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Journal of Modern Optics

Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Jan Peřina, J. Bajer

Published Nov 1, 1995• 24 citations
Publisher

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.

DOI
10.1080/09500349514552031

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We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.
We derive the quantum statistical properties of light beams involved in an asymmetric nonlinear coupler composed of a linear waveguide and a nonlinear waveguide operating using second harmonic generation. Examining quadrature and integrated intensity fluctuations, photon number distribution, reduced factorial moments and the uncertainty product, we demonstrate non-classical behaviour of single and compound modes. We show that squeezing of vacuum fluctuations, sub-Poissonian photon statistics and oscillations in photon number distribution created by nonlinear dynamics can be transferred to the linear signal mode. Also effects of non-classical incident beams and smoothing effects of external noise are demonstrated.
We examine a contradirectional asymmetric nonlinear coupler composed of a linear waveguide and a nonlinear waveguide operating by second harmonic generation. For this we develop a new consistent approach to quantum contradirectional propagation. Using a short-length approximation or a strong stimulating field in the second harmonic mode, we can demonstrate an effective transfer of non-classical properties of light from nonlinear to linear waveguides analysing quadrature and integrated intensity fluctuations, photon number distribution, reduced factorial moments and uncertainty product. Effects of non-classical behaviour of incident beams and of external noise are involved.
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 investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.
Higher-order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher-order antibunching, higher-order squeezing, and higher-order two-mode and multimode entanglement in the asymmetric nonlinear optical coupler. It is also shown that nonclassical properties of light can transfer from a nonlinear waveguide to a linear waveguide.