Abstract

The parametric equations for periodic rays in degenerate astigmatic laser resonators are derived in a generalized way. The derived parametric equations clearly reveal the formation of Lissajous geometric modes with phase variation along the propagation. Using the representation of a quantum coherent state, a generalized wave-packet formula is derived to connect with the periodic rays of geometric modes. The derived wave-packet formula is not only validated through comparing with various experimental patterns, but also is directly exploited to manifest the spatial asymmetries of Lissajous lasing modes due to a highly transmissive output coupler.

© 2019 Optical Society of America

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