Analysis of electromagnetic scattering from array of time-modulated graphene ribbons.

An accurate and fast method is presented for the analysis of scattering of electromagnetic waves from an array of time-modulated graphene ribbons. We derive a time-domain integral equation for induced surface currents under subwavelength approximation. Using the method of harmonic balance, this equation is solved for a sinusoidal modulation. The solution of the integral equation is then used to obtain the transmission and reflection coefficients of time-modulated graphene ribbon array. The accuracy of the method was verified through comparison with results of full-wave simulations. In contrast with previously reported analysis techniques, our method is extremely fast and can analyze structures with a much higher modulation frequency. The proposed method also provides interesting physical insights useful for designing novel applications and opens up new vistas in the fast design of time-modulated graphene-based devices.

Investigating non-reciprocity in time-periodic media using a perturbative approach.

Lorentz famous theorem leads to clear reciprocity conditions for linear, time-invariant media based on their constitutive parameters. By contrast, reciprocity conditions for linear time-varying media are not fully explored. In this paper, we investigate whether, and how a structure containing a time-periodic medium can be truly identified as reciprocal or not. To that end, a necessary and sufficient condition is derived which requires both the constitutive parameters and the electromagnetic fields inside the dynamic structure. As solving for the fields for such problems is challenging, a perturbative approach is proposed which expresses the aforementioned non-reciprocity condition in terms of the electromagnetic fields and the Green's functions of the unperturbed static problem and is particularly applicable for the case of structures with weak time modulation. Reciprocity of two famous canonical time-varying structures are then studied using the proposed approach and their reciprocity/non-reciprocity is investigated. In the case of one-dimensional propagation in a static medium with two point-wise modulations, our proposed theory clearly explains the often observed maximization of non-reciprocity when the modulation phase difference between the two points is 90 degrees. In order to validate the perturbative approach, analytical and Finite-Difference Time-Domain (FDTD) methods are employed. Then, solutions are compared and considerable agreement between them is observed.

Analytical method for diffraction analysis and design of perfect-electric-conductor backed graphene ribbon metagratings.

Graphene-based gratings and metagratings have attracted great interest in the last few years because they could realize various multi-functional beam manipulation, such as beam splitting, focusing, and anomalous reflection in the terahertz (THz) regime. However, most of graphene-based metagratings are designed through numerical simulations, which are very time-consuming. In this paper, an accurate analytical method is proposed for diffraction analysis of a perfect electric conductor (PEC)-backed array of graphene ribbons. In contrast to previous analytical treatments, the proposed method can predict the electromagnetic performance of graphene ribbons not only in the subwavelength regime, but also for wavelengths shorter than the array constant. Results are obtained by first deriving the surface current density induced on graphene ribbons by an obliquely incident transverse-magnetic (TM) polarized plane wave. Closed-form expressions for reflection coefficients of diffracted orders are then obtained using the surface current distribution. We validate the proposed method through comparison with full-wave simulation results. Finally, a tunable beam splitter and a tunable retroreflector in the THz regime are designed using the method proposed. The designed structures have good power efficiency (80% for beam splitter and 90% for retroreflector). Moreover, their operating frequency and angle may be controlled by changing the bias voltage of graphene ribbons. The proposed method paves the path for analytical design of tunable metagratings with widespread potential for THz and optical beam-manipulation applications.

Spin-polarized unidirectional cylindrical waveguide in bianisotropic media.

In this paper, we analyze a cylindrical waveguide consisting of two layers of bianisotropic material with anti-symmetric magnetoelectric coupling tensors. The analysis is carried out in terms of pseudo-electric and pseudo-magnetic fields which satisfy Maxwells' equations with gyrotropic permittivity and permeability tensors. We show that the rotationally symmetric modes of the waveguide are unidirectional with transverse pseudo-electric and transverse pseudo-magnetic modes propagating in opposite directions. These modes are surface waves whose electromagnetic field is concentrated near the interface between the two anisotropic materials. They follow the contour of the interface even in the case of sharp discontinuities and pass through an obstacle without backscattering if the obstacle does not change the polarization of the wave. Higher-order modes of the waveguide are also investigated. Although these modes are hybrid modes and not, strictly speaking, unidirectional, they practically behave as the rotationally symmetric mode.

Frequency conversion and parametric amplification using a virtually rotating metasurface.

We analyze the scattering of circularly polarized electromagnetic waves from a time-varying metasurface having a time-dependent surface susceptibility that locally mimics a rotating, anisotropic surface. Such virtually rotating metasurfaces (VRM) can be realized by means of electronically tunable surface elements and reach microwave-range rotation frequencies. It is shown that the scattered field contains the incident tone, as well as a single up-or down converted tone which differs by twice the rotation frequency of the surface. A simple full frequency converter is then proposed by augmenting the VRM with a metal screen separated by a proper distance. It is shown that after reflection from this system, the incident tone is fully converted to a single down- or up-converted tone, and shows amplification in the case of up conversion. The analysis of these time-rotating scenarios is carried out by switching to a rotating frame for the fields, leading to time-invariant equations, and thus using common phasor-representation. All results are also validated against an in-house 1D-FDTD code showing excellent agreement. A lumped element model using a 2D periodic metal mesh grid loaded with time-varying capacitive nodes is also presented that enables the VRM concept. This model is then further used to design a 3D realization, verified with static full-wave simulations for different values of the capacitor arrangement. Furthermore, the effect of piece-wise constant changes of surface susceptibility in a general virtually rotating metasurface is studied and it is shown to operate with acceptable results, which is of practical importance. The results of this paper can open new ways for realization of frequency conversion and amplification, in a magnetless and linear time-varying system.

Analytical and rigorous method for analysis of an array of magnetically-biased graphene ribbons.

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to an incident plane wave, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict resonant spectral effects that cannot be accounted for by existing semi-analytical methods. Finally, we extract an analytical, closed form solution for the Faraday rotation of magnetically-biased graphene ribbons. In contrast to previous studies, this paper presents a fast, precise and reliable technique for analyzing magnetically-biased array of graphene ribbons, which are one of the most popular graphene-based structures.

Propagation and refraction of left-handed plasmons on a semiconducting substrate covered by graphene.

We show that a plasmonic semiconductor substrate can support highly confined surface plasmons when it is covered by a graphene layer. This occurs when the imaginary part of graphene conductivity and real part of the effective permittivity of the surrounding medium become simultaneously negative. Full-wave electromagnetic simulations demonstrate the occurrence of negative refraction and two-dimensional lensing at the interface separating regions supporting conventional right-handed graphene plasmons and left-handed surface plasmon polaritons.