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Annual Meeting Optical Society of America

Fluctuation properties of intracavity second-harmonic generation

Reeta Vyas

Published Jan 1, 1990• 0 citations
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Abstract

Fluctuation properties of the fundamental light beam in intracavity second harmonic generation (ISHG) are studied theoretically. It is shown that the field produced by the ISHG can be described as a superposition of a coherent component and bivariate Gaussian noise field. Using this property of the ISHG field a generating function for photon counting statistics is obtained. From this generating function various expressions for quantities characterizing statistical properties such as photon counting distribution, factorial moments, and statistics of times are calculated. Curves are presented to illustrate the behavior. These results for the ISHG are also compared with those obtained for the optical parametric oscillators.

DOI
10.1364/oam.1990.wq5

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Fluctuation properties of the fundamental light beam in intracavity second harmonic generation (ISHG) are studied theoretically. It is shown that the field produced by the ISHG can be described as a superposition of a coherent component and bivariate Gaussian noise field. Using this property of the ISHG field a generating function for photon counting statistics is obtained. From this generating function various expressions for quantities characterizing statistical properties such as photon counting distribution, factorial moments, and statistics of times are calculated. Curves are presented to illustrate the behavior. These results for the ISHG are also compared with those obtained for the optical parametric oscillators.
Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.
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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.
Homodyne statistics when the light from a degenerate parametric oscillator (DPO) is mixed with coherent light from a local oscillator are discussed. By using dynamical models of these beams we discuss the photon sequences underlying the superposed beam in terms of photoelectric pulse sequences recorded by a detector. The field produced by the parametric oscillator is expressed in terms of two independent real Gaussian random variables. Using this property of the field variables, we derive the generating function for the photoelectron statistics analytically. From this generating function, expressions for the photoelectron-counting distribution, factorial moments, and the waiting-time distribution are derived. These quantities are directly measurable in photon-counting experiments. The results reported here are applicable to arbitrary strengths of the signal and the local-oscillator fields. We also show that, depending on the relative strength and relative phase between coherent light from the local oscillator and squeezed light from the DPO, the superposed light beam may exhibit many interesting nonclassical features. These and other effects are described and curves are presented to illustrate the behavior.