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Journal of Optics B Quantum and Semiclassical Optics

Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image

A. S. Chirkin, E. V. Makeev

Published Nov 4, 2005• 12 citations
Publisher

Abstract

We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.

DOI
10.1088/1464-4266/7/12/010

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A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.
We develop for the first time the quantum theory of parametric image amplification at low-frequency pumping. Such a process can be implemented by coupled consecutive three-frequency optical interactions. As a result, besides the amplified optical image on the signal frequency, there are two other images with frequencies which are below the pumping frequency. The theory developed takes into account the diffraction effect and group mismatch of interacting waves. For the interacting waves the expressions for mean photon numbers and signal-to-noise ratios are deduced and the dependence of these parameters on the interaction length and coordinate at the image plane are studied.
A two-step nonlinear optical interaction consisting of (i) a spontaneous frequency down-conversion process coupled with (ii) a frequency up-conversion process is treated quantum mechanically in the experimentally observed case of simultaneous collinear phase matching of both processes. The temporal behavior of the output signals is found to depend on which process, (i) or (ii), predominates. The nature of the photon statistics for each of the output modes is found to be "super-Poisson," regardless of which process, (i) or (ii), is dominant, and the zero-point fluctuations characteristic of parametric amplification are exhibited.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.