of wave fields in systems containing small arbitrary shaped nonlinear particles is presented. The analysis is based on the local perturbations method (LPM). Approximate expres- sions, valid when the particles are small compared to the wavelength of radiation in surrounding media, are obtained for the scattered fields in the free space and different types of metallic waveguides. The ex- pressions show that, while in infinite media and planer waveguides the fields have well pronounced maxima (resonances) at some frequencies, in a rectangular tube the maxima are smeared out and the frequency dependence of the scattered field is rather smooth. The resonance fre- quencies are calculated and are shown to be dependent not only on the internal parameters of the system, but on the intensity of the incident field as well. Shifts of the eigen frequencies of a resonator caused by the presence of nonlinear scatterers are also calculated.