The Fourier Modal Method equipped with the concept of Adaptive Spatial Resolution (FMMASR) is derived and presented, in details, in the case of lamellar diffraction gratings under conical mounting. In the present work, we focus on efficiency and reduction of the numerical load.

The radiative heat transfer between two dielectrics can be strongly enhanced in the near field in the presence of surface phonon-polariton resonances. Nevertheless, the spectral mismatch between the surface modes supported by two dissimilar materials is responsible for a dramatic reduction of the radiative heat flux they exchange. In the present paper we study how the presence of a graphene sheet, deposited on the material supporting the surfacewave of lowest frequency, allows us to widely tune the radiative heat transfer, producing an amplification factor going up to one order of magnitude. By analyzing the Landauer energy transmission coefficients we demonstratethat this amplification results from the interplay between the delocalized plasmon supported by graphene and the surface polaritons of the two dielectrics. We finally show that the effect we highlight is robust with respect to the frequency mismatch, paving the way to an active tuning and amplification of near-field radiative heat transfer in different configurations.

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 withhyperbolic 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 enable more hyperbolic polaritons that enhance the photon tunneling and hence the near-fieldheat 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 effectivehyperbolic 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 transfer 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.

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.

We calculate the radiative heat transfer between two identical metallic one-dimensional lamellar gratings. To this aim we present and exploit a modification to the widely-used Fourier modal method, known as adaptive spatial resolution, based on a stretch of the coordinate associated to the periodicity of the grating. We first show that this technique dramatically improves the rate of convergence when calculating the heat flux. We then present a study of heat flux as a function of the grating height, highlighting a remarkable amplification of the exchanged energy, ascribed to the appearance of spoof-plasmon modes, whose behavior is also spectrally investigated. Differ- ently from previous works, our method allows us to explore a range of grating heights extending over several orders of magnitude. By comparing our results to recent studies we find a consis- tent quantitative disagreement with some previously obtained results going up to 50%. In some cases, this disagreement is explained in terms of an incorrect connection between the reflection operators of the two gratings.

We study the coupling between surface plasmons of a doped graphene sheet and those of a metal-like/dielectric/ metal-like plasmonic waveguide. In order to allow such a coupling, the metal-like media are chosen to be doped semiconductors with plasma energies close to the Fermi level of the doped graphene. We derive and compute numerically the full dispersion relation and study in detail the characteristics of the hybrid modes emerging from strong coupling.

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 forisolated 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.