The wave impedance of an atomically thin crystal

I propose an expression for the electromagnetic wave impedance of a two-dimensional atomic crystal, and I deduce the Fresnel coefficients in terms of this quantity. It is widely known that a two-dimensional crystal can absorb light, if its conductivity is different from zero. It is less emphasized that they can also store a certain amount of electromagnetic energy. The concept of impedance is useful to quantify this point

Role of the radiation-reaction electric field in the optical response of two-dimensional crystals

A classical theory of a radiating two-dimensional crystal is proposed and an expression for the radiative-reaction electric field is derived. This field plays an essential role in connecting the microscopic electromagnetic fields acting on each dipole of the crystal to the macroscopic one, via the boundary conditions for the system. The expression of the radiative-reaction electric field coincides with the macroscopic electric field radiating from the crystal and, summed to the incident electric field, generates the total macroscopic electric field.Comment: Two-dimensional crystal, metasurface, local field, radiative-reaction, Fresnel, boundary conditio

Observing angular deviations in light beam reflection via weak measurements

An optical analog of the quantum weak measurement scheme proved to be very useful for the observation of optical beam shifts. Here we adapt the weak value amplification method for the observation of the angular Goos-Hanchen shift. We observe this effect in the case of external air-dielectric reflection, the more fundamental case in which it occurs.We show that weak measurements allow for a faithful amplification of the effect at any angle of incidence, even at the Brewster angle of incidence

Fresnel coefficients of a two-dimensional atomic crystal

In general the experiments on the linear optical properties of a single-layer two-dimensional atomic crystal are interpreted by modeling it as a homogeneous slab with an effective thickness. Here I fit the most remarkable experiments in graphene optics by using the Fresnel coefficients, fixing both the surface susceptibility and the surface conductivity of graphene. It is shown that the Fresnel coefficients and the slab model are not equivalent. Experiments indicate that the Fresnel coefficients are able to simulate the overall experiments here analyzed, while the slab model fails to predict absorption and the phase of the reflected light

How orbital angular momentum affects beam shifts in optical reflection

It is well known that reflection of a Gaussian light beam ($\text{TEM}_{00}$) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-H\"{a}nchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with Orbital Angular Momentum (OAM) leads to coupling of these four shifts; this is described by a $4 \times 4$ mixing matrix.Comment: v2 Version accepted for publication in Phys. Rev.

Orbital angular momentum induced beam shifts

We present experiments on Orbital Angular Momentum (OAM) induced beam shifts in optical reflection. Specifically, we observe the spatial Goos-H\"anchen shift in which the beam is displaced parallel to the plane of incidence and the angular Imbert-Fedorov shift which is a transverse angular deviation from the geometric optics prediction. Experimental results agree well with our theoretical predictions. Both beam shifts increase with the OAM of the beam; we have measured these for OAM indices up to 3. Moreover, the OAM couples these two shifts. Our results are significant for optical metrology since optical beams with OAM have been extensively used in both fundamental and applied research.Comment: 7 pages, 7 figure

Weak measurements of a large spin angular splitting of light beam on reflection at Brewster angle

We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to explore this angular splitting. Remarkably, the directions of the spin accumulations can be switched by adjusting the initial handedness of polarization.Comment: 7 pages, 4 figure

Measurement of the surface susceptibility and the surface conductivity of atomically thin MoS2\rm MoS_2 by spectroscopic ellipsometry

We show how to correctly extract from the ellipsometric data the surface susceptibility and the surface conductivity that describe the optical properties of monolayer $\rm MoS_2$. Theoretically, these parameters stem from modelling a single-layer two-dimensional crystal as a surface current, a truly two-dimensional model. Currently experimental practice is to consider this model equivalent to a homogeneous slab with an effective thickness given by the interlayer spacing of the exfoliating bulk material. We prove that the error in the evaluation of the surface susceptibility of monolayer $\rm MoS_2$, owing to the use of the slab model, is at least 10% or greater, a significant discrepancy in the determination of the optical properties of this material.Comment: Keywords: Ellipsometry, graphene, MoS2, two dimensional crystals, optical contrast, absorption, transition metal dichalcogenide monolayer

Duality Between Spatial and Angular Shift in Optical Reflection

We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam reflection. In the Goos-Hanchen case we show theoretically and experimentally that this unification naturally arises in the context of reflection from a lossy surface (e.g., a metal).Comment: 4 pages, 3 figure

Observation of Goos-H\"{a}nchen shifts in metallic reflection

We report the first observation of the Goos-H$\rm \ddot{\textbf{a}}$nchen shift of a light beam incident on a metal surface. This phenomenon is particularly interesting because the Goos-H$\rm \ddot{\textbf{a}}$nchen shift for $p$ polarized light in metals is negative and much bigger than the positive shift for $s$ polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a $p$ polarized beam of light.Comment: The parer was published on Optics Express. The new version is modified according to the reviewers suggestion