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Annual Meeting Optical Society of America

Coherence properties of optical parametric oscillators

Surendra Singh, Reeta Vyas

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Most treatments of noise characteristics of optical parametric oscillators (OPOs) have been based on linearization of the equations of motion. This approach, valid far below and far above threshold, breaks down in the threshold region as it ignores the nonlinearity of interaction. We present a treatment that takes into account both the nonlinearity and the quantum mechanical nature of noise in these oscillators. Analytical expressions for the steady-state amplitude distribution functions are derived. Both the degenerate and the nondegenerate OPOs are considered. These steady-state distributions are used to study the coherence properties of the OPOs in the threshold region. These studies bridge the noise characteristics of the OPOs below and above threshold. Results are compared with classical oscillators and differences and similarities are discussed. Special attention is given to quantum mechanical features that survive even as the oscillator amplitude grows and reaches macroscopic proportions.

DOI
10.1364/oam.1993.wxx.6

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Most treatments of noise characteristics of optical parametric oscillators (OPOs) have been based on linearization of the equations of motion. This approach, valid far below and far above threshold, breaks down in the threshold region as it ignores the nonlinearity of interaction. We present a treatment that takes into account both the nonlinearity and the quantum mechanical nature of noise in these oscillators. Analytical expressions for the steady-state amplitude distribution functions are derived. Both the degenerate and the nondegenerate OPOs are considered. These steady-state distributions are used to study the coherence properties of the OPOs in the threshold region. These studies bridge the noise characteristics of the OPOs below and above threshold. Results are compared with classical oscillators and differences and similarities are discussed. Special attention is given to quantum mechanical features that survive even as the oscillator amplitude grows and reaches macroscopic proportions.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
Quantum images, that is inhomogeneous field distributions purely generated by quantum fluctuations, persist when passing from the degenerate to the non-degenerate case of optical parametric oscillators (OPO). Below the threshold for parametric oscillation where the near-field distributions are homogeneous both in intensity and phase, appropriate spatial correlation functions anticipate the transverse spatial pattern that appears above threshold. In particular, the angular dependence of the far field spatial correlation function is able to reveal the travelling-wave nature of the phase pattern above threshold typical of nondegenerate OPOs. Cross-correlation functions between signal and idler intensities show clear evidence of the non-classical nature of the output light.
A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO's). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.
We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive PPP representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.
A semi-classical analysis of the noise characteristics of a non degenerate, above threshold, optical parametric oscillator is presented, yielding expressions for the quantum fluctuations of the output field intensities and phases. Particular emphasis is given to the study of the noise on the intensity difference between the two generated fields. The effect of losses, unbalance, detunings and excess pump noise is investigated. A significant quantum noise reduction is found over a broad domain of the parameter space.
We perform a theoretical analysis of steady-state solutions and quantum noise in a below-threshold optical parametric oscillator (OPO) operating as an amplifier with an input seed wave. Both the amplitude-squeezed and phase-squeezed states of the output field are considered. We take into account the intracavity nonlinear losses due to intracavity frequency doubling of the signal wave and the quantum fluctuations of the seed and pump waves. Unlike the preceding theoretical studies of the problem, we show that squeezing in bright beams produced by the OPO depends on their intensity. For the amplitude-squeezed state, squeezing strongly degrades with increasing output intensity. In contrast, one can obtain good squeezing for phase-squeezed beams of high output intensity.