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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Substituting scheme for nonlinear couplers

Jaromı́r Fiurášek, Jan Peřina

Published Mar 7, 2001• 0 citations
Publisher

Abstract

We propose a substituting scheme for nonlinear optical couplers operating by means of degenerate parametric down- conversion with strong coherent pumping. The scheme, which provides the same unitary input-output transformation as the original coupler, consists of simple linear and nonlinear optical devices: beam splitter and optical parametric amplifiers. Using group theoretical approach, we find analytical formulas for parameters of these optical elements. The scheme allows us to get a better insight into the coupler behavior, because the complex dynamics of the coupler is transformed into a sequence of simpler evolutions governed by the beam splitter and parametric amplifiers, whose properties are well known and understood.

DOI
10.1117/12.417841

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We propose a substituting scheme for nonlinear optical couplers operating by means of degenerate parametric down- conversion with strong coherent pumping. The scheme, which provides the same unitary input-output transformation as the original coupler, consists of simple linear and nonlinear optical devices: beam splitter and optical parametric amplifiers. Using group theoretical approach, we find analytical formulas for parameters of these optical elements. The scheme allows us to get a better insight into the coupler behavior, because the complex dynamics of the coupler is transformed into a sequence of simpler evolutions governed by the beam splitter and parametric amplifiers, whose properties are well known and understood.
We consider a substituting scheme for nonlinear optical couplers operating by means of degenerate parametric down-conversion with strong coherent pumping. The proposed scheme, which provides the same unitary input-output transformation as the original coupler, consists of simple linear and nonlinear optical devices: beam splitter and optical parametric amplifiers. Using a group-theoretical approach, we find analytical formulas for parameters of these optical elements. The scheme allows us to get a better insight into the coupler behavior, because the complex dynamics of the coupler is transformed into a sequence of simpler evolutions governed by the beam splitter and parametric amplifiers, whose properties are well known and understood. We demonstrate that various dynamical regimes of the coupler are clearly reflected by the substituting device.
We provide two quantum descriptions of a beam splitter with second-order nonlinearity. Models of nonlinear couplers could be the same. For simplicity, a symmetry of the device is assumed, which does not exclude various reflectivities. The models differ in taking into account the co-propagation of beams and replacing it by their counter-propagation. The unitary operators that evolve the input states into the output ones are calculated by using a momentum operator and the effective distance of presumed co-propagation and counter-propagation, respectively.
In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.
We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.
We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.
The quantum-limited noise figure (NF) for a general combination of linear optical elements is obtained in a compact form. The entries in this expression are obtained from the classical input–output transmission coefficient of the signal, and of the various transmission coefficients from the noise inputs to the output. The same result is also obtained by means of a semiclassical derivation. The linear elements can be: population-inversion amplifiers, parametric amplifiers and/or wavelength converters, beam splitters, lossy fibers, etc. They form a network with a simple directed graph (no loops). We identify a class of networks for which Friis’ formula for concatenated elements holds. We verify the general formula for a variety of well-known cases. We also verify that the NF for an optical communication link periodically amplified by nondegenerate phase-sensitive parametric amplifiers (PSAs) is only about half of that for a similar system using degenerate PSAs.