Discrete Energy Level of Bright Soliton in Lithium Niobate Ferroelectrics

Abstract:                                                                           

In the framework of a simple model of one dimensional array of ferroelectric slab of domains, the polarization with time and space is explained by Klein-Gordon equation. A perturbation of K-G equation makes it possible to use this continuum model through progressive wave nonlinear Schrodinger equation (NLSE). The latter gives rise to bright soliton that moves with certain velocity. The bright soliton controls itself so that both bright and dark solitons appear at the same time with discrete energy levels that is estimated from a hypergeometric function, but dark soliton is not visible as it is part of the complex solution that indicates absorption of energy, i.e. the presence of an energy-gap. The pulse width for switching of ferroelectrics can be estimated from the analysis of NLSE that matches with that calculated from this model.

Keyword: Bright Soliton, Discrete Energy Level, Hypergeometric Function, Ferroelectrics.

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In this work, the validity of NLSE breaks down near collapse where the assumption of small amplitude and large scale of modulation no longer holds. The effects of perturbations that can modify or even arrest the collapse are also considered. These include dissipation, normal dispersion and saturated nonlinearity. Both bright and dark solitons are the solutions of NLSE under the conditions: group velocity is higher or lower than coupling. The bright soliton moves with a velocity of 37.73 m/see and dark soliton moves with a velocity of 0.43 m/see for coupling=10. The soliton has self-energy or amplitude and this has important role in controlling bright soliton so that bright soliton has discrete energy levels. When wave packet passes through lithium niobate ferroelectrics, the dispersion will take place near the domain wall and in the absence of dispersion, the soliton will appear near the domain wall. When bright soliton passes through self-energy barrier, it splits into real and imaginary parts, i.e. bright and dark solitons respectively with discrete energy levels. It also implies a band-gap for the complex solution.

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Phys. Rev. B, Vol. 86, 184101, (2012)