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Nonlinear Optics

How quickly self-Raman effects and third-order dispersion destroy squeezing

Yinchieh Lai, Shinn-Sheng Yu

Published Dec 17, 2002• 0 citations
Publisher

Abstract

We have developed a general quantum theory of nonlinear pulse propagation and a self-consistent quantum theory of self-Raman effects in optical fibers. Our approach is based on the linearization approximation, the conservation of commutator brackets, and the concept of adjoint systems. A general, self-consistent scheme is developed to quantize nonlinear optical pulse propagation problems and a general computation procedure ("the backpropagation method") is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. By utilizing these results, we can calculate the magnitude of squeezing when an optical pulse propagates through an optical fiber in the presence of self-Raman effects and third-order dispersion.>

DOI
10.1109/nlo.1994.470775

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We have developed a general quantum theory of nonlinear pulse propagation and a self-consistent quantum theory of self-Raman effects in optical fibers. Our approach is based on the linearization approximation, the conservation of commutator brackets, and the concept of adjoint systems. A general, self-consistent scheme is developed to quantize nonlinear optical pulse propagation problems and a general computation procedure ("the backpropagation method") is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. By utilizing these results, we can calculate the magnitude of squeezing when an optical pulse propagates through an optical fiber in the presence of self-Raman effects and third-order dispersion.>
Based on the linearization approximation and the conservation of commutation brackets, a general, self-consistent scheme is developed to quantize nonlinear optical-pulse propagation problems. A general computation procedure is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. As an illustration, a self-consistent quantum theory of the self-Raman effect in optical fibers is presented. The influence of the self-Raman effect on soliton squeezing is examined.
Based on a newly developed general quantum theory of nonlinear optical pulse propagation, the influences of the self-Raman effect and third-order dispersion on the achievable squeezing ratio in squeezing experiments with optical fibers at both the 1.3- and 1.55-μm wavelengths are studied. In the presence of these effects, squeezing still survives, but the achievable squeezing will reach a limit as the propagation distance increases. Temperature dependence of the squeezing ratio is also examined.
The fiber Bragg gratings (FBGs) with Kerr nonlinearity exhibit optical soliton like phenomena known as the Bragg solitons. Due to the high dispersion of FBGs near the band edge, optical solitons in the anomalous dispersion side is produced when the input pulse has suitable pulse-width and peak intensity. The Bragg solitons belong to the class of bi-directional pulse propagation problems. In this paper, general quantum theory for bi-directional pulse propagation problems is developed and applied to the Bragg solitons. The output Bragg soliton pulses are quantum-mechanically squeezed and their squeezing ratios calculated.
We theoretically reveal the potential of the parallelism of squeezed state generation by nonlinear pulse propagation in an optical fiber. Starting from a nonlinear Schr\"odinger equation coupling with phonon modes that cause Raman noise, we develop a multimode quantum theory of nonlinear propagation in an optical fiber. Based on our proposed method, we numerically simulate fiber nonlinear propagation in two conditions: solitonlike and zero-group-delay-dispersion (zero-GVD) propagation. As a result, we find that zero-GVD propagation enables the large-scale parallel generation of squeezed states relative to solitonlike propagation owing to the broadband phase matching of the four-wave mixing process.
The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.