Ferroelectric Optics:Optical Bistability in Nonlinear Kerr Ferroelectric Materials

Ferroelectric oxides with perovskite structure such as PbLaTiO3 (PLT), BaTiO3, PbTiO3, SrBi2Ta2O9 and LiNbO3 are very attractive class of materials which possess numerous useful properties such as high dielectric constant, large spontaneous polarization, and remarkable optical nonlinearity. Potential applications of these materials include real-time holography, correlation filtering and various novelty filter applications (Sutherland 1996 and Eaton 1991). They are also popular materials for the fabrication of nonvolatile memories (Ramesh 2001). Over the past few years, ferroelectric oxides have been widely investigated for various nonlinear optical applications (Shi 2006; Xuan 1998; Zhang 1999; Zhao 1996) especially for optical switches. Optical switches are devices invented to perform multiplexing at very fast speeds and with less delay than the customary switches works with electronic signals. A ferroelectric optical switch is expected to allow the processing of millions of signals at a speed of terahertz. To obtain optical bistability phenomenon, two ingredients are necessary, a nonlinear process and a feedback mechanism (Gibbs, 1977, 1979, and 1985). In all optical systems, the feedback can be “distributed”, “extrinsic” or “intrinsic”. In multilayer systems with alternating nonlinear materials, the feedback is “distributed”; it arises from the interaction of the propagating wave with many cross-sections of a nonlinear medium. In a Fabry-Perot (FP) resonator, the feedback is “extrinsic”; it arises as a result of reflection from the mirrors placed at its interface. In a single nonlinear layer, the feedback can be “intrinsic” or “mirrorless”; it arises in each elementary oscillator due to the strong local nonlinear response of an individual atom or molecule. In the usual or the standard analysis to study the optical bistability (Marburger 1978, Gupta 1987, Biran 1990, Danckaert 1989, Shen 1984, and Haelterman 1989) in nonlinear optics, the governing equation for optical propagation within the nonlinear medium is a nonlinear wave equation in the electric field derived from Maxwell’s equations. The usual constitutive relation between the nonlinear polarization and the electric field is then obtained by expanding the nonlinear polarization as a Taylor series in the electric field. The usefulness of this constitutive relation is that the polarization is a natural source term in the Maxwell’s