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Physical Review A

(2+1) -dimensional stable spatial Raman solitons

Miro Y. Shverdin, Deniz D. Yavuz, D. R. Walker

Published Mar 3, 2004• 18 citations
Publisher

Abstract

We analyze the formation, propagation, and interaction of stable two-frequency $(2+1)$-dimensional solitons, formed in a Raman media driven near maximum molecular coherence. The propagating light is trapped in the two transverse dimensions.

DOI
10.1103/physreva.69.031801

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•Oct 5, 2012•1 citation
We analyze the formation, propagation, and interaction of stable two-frequency (2+1)(2+1)(2+1)-dimensional solitons, formed in a Raman media driven near maximum molecular coherence. The propagating light is trapped in the two transverse dimensions.
We propose a scheme to produce stable high-dimensional spatial optical solitons and vortices in an M-type five-level active Raman gain medium at room temperature. We derive a (2+1)-dimensional [(2+1)D] nonlinear Schrödinger (NLS) equation with a 2D trapping potential, which is contributed by an assisted field. We show that by adjusting the system parameter, the signs of the Kerr nonlinearity and the external potential can be manipulated at will. We then present three types of NLS equation, provide their soliton solutions, and analyze their stabilities. We finally discuss the differences in the soliton solutions between (2+1)D and (3+1)D systems with the same 2D trapping potential.
Investigating the behavior of an atom in response to the applied electric field when the latter frequency is in resonance with the natural frequency of the atom is an interesting subject. Near resonance, some of the most interesting optical phenomena such as dispersion, and absorption are more pronounced. Moreover, considering resonant and near resonant interaction of light with two-level atoms, uncovers fascinating physical phenomena such as area theorem and self-induced transparency describing stable pulse propagation regimes in which the pulses maintain their identity. Existence of these optical structures in on-resonance optical media has not been investigated in detail. In this thesis, the on-resonance interaction of optical field with atoms is considered and the formation of several novel self-similar and kink waves in linear and nonlinear resonant media is discovered and theoretically explored. First, self-similar pulse formation in homogeneous broadened linear amplifiers in a vicinity of an optical resonance is analyzed. It is demonstrated that the self-similar pulses serve as universal asymptotics of any near resonance short pulses propagating in coherent linear amplifiers. Second, ultrashort self-similar pulse propagation in coherent linear absorbers near optical resonance is investigated. Third, existence of self-similar optical waves with kink structure in resonant optical systems is discovered. Fourth, it is found that self-induced transparency quadratic solitons are realizable in the media with quadratic optical nonlinearities, doped with resonant impurities. Finally, stable spatial similaritons supported by homogeneous conservative optical media with quintic nonlinearities are explored. To experimentally realize the presented results, physical models are presented for all systems under consideration. The stability of the proposed near resonance optical systems is demonstrated through a series of numerical case studies.