Electromagnetic scattering by a partially graphene-coated dielectric cylinder: Efficient computation and multiple plasmonic resonances.

We present a numerical approach for the solution of electromagnetic scattering from a dielectric cylinder partially covered with graphene. It is based on a classical Fourier-Bessel expansion of the fields inside and outside the cylinder to which we apply ad hoc boundary conditions in the presence of graphene. Due to the singular nature of the electric field at the edges of the graphene sheet, we introduce auxiliary boundary conditions. The result is a particularly simple and efficient method allowing the study of diffraction from such structures. We also highlight the presence of multiple plasmonic resonances that we ascribe to the surface modes of the coated cylinder.

Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms.

We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell's equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale surface under any kind of incident excitation. In the proposed approach, a large-size surface is decomposed into square sub-cells, and a projector, linking the set of eigenvectors of the large-scale problem to those of the small-size sub-cells, is defined. This projector allows one to associate univocally the spectrum of any electromagnetic field of a problem stated on the large-size domain with its footprint on the small-scale problem eigenfunctions. This approach is suitable for parallel computing, since the spectrum of the electromagnetic field is computed on each sub-cell independently from the others. In order to demonstrate the method's ability, to simulate both near and far fields of a full three-dimensional (3D) structure, we apply it to design large area diffractive metalenses with a conventional personal computer.

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings.

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

Giant Casimir Torque between Rotated Gratings and the θ=0 Anomaly.

We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle θ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at θ=0, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only ten period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nanomechanical devices.

Strong Thermal and Electrostatic Manipulation of the Casimir Force in Graphene Multilayers.

We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage of the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also achieve the anomalous nonmonotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi level. In addition to a strong thermal modulation occurring at short separations, in a region where the force is orders of magnitude larger than the one occurring at large distances, the force can be also adjusted by varying the number of graphene layers as well as their Fermi levels, allowing for relevant force amplifications which can be tuned, very rapidly and in situ, by simply applying an electric potential. Our predictions can be relevant for both Casimir experiments and micro- or nanoelectromechanical systems and in new devices for technological applications.

Polariton condensation threshold investigation through the numerical resolution of the generalized Gross-Pitaevskii equation.

We present a numerical approach for the solution of the dissipative Gross-Pitaevskii equation coupled to the reservoir equation governing the exciton-polaritons Bose-Einstein condensation. It is based on the finite difference method applied to space variables and on the fourth order Range-Kutta algorithm applied to the time variable. Numerical tests illustrate the stability and accuracy of the proposed scheme. Then results on the behavior of the condensate under large Gaussian pumping and around the threshold are presented. We determine the threshold through the particular behavior of the self-energy and characterize it by tracking the establishment time of the steady state.

Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates implementation.

In this paper we present an extension of the modal method by Gegenbauer expansion (MMGE) [J. Opt. Soc. Am. A28, 2006 (2011)], [Progress Electromagn. Res.133, 17 (2013)] to the study of nonperiodic problems. The nonperiodicity is introduced through the perfectly matched layers (PMLs) concept, which can be introduced in an equivalent way either by a change of coordinates or by the use of a uniaxial anisotropic medium. These PMLs can generate strong irregularities of the electromagnetic fields that can significantly alter the convergence and stability of the numerical scheme. This is the case, e.g., for the famous Fourier modal method, especially when using complex stretching coordinates. In this work, it will be shown that the MMGE equipped with PMLs is a robust approach because of its natural immunity against spurious modes.

Broadband computation of the scattering coefficients of infinite arbitrary cylinders.

We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.

Fourier modal method with spatial adaptive resolution for structures comprising homogeneous layers.

A numerical improvement of the Fourier modal method with adaptive spatial resolution is obtained. It is shown that the solutions of all the eigenvalue problems corresponding to homogeneous regions can be deduced straightforwardly from the solution of one of these problems. Numerical examples demonstrate that computation time saving can be substantial.

What is the direction followed by a beam in a photonic medium?

The direction of propagation followed by a monochromatic beam in a periodic structure is generally deduced from the isofrequency diagram, which is related to the group velocity. However, the group velocity is the derivative of omega with respect to the wavenumber, while the behavior of the beam should depend on omega only. In the subwavelength regime, a method for choosing the relevant branch of the isofrequency diagram and relying on the behavior of the system at omega only is described.

An angle-independent Frequency Selective Surface in the optical range.

We suggest and numerically demonstrate a design for Frequency Selective Surfaces (FSS) operating in the optical (visible and near-infrared) range. The position and width of the FSS bandpass do not depend on the angle of incidence and polarization state of the incoming light, allowing high transmission at any angle. The FSS is formed by annular apertures perforated in a metal film and arranged in a square array. Angle- and polarization-independent transmission properties are demonstrated for silver. These results can be extended to other metals as well as to other frequency domains.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Enhanced confined light transmission by single subwavelength apertures in metallic films.

The diffraction of light that emerges from a metallic circular aperture is studied. Near- and far-field results are presented. Spectral angular transmitted intensities are performed versus the incident wavelength for four kinds of aperture. It is shown that, for a definite configuration, a large enhancement of transmission--compared with the basic case of a single hole--occurs combined with a spectacular angular confinement of light. Such effects are, for example, of great interest in optical near-field microscopy for which the probe is a nanosource.