Multiple Time-Scale Analysis for Non-Linear Modes in Lithium Niobate Ferroelectrics

Abstract:

A model of a ferroelectric crystal in terms of a one-dimensional array of ferroelectric slab domains is treated theoretically for the dynamics of the ‘array of domains’.  Two approaches are considered.  In a first, the system is treated within a continuum limit in which the space and time evolution of the polarization of the crystal are described by a non-linear Klein-Gordon equation.  A multiple time-scale analysis (MTSA) is used to determine the linear and non-linear parts of the frequencies and amplitudes of the extended modes of oscillation of the array of domains.  An application is also made to study these modes in the presence of impurities in inhomogeneous ferroelectric materials such as lithium niobate.  In a second approach, the discrete equations for the coupling of neighboring ferroelectric slab domains are used to study intrinsic localized modes (ILM) of the ferroelectric crystal.  These are highly localized modes that arise from self-consistent interactions with the non-linearity of the system.

Keywords: Multiple-Time Scale Analysis (MTSA), Domains in Ferroelectrics, Linear & Nonlinear Modes.

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Intrinsic Localised Modes (ILM) was shown for the first time in ferroelectric materials with our discrete Hamiltonian. In this discrete model, ILM was formed also due to nonlinearity in the Klein-Gordon lattice.

(Phys. Rev. B, Vol. 81 (2010) 064104)