Optimization of third harmonic generation for two coupled three-frequency interactions of waves with multiple frequencies in periodic crystals

Third harmonic generation with simultaneous excitation of degenerate two-frequency (2ω = ω + ω) and three-frequency (3ω = 2ω + ω) interactions of collinear waves in periodic crystals is considered. It is shown that the optimal condition for third harmonic generation, in this case, is determined by the ratio of the amplitudes of the fundamental and second harmonics at the entrance of the crystal. The optimal value of this ratio, for which the efficiency of the third harmonic generation may reach 96%, is found.     

On a classical analog of the isospectral Schrödinger problem

It is shown that the problem of potential deformations that preserve the energy dependence of the oscillation frequency corresponds in the classical limit to the isospectral problem for the Schrödinger equation. The solutions of the corresponding evolutionary equations for the potential (with respect to the deformation parameter) are simple Riemann waves. The relation between such solutions and the solutions of the inverse problem of mechanics — the problem of reconstructing the potential given the energy dependence of the oscillation frequency — is determined.     

Classification of soliton solutions in an infinite-dimensional phase space on the basis of the theory of dynamical systems

Theoretical and Mathematical Physics -     

Natural fluctuations in a quartz crystal oscillator with automatic gain control

A method is developed for calculation of natural fluctuations in oscillators with automatic gain control (AGC). As an example, a three-terminal capacitive transistor crystal oscillator is considered. It is shown that the AGC system permits stabilization of the amplitude and frequency of the oscillator output signal.