Optical bistability in nonlinear kerr dielectric and ferroelectric materials
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Date
2009
Authors
Abdel-Hamid Ibrahim, Abdel-Baset Mohamed Elnabawi
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Abstract
The optical bistability (OB) and multistability in Kerr nonlinear crystals are investigated. Two types of ionic insulating crystals are considered: a typical dielectric and a ferroelectric (FE). Both extrinsic and intrinsic optical instabilities are investigated. An alternative analysis is used to model the OB; rather than the conventional analysis where the nonlinear polarization is usually expanded as the Taylor series in the electric field. The alternative formalism proves to be more suitable for highly nonlinear materials such as FE and for resonant-nonlinearities. The OB has its manifestation in various physical variables such as polarization, reflectance and transmittance coefficients. The effects of system thickness, operating frequency, damping parameter, and nonlinearity coefficient, on the OB of each crystal system are investigated.
The Duffing equation describing an anharmonic oscillator and the wave equation are used to model the nonlinear response of the material. Application of standard boundary conditions leads to analytical expressions for both reflectance and transmittance expressed in terms of the electric field incident amplitude, polarization and other material parameters. Numerical simulations show that the OB is dependent on the material thickness, nonlinear coefficient, and the angle of incidence. In the case of a dielectric Fabry-Pérot resonator, the OB is also found to be mirror reflectivity dependent.
For FE material, the nonlinear response is modeled using the Landau-Khalatnikov (LK) dynamical equation. The nonlinear anharmonic potential is obtained from the Landau-Devonshire (LD) free energy expressed in terms of polarization. The LK equation and the wave equation are then used to produce a nonlinear polarization equation. This technique makes the OB becomes temperature-dependent. Input parameters from available experimental data of a BaTiO3 single crystal are used in the numerical simulations. The simulation results agree in principle with the recent experimental observations of intrinsic OB in BaTiO3 monocrystal and other FE photorefractive materials. It is found that FE always exhibits a threshold-type of bistability.
The last part of this work is devoted to studies of dielectric susceptibilities of bulk FE materials in the vicinity of the morphotropic phase boundary (MPB). It includes studies on linear and nonlinear (second-order and third-order) susceptibilities for both the dynamic and static limit. The behaviour of the susceptibilities near the MPB is investigated using the LD free energy and LK dynamical equation. The susceptibility magnitudes are plotted as a function of the material parameter*21βββ= where 1βand 2βare the coefficients in the LD free energy expression. In the static limit, the MPB is represented by. In this limit, the linear dielectric constant, the second third-order nonlinear susceptibilities diverge at the MPB. The dynamic dielectric susceptibility assumes a resonance-like peak(s) or peaks at certain value(s) of *1β=*β. The enhancement is explained using the concept of FE soft-mode. The enhancement of the nonlinear susceptibility may have its potential in engineering new materials for various optical device applications.
Description
PhD
Keywords
Science Physic , Optical bistability , Nonlinear kerr dielectric , Ferroelectric