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The International Journal of Physics

Properties of Optical Soliton in a Three Level Medium with Quintic Nonlinearity

Preeti Agarwal, Aditi Ray, Anirban Chowdhury

Published Jan 23, 2015• 5 citations
Publisher

Abstract

Propagation characteristics of optical soliton in a three level atomic medium are analyzed by treating the material medium quantum mechanically, but the electromagnetic wave classically. Both the cubic and quintic components of the nonlinear polarization of the electromagnetic field are considered along with those generated due to the dipole formation of the material. A numerical simulation is carried out with the help of split-step technique. It is observed that the power of the pulse, distance of propagation and degree of dispersion are intimately related. The role of polarization due to the material is duely compensated by keeping higher order dispersive terms. In this connection we have seen that keeping the higher order dispersive terms, up to the eighth order, which is actually the phenomenon of continuum generation, results in a better form of the pulse. In our paper, we have analyzed the effects in both the cases, that is, including and excluding the quintic terms and in each case we have considered the effects of second-order dispersion (β2) as well as the higher order dispersion terms ( 8 2 j j β =

DOI
10.12691/ijp-3-2-1

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Propagation characteristics of optical soliton in a three level atomic medium are analyzed by treating the material medium quantum mechanically, but the electromagnetic wave classically. Both the cubic and quintic components of the nonlinear polarization of the electromagnetic field are considered along with those generated due to the dipole formation of the material. A numerical simulation is carried out with the help of split-step technique. It is observed that the power of the pulse, distance of propagation and degree of dispersion are intimately related. The role of polarization due to the material is duely compensated by keeping higher order dispersive terms. In this connection we have seen that keeping the higher order dispersive terms, up to the eighth order, which is actually the phenomenon of continuum generation, results in a better form of the pulse. In our paper, we have analyzed the effects in both the cases, that is, including and excluding the quintic terms and in each case we have considered the effects of second-order dispersion (β2) as well as the higher order dispersion terms ( 8 2 j j β =
For pt.I see ibid., vol.10, p.425 (1977). The effect of spatial dispersion or exciton formation on the steady propagation of a coherent light pulse in a dielectric medium is studied. The optical Bloch equation for a lattice of atomic dipoles coupled to one another by an exchange-type interaction is solved simultaneously with the Maxwell equation by the method of power-series expansion developed in the preceding paper. Two kinds of pulse solutions are obtained in general: one propagating by the medium of the radiation field and the other by excitation transfer between atomic dipoles. The former solution is SIT-like in the short pulse limit, but a polariton-soliton or a standing wave of non-linear polariton if the pulse width is long. The latter is an exciton-soliton containing little photon component. When the pulse width is extremely long, there appears a polariton-soliton of a new type in which the two propagation mechanisms are mixed. It is found that the spatial dispersion prevents the polariton-soliton solutions from existing in a certain frequency range. This effect is explained on the basis of the functional behavior of the dispersion relation of the non-linear polariton.
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In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
The influence of high-order effects on the stability of the optical soliton in a semiconductor three-quantum-dot molecular system under the excitation of narrow pulse probe light is analyzed analytically by using the multi-scale method. The results show that optical soliton described by the standard nonlinear Schrödinger equation will have a large attenuation in the propagation process, while the optical soliton described by the high-order nonlinear Schrödinger equation has relatively good stability. In addition, numerical simulations of the interaction between optical solitons show that the amplitudes of the two optical solitons described by the standard nonlinear Schrödinger equation attenuate rapidly after the collisions and radiation of more serious dispersion waves, while the shapes of the two optical solitons described by the high-order nonlinear Schrödinger equation hardly changes after the collision. This is mainly because when the incident probe light pulse is narrow enough, the system must be described by a higher-order equation. The physical reason is that the higher-order effects in the equation, including non-instantaneous effects and third-order dispersion effects, cannot be ignored or treated as perturbations. This kind of stable optical soliton has potential application value for future optical information processing and transmission technology.
The coherent propagation of a pair of matched pulses in a doped two-mode nonlinear dispersive waveguide is investigated, where the dopant is modeled by a V-type three-level system. Relations involving the parameters of the pulses and the propagation medium that allow us to observe the formation of coupled bright solitons are derived. The analytical result is verified by numerically solving the propagation equations together with the evolution of the three-level system. The numerical results show a stable propagation of the pair of pulses corroborating the theoretical result.
This paper investigates the stability of higher-order nonlinear optical systems using cold atomic gases. We explore the behavior of optical solitons in such systems by analyzing the Schrödinger equation (NLSE) and its third-(cubic) and fifth-order(quintic) nonlinear effects. Firstly, we solve the travelling wave solutions of bright solitons in the third-order nonlinear regime by the F-expansion method. We then consider the fifth-order nonlinear case to compare and analyze the important influence of higher-order effects on the soliton morphology and stability. Finally, we analyze the stability of bright solitons in the resulting fiber system. We find that higher-order effects play a critical role in maintaining the long-distance transport of solitons. This study definitively guides experimental studies of steady-state optical soliton teleportation in fiber-optic systems containing higher-order nonlinear interactions.