Frequency locking of two transverse optical modes of a laser

The interaction of nearly degenerate TE${\mathrm{M}}_{01}$ and TE${\mathrm{M}}_{10}$ modes of a laser is investigated. When the difference between the oscillation frequencies of the two modes is decreased, a transition occurs from a nearly sinusoidal "mode-beating" intensity modulation via periodic and irregular pulsing to frequency-locked steady-state emission in a TE${\mathrm{M}}_{01}^{*}$ hybrid mode. The formation of this hybrid mode by frequency locking is a simple example of the recently predicted emergence of stable transverse patterns in nonlinear optical resonators, brought about by frequency locking of near-degenerate, competing transverse modes.