A review is presented of phenomena involving thermal focusing and optical bistability arising from the temperature dependence of the refractive index in ferroelectrics. Aperiodic spatio-temporal oscillations have been observed in the light transmitted and reflected by parallel-sided crystal and ceramic samples of the thermo-optic ferroelectrics PMN (lead magnesium niobate, Pb(Mg1/3Nb2/3)O3), PLZT (lanthanum doped lead zirconium titanate, Pb(Zr1-xTix)O3:La), BNN (barium sodium niobate, Ba2NaNb5O15) and Ce:SBN (cerium doped strontium barium niobate, Ce3+:Srx Ba1-xNb2O6) under steady illumination by an incident c.w. laser beam of finite beamwidth. Such materials focus the incident beam due to the temperature dependence of the refractive index and the establishment of a radial temperature gradient. The shape of the resulting thermal lens varies in time as a result of variation in the absorbed energy arising from both thermal focusing and optical bistability (Fabry-Perot resonance). Whereas PMN and PLZT exhibit relaxation oscillations, the beam oscillations produced by BNN and Ce:SBN have equal rise and fall times. We compare the predictions of theoretical models with experimental results for ferroelectric ceramics and crystals. The principal conclusions from the present work are that (1) there are two distinct mechanisms for aperiodic oscillation in dispersively nonlinear plates, viz., focusing oscillations and Fabry-Perot switching oscillations, of which only the latter involves bistability; (2) in Fabry-Perot etalons with a diffusive nonlinearity, as contrasted with the systems (e.g. laser tubes) originally described by Gordon et al, the diffusive quantity (i.e. temperature) can exhibit bistable and multistable switching behaviour, leading to regenerative oscillations in other variables (e.g. light output); (3) there are two characteristic relaxation times involved in these oscillations, differing by several orders of magnitude; (4) the spatio-temporal characteristics of the transmitted beam patterns in the near and far fields can be quantitatively predicted and (5) comparison between theory and experiment can provide information on the temperature dependence of conductivity and thermo-optic coefficient near the ferroelectric phase transition.

https://iopscience.iop.org/article/10.1088/0953-8984/13/12/202/pdf

Thermal focusing and optical bistability in ferroelectrics

Based on the phase field simulations, effects of the surface charge screening and temperature on the vortex domain structure of the ferroelectric nanodot have been investigated. Our calculations show that the ferroelectric nanodot adopts a rhombohedral vortex domain pattern under an ideal open-circuit boundary condition. With the increase of the surface charge screening, the dipole vortex gradually rotates and appears rhombohedral-orthorhombic-tetragonal transformation. By adjusting the surface charge screening, the polar single domain and multi-vortices domain patterns with zero toroidal moment have been obtained near the phase transition temperature. More importantly, temperature and charge screening “T-C” phase diagram has been summarized, which indicates an effective method to control the vortex domain structure in the low-dimensional ferroelectric nanostructures.

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Effects of the surface charge screening and temperature on the vortex domain patterns of ferroelectric nanodots

Three fundamental problems in ferroelectricity

Effects of size and hydrostatic pressure on the formation of vortex domain structures (VDSs) in ferroelectric nanodots under the open circuit condition have been simulated using the effective Hamiltonian method. Our calculations indicate promising controllability of VDS in the nanodots. Interestingly, it is found that the VDS holds rhombohedral at various sizes and pressures. Furthermore, the paraelectric-ferrotoroidic phase transition temperature (TFD) is very sensitive to size and pressure, manifesting with near linear relationships in most investigated range. At high pressure range, we found that the TFD-pressure curves become nonlinear. It indicates that the traditional Landau potentials with polarization-strain coupling term up to ∼Pe2 are not sufficient to describe the high pressure effect and the expansion coefficients should be modified as pressure dependent.

The formation and phase transition of vortex domain structures in ferroelectric nanodots: First-principles-based simulations

A theoretical model of a nonlinear Fabry-Perot cavity for a Gaussian beam with transverse diffraction is used to simulate the static and dynamic response of optical multistability in ferroelectrics. The model is applied using material parameters of ceramic lead magnesium niobate, Pb(Mg03Nb06Ti0.09)O3, for its application as photonic sensors. The theoretical results are in good agreement with the experimental results.

Theoretical models of ferroelectric-photonic sensors

Optical bistability in ferroelectric ceramic lead magnesium niobate at room temperature was discovered recently (Chen et al., Applied Physics Letters, 60, 332, 1992) and characterized in detail as a function of laser power, sample temperature, pressure and flow rate of the ambient air (Scott and Chen, Integrated Ferroelectrics, 1, March 1992). In all these experiments the laser light was incident on the PMN sample with a very fast rise time; thus the switched thermal response of the system was isothermal, with relatively rapid relaxation to steady-state temperatures that are functions of input power. By comparison, in the present study the laser light intensity is ramped up slowly and linearly (slowly compared to the thermal relaxation time of the system, which is typically 200 ms). Under these circumstances the thermal focussing responds adiabatically, and different spatial and temporal patterns are observed. Notable is the hysteretic behavior associated with each switching event; the onset of s...

Ting Chen

Papers

Ferroelectric PMN photonic sensors: Adiabatic response