Ab initio approach to description of nonlinear dynamics of individual and coupled microdisk whispering-gallerymode
resonators is developed for the nonlinearities of Kerr type. Distinction between scattering resonances and
eigenfrequencies, which is important for resonators with moderate quality factors is discussed. Properties of
various parameters important for nonlinear dynamics, such as coupling to external radiation, linear inter-disk
coupling parameter, nonlinear mode overlap coefficients are discussed from the point of view of the ab initio
Using ab initio approach to the theory of electromagnetic interaction of a small particle and spherical whispering
gallery mode resonator, we derive the optical forces experienced by the particle and it's resulting motion. The
form of the forces differs from that expected by the traditional gradient/scattering approach due to the modification
of the field by the particle. The main effect of the confinement of the field in a cavity consists in making
the component of the optical force usually interpreted as gradient, manifestly non-conservative, and hence not
presentable in the gradient form. It is shown how the standard gradient/scattering formalism can be modified
for the cavity confined optical field.
Recent observation of two-mode lasing in random lasers is discussed in the context of the problem of distinguishing between lasing with coherent and non-coherent feedback. A general semiclassical theory of lasing in cavities with a spatially non-uniform dielectric constant is developed. It is shown that the non-uniformity causes a radiative coupling between modes of the empty cavity, which results in a renormalization of the coefficients responsible for non-linear interaction between lasing modes. One of the consequences of this renormalization is the enhancement of the effects of spatial hole burning and promotion of the multi-mode lasing.
An array of quantum dots in a microcavity is considered. It is shown that a vacancy in the array may give rise to one or two quasi-local states with a long life-time depending upon the structure of the array. One state always splits off the top of the polariton gap, and the other one may appear closer to the bottom of the gap. The life-time of the state is mostly determined by the exciton non-radiative relaxation and depends only weakly upon the properties of the cavity mirrors.