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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum correlation in multimode OPO

Mikael Lassen, Preben Buchhave

Published May 25, 2004• 0 citations
Publisher

Abstract

Fluctuations in the field of a 2nd order nonlinear multi-mode parametric downcoverter exhibit nonclassical correlations in the transverse plane. We present results of measurements of the classical pattern for a degenerate, multi-mode parametric optical parametric oscillator (OPO) operating above threshold. We also present results of autocorrelation measurements of intensity fluctuations in the transverse plane both in the near field and in the far field with the OPO operating both below and above threshold -- a method we believe will ultimately enable us to display the nonclassical correlations of the OPO output.

DOI
10.1117/12.546906

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Fluctuations in the field of a 2nd order nonlinear multi-mode parametric downcoverter exhibit nonclassical correlations in the transverse plane. We present results of measurements of the classical pattern for a degenerate, multi-mode parametric optical parametric oscillator (OPO) operating above threshold. We also present results of autocorrelation measurements of intensity fluctuations in the transverse plane both in the near field and in the far field with the OPO operating both below and above threshold -- a method we believe will ultimately enable us to display the nonclassical correlations of the OPO output.
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 the results of an experimental investigation of multimode intensity patterns from an optical parametric oscillator operating above threshold and show that it oscillates in 10--15 transverse modes strongly coupled through the nonlinear crystal, which makes this setup useful for future investigation of quantum correlations in the transverse plane. We describe the experimental setup for simultaneous measurements of signal and idler near- and far-field patterns and analyze the effects of various experimental complications such as walk-off and thermal index changes on the generated patterns. We also show that the oscillator can be stabilized by optical feedback, indicating a possible route for controlling the generated intensity patterns.
The visibility and quality of optical images is ultimately limited not by diffraction but by the quantum noise affecting each pixel of a detector. Multimode non-classical states of light, characterized by spatial quantum correlation or local reduced quantum noise, permit in principle to go beyond the standard quantum limit and therefore to improve transverse optical resolution. It has been predicted that Optical Parametric Oscillators (OPO) operating simultaneously on many transverse modes are good candidates for generating multimode non-classical states of light. We perform an experiment showing that a c.w. confocal OPO above threshold emits such states. Below threshold, the OPO is turned to a multimode optical parametric amplifier.