An electrodynamic approach is developed to solve the problem of stimulated Raman scattering (SRS) in a transparent dielectric spherical particle. In this approach it is proposed that optical fields for time-dependent amplitudes of coupled waves at Stokes and pump frequencies in a spherical particle be represented as an expansion in terms of eigenfunctions of the stationary scattering problem in which the expansion coefficients determine the temporal behavior of the field and comply with inhomogeneous differential equations. Solutions of these equations for initial phase SRS and under steady-state conditions are analyzed. The SRS threshold is determined, and the threshold for steady-state SRS at a given intensity is found for when there is double resonance between the fields. It is shown that, to excite SRS, one should compensate for the loss of the Stokes wave that is due to absorption and emission through the particle surface. To provide steady-state SRS generation it is necessary to compensate additionally for the energy loss that is due to depletion of pump intensity.
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