Излучение резонансной среды, возбуждаемое лазерным излучением с периодической фазовой модуляцией в режиме сильной связи поля и вещества

In this paper, the radiation of a two-level resonant medium placed in a cavity and excited by a laser pulse with periodic phase modulation is studied theoretically. The analysis is carried out on the basis of an analytical and numerical solution of the system of Maxwell-Bloch equations under conditions when the regime of strong coupling of the field and matter is realized. Under these conditions, this system is similar to a polariton laser. A high excitation efficiency of a polariton laser by a phase-modulated radiation pulse compared with a pulse without phase modulation of the carrier frequency is shown. It is shown that the main reason for the effective excitation of polariton modes of the medium is the occurrence of a difference combination parametric resonance. The results obtained open up new possibilities in the excitation of radiation from polariton lasers by low-power pumping laser radiation with frequency modulation.

THE RESPONSE OF A NONLINEAR SYSTEM WITH A NONSEMISIMPLE ONE-TO-ONE RESONANCE TO A COMBINATION PARAMETRIC RESONANCE

The Galerkin procedure is used to discretize the nonlinear partial differential equation and boundary conditions governing the flutter of a simply supported panel in a supersonic stream. These equations have repeated natural frequencies at the onset of flutter. The method of multiple scales is used to derive five first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the excited modes. Then, the modulation equations are used to calculate the equilibrium solutions and their stability, and hence to identify the excitation parameters that suppress flutter and those that lead to complex motions. A combination of a shooting technique and Floquet theory is used to calculate limit cycles and their stability. The numerical results indicate the existence of a sequence of period-doubling bifurcations that culminates in chaos. The complex motions are characterized by using phase planes, power spectra, Lyapunov exponents, and dimensions.