Ferroelectric
belongs to an important class of materials showing very interesting non-linear
optical properties that have a variety of application in photonic devices In a
discrete Hamiltonian, if we consider the space and time dependence of
polarization vectors with an interaction term between two polarization domains,
it gives rise to a nonlinear Klein-Gordon (K-G) equation that has been shown in
some systems [Phys. Rev. B 86,
184101 (2012), and Phys.
Rev.-B 81, 064104 (2010)]. This
equation as a governing equation enables multiple time-scale analysis (MTSA) to
be performed on a real ferroelectric material that reveals new type of
information on both linear (known as soft modes) and the nonlinear parts of
frequencies and amplitudes of oscillations. MTSA was described in a K-G system
based on staggered polarization where more emphasis was given to reveal the
presence of intrinsic localized modes (ILM). Here, detailed results for the
first three linear modes and their frequencies as a function of a wide range of
niobium antisite defects or, impurities in lithium niobate ferroelectric are
presented. It is found that when an external excitation (i.e. the input) is only harmonic
in nature, it could not be ascertained whether the even modes of the solitonic
waves (i.e. the output) will have phase-locking with this type of harmonic
external force.
The paper is organized as follows: In Section II, a brief description of the MTSA technique is given, in
both linear and nonlinear forms, and at the end of this section three cases are
presented for electric field and damping. In Section III, the results and discussion are given for linear modes
and frequencies that are shown to depend on impurity content of lithium niobate
as well as on upper limit of domain wall width. In Section III, the nonlinear modes, their frequencies and amplitudes
are also shown. In Section IV, the
conclusions are given.
A Bhattacharya, K Choudhary, S
Das , L Vu-Quoc, and A K Bandyopadhyay - arXiv preprint arXiv: …,
2016
