Beam dynamics in quadratically nonlinear waveguides with gain and losses

E. N. Tsoy, F. Kh. Abdullaev, and V. E. Eshniyazov

Tsoy E. N., Abdullaev F. Kh., Eshniyazov V. E. Beam dynamics in quadratically nonlinear waveguides with gain and losses. // PHYSICAL REVIEW A 98, 043854 (2018)

A propagation of optical beams in active waveguides with quadratic nonlinearity is considered. It is shown that gain in one harmonic can compensate losses in the other harmonic. As a result of this process, stationary beams can be formed in the system. Exact solutions for stationary modes of a single waveguide are obtained, and their stability is analyzed. A possibility of the Hopf bifurcation that results in emergence of stable periodic regimes in a monomer is demonstrated. Stationary solutions are also found for a dimer with identical waveguides and a dimer with parity-time symmetry. The stability analysis demonstrates that stable beams exist in a wide range of the system parameters.

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