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The European Physical Journal D

Dependence on crystal parameters of the correlation time between signal and idler beams in parametric down conversion calculated in the Wigner representation

Alberto Casado, A. Fernández-Rueda, Trevor W. Marshall, J. Martínez, Ramón Risco, Emilio Santos

Published Aug 1, 2000• 15 citations
Publisher
DOI
10.1007/s100530070074

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We study modal characteristics of a customized ridge waveguide in Lithium Niobate designed to generate twin photons at telecom wavelength. A quantum analysis of SPDC predicts the possible down conversion processes and optimizes the input beam parameters for fundamental mode emission. Further, a Joint Spectral Amplitude (JSA) analysis ensures the generation of signal/idler at 1550 nm in the customized LN waveguide. A calculation of the parametric down conversion (PDC) signal power shows a dependence of L^(3/2) for a waveguide compared to a linear dependence in case of bulk crystal.

•Sep 27, 2017•0 citations
In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].
The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.
We study modal characteristics of a customized ridge waveguide in Lithium Niobate designed to generate twin photons at telecom wavelength. A quantum analysis of SPDC predicts the possible down conversion processes and optimizes the input beam parameters for fundamental mode emission. Further, a Joint Spectral Amplitude (JSA) analysis ensures the generation of signal/idler at 1550 nm in the customized LN waveguide. A calculation of the parametric down conversion (PDC) signal power shows a dependence of L^(3/2) for a waveguide compared to a linear dependence in case of bulk crystal.