Flexible control of laser transverse modes using a Fox-Smith mirror

The Fox-Smith mirror (FSM) has long been used in a three-mirror laser cavity arrangement for forcing the laser oscillation on a single-longitudinal mode. However, its transverse properties are very little studied, and we report three interesting transverse features. First, the FSM gives the possibility to change the order p of the oscillating radial Laguerre–Gaussian LG p0 mode by adjusting the microscopic position of one of its mirrors. These results help for understanding non-interpreted experimental observations of interferometric control of the oscillating transverse mode reported by Smith in 1965. Second, we have shown that otherwise values of FSM parameters allow an equal FSM reflectivity of LG 00 and LG 01 (doughnut) modes. This would in effect give, to a laser using a FSM as rear mirror, a simultaneous oscillation of these two transverse modes giving rise to a shape-invariant flat-top laser beam. The latter having the interesting property to keep its uniform transverse intensity profile as it propagates inside and outside the laser cavity. Third, we have shown that the beam emerging from the FSM output through its beam splitter can be an Optical Bottle Beam by an adequate choice of parameters.