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Conference on Lasers and Electro-Optics

Spatial behavior of nonclassic light

Mikhail I. Kolobov

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.It has previously been shown that a traveling-wave optical parametric amplifier can generate multimode squeezed states of light. Homodyne detection of multimode squeezed light, under certain physical conditions, results in sub-Poissonian statistics of photons not only in time but also in the transverse plane of the light beam. Of particular relevance to applications is a situation when the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons within each of them. Under photodetection of such a beam of light, several sub-shot-noise photocurrents can be produced according to the number of independent areas with sub-Poissonian statistics. This is in drastic contrast to the case of a single-mode sub-Poissonian light beam, where any attempt to collect light only from a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of new interesting applications in optical imaging, optical parallel processing of information, parallel computing, and many other phenomena where it is desirable to have the regular statistics of photons across the transverse plane of the electromagnetic wave. We describe the application of multimode squeezed light in sub-shot-noise microscopy, noiseless amplifications of optical images, and optical imaging. We also consider the possibility of improving the resolution in optical imaging and microscopy beyond the Rayleigh limit via multimode squeezed light.

DOI
10.1109/iqec.1998.680402

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Summary form only given.It has previously been shown that a traveling-wave optical parametric amplifier can generate multimode squeezed states of light. Homodyne detection of multimode squeezed light, under certain physical conditions, results in sub-Poissonian statistics of photons not only in time but also in the transverse plane of the light beam. Of particular relevance to applications is a situation when the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons within each of them. Under photodetection of such a beam of light, several sub-shot-noise photocurrents can be produced according to the number of independent areas with sub-Poissonian statistics. This is in drastic contrast to the case of a single-mode sub-Poissonian light beam, where any attempt to collect light only from a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of new interesting applications in optical imaging, optical parallel processing of information, parallel computing, and many other phenomena where it is desirable to have the regular statistics of photons across the transverse plane of the electromagnetic wave. We describe the application of multimode squeezed light in sub-shot-noise microscopy, noiseless amplifications of optical images, and optical imaging. We also consider the possibility of improving the resolution in optical imaging and microscopy beyond the Rayleigh limit via multimode squeezed light.
Nonclassical effects such as squeezing, antibunching, and sub-Poissonian statistics of photons have been attracting attention in quantum optics over the last decade. Up to now most theoretical and experimental investigations have been carried out exclusively in the time domain while neglecting the spatial aspects by considering only one spatial mode of the electromagnetic field. In many situations such an approximation is well justified. There are, however, problems that do not allow in principle a single-mode consideration. This is the case when one wants to investigate the quantum fluctuations of light at different spatial points in the plane perpendicular to the direction of propagation of the light beam. Such an investigation requires a complete description of quantum fluctuations of light in both time and space and cannot be done within a single-mode theory. This space-time description brings about a natural generalization into the spatial domain of such notions as the standard quantum limit, squeezing, antibunching, etc. It predicts, for example, the possibility of generating a light beam with sub-Poissonian statistics of photons not only in time but also in the beam's transverse plane. Of particular relevance to the applications is a situation in which the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons in each. Photodetection of such a beam produces several sub-shot-noise photocurrents depending on the number of independent areas with sub-Poissonian statistics. This is in marked contrast to the case of a single-mode sub-Poissonian light beam in which any attempt to collect light from only a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of interesting new applications in optical imaging, optical parallel processing of information, parallel computing, and many other areas in which it is desirable to have a light beam with regular photon statistics across its transverse area. The aim of this review is to describe the recent development in this branch of quantum optics.
This paper provides a simple physical consideration of a new type of squeezed state of light: space-time squeezed state. As it was shown recently, spatial-multimode broadband squeezed light can generate (by homodyne detection) photon counting statistics that are regular not only in time, but also in the plane of observation. A possible advantage of application of space-time squeezed light in a number of areas of quantum optics (i.e., low-noise generation, detection of optical images, Fourier optics, and holography) is discussed from an elementary point of view.
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.
Quantum imaging can be defined as an area of quantum optics that investigates the ultimate performance limits of optical imaging allowed by the quantum nature of light. Quantum Imaging techniques possess a high potential for improving the performance in recording, storage, and readout of optical images beyond the limits set by the standard quantum level of fluctuations known as the shot noise. This talk aims at giving an overview of the fundamentals of Quantum Imaging as well as its most important directions. We shall discuss generation of the spatially multimode squeezed states of light be means of a travelling-wave optical parametric amplifier. We shall demonstrate that this kind of light allows us to reduce the spatial fluctuations of the photocurrent in a properly chosen homodyne detection scheme with a highly efficient CCD camera. It will be shown that using the amplified quadrature of the light wave in a travelling-wave optical parametric amplifier, one can perform noiseless amplification of optical images. We shall provide recent experimental results demonstrating a single-shot noiseless image amplification by a pulsed optical parametric amplifier. One of important experimental achievements of Quantum Imaging, coined in the literature as quantum laser pointer, is a precise measurement of position and transverse displacement of a laser beam with resolution beyond the limit imposed by the shot noise. We shall describe briefly the idea of the experiment in which the transverse displacement of a laser beam was measured with resolution of the order of Angstrom. The problem of precise measurement of transverse displacement of a light beam brings us to a more general question about the quantum limits of optical resolution. The classical resolution criterion, derived in the nineteen century by Abbe and Rayleigh, states that the resolution of an optical instrument is limited by diffraction and is related to the wavelength of the light used in the imaging scheme. However, it was for a long time recognised in the literature that in some cases when one has some a priori information about the object, one can improve the resolution beyond the Rayleigh limit using the so-called super-resolution techniques. As a final topic in this talk, we shall discuss the quantum limits of optical super-resolution. In particular, we shall formulate the standard quantum limit of super-resolution and demonstrate how one can go beyond this limit using specially designed multimode squeezed light.
Theoretical and experimental results of investigations into the quantum noise of multimode laser radiation are considered. The feasibility of generating light with a photon-number-squeezed (sub-Poissonian) photon distribution by a multimode laser with a homogeneously broadened line is analyzed. The conditions of noisy and noiseless (regular) pumping are considered. Photon-number fluctuations of the net laser radiation summed over all generated modes are calculated in the approximation of equidistant equal modes, as are photon-number fluctuations in an individual mode inside and outside the resonator. Output-radiation noise spectra and photon-number fluctuations are calculated for solid-state (neodymium glass, Nd:YAG) and semiconductor lasers. Theoretical results are compared with a number of experimental data obtained for semiconductor lasers in recent years.