A. K. Bandyopadhyay

An approach to the Klein–Gordon equation for a dynamic study in ferroelectric materials

Ferroelectric materials such as lithium niobate and lithium tantalate show a non-linear hysteresis behaviour, which may be explained by dynamical system analysis. The behaviour of these ferroelectrics is usually explained by domains and domain wall movements. So, the spatial variation of the domain wall was studied previously in order to see its effect on the domain wall width in the context of the Landau-Ginzburg functional. In the present work, both temporal and spatial variations of polarization are considered, and by using the Euler-Lagrange dynamical equation of motion, a Klein-Gordon equation is derived by taking the ferroelectrics as a Hamiltonian system. An interaction has been considered between the nearest neighbour domains, which are stacked sideways in a parallel array with uniform polarization. This interaction term is associated with the spatial term and when this interaction is assumed to be zero, the spatial term vanishes, giving rise to a Duffing oscillator differential equation, which can be also studied by a dynamic system analysis.

Discrete breathers in nonlinear LiNbO3-type ferroelectrics

Ferroelectric materials, such as lithium niobate, show interesting nonlinear hysteresis behavior that can be explained by a dynamical system analysis by using a nonlinear Klein- Gordon equation previously constructed from the Hamiltonian with Landau-Ginzburg two-well potential. In the discrete case [Phys. Rev. B 81, 064104 (2010)], the intrinsic localized modes were shown to exist above the linear modes. Nonlinearity and discreteness of domain structures in ferroelectrics slab domains arrayed in the x-direction lead to breather solutions under different values of controlling parameters, such as interaction between the domains and damping term mainly due to pinning effect. Different types of classical breather solution, namely Hamiltonian, dissipative and moving breather solutions are shown by numerical simulation with data on actual ferroelectric materials.

Dynamical systems analysis for polarization in ferroelectrics

The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization “domain wall width” was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energy functional. In the present work, the temporal dynamics of the domains themselves are considered by taking the time variation through Euler-Lagrange dynamical equation of motion, which gives rise to a Duffing oscillator differential equation as a governing equation. From this nonlinear Duffing oscillator equation, three cases are studied theoretically: First, with no electric field with and without any damping; secondly, taking the external field as static with damping; and finally, taking an oscillatory electric field with damping. After giving perturbation at the coercive field, the eigenvalues deduced through a ...

Quantum pinning-transition due to charge defects in ferroelectrics

We investigate the pinning of domain walls in ferroelectrics on the basis of the two phonon bound state (TPBS) or discrete breather state due to impurity energy levels above the phonon continua in ferroelectrics such as LiNbO3 in order to show the pinning transition, which indicates the point of easiest switching. We predict, with the help of our quantum calculations, that every ferroelectric material has such a critical point of easy switching. Here we describe the quantum origin of pinning through the findings of analytical and numerical calculations, as interpreted by a TPBS concept by such impurity or nonlinearity induced modes, by plotting various TPBS parameters against the Landau coefficient and percent impurity content. This new approach might lead to many interesting applications for device manufacturing.

Quantum breathers in Klein-Gordon lattice: Non-periodic boundary condition approach

The presence of classical breathers and two-phonon bound state (TPBS) or quantum breather (QB) state through detailed quantum calculations have already been shown in technologically important ferroelectric materials, such as lithium niobate with antisite niobium charge defects concerning pinning transition, its control, and application. The latter was done in a periodic boundary condition with Bloch function in terms of significant variations of TPBS parameters against impurity, which is related to nonlinearity. In further extension of this work, in a non-periodic boundary condition and number-conserving approach, apart from various techniques available, only the temporal evolution of the number of quanta (i.e., phonons) in more sites is detailed in this present investigation for a generalized Klein-Gordon system with applications in ferroelectrics, metamaterials, and DNA. The critical time of redistribution of quanta that is proportional to the QB’s lifetime in these materials shows different types of be...

Fano resonance due to discrete breather in nonlinear Klein–Gordon lattice in metamaterials

The richer variety of Klein–Gordon basis is already established for discrete breathers in metamatetrials. Based on this attempt, we show various anomalous Fano resonance behaviors that have been experimentally observed, but cannot be explained by nonlinear Schrodinger model. Certain material parameters of Klein–Gordon lattice in metamaterials are related for the first time with characteristics of Fano resonance, which can be utilized for beam filtering and for high-resolution biological sensing technology. Although relations with coupling and other parameters exist, the most remarkable relation is observed with linear permittivity that could control the wave transmission characteristics in metamaterials for applications in optical engineering.

Role of coupling of discrete breathers in split-ring-resonator-based metamaterials

Through detailed quantum calculations, the presence of classical discrete breathers and, subsequently, a two-phonon bound state (TPBS) or quantum breather (QB) state have already been shown in nonlinear photonic materials such as ferroelectrics. The latter was done in a periodic boundary condition in terms of the variations of TPBS parameters against impurity that is related to nonlinearity. Metamaterials are also nonlinear optical materials for applications as a split-ring-resonator (SRR) in antenna arrays. By using a Klein–Gordon approach, first multi-solitons and classical breathers are shown. For QBs, by using a periodic boundary condition, the variation of the TPBS parameters with coupling within the SRR elements is observed. Finally, in a non-periodic boundary condition approach, the temporal evolution of the number of quanta is shown eventually in order to derive the critical time of redistribution of quanta that is proportional to the QBs lifetime in femtoseconds, which also shows variation with coupling in the SRR system.

Bound to unbound state route and propagation of dark solitons showing acoustical memory

The dark and bright solitons in different systems are already known. If the intrinsic field is only considered, then the modal dynamics for small oscillations could be characterized by the bound state in a limited range of frequency, revealed via associated Legendre polynomial. The pairing and interplay between the dark and bright solitons occur. The disappearance of the bound state after a critical frequency gives rise to dark solitons in the unbound states that propagate through the domains. Above the upper boundary of the bound states, the estimated frequencies of dark solitons match with those experimentally found for ‘acoustical memory’.

Quantum Breathers in Nonlinear Metamaterials

The goal of this paper is to explore whether SRR system, through engineering of their geometry (i.e. change of coupling) and permittivity, shows any sensitivity on the femtosecond response of quantum breathers by quantum calculations hitherto not done in metamaterials. This study is quite realistic to understand quantum localization by nonlinearity that is essential for many small-structured nano-devices. Therefore, this study should be viewed as working towards understanding of many nano structured devices.

Quantum breathers in lithium tantalate ferroelectrics

Lithium tantalate is technologically one of the most important ferroelectric materials with a low poling field that has several applications in the field of photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the polarization behavior of such ferroelectrics can be well-modeled by Klein–Gordon (K-G) equation. Due to strong localization coupled with discreteness in a nonlinear K-G lattice, there is a formation of breathers and multi-breathers that manifest in the localization peaks across the domains in polarization–space–time plot. Due to the presence of nonlinearity and also impurities (as antisite tantalum defects) in the structure, dissipative effects are observed and hence dissipative breathers are studied here. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition. The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite tantalum defects in the system, i.e., a point of easier switching within the limited amount of data on poling field, which is related to Landau coefficient (read, nonlinearity). Secondly, in a non-periodic boundary condition, the temporal evolution of quanta shows interesting behavior in terms of ‘critical’ time of redistribution of quanta that is proportional to QB’s lifetime in femtosecond having a possibility for THz applications. Hence, the importance of both the methods for characterizing quantum breathers is shown in these perspectives.