Stability and asymptotic properties of a linearized hydrodynamic medium model for dispersive media in nanophotonics

We analyze the stability of a linearized hydrodynamical model describing the response of nanometric dispersive metallic materials illuminated by optical light waves that is the situation occurring in nanoplasmonics. This model corresponds to the coupling between the Maxwell system and a PDE describing the evolution of the polarization current of the electrons in the metal. We show the well posedness of the system, polynomial stability and optimal energy decay rate. We also investigate the numerical stability for a discontinuous Galerkin type approximation and several explicit time integration schemes.

Stability and asymptotic properties of a linearized hydrodynamic medium model for dispersive media in nanophotonics

International audienceWe analyze the stability of a linearized hydrodynamical model describing the response of nanometric dispersive metallic materials illuminated by optical light waves that is the situation occurring in nanoplasmonics. This model corresponds to the coupling between the Maxwell system and a PDE describing the evolution of the polarization current of the electrons in the metal. We show the well posedness of the system, polynomial stability and optimal energy decay rate. We also investigate the numerical stability for a discontinuous Galerkin type approximation and several explicit time integration schemes.

Discontinuous Galerkin Finite Element Methods for Maxwell\u27s Equations in Dispersive and Metamaterials Media

Discontinuous Galerkin Finite Element Method (DG-FEM) has been further developed in this dissertation. We give a complete proof of stability and error estimate for the DG-FEM combined with Runge Kutta which is commonly used in different fields. The proved error estimate matches those numerical results seen in technical papers. Numerical simulations of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. We propose a leap-frog discontinuous Galerkin Finite Element Method to solve the time-dependent Maxwell\u27s equations in metamaterials. The stability and error estimate are proved for this scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided. The wave propagation simulation in the double negative index metamaterials supplemented with perfectly matched layer (PML) boundary is given with one discontinuous Galerkin time difference method (DGTD), of which the stability and error estimate are proved as well in this dissertation. To illustrate the effectiveness of this DGTD, we present some numerical result tables which show the consistent convergence rate and the simulation of PML in metamaterials is tested in this dissertation as well. Also the wave propagation simulation in metamaterals by this DGTD scheme is consistent with those seen in other papers. Several techniques have appeared for solving the time-dependent Maxwell\u27s equations with periodically varying coefficients. For the first time, I apply the discontinuous Galerkin (DG) method to this homogenization problem in dispersive media. For simplicity, my focus is on obtaining a solution in two-dimensions (2D) using 2D corrector equations. my numerical results show the DG method to be both convergent and efficient. Furthermore, the solution is consistent with previous treatments and theoretical expectations

Arbitrary High Order Finite Difference Methods with Applications to Wave Propagation Modeled by Maxwell\u27s Equations

This dissertation investigates two different mathematical models based on the time-domain Maxwell\u27s equations: the Drude model for metamaterials and an equivalent Berenger\u27s perfectly matched layer (PML) model. We develop both an explicit high order finite difference scheme and a compact implicit scheme to solve both models. We develop a systematic technique to prove stability and error estimate for both schemes. Extensive numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel and provide the first error estimate for the high-order finite difference methods for Maxwell\u27s equations

Plasmonic Nanoplatforms for Biochemical Sensing and Medical Applications

Plasmonics, the science of the excitation of surface plasmon polaritons (SPP) at the metal-dielectric interface under intense beam radiation, has been studied for its immense potential for developing numerous nanophotonic devices, optical circuits and lab-on-a-chip devices. The key feature, which makes the plasmonic structures promising is the ability to support strong resonances with different behaviors and tunable localized hotspots, excitable in a wide spectral range. Therefore, the fundamental understanding of light-matter interactions at subwavelength nanostructures and use of this understanding to tailor plasmonic nanostructures with the ability to sustain high-quality tunable resonant modes are essential toward the realization of highly functional devices with a wide range of applications from sensing to switching. We investigated the excitation of various plasmonic resonance modes (i.e. Fano resonances, and toroidal moments) using both optical and terahertz (THz) plasmonic metamolecules. By designing and fabricating various nanostructures, we successfully predicted, demonstrated and analyzed the excitation of plasmonic resonances, numerically and experimentally. A simple comparison between the sensitivity and lineshape quality of various optically driven resonances reveals that nonradiative toroidal moments are exotic plasmonic modes with strong sensitivity to environmental perturbations. Employing toroidal plasmonic metasurfaces, we demonstrated ultrafast plasmonic switches and highly sensitive sensors. Focusing on the biomedical applications of toroidal moments, we developed plasmonic metamaterials for fast and cost-effective infection diagnosis using the THz range of the spectrum. We used the exotic behavior of toroidal moments for the identification of Zika-virus (ZIKV) envelope proteins as the infectious nano-agents through two protocols: 1) direct biding of targeted biomarkers to the plasmonic metasurfaces, and 2) attaching gold nanoparticles to the plasmonic metasurfaces and binding the proteins to the particles to enhance the sensitivity. This led to developing ultrasensitive THz plasmonic metasensors for detection of nanoscale and low-molecular-weight biomarkers at the picomolar range of concentration. In summary, by using high-quality and pronounced toroidal moments as sensitive resonances, we have successfully designed, fabricated and characterized novel plasmonic toroidal metamaterials for the detection of infectious biomarkers using different methods. The proposed approach allowed us to compare and analyze the binding properties, sensitivity, repeatability, and limit of detection of the metasensing device

Metamaterial

In-depth analysis of the theory, properties and description of the most potential technological applications of metamaterials for the realization of novel devices such as subwavelength lenses, invisibility cloaks, dipole and reflector antennas, high frequency telecommunications, new designs of bandpass filters, absorbers and concentrators of EM waves etc. In order to create a new devices it is necessary to know the main electrodynamical characteristics of metamaterial structures on the basis of which the device is supposed to be created. The electromagnetic wave scattering surfaces built with metamaterials are primarily based on the ability of metamaterials to control the surrounded electromagnetic fields by varying their permeability and permittivity characteristics. The book covers some solutions for microwave wavelength scales as well as exploitation of nanoscale EM wavelength such as visible specter using recent advances of nanotechnology, for instance in the field of nanowires, nanopolymers, carbon nanotubes and graphene. Metamaterial is suitable for scholars from extremely large scientific domain and therefore given to engineers, scientists, graduates and other interested professionals from photonics to nanoscience and from material science to antenna engineering as a comprehensive reference on this artificial materials of tomorrow