Theory of mode pulling in a stokes Raman oscillator. I

Abstract

In the present paper frequency shifts and other characteristic properties of the Stokes modes in a solid Raman-active sample are investigated theoretically. The Raman process is described by nonlinear Heisenberg equations for running waves, which is convenient in order to satisfy the momentum conservation condition. The Stokes shifted electromagnetic waves are assumed to be reflected at the endfaces of the crystal to establish standing waves (modes), whereas the vibrational waves are treated as running waves because of their large damping. The calculations are done for (a) one mode in the 1. Stokes line, (b) one mode in the 1. and one mode in the 2. Stokes line and (c) two modes in the 1. Stokes line. Case (c) can be established only if the two modes are placed symmetrically with respect to the center of the line. In all three cases homogeneously broadened lines are assumed. The frequency shifts in (a) and (c) are power-independent. Only in (b) the shift of the 1. Stokes mode depends on the incident laser flux. Nonlinear pulling and power-dependent pushing of arbitrarily situated modes in the 1. Stokes line occur if additonal modes oscillate simultaneously in the higher order lines. Detailed calculations of these interesting cases are given in a forthcoming paper.