  Light injected into a spherical dielectric body may be confined very
efficiently via the mechanism of total internal reflection. The frequencies
that are most confined are called resonances. If the shape of the body deviates
from the perfect spherical form the resonances change accordingly. In this
thesis, a perturbation theory for the optical resonances of such a deformed
sphere is developed. The optical resonances of such an open system are
characterized by complex eigenvalues, where the real part relates to the
frequency of the resonant light and the imaginary part to the energy leakage
out of the system. As unperturbed and analytically solvable problem serves the
homogeneous dielectric sphere, and the corrections to its eigenvalues are
determined up to and including second order for any polarization of light. For
each order, the corrections of the optical resonances are determined by a
finite-dimensional linear eigenvalue equation, similar to degenerate
time-independent perturbation theory in quantum mechanics. Furthermore,
geometrically intuitive applicability criteria are derived. To check the
validity of the presented method, it is applied and compared to an analytically
solvable problem.
