Scattering coefficients of surface plasmon polaritons impinging at oblique incidence onto one-dimensional surface relief defects

4 pages, 4 figures.-- PACS number(s): 73.20.Mf, 78.67. n, 41.20.JbWe present a theoretical analysis of surface plasmon polariton (SPP) scattering by shallow one-dimensional surface relief defects for oblique incidence, applying both surface impedance boundary conditions and Rayleigh expansion. Using this method, nontrivial angular dependences for transmission, reflection, and out-of-plane scattering are obtained. For the case of a defect with rectangular shape, we give an analytical description of the interference phenomena caused by the SPP diffraction for both a single defect (either protrusion or indentation) and a finite array of them.The authors acknowledge financial support from the INTAS YS Grant No. 05-109-5206, the European Network of Excellence Plasmo-Nano-Devices (Grant No. FP6-2002-IST- 1-507879 , the STREP “Surface Plasmon Photonics” Grant No. FP6-NMP4-CT2003-505699), and the Spanish MCyT Project No. MAT2005-06608-C02.Peer reviewe

Special issue on graphene nanophotonics

Editorial.Peer Reviewe

Observation of enhanced transmission for s-polarized light through a subwavelength slit

6 páginas, 4 figuras.-- et al.Enhanced optical transmission (EOT) through a single aperture is usually achieved by exciting surface plasmon polaritons with periodic grooves. Surface plasmon polaritons are only excited by p-polarized incident light, i.e. with the electric field perpendicular to the direction of the grooves. The present study experimentally investigates EOT for s-polarized light. A subwavelength slit surrounded on each side by periodic grooves has been fabricated in a gold film and covered by a thin dielectric layer. The excitation of s-polarized dielectric waveguide modes inside the dielectric film strongly increases the s-polarized transmission. A 25 fold increase is measured as compared to the case without the dielectric film. Transmission measurements are compared with a coupled mode method and show good qualitative agreement. Adding a waveguide can improve light transmission through subwavelength apertures, as both s and p-polarization can be efficiently transmitted.This work was funded by the European Community, project no. IST-FP6- 034506 'PLEAS'. AYN acknowledges MICINN for a Juan de la Cierva Grant.Peer reviewe

Analytical solution for the diffraction of an electromagnetic wave by a graphene grating

arXiv:1307.0310v1An analytical method for diffraction of a plane electromagnetic wave at a periodically modulated graphene sheet is presented. Both interface corrugation and a periodic change in the optical conductivity are considered. Explicit expressions for reflection, transmission, absorption and transformation coefficients in arbitrary diffraction orders are presented. The dispersion relation and decay rates for graphene plasmons of the grating are found. Simple analytical expressions for the value of the bandgap in the vicinity of the first Brillouin zone edge are derived. The optimal amplitude and wavelength, guaranteeing the best matching of the incident light with graphene plasmons are found for the conductivity grating. The analytical results are in a good agreement with first-principles numeric simulations. © 2013 IOP Publishing Ltd.Peer Reviewe

Twisted Nano-optics: Manipulating Light at the Nanoscale with Twisted Phonon Polaritonic Slabs

Recent discoveries have shown that when two layers of van der Waals (vdW) materials are superimposed with a relative twist angle between their respective in-plane principal axes, the electronic properties of the coupled system can be dramatically altered. Here, we demonstrate that a similar concept can be extended to the optics realm, particularly to propagating polaritons, hybrid light-matter interactions. To do this, we fabricate stacks composed of two twisted slabs of a polar vdW crystal (MoO3) supporting low-loss anisotropic phonon polaritons (PhPs), and image the propagation of the latter when launched by localized sources (metal antennas). Our images reveal that under a critical angle the PhPs isofrequency curve (determining the PhPs momentum at a fixed frequency) undergoes a topological transition. Remarkably, at this angle, the propagation of PhPs is strongly guided along predetermined directions (canalization regime) with no geometrical spreading (diffraction-less). These results demonstrate a new degree of freedom (twist angle) for controlling the propagation of polaritons at the nanoscale with potential for nano-imaging, (bio)-sensing, quantum applications and heat management

Twisted polaritonic crystals in thin van der Waals slabs

Polaritons - hybrid light-mater excitations - are very appealing for the confinement of light at the nanoscale. Recently, different kinds of polaritons have been observed in thin slabs of van der Waals (vdW) materials, with particular interest focused on phonon polaritons (PhPs) - lattice vibrations coupled to electromagnetic fields in the mid-infrared spectral range with - in biaxial crystals, such as e.g. MoO3. In particular, hyperbolic PhPs - having hyperbola-like shape of their isofrequency curves - in MoO3 can exhibit ultra-high momenta and strongly directional in-plane propagation, promising novel applications in imaging, sensing or thermal management at the nanoscale and in a planar geometry. However, the excitation and manipulation of in-plane hyperbolic PhPs have not yet been well studied and understood. Here we propose a technological platform for the effective excitation and control of in-plane hyperbolic PhPs based on polaritonic crystals (PCs) - lattices formed by elements separated by distances comparable to the PhPs wavelength -, twisted with respect to the natural vdW crystal axes. In particular, we develop a general analytical theory valid for an arbitrary PC made in a thin biaxial slab. As a practical example, we consider a twisted PC formed by rectangular hole arrays made in MoO3 slab and demonstrate the excitation of Bragg resonances tunable by the twisting angle. Our findings open novel avenues for both fundamental studies of PCs in vdW crystals and the development of mid-infrared sensing and photodetection application

Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition

Recent discoveries of polaritons in van der Waals (vdW) crystals with directional in-plane propagation, ultra-low losses, and broad spectral tunability have opened the door for unprecedented manipulation of the flow of light at the nanoscale. However, despite their extraordinary potential for nano-optics, these unique polaritons also present an important limitation: their directional propagation is intrinsically determined by the crystal structure of the host material, which imposes forbidden directions of propagation and hinders its control. Here, we theoretically predict and experimentally demonstrate that directional polaritons (in-plane hyperbolic phonon polaritons) in a vdW biaxial slab (alpha-phase molybdenum trioxide) can be steered along previously forbidden directions by inducing an optical topological transition, which naturally emerges when placing the slab on a substrate with a given negative permittivity (4H-SiC). Importantly, due to the low-loss nature of this topological transition, we are able to visualize in real space exotic intermediate polaritonic states between mutually orthogonal hyperbolic regimes, which permit to unveil the unique topological origin of the transition. This work provides new insights into the emergence of low-loss optical topological transitions in vdW crystals, offering a novel route to efficiently steer the flow of energy at the nanoscale

Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range-too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.We acknowledge financial support from the European Commission under the Graphene Flagship (GrapheneCore1, grant no. 696656), the ERC starting grant SPINTROS (grant no. 257654), and the Spanish Ministry of Economy and Competitiveness (National plans MAT2014-53432-C5-4-R, MAT2015-65159-R, MAT2015-65525-R, and FIS2016-80174-P). A.K. also thanks for the Czechoslovak Microscopic Society/FEI scholarship.Peer Reviewe

Extracting the infrared permittivity of SiO2 substrates locally by near-field imaging of phonon polaritons in a van der Waals crystal

Layered materials in which individual atomic layers are bonded by weak van der Waals forces (vdW materials) constitute one of the most prominent platforms for materials research. Particularly, polar vdW crystals, such as hexagonal boron nitride (h-BN), alpha-molybdenum trioxide (α-MoO3) or alpha-vanadium pentoxide (α-V2O5), have received significant attention in nano-optics, since they support phonon polaritons (PhPs)―light coupled to lattice vibrations― with strong electromagnetic confinement and low optical losses. Recently, correlative far- and near-field studies of α-MoO3 have been demonstrated as an effective strategy to accurately extract the permittivity of this material. Here, we use this accurately characterized and low-loss polaritonic material to sense its local dielectric environment, namely silica (SiO2), one of the most widespread substrates in nanotechnology. By studying the propagation of PhPs on α-MoO3 flakes with different thicknesses laying on SiO2 substrates via near-field microscopy (s-SNOM), we extract locally the infrared permittivity of SiO2. Our work reveals PhPs nanoimaging as a versatile method for the quantitative characterization of the local optical properties of dielectric substrates, crucial for understanding and predicting the response of nanomaterials and for the future scalability of integrated nanophotonic devices