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Optics Communications

Phase properties of second harmonics generated by different initial fields

R. Tanaś, Ts. Gantsog, Roman Zawodny

Published Jun 1, 1991• 10 citations
Publisher
DOI
10.1016/0030-4018(91)90177-f

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Quantum Optics Journal of the European Optical Society Part B•Aug 1, 1991•20 citations
The effect of saturable absorption on second-harmonic generation in a quasi-phase-matched structure is studied, including both plane-wave and diffractive coupling of the fields and detuning of the pump field from resonance. In the regime of large Fresnel numbers, the main effect of saturable absorption is to suppress the parametric instability, which limits the efficiency of the second-harmonic generation and places a bound on the device length in order to fit sufficient harmonic power. The optical limiting nature of resonance absorption places an upper bound on the gain that quasi-phase-matching can achieve. In the diffractive regime, a variety of output transverse structures may be initiated by modulation of the relative phase and mutual displacement between the input beams of the pump and seeding harmonic signal. In particular, second-harmonic dragging, i.e., the asymmetric interaction between initially overlapping pump and second-harmonic beams propagating at different angles, is observed such that a pump beam can drag a second-harmonic one out a spatial aperture, thereby implementing a colored logical switch with gain.
We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.
Photon number and phase fluctuations and correlations in the second harmonic generation are discussed. The new Pegg-Barnett Hermitian phase formalism is used to deal with the phase properties of the field. The method of numerical diagonalization of the interaction Hamiltonian is applied to find the state evolution and, consequently, the number and phase quantum fluctuations. It is shown that the joint phase probability distribution evolves into a multi-peak structure indicating clearly the transition from the second harmonic to the down-conversion regime, and back. The evolution of all relevant quantities is illustrated graphically, and their dependence on the mean number of photons of the initial field is shown explicitly. The number-phase uncertainty product for the fundamental mode is plotted making evident the abrupt transition from the low to the high level of quantum fluctuations.