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Journal of Contemporary Physics (Armenian Academy of Sciences)

Distribution of numbers of photons in the region of unstable behavior in the process of intracavity second harmonic generation

S. T. Gevorgyan, M. S. Gevorgyan

Published Feb 26, 2011• 0 citations
Publisher

Abstract

For the process of intracavity second harmonic generation we investigate in positive P-representation with simulation of Langevin noise sources the distribution functions of numbers of photons in fundamental and second harmonic modes in the region of unstable behavior of the system. It is shown that in the unstable region, as distinct from the stable, the functions of distribution have two-peak structure. We also study the joint function of distribution of photon numbers in interacting modes.

DOI
10.3103/s1068337211020010

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For the process of intracavity second harmonic generation we investigate in positive P-representation with simulation of Langevin noise sources the distribution functions of numbers of photons in fundamental and second harmonic modes in the region of unstable behavior of the system. It is shown that in the unstable region, as distinct from the stable, the functions of distribution have two-peak structure. We also study the joint function of distribution of photon numbers in interacting modes.
For the process of intracavity second-harmonic generation in the region of unstable dynamics, the joint fluctuations of numbers of photons and phases of the fundamental mode and second harmonic are studied in positive P representation. It is shown that above the bifurcation point of the optical system the distribution functions of the phases of the fundamental mode and second harmonic have a two-component structure. The quantum trajectories of the phases of these modes are not localized in the components of their states, which demonstrates the presence of quantum-mechanical interference between these components. In both components of each state the same values of numbers of photons are realized. It is shown that in the case of coherent initial states of both modes the joint distribution functions of the numbers of photons and phases are in the oscillatory regime. With time, the modes pass from a two-component delocalized state to a one-component one and then back to the two-component state. The time of oscillation of the distribution function is of the order of the photon's lifetime in the cavity volume. Self-matching of phases of interacting modes is investigated above the bifurcation point.
We study the quantum dynamics of the number of photons of the interacting modes, the dynamics of the quantum entropy, and the Wigner function of the states of the fundamental and the third harmonic modes for the process of intracavity third harmonic generation. It is shown that the quantum dynamics of the system strongly depends on the external resonant perturbation of the fundamental mode and on the coupling coefficient of the interacting modes. In the region of long interaction times, the modes of the field can be both in stable and in unstable states—depending on the above-mentioned quantities. In the paper, we also investigate the dynamics of transition of the system from stable to unstable states.