RADIATIVE RELAXATION-TIME OF QUASI-NORMAL OPTICAL MODES IN SMALL DIELECTRIC PARTICLES

Radiative relaxation times of optical states in small dielectric parti cles of arbitrary shape are calculated in the quasistatic limit up to the second order of perturbation theory, assuming that the polarizatio n distribution for the optical states is known. The concept of antisym metrical optical states, previously developed for a system of discrete dipoles, is generalized for the case of a bulk dielectric particle. W e use the integral form of Maxwell's equations to obtain a general exp ansion of solutions for the polarization function inside a particle in terms of eigenfunctions of the integral interaction operator. Then we calculate imaginary parts of corresponding eigenvalues, which determi ne the radiative relaxation times of optical excitations, treating the non-Hermitian part of the interaction operator as a perturbation. The imaginary parts of eigenvalues are expanded in terms of total multipo le moments of corresponding eigenmodes. Particles with special propert ies of symmetry can possess polarization modes with very large radiati ve relaxation time. We also discuss the possibility of application of the eigenfunction decomposition to numerical calculations of optical c ross-sections for some particles of non-spherical shape.