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MULTIMODE SQUEEZING PROPERTIES OF A CONFOCAL OPO: BEYOND THE THIN CRYSTAL APPROXIMATION

Lopez, Laurent, Sylvain Gigan, Nicolas Treps, Agnès Maître, Claude Fabre, Gatti, Alessandra

Published Jan 1, 2005• 0 citations
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Abstract

Up to now, transverse quantum effects (usually labelled as "quantum imaging" effects) which are generated by nonlinear devices inserted in resonant optical cavities have been calculated using the "thin crystal approximation", i.e. taking into account the effect of diffraction only inside the empty part of the cavity, and neglecting its effect in the nonlinear propagation inside the nonlinear crystal. We introduce in the present paper a theoretical method which is not restricted by this approximation. It allows us in particular to treat configurations closer to the actual experimental ones, where the crystal length is comparable to the Rayleigh length of the cavity mode. We use this method in the case of the confocal OPO, where the thin crystal approximation predicts perfect squeezing on any area of the transverse plane, whatever its size and shape. We find that there exists in this case a "coherence length" which gives the minimum size of a detector on which perfect squeezing can be observed, and which gives therefore a limit to the improvement of optical resolution that can be obtained using such devices.

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Up to now, transverse quantum effects (usually labelled as "quantum imaging" effects) which are generated by nonlinear devices inserted in resonant optical cavities have been calculated using the "thin crystal approximation", i.e. taking into account the effect of diffraction only inside the empty part of the cavity, and neglecting its effect in the nonlinear propagation inside the nonlinear crystal. We introduce in the present paper a theoretical method which is not restricted by this approximation. It allows us in particular to treat configurations closer to the actual experimental ones, where the crystal length is comparable to the Rayleigh length of the cavity mode. We use this method in the case of the confocal OPO, where the thin crystal approximation predicts perfect squeezing on any area of the transverse plane, whatever its size and shape. We find that there exists in this case a "coherence length" which gives the minimum size of a detector on which perfect squeezing can be observed, and which gives therefore a limit to the improvement of optical resolution that can be obtained using such devices.
Up to now, transverse quantum effects (usually labeled as ``quantum imaging'' effects) which are generated by nonlinear devices inserted in resonant optical cavities have been calculated using the ``thin-crystal approximation,'' i.e., taking into account the effect of diffraction only inside the empty part of the cavity, and neglecting its effect in the nonlinear propagation inside the nonlinear crystal. We introduce in the present paper a theoretical method which is not restricted by this approximation. It allows us in particular to treat configurations closer to the actual experimental ones, where the crystal length is comparable to the Rayleigh length of the cavity mode. We use this method in the case of the confocal optical parametric oscillator, where the thin-crystal approximation predicts perfect squeezing on any area of the transverse plane, whatever its size and shape. We find that there exists in this case a ``coherence length'' which gives the minimum size of a detector on which perfect squeezing can be observed, and which gives therefore a limit to the improvement of optical resolution that can be obtained using such devices.
Summary form only given. To achieve super-resolution one must take into account a priori information about localization of the object. Such an a priori information exists in the case of an object of finite size. Its Fourier transform located in the focal plane of the lens is an entire analytic function, and analytic continuation of the object spectrum outside the spatial-frequency band allows for unlimited resolution. However such a super-resolution is extremely sensitive to the noise in the detected image. The ultimate limit of super-resolution is determined by the quantum fluctuations of light in the detection plane. We present the quantum theory of super-resolution for a one-dimensional coherent optical imaging scheme and discuss possibilities of improving the resolution limit by using multimode squeezed light. For quantum-mechanical description of this scheme we take into account the vacuum fluctuations of the electromagnetic field in the input plane outside the object. Interference of these vacuum fluctuations with the field amplitude of the object in the detection plane is the origin of the standard quantum limit or shot noise of photodetection in the image. To go beyond this limit we suggest to illuminate the object with multimode squeezed light having the spot size much larger than the object area. Then the vacuum fluctuations outside the object can be effectively suppressed resulting in sub-shot-noise detection of the image.
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.
In this paper, experimental evidence of cw amplification of images in the quantum regime, using a phase sensitive optical parametric amplification operating inside transverse degenerate cavities. Injecting various images (mismatched Gaussian modes and double slits of different orientations) at the input of the device, showed that the output image was amplitude squeezed by 30% in the regime of deamplification of a type II frequency-degenerate OPO operating below threshold in a semi-confocal cavity, when the polarization of the input image is at 45deg from the crystal axes. The authors showed also that, in the regime of amplification, the two polarization components along the signal and idler axes had quantum correlated intensity fluctuations (intensity difference fluctuations measured at 30% below the standard quantum noise level).