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Physical Review A

Quantum analysis of light propagation in a parametric amplifier

B. Hüttner, Sergio D. Serulnik, Y. Ben-Aryeh

Published Nov 1, 1990• 132 citations
Publisher

Abstract

We develop a quantization procedure for treating the propagation of light. This formalism is particularly effective in a dispersive nonlinear medium characterized by its macroscopic linear and nonlinear polarizability. We demonstrate it by analyzing the propagation of light in a multimode degenerate parametric amplifier.
DOI
10.1103/physreva.42.5594

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We present the main theoretical results on spatial propagation of quantum light in nonlinear waveguiding devices together with a few applications. We show that the quantization of the classical momentum provides a consistent quantum mechanical formulation of both the linear and the nonlinear quantum light propagation in waveguiding devices. The momentum operator allows us to derive the correct spatial Heisenberg's equations for the forward and backward absorption and emission operators and consequently to analyze the spatial propagation in the multimode optical-field strength space. For that purpose we use the Feynman's path integral method in order to derive the quantum spatial optical propagators of different nonlinear waveguiding devices and accordingly to calculate the spatial propagation of the optical-field strength probability amplitude of quantum states in these nonlinear devices. Likewise, we present a preliminary and heuristic formulation of quantum dissipation in order to take into account the losses under spatial quantum propagation in lossy nonlinear waveguiding devices. It must be stressed that these optical-field strength probabilities have the advantage of being measured by homodyne techniques and therefore their theoretical analysis is of a remarkable interest in the optical characterization of quantum states obtained under linear and nonlinear propagation in waveguiding devices.
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