An analytic method predicts beating phenomena in asymmetric Gaussian beams

The widths of asymmetric Gaussian beams oscillate in a phenomenon known as “beating.” Simple generalized non-linear Schrödinger (GNLS) equations describe this process. Physicists found that marginal alterations in initial parameters caused changes in beating behavior to occur in non-linear optical beams, but at distances far from propagation point. They report the analytic model they developed to describe these beating transitions in Chaos: An Interdisciplinary Journal of Nonlinear Science.

Two degree-of-freedom Hamiltonian systems helped approximate the location of beating transitions. Parameters were selected using coincidences of roots of a pair of quadratic equations, and its coefficients were determined by internal parameters and the initial conditions of the original system. The roots of the quadratic equations could coincide in three different ways, predicting three different types of transitions, all of which were occurred in the physical beam. “We found this incredible mathematical phenomenon inside these really quite simple equations that describe the evolution of a beam down an optic fiber,” said co-author Jeremy Schiff.

Results from the model align with numeric descriptions of the original system over large parameter ranges, and the method is now being used to accurately predict transition behavior. “We were able to map out the behavior in a way that would have been too time-consuming using the numerics,” Schiff said.

The beams rely on propagation within non-linear Kerr media and with the identification of promising new non-linear Kerr materials, these beams could be supported within the next few years. The authors are also beginning to apply their models to different types of beams. Looking beyond optics, the mathematical methods have promising applications for vibrating mechanical systems and astronomy.

Source: “Analytic methods to find beating transitions of asymmetric Gaussian beams in GNLS equations,” by David Ianetz and Jeremy Schiff, Chaos: An Interdisciplinary Journal of Nonlinear Science (2018). The article can be accessed at https://doi.org/10.1063/1.5001484 .