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)
