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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Quantum statistics of a nonlinear asymmetric coupler with strong pumping

Jan Peřina, Jan Peřina

Published Aug 1, 1995• 27 citations
Publisher

Abstract

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.

DOI
10.1088/1355-5111/7/4/011

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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.
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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. Quantum statistical characteristics, such as photon number distribution, its factorial moments, quadrature and integrated intensity vari- ances and quadrature uncertainty product can demonstrate effects of transmission of light between waveguides. Incident beams can be assumed to be coherent, squeezed and mixed with external noise. Second harmonic modes are assumed to be pumped with strong coherent beams. Nonclassical behavior 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 nonclassical states can be generated.
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.
The authors examine both codirectional and contradirectional nonlinear couplers operating by second harmonic generation with particular attention to the effect of linear and nonlinear phase mismatches under the assumption that the second harmonic mode is stimulated by a strong coherent field. Quantum statistical properties are described by a photocount distribution, its factorial moments, quadrature and integrated intensity variances and the uncertainty product, with particular attention to generation and transmission of nonclassical light. Incident beams can be coherent or squeezed with mixed external noise. It is shown that, in general, the nonlinear phase mismatch, which effectively makes the interaction weaker, may reduce nonclassical effects and their transmission to signal linear waveguide. However, as a consequence of the phase mismatches some initial regimes of the interaction can be repeated, which leads to new interesting nonclassical effects.