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arXiv:0807.3946 · Physical Review A

Four-photon scattering in birefringent fibers

Edouard Brainis

Published Feb 26, 2009• 57 citations
arXivHTMLPDF

Abstract

Four-photon scattering in nonlinear waveguides is an important physical process that allows photon-pair generation in well-defined guided modes, with high rate and reasonably low noise. Most of the experiments to date used the scalar four-photon scattering process in which the pump photons and the scattered photons have the same polarization. In birefringent waveguides, vectorial four-photon scatterings are also allowed: these vectorial scattering processes involve photons with different polarizations. In this paper, the theory of four-photon scattering in nonlinear, birefringent, and dispersive fibers is developed in the framework of the quantum theory of light. The work focuses on the spectral properties and quantum correlations (including entanglement) of photon pairs generated in high-birefringence and low-birefringence fibers.

DOI
10.1103/physreva.79.023840

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Four-photon scattering in nonlinear waveguides is an important physical process that allows photon-pair generation in well-defined guided modes, with high rate and reasonably low noise. Most of the experiments to date used the scalar four-photon scattering process in which the pump photons and the scattered photons have the same polarization. In birefringent waveguides, vectorial four-photon scatterings are also allowed: these vectorial scattering processes involve photons with different polarizations. In this paper, the theory of four-photon scattering in nonlinear, birefringent, and dispersive fibers is developed in the framework of the quantum theory of light. The work focuses on the spectral properties and quantum correlations (including entanglement) of photon pairs generated in high-birefringence and low-birefringence fibers.
Spontaneous four-wave mixing (SFWM) in optical fibers is an important way to generate correlated/entangled photon pairs. When the pulsed pump light passes through the optical fiber, two kinds of SFWM will take place simultaneously. One is scalar scattering processes, in which two annihilated pump photons and generated photon pair are all polarized along the same fiber polarization axis. The other is vector scattering processes, in which two annihilated pump photons are polarized along different fiber polarization axes, either to the two photons of the generated pair. If the fiber has large group birefringence, the intensity of vector scattering processes will be suppressed at the phase matching frequencies of the scalar scattering processes. On the other hand, the walk-off effect of the pump pulse components polarized along the two fiber polarization axes also suppresses the vector scattering processes. Hence, by proper pump polarization and signal/idle frequency selection, photon pairs can be generated only by the two independent scalar scattering processes in optical fibers with birefringence, which provide a simple way to realize polarization entangled photon pair generation. In this paper, related experiments based on the high nonlinearity microstructure fiber (HN-MSF) with group birefringence and polarization maintained dispersion shifted fiber (PM-DSF) are introduced, showing their potential on developing practical quantum light sources.
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.
We investigate the impact of fiber birefringence and spontaneous Raman scattering on the properties of photon pairs that are generated by the spontaneous four-wave mixing process in birefringent fibers. Starting from the formulation of the theory of four-wave mixing, we show a theoretical model for a generated optical field with the consideration of the Raman scattering and a Gaussian-distributed pump. The theoretical model is then applied for deriving the closed expressions of the photon-pair spectral properties as a function of the fiber birefringence. Also, with the modeled Raman gain, we evaluate the reduction of the pair production rate due to the presence of the Raman effect as well as the contributions of the Raman-scattered photons over a broad wavelength range. The predictions are experimentally verified with a commercial polarization-maintaining fiber.
We present a general quantum theory capable of describing photon statistics under the combined effects of four-wave mixing and Raman scattering inside optical fibers. Our theory is vectorial in nature and includes all polarization effects. Our analysis shows that spontaneous Raman scattering degrades the pair correlation in all cases but the extent of degradation depends on the pumping configuration employed. In a single-pump configuration, photon pairs can be created with polarization either parallel or orthogonal to the pump. Our results show that the orthogonal configuration can improve the extent of quantum correlation considerably over a broad bandwidth. In the case of a dual-pump configuration, we show that imbalance of two pump powers can be used to improve the quality of photon pairs. We show that orthogonally polarized pumps can generate photon pairs automatically in a polarization-entangled state. In particular, orthogonal pumping with circular polarizations produces such an entangled state with relatively high quality. We also quantify the quality of polarization entanglement as well as energy-time entanglement constructed using correlated photon pairs.