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We investigated phase-locking effects between longitudinal modes in lasers. In order to show the general trend to be expected for a large number of oscillating modes, we treat three-, four-, and five-mode oscillations. The expected phases depend in a complicated manner upon the relaxation times T1 and T2 of the medium, on the degree of inhomogeneous broadening, the mode separation and location of the medium in the cavity. Simple formation of sharp output spikes at the fundamental frequency are expected where crystals like ruby or YAG are placed near the edges of the cavity. Sharp spikes at twice the fundamental frequency are expected when these solids are placed in the center of a cavity. Certain filters, when placed near the edge or center of the cavity are expected to cause similar locking effects. Gases and solids are expected to act quite differently. The calculations are based on the maximum-emission principle. This principle will be discussed in a later publication. Some experimental results are also presented.
Statz et al. (Sat,) studied this question.