Metamaterials are mostly studied using the time-harmonic approach, where the wave propagation is spatially described. Recently, studies of media having electromagnetic properties that change in time have been given the attention of the scientific community, aiming to describe wave-matter interaction in both space and time. In the present paper, we use the space-harmonic method for the general description of wave propagation in time. Such a method can be used to effectively describe a "temporal multilayered" (or temporal multi-stepped) metamaterial by alternating the effective material parameters of the medium in time between two values. We obtain the exact analytical solution for the fields in two examples of temporally periodic metamaterials. Numerical simulations for the impedance-matched scenario are also carried out, showing an excellent agreement when compared to the exact analytical field. Our results also demonstrate the duality between the descriptions of the temporally periodic metamaterial and its spatial counterpart, spatially periodic metamaterials.

We study TE-wave propagation in a circular waveguide with a graded transition from a lossy right-handed material (RHM) filling the left-hand half of the waveguide to the impedance-matched lossy left-handed material (LHM) filling the right-hand half of the waveguide. We obtain exact analytical solutions to Maxwell's equations and perform corresponding numerical simulations in COMSOL. An excellent agreement is obtained between the numerical simulations and analytical results. The presented method can model smooth realistic material transitions, where the interface width is an additional degree of freedom in the design of practical RHM-LHM interfaces.

A theoretical study of TE-wave propagation in a hollow circular waveguide with a graded dielectric medium is presented. The medium is modeled using a squared cosine function that oscillates between two unique complex dielectric media to simulate a periodic multilayer structure. The proposed model is applicable to arbitrary complex permittivities of the two media, including negative values for chiral metamaterials. The exact analytical result for the longitudinal magnetic field component H-z is obtained, while the transverse electric and magnetic field components could be determined using the appropriate Maxwell's equations.

We present a parametric analysis of the absorption cross-section of small ellipsoidal composite structures (particles) with gold nanoparticles (GNP) embedded in lossy human tissue. The optimal permittivity of the ellipsoidal particle that maximizes the absorption at any given frequency, derived in our previous work with the surrounding tissue as a saline water, is used. We present new results for realistic tissue material parameters and for different GNP-host media and surrounding media. Present results are useful to assess the feasibility of the proposed radiotherapeutic hyperthermia-based methods to treat cancer, based on electrophoretic heating of gold nanoparticle suspensions using microwave radiation, as well as to improve the general understanding of plasmonic resonances in lossy media.

In recent years, several researchers and research groups have proposed and studied a novel method of using gold nanoparticles (AuNPs) for radio frequency (RF) hyperthermia treatment of cancer. Such a method is occasionally described as a very promising new method for cancer treatment, without the side effects that are typical for other radiation treatments. It is well established that optical heating of AuNPs is caused by localized surface plasmon resonances. However, the physical mechanism behind RF heating of AuNP-fed biological tissue is a subject of some controversy. It is believed that the applied RF radiation drives the AuNPs into resonant oscillation, leading to relatively high dielectric losses, such that Joule and inductive heating is found to be negligible. In the present paper, we therefore perform an in-depth investigation of the parameter ranges and limitations that exist for the proposed methods of using AuNPs for RF hyperthermia treatment of cancer. Thereby, we show that a number of claims made so far about the potential of the proposed method are uncertain, and require further quantitative investigation.

In this paper, we perform analytical and numerical studies of TEM-wave propagation in an elliptic coaxial waveguide filled with a graded inhomogeneous RHM-LHM composite. Within the composite, the real parts of the effective permittivity and permeability vary along the propagation direction (chosen to be the z-direction) according to a hyperbolic tangent function. The present model introduces the transition width as an additional degree of freedom in the graded metamaterial composite design, which allows for tailoring of the electromagnetic wave propagation. An excellent agreement is obtained between the analytical results and numerical results obtained using the COMSOL Multiphysics software.

We study TEM-wave propagation inside a hollow coaxial waveguide filled with a periodic composite of lossy impedance-matched right-handed (RHM) and left-handed (LHM) media. The z-direction, chosen as the direction perpendicular to the boundaries between the two media, is where the transitions and TEM-wave propagation take place. The relative permittivity epsilon(omega, z) and permeability mu(omega, z) of the periodic RHM-LHM composite vary according to an arbitrary periodic function f(z) along the z-direction. In particular, we consider two specific periodic permittivity and permeability profiles: one with abrupt RHM-LHM transitions and one with linear RHM-LHM transitions. The expected properties of impedance-matched periodic RHM-LHM structures are confirmed by the derived precise analytical solutions to Maxwell's equations, which also include solutions for the wave behavior and field components. Furthermore, a numerical study of the wave propagation over the impedance-matched graded RHM-LHM composites is performed using the COMSOL Multiphysics software. The resulting numerical simulations and analytical results were virtually identical. The present method can model smooth, realistic material transitions and includes the abrupt transition as a limiting case.

This paper presents analytical and numerical studies of electromagnetic wave propagation through an interface between a regular right-handed material (RHM) and a left-handed metamaterial (LHM). The interface is graded along the direction perpendicular to the boundary plane between the two materials, chosen to be the x-direction. The permittivity epsilon(omega, x) and permeability mu(omega, x) are chosen to vary according to hyperbolic tangent functions. We show that the field intensities for both TE-and TM-cases satisfy the same differential equations, and we obtain remarkably simple exact analytical solutions to Helmholtz' equations for lossy media. The obtained exact analytical results for the field intensities along the graded RHM-LHM composite confirm all the expected properties of RHM-LHM structures. Finally, we perform a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using the software COMSOL Multiphysics, and obtain an excellent agreement between the numerical simulations and analytical results. The results obtained in the present paper are not limited to any particular application, and are generally useful for all cases of wave propagation over impedance-matched two-and three-dimensional interfaces between RHM and LHM media. The advantage of the present method is that it can model smooth realistic material transitions, while at the same time including the abrupt transition as a limiting case. Furthermore, unlike previously existing solutions, the interface width is included as a parameter in the analytical solutions in a very simple way. This enables the use of the interface width as an additional degree of freedom in the design of practical RHM-LHM interfaces.

In this paper, we study TEM-wave propagation inside a hollow coaxial waveguide filled with an inhomogeneous metamaterial composite, with a graded transition between a right-handed material (RHM) and an impedance-matched left-handed material (LHM). The graded transition and the TEM-wave propagation occur in the direction perpendicular to the boundary between the two media, which has been chosen to be the z-direction. The relative permittivity epsilon(omega, z) and permeability mu(omega, z) of the RHM-LHM composite vary according to hyperbolic tangent functions along the z-direction. The exact analytical solutions to Maxwell's equations are derived, and the solutions for the field components and wave behavior confirm the expected properties of impedance-matched RHM-LHM structures. Furthermore, a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using the COMSOL Multiphysics software, is performed. An excellent agreement between the analytical results and numerical simulations is obtained, with a relative error of less than 0.1%. The present method has the ability to model smooth realistic material transitions, and includes the abrupt transition as a limiting case. Finally, the RHM-LHM interface width is included as a parameter in the analytical and numerical solutions, allowing for an additional degree of freedom in the design of practical devices using RHM-LHM composites. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

We study TEM-wave propagation in a parallel plate waveguide with a graded transition between a lossy right-handed material (RHM) and an impedance-matched lossy left-handed material (LHM). The transition between the two media is graded along the direction perpendicular to the boundary between the two materials, and the permittivity and permeability vary according to hyperbolic tangent functions. We obtain exact analytical solutions to Maxwell's equations for lossy media, and the solutions for the field components confirm the expected properties of RHM-LHM structures. Finally, we perform a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using COMSOL, and obtain an excellent agreement between the numerical simulations and analytical results.