We describe simultaneous measurements of signal/idler near field and far field patterns of a 2nd order nonlinear multi-mode parametric downconverter. We also describe the use of auto- and cross correlation techniques to obtain statistical data.
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.
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.
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.
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.
We measure the complete quantum state for six modes of the electromagnetic field produced by an optical parametric oscillator. The investigation involves the sideband of the intense pump, signal, and idler fields generated by stimulated parametric downconversion inside a triply resonant optical resonator. We develop a theoretical model to successfully interpret the experimental results. The model takes into account the coupling of the field modes to the phonon bath of the nonlinear crystal, clearly showing the roles of different physical effects in shaping the structure of the quantum correlations between the six optical modes.
Summary form only given.We study spatiotemporal fluctuations of the signal field in the output from a degenerate optical parametric oscillator using the Langevin model of A. Gatti et al. (1997). The spatial structure of the output signal is calculated for pump values just below the threshold for the formation of patterns with a critical wave vector. We consider the effects of a squeezed input signal, both homogeneous and spatially varying, on the output correlations, which can be measured in both the near- and far-field.