Time-dependent Permittivity Research Articles

Electronic-Based Model of the Optical Nonlinearity of Low-Electron-Density Drude Materials

Low-electron-density Drude (LEDD) materials such as indium tin oxide (ITO) are receiving considerable attention for their combination of CMOS compatibility, unique epsilon-near-zero (ENZ) behavior, and giant ultrafast nonlinear thermo-optic response. However, current understanding of the electronic and optical response of LEDD materials is limited due to the simplistic modeling that extends only the known models of noble metals without considering the interplay among the lower electron density, relatively high Debye energy, and the nonparabolic band structure. We bridge this knowledge gap and provide a complete understanding of the nonlinear electronic-thermal-optical response of LEDD materials. In particular, we rely on state-of-the-art electron dynamics modeling, as well as a time-dependent permittivity model for LEDD materials under optical pumping within the adiabatic approximation. We find the electron temperature may reach values much higher than realized before, even exceeding the Fermi temperature, in which case the effective chemical potential dramatically decreases and even becomes negative, thus, transient giving the material some characteristics of a semiconductor. We further show that the nonlinear optical response of LEDD materials originating from the changes to the real part of the permittivity is associated with changes of the population. This resolves the argument about the rise time of the permittivity, showing that it is instantaneous. In this vein, we show that referring to the LEDD permittivity as having a Kerr or ``saturable'' nonlinearity is unsuitable since its permittivity dynamics is absorptive rather than nonresonant and does not originate from population inversion. Finally, we analyze the probe-pulse dynamics and unlike previous work, we obtain a quantitative agreement with the results of recent experiments.

Antireflection temporal coatings

It is known that complete transmission of waves through the interface between two different media can be achieved by proper impedance matching between them. One of the most common techniques for such reflectionless propagation is the quarter-wave impedance transformer, where an additional slab of material with proper material parameters and carefully engineered dimensions is added between the two media, minimizing reflections. Metamaterials, with properly designed spatial inhomogeneity, have exhibited unprecedented ability to tailor and manipulate waves, and recently temporal metamaterials have also gained much attention, enabling spatiotemporal control of wave propagation. Here a temporal analogue of the quarter-wave impedance transformer technique, which we name “antireflection temporal coating,” is proposed using time-dependent materials. The proposed technique is demonstrated, analytically and numerically, using metamaterials with a time-dependent permittivity. Comparison with the conventional (spatial) impedance-matching technique is shown, demonstrating that both impedance matching and frequency conversion are achieved with our proposed temporal version. As an illustrative example, the present technique is also applied to match two waveguides with different cross sections, demonstrating an example of scenarios where it may be applied.

Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling

This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.

Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell׳s equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light–matter interaction in time-varying structures.

Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects.

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.

On the electrodynamics in time-dependent linear media

In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to an additional term in the Ampere-Maxwell equation and an asymmetry between the electric and magnetic field wave equations. As special cases we consider a linear and an exponential growth of the permittivity, as well as a sinusoidal time-dependent permittivity.

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Time-domain electromagnetic modelling of complex structures which include both non-dispersive media and media exhibiting electromagnetically induced transparency (EIT) require a general, robust calculation method such as finite-difference time-domain (FDTD). We propose a complex-valued, exact two-pole representation of the permittivity of a three-level system which is suitable for integration into the FDTD algorithm via the auxiliary differential equation method. Our calculation model confirmed reported results which were calculated with an approximate representation of the EIT permittivity. Additionally, propagation calculations which mimic slow light experiments were performed. A major advantage of our representation is the ease with which changes in the control field Rabi frequency can be implemented by using a time-dependent permittivity.

Dielectric characterization and conduction modelling of a water tree degraded LDPE

Distribution of electric energy by extruded polymer insulated cables continues to be a subject of outstanding relevance in modern industrialized countries all over the world. Dielectric characterization, conduction modelling and finally diagnostics of polymeric insulations are necessary steps towards the development of reliable and less expensive robust technologies of electric power distribution. This paper is devoted to a detailed experimental/theoretical study of the conductive properties of LDPE affected by different levels of degradation by water trees. Water tree layers of different lengths were grown in accelerated conditions and were characterized by water tree kinetics, time-dependent permittivity and polarization current. The polarization current was found to obey a Curie-von Schweidler law whose parameters were used to characterize the effect of ageing time. A new conduction model that takes into account dipole interactions and was obtained from a two-wells Debye model is presented which allows us to give an interpretation of the effect of ageing. This laboratory study was intended to improve the characterization of service power cables aged by water trees

Reflection from 1D quasi-periodical structures

A theoretical investigation of 1D stationary and transient quasi-periodical dielectric structures is presented. A new approach for solving the problem of field interaction with such structures common for both stationary and transient cases, based on integral equations for the fields in transient media, is proposed. Some special cases of quasi-periodical structures with doubled quasi-periodicity are investigated numerically, showing that an additional complexity of the structure allows to obtain good filtering properties with a small number of quasi-periods. Transient structures with the same spatial dependencies, but with a time-dependent permittivity were also investigated.

Transient Processes in a Resonator Filled with a Medium with Time-Dependent Permittivity and Permeability

Transient Processes in a Resonator Filled with a Medium with Time-Dependent Permittivity and Permeability