We present a semi-analytical model of the resonance phenomena occurring in a hybrid system made of a 1D array of periodic subwavelength slits deposited on an insulator/graphene layer. We show that the spectral response of this hybrid system can be fully explained by a simple semi-analytical model based on weak and strong couplings between two elementary sub-systems.

The Casimir force arises from the quantum fluctuations of the electromagnetic field. It leads to an attraction between electrically neutral bodies with a vacuum gap that be- comes measureable at nanoscale separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in nanomechanical devices. One remarkable property of the Casimir force is its non-trivial dependence on the shape of the in- teracting bodies. Experiments using the corrugated surface of gratings have demonstrated the deviation of the Casimir force from the proximity force approximation. In these experiments, it was necessary to choose one of the bodies to be a sphere to circumvent alignment difficulties.Here, we present measurement of the Casimir force gradient between two microfabricated silicon beams, both of which contain rectangular corrugations. One of the beams acts as the forcesensing element. As it vibrates in a perpendicular magnetic field, a back electromotive force is generated and the corresponding change in the current is measured. The force gradient exerted on this beam is measured from the resonance frequency shift. The distance to the other beam is controlled using a comb actuator integrated on the same substrate, where electrostatic forces push the second beam towards the force-sensing beam. By using lithography to define the structures, they are aligned to allow the two gratings to interpenetrate when the separation between them is reduced. Our data shows a number of novel features, including strong deviations of the force gradient from the proximity force approximation and a non-zero, distance-independent Casimir force over certain range of displacement.We will also discuss the design of a bridge to measure the difference in Casimir forces on two types of surfaces. By fabricating an additional sensing beam next to the original one and measuring their resonant frequency shifts simultaneously in the same experimental run, the difference in the Casimir force gradient of two different geometries can be compared.

Metasurfaces are planar metamaterials that consist of a single or a few stack of subwavelength thickness metal-dielectric layers. They could be periodically structured or not with subwavelength scale patterns according to the transverse directions. The strong interac- tion between an electromagnetic field components and these surfaces, exhibits some properties that could not be found in nature. These artificial properties strongly depend on the shape and arrangement of the elementary patterns and they are often linked to a plasmon resonance phe- nomenon. Metasurfaces working in the visible range generally consist in periodical arrangments of plasmonic resonators. These resonators are inherently muti-scale, as their responses relie on the excitation of resonances in very small gaps, like in the case of gap-plasmon resonators [1] or for bow-tire antennas. The simulation of their electromagnetic response can be very challeng- ing and may be successfully treated thanks to a modal method holding the complexity of the patterns shape. Here we present a polynomial modal method [2–5] that is particularly suited for the simulation of metallic structures. Advanced coordinates transformation such as matched coordinates and tilted coordinates are included in order to hold efficiently the complexity of the geometry without any approximation. Such a tool even offers the possibility to control the way the resonators are periodically arranged.

We study the radiative heat transfer between multilayer structures made by a periodic repetition of a graphene sheet and a hexagonal boron nitride (hBN) slab. Surface plasmons in a monolayer graphene can couple with hyperbolic phonon polaritons in a single hBN film to form hybrid polaritons that can assist photon tunneling. For periodic multilayer graphene/hBN structures, the stacked metallic/dielectric array can give rise to a further effective hyperbolic behavior, in addition to the intrinsic natural hyperbolic behavior of hBN. The effective hyperbolicity can en- able more hyperbolic polaritons that enhance the photon tunneling and hence the near-field heat transfer. However, the hybrid polaritons on the surface, i.e., surface plasmon-phonon polaritons, dominate the near-field heat transfer between multilayer structures when the topmost layer is graphene. The effective hyperbolic regions can be well predicted by the effective medium theory (EMT), thought EMT fails to capture the hybrid surface polaritons and results in a heat trans- fer rate much lower compared to the exact calculation. The chemical potential of the graphene sheets can be tuned through electrical gating and results in an additional modulation of the heat transfer. We found that the near-field heat transfer between multilayer structures does not increase monotonously with the number of layers in the stack, which provides a way to control the heat transfer rate by the number of graphene layers in the multilayer structure. The results may benefit the applications of near-field energy harvesting and radiative cooling based on hybrid polaritons in two-dimensional materials.

The polynomial modal method (PMM) is one of the most powerful methods for modeling diffraction from lamellar gratings. In the present work, we show that applying it to the so-called matched coordinates leads to important improvement of convergence for crossed lamellar gratings with patterns that are not parallel to the coordinates’ axes. After giving the new formulation of the PMM under matched coordinates in the general framework of biperiodic structures, we provide numerical examples to demonstrate the effectiveness of the proposed approach.

We calculate the radiative heat transfer between two metallic gratings by exploiting the Adaptive Spatial Resolution metod. This technique dramatically improves the rate of convergence allowing to explore smaller separations. The heat flux shows a remarkable amplification of the exchanged energy, due to spoof-plasmon modes. We find a consistent disagreement with some previously obtained results going up to 50% (this disagreement is explained in terms of an incorrect connection between the reflection operators of the two gratings).

The Fourier Modal Method (FMM) is used to obtain the band structure of a 1D graphene based photonic crystal. The structure consists of graphene layers periodically inlayed in a homogeneous dielectric medium. In the model, the graphene sheet is considered as layer with atomic thickness. Under these conditions, we show that it is possible to use the FMM in order to obtain a polynomial eigenvalue problem allowing the computation of the band structure.