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Physical Review E

Theory of incoherent optical solitons: Beyond the mean-field approximation

Sergey A. Ponomarenko, Natalia M. Litchinitser, Govind Prasad Agrawal

Published Jul 27, 2004• 17 citations
Publisher

Abstract

We present a general theory of partially coherent optical solitons in slow-responding nonlinear media that takes into account intensity fluctuations of the light sources generating such solitons. If intensity fluctuations of the source are negligible, the theory reduces to the previously reported mean-field theory of partially coherent solitons. However, when such fluctuations are significant, our theory shows that the properties of partially coherent solitons in saturable nonlinear media can be qualitatively different from those predicted by the mean-field theory.

DOI
10.1103/physreve.70.015603

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We present a general theory of partially coherent optical solitons in slow-responding nonlinear media that takes into account intensity fluctuations of the light sources generating such solitons. If intensity fluctuations of the source are negligible, the theory reduces to the previously reported mean-field theory of partially coherent solitons. However, when such fluctuations are significant, our theory shows that the properties of partially coherent solitons in saturable nonlinear media can be qualitatively different from those predicted by the mean-field theory.
We develop a quantum theory of propagation in dispersive nonlinear media from the foundations of a correctly quantized field theory. Quantum fluctuations are handled by coherent-state expansions of localized field states. A stochastic nonlinear Schrödinger equation in the field variables is obtained for media with an intensity-dependent refractive index. This predicts squeezing for a continuous-wave input, over a wide bandwidth with anomalous dispersion, and over a gradually reducing bandwidth with normal dispersion. The equation is easily modified to include thermal-noise sources as well. For solitons, fluctuations are reduced over the soliton bandwidth. This leads to quantum solitons that have quadrature fluctuations less than the level of vacuum fluctuations. The complementary quadrature has a correspondingly increased fluctuation level.
In the framework of the nonlinear lambda model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the lambda-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the lambda-type media. We provide an exact analytic description of decelerating, stopping and reaccelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the field; we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We discuss physically interesting features of our solution, which are in a good agreement with recent experiments.
Optical experiments reveal the fact that real laser pulses have random fluctuations in their amplitude and phase that crucially affect pulse evolution. Statistical optics considers the random nature of light to give a more realistic description of laser pulses behavior. Generation of ultrashort pulses, operating at frequencies close to internal transition frequencies of medium atoms, motivated the growing interest in studying on-resonance light-matter interactions. Moreover, there exist optical phenomena that only occur at optical resonance. Thus, near resonance light-matter interactions are of great importance. In this dissertation, statistical properties of ultrashort pulses propagating in different linear and nonlinear media near optical resonance is studied. Various partially coherent pulses are simulated and effects of initial statistical properties of pulses on their propagation in resonant absorbing and amplifying media are explored. The research performed throughout this thesis leads to following results. 1- Various classes of ultrashort self-similar partially coherent pulses are explored along with closed form expressions for their correlation functions. Also, the evolution of coherence properties of pulses upon their short-distance and long-distance propagation is investigated. 2- Generic partially coherent pulses are simulated and their global and local correlation properties upon propagation in resonant linear absorber media are studied. The evolution of the coherence functions of pulses shows that partially coherent pulses are strongly affected by the medium regarding to their coherence levels. A correlation area theorem is also derived to describe global correlation properties of stochastic pulses propagating in such media. 3- Evolution of small-area pulse coherence properties, propagating in linear amplifiers near optical resonance, is studied. Our simulation results reveal that more coherent pulses are amplified more effectively by the medium than are their less coherent counterparts. 4- Propagation of partially coherent pulses in resonant, inhomogenously broadened nonlinear media is simulated. Stochastic pulses of different coherence levels are generated to investigate effects of initial properties of pulses on their long-term evolution. We also provide evidence of self-induced transparency phenomena and soliton formation for relatively coherent pulses. Also, evolution of the coherence functions reveal that low-coherence pulses lose their coherence level upon propagation faster than do highly coherent pulses.
The physics of slow-light propagation in atomic Lambda systems is described by the theory of integrable systems, which allows the existence of solitons. Slow-light solitons are stable polarization structures that propagate through the atomic medium at a controllable speed. They represent generalizations of the experimentally demonstrated slow-light pulses in atomic media where one light polarization dominates the other, the probe, and controls its group velocity. In the general case, the overall intensity controls the speed of the entire polarization structure. For zero detuning between light and atoms, even more general shape-preserving pulses exist. Quantum fluctuations of slow-light pulses can be stored in atomic media. In the case of solitons, these are fluctuations of the soliton parameters.