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Applied Physics B

Assessment of image resolution improvement by phase-sensitive optical parametric amplification

Zhifeng Huang, D. French, Hsueh‐Yuan Pao, Igor Jovanovic

Published Jun 17, 2010• 3 citations
Publisher

Abstract

Classical information theory can be used to quantify the resolution performance of optical imaging systems. When an optical parametric amplifier (OPA) operated as a phase-sensitive amplifier (PSA) in the transverse spatial domain is used for point source imaging, the angular resolution improvement can approach the de Broglie resolution (i.e. Heisenberg limit). In this paper, classical information theory is employed to quantify the signal-to-noise ratio (SNR) improvement for both an ideal and a realistic multimode PSA applied to the problem of sub-Rayleigh imaging. When only considering the noise originating from the detector, the SNR improvement is found to scale quadratically as a function of the PSA gain, in the limit of noise power comparable to signal power. Differences in performance of an ideal PSA and a realistic PSA are discussed.

DOI
10.1007/s00340-010-4101-z

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Classical information theory can be used to quantify the resolution performance of optical imaging systems. When an optical parametric amplifier (OPA) operated as a phase-sensitive amplifier (PSA) in the transverse spatial domain is used for point source imaging, the angular resolution improvement can approach the de Broglie resolution (i.e. Heisenberg limit). In this paper, classical information theory is employed to quantify the signal-to-noise ratio (SNR) improvement for both an ideal and a realistic multimode PSA applied to the problem of sub-Rayleigh imaging. When only considering the noise originating from the detector, the SNR improvement is found to scale quadratically as a function of the PSA gain, in the limit of noise power comparable to signal power. Differences in performance of an ideal PSA and a realistic PSA are discussed.
The Rayleigh criterion sets a classical limit on the resolution of optical imaging systems, which brings challenges in remote sensing of spatial information. According to the Rayleigh criterion, only a limited control of resolution can be accomplished by adjusting the optical wavelength or aperture diameter. The resolvability of optical imaging systems can also be represented in terms of the signal-to-noise ratio (SNR). The optical parametric amplier (OPA) is a common nonlinear device used in a variety of applications, such as imaging, quantum information, and ultrafast laser science. It has been shown that when the OPA is operated as a phase-sensitive amplifier (PSA), no quantum noise is added thus preserving the SNR. In this thesis, the hypothesis testing from the classical information theory has been applied to the problem of distinguishing distant point sources. It is numerically demonstrated that an improvement of resolution beyond the classical limit and SNR enhancement could be achieved by utilizing the PSA operated in spatial domain. Plasma diagnostics deducts information of important parameters (such as temperature, plasma density and confinement) in magnetic confinement fusion (MCF) reactions. Interferometer can be used to measure the refractive index of plasma which is correlated with the plasma density. A Mach-Zehnder type interferometer enhanced by the PSA is studied. It has been found that the effect of the PSA is to increase the minimum resolvable interference fringe shift caused by plasma density perturbation so that a better resolution of the interferogram can be obtained. This method may enable significant improvement in plasma density measurement.
Optical parametric amplifiers (OPAs) configured as phase-sensitive amplifiers (PSAs) can be used for noiseless optical image amplification, generation of non-classical states of light, and, in particular, for multimode squeezed light generation. For all these applications and for effective use of the quantum properties of the multimode PSA, we need to know its independently squeezed (or amplified) eigenmodes. First we present the quantum theory of a spatially multimode traveling-wave PSA pumped by a high-power pump beam with arbitrary spatial profile. To quantitatively identify the Green's function of the PSA, we have developed a semi-analytical coupled-mode-theory of the PSA using 2D Hermite-Gaussian mode expansions of the signal- and pump-beam spatial distributions. By using Green's functions of the classical OPA, we calculate the normallyordered quadrature correlators at its output, which provide complete quantum description of the phase-sensitive OPA and enable determination of its independently squeezed eigenmodes. We find the number of the supported eigenmodes and their shapes for a spatially broadband frequency-degenerate optical parametric amplifier with elliptical Gaussian pump. We conclude by discussing our recent extensions of the coupled-mode-theory to study higher-order pump modes, compact representation of the PSA eigenmodes (especially convenient for experiments), and effect of non-zero phase mismatch on the PSA eigenmodes. We expect that the results from our model can be used for optimum mode matching in phase-sensitive image amplification and multimode squeezing generation.