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Physical Review A

General quantum theory of nonlinear optical-pulse propagation

Yinchieh Lai, Shinn-Sheng Yu

Published Jan 1, 1995• 64 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.51.817

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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.
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.>
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.
Based on the linearization approximation, a unified approach to the quantum effects of soliton propagation is developed. The new formulation provides a clearer picture. The real and imaginary parts of the perturbation field are expanded in different basis sets. Orthogonality relations are used to project out the soliton parameters. The new formulation also provides a general numerical approach to the calculation of detection noise. Numerical analyses of fiber ring gyros that use squeezed solitons are presented.
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.
A quantum treatment of soliton squeezing based on the linearization approximation has been carried out numerically.2 are recast more naturally. The new formulation also provides a general approach to calculation of detection noise. With the projection interpretation of homodyne detection, the squeezing ratio can be easily calculated by applying the propagation operator to the characteristic function of homodyne detection instead of the perturbation field operator. All the results in Ref. 1 also can be reproduced naturally. Finally, numerical analysis of fiber ring gyros using squeezed solitons and analysis of modelocked lasers are presented.
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.