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International Conference on Optoelectronic Information and Functional Materials (OIFM)

Analytical study of higher-order nonlinear effects on the steady-state optical solitons in optical fiber filled with cold atomic gases

HUIPING OU, Ying Wang, Mitra Ghergherehchi, C. H. Raymond Ooi

Published Aug 19, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3072687

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We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.
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.
We present a systematic study on the dynamics of a ultraslow optical soliton in a cold, highly resonant three-state atomic system under Raman excitation. Using a method of multiple scales we derive a modified nonlinear Schrödinger equation with high-order corrections that describe effects of linear and differential absorption, nonlinear dispersion, delay response of nonlinear refractive index, diffraction, and third-order dispersion. Taking these effects as perturbations we investigate in detail the evolution of the ultraslow optical soliton using a standard soliton perturbation theory. We show that due to these high-order corrections the ultraslow optical soliton undergoes deformation, change of propagating velocity, and shift of oscillating frequency. In addition, a small radiation superposed by dispersive waves is also generated from the soliton. The results of the present work may provide a guidance that is useful for experimental demonstration of ultraslow optical soliton in cold atomic systems.
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 =
We investigate dark-bright vector solitary wave solutions to the coupled nonlinear Schrödinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in nonlinear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effect of controllably different interparticle scattering lengths is examined, and stability against three-dimensional deformations is considered.
We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.