Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing anomalous reflection and refraction for all polarizations of incident light.

Generalized laws of reflection and refraction from transformation optics

Optical edge detection is a useful method for characterizing boundaries, which is also in the forefront of image processing for object detection. As the field of metamaterials and metasurface is growing fast in an effort to miniaturize optical devices at unprecedented scales, experimental realization of optical edge detection with metamaterials remains a challenge and lags behind theoretical proposals. Here, we propose a mechanism of edge detection based on a Pancharatnam-Berry-phase metasurface. We experimentally demonstrated broadband edge detection using designed dielectric metasurfaces with high optical efficiency. The metasurfaces were fabricated by scanning a focused laser beam inside glass substrate and can be easily integrated with traditional optical components. The proposed edge-detection mechanism may find important applications in image processing, high-contrast microscopy, and real-time object detection on compact optical platforms such as mobile phones and smart cameras.

https://www.pnas.org/content/pnas/116/23/11137.full.pdf

Optical edge detection based on high-efficiency dielectric metasurface

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing1, topological protection2,3 and dipole-forbidden absorption4. A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes5. Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications.The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

Fundamental Limits to graphene plasmonics

Two-dimensional graphene monolayers and bilayers exhibit fascinating electrical transport behaviors. Using infrared spectroscopy, we find that they also have strong interband transitions and that their optical transitions can be substantially modified through electrical gating, much like electrical transport in field-effect transistors. This gate dependence of interband transitions adds a valuable dimension for optically probing graphene band structure. For a graphene monolayer, it yields directly the linear band dispersion of Dirac fermions, whereas in a bilayer, it reveals a dominating van Hove singularity arising from interlayer coupling. The strong and layer-dependent optical transitions of graphene and the tunability by simple electrical gating hold promise for new applications in infrared optics and optoelectronics.

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Gate-Variable Optical Transitions in Graphene

Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorial-field computation and perform edge detection for ultra-fast and energy-efficient image processing.

Generalized spatial differentiation from spin Hall effect of light

In this letter, a new approach to perform edge detection is presented using an all-dielectric complimentary metal–oxide–semiconductor-compatible metasurface. Our design is based on the guided-mode resonance, which provides a high quality factor resonance to make the edge detection experimentally realizable. The proposed structure is easy to fabricate, and it can be exploited for detection of edges in two dimensions due to its symmetry. In addition, a tradeoff between gain and the resolution of edge detection is discussed, which can be adjusted using appropriate design parameters. The proposed edge detector potentially can be used in ultrafast analog computing and image processing.

Two-Dimensional Edge Detection by Guided Mode Resonant Metasurface

In this paper, we extract the fundamental resonant mode of a graphene patch using a variational method. We use 2-D eigenvalue problem obtained from the integral equation governing the surface current on graphene patterns under quasi-static approximation. To compute the eigenvalues, we propose three trial eigenfunctions, which meet the boundary conditions. We investigate the accuracy of these eigenfunctions with comparing to the results obtained by full wave simulations. Finally, we analyze square-lattice arrangements of graphene patches using the most accurate proposed eigenfunction and derive a very accurate surface impedance for it. The proposed surface impedance is much more precise than the surface impedance already reported by Padooru et al. for this structure.

Deriving Surface Impedance for 2-D Arrays of Graphene Patches Using a Variational Method

We propose a novel graphene-dielectric-based metasurface for manipulating the polarization of the incident light in the terahertz regime. The proposed structure comprised two orthogonally oriented periodic array of graphene ribbons (PAGRs) which are separated by a dielectric spacer and deposited on an Au-backed dielectric substrate. Based on the transmission line theory, an equivalent model with excellent accuracy is suggested for the proposed structure. By leveraging the simplicity of the model, we design a three-state quarter wave plate that is able to dynamically switch the polarization of the reflected wave to linear, right-, and left-hand polarizations while keeping the reflected amplitude remarkably high. Thanks to the simplicity of the model, the proposed structure can be easily used for designing other metasurfaces for light propagation control applications in imaging, sensing, and telecommunication.

Terahertz Quarter Wave-Plate Metasurface Polarizer Based on Arrays of Graphene Ribbons

In this paper, we propose a graphene-covered subwavelength metallic grating where the Fermi level of graphene is sinusoidally modulated as a leaky-wave antenna at terahertz frequencies. This structure can convert spoof surface plasmon guided waves to free-space radiation due to the tunability of graphene. Analysis and design of the proposed leaky-wave antenna are discussed based on sinusoidally modulated surface impedance. The surface impedance is obtained by an analytical circuit model. The sinusoidal surface impedance is realized using modulation of the conductivity of graphene by applying a bias voltage. The proposed leaky-wave antenna is capable of electronic beam scanning with an almost constant gain and low sidelobe level by tuning the graphene Fermi level. In addition, a mode-converting section is proposed that drastically improves the return loss of the antenna.

Tunable leaky-wave radiation by graphene-covered corrugated surfaces.

We introduce a new metasurface structure for controlling the polarization of light by leveraging a well-harmonized combination of graphene and dielectric. The proposed metasurface is composed of an array of rectangular pillars laterally sandwiched by ribbons of graphene. Being able to dynamically change the polarization state of the reflected wave, the proposed structure is employed to realize a switchable polarization converter, which is able to act as a reflector (co-polarizer)/right-hand circular (RHC) quarter-wave plate or RHC/cross/left-hand circular (LHC) polarizer based on its design configuration. The reflected amplitude in all states of functionality is remarkably high. It is also shown that, for some states, the proposed polarization converter demonstrates broad working bandwidth both spatially and spectrally. Therefore, it could find applications in terahertz imaging, sensing, and communication and also could be easily used to realize other beam-shaping functionalities such as lensing.

Mohammad Reza Tavakol

Papers

Two-Dimensional Edge Detection by Guided Mode Resonant Metasurface

Deriving Surface Impedance for 2-D Arrays of Graphene Patches Using a Variational Method

Terahertz Quarter Wave-Plate Metasurface Polarizer Based on Arrays of Graphene Ribbons

Tunable leaky-wave radiation by graphene-covered corrugated surfaces.

Tunable polarization converter based on one-dimensional graphene metasurfaces