On the Conditions for Self-Locking of Modes in Lasers

Abstract

Before self‐locking of modes can be accomplished in a laser, all adjacent longitudinal modes must have the same frequency separation. It can be shown that the dispersion associated with the laser transition generally causes longitudinal modes to have slightly different frequency separations. For homogeneously broadened lines these differences are indeed very small, but for inhomogeneously broadened lines they become significant. An equidistant mode separation can be produced when the mode oscillations shift slightly in frequency and lock onto nonlinear polarization source terms produced by the interaction of three modes. The question as to whether mode locking is actually achieved depends upon the relative size of the required frequency shift and the amplitude of the nonlinear source terms. Among other variables, the nonlinear polarization is proportional to the fourth power of the dipole matrix element between the two states in question, and thus depends strongly on their radiative lifetime. For example, in Nd³⁺‐doped glass the matrix element between the laser states is too small for locking, but a short‐lifetime saturable absorber inserted into the cavity will produce self‐locking.