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Ferroelectric belongs to an important class of materials showing veryinteresting nonlinear optical properties that have a variety of application inphotonic devices In a discrete Hamiltonian, if we consider the space and timedependence of polarization vectors with an interaction term between twopolarization domains, it gives rise to a nonlinear Klein-Gordon (K-G) equationthat has been shown in some systems [1]. This equation as a governing equationenables multiple time-scale analysis (MTSA) to be performed on a realferroelectric material that reveals new type of information on both linear(known as soft modes) and the nonlinear parts of frequencies and amplitudes ofoscillations. MTSA was described in a K-G system based on staggeredpolarization where more emphasis was given to reveal the presence of intrinsiclocalized modes (ILM). Here, detailed results for the first three linear modesand their frequencies as a 2 function of a wide range of niobium antisitedefects or, impurities in lithium niobate ferroelectric are presented. It isfound that when an external excitation (i.e. the input) is only harmonic innature, it could not be ascertained whether the even modes of the solitonicwaves (i.e. the output) will have phase-locking with this type of harmonicexternal force.

Non-Linear Modes in Lithium Niobate Ferroelectrics with niobium antisite defects