We propose in this article an unambiguous definition of the local density of electromagnetic states (LDOS) in a vacuum near an interface in an equilibrium situation at temperature $T$. We show that the LDOS depends only on the electric field Green function of the system but does not reduce in general to the trace of its imaginary part as often used in the literature. We illustrate this result by a study of the LDOS variations with the distance to an interface and point out deviations from the standard definition. We show nevertheless that this definition remains correct at frequencies close to the material resonances such as surface polaritons. We also study the feasability of detecting such a LDOS with apetureless SNOM techniques. We first show that a thermal near-field emission spectrum above a sample should be detectable and that this measurement could give access to the electromagnetic LDOS. It is further shown that the apertureless SNOM is the optical analog of the scanning tunneling microscope which is known to detect the electronic LDOS. We also discuss some recent SNOM experiments aimed at detecting the electromagnetic LDOS.
We study the propagation properties and light-matter interactions of the focused doughnut pulses, broadband, single-cycle electromagnetic perturbations of toroidal topology first described by Hellwarth and Nouchi in 1996. We show how focused doughnuts are reflected and refracted at planar metallic and vacuum-dielectric interfaces leading to complex distortions of the field structure. We also identify the conditions under which these toroidal pulses excite dominant dynamic toroidal dipoles in spherical dielectric particles.
Discovery of Electromagnetic Surface Waves at the Interface Between Perfect Electric Conductor and Perfect Magnetic Conductor Parallel-Plate Waveguides
It is shown that the generally accepted definition of the Poynting vector and the energy flux vector defined by means of the energy density of the electromagnetic field (Umov vector) lead to the prediction of the different results touching electromagnetic energy flux. The experiment shows that within the framework of the mentioned generally accepted definitions the Poynting vector adequately describes the electromagnetic energy flux unlike the Umov vector. Therefore one can conclude that a generally accepted definitions of the electromagnetic energy density and the Poynting vector, in general,…
In this paper the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view the consequences of the boundary conditions at such interfaces are addressed in two different ways. First, we analyze a restricted class of reflectionless interfaces, for which the tools of transformation optics allow to describe the electromagnetic fields on both sides of the interface by means of the same vacuum solution of the Maxwell equations. In a second step, we examine interfaces between two arbitrary transformation…
Electromagnetic wave is reflected and refracted at interfaces, satisfying Fresnel-Snell law which is required by conservations of energy and momentum. If the incident angle is lower than the critical angle, we can use this Fresnel-Snell law, but the Fresnel-Snell law is modified in the case of existence of dissipation ($\tilde{n} = n + iκ, κ> 0$) or in the condition of total internal reflection. In the cases, we have to extend the angle of refraction from real number to complex number ($θ\rightarrow \tildeθ = θ+ iψ, ψ\neq 0$). In this paper, by using complex-angle approach, we analyse the beha…
We investigate single interface surface plasmon polaritons (SPPs) excited by electromagnetic waves under general electromagnetic boundary conditions that allow for non-zero surface charge and surface current densities. Incorporating these, we derive general conditions for single interface SPPs and solve both the surface source distributions and the surface electromagnetic waves for such SPPs when excited by electromagnetic waves.
Focusing through a tilted dielectric interface is studied, and an explicit expression for the electric field in the focal region is found. In the case of small tilt angles, one obtains a focal shift, and only a simple aberration term remains.
A low loss propagating electromagnetic wave is shown to exist at a gradual interface between two lossy conductive media. The electromagnetic frequency range of this phenomenon may span from UV optics to RF range. In particular, it is demonstrated that such a surface wave may be guided by a seafloor-seawater interface and it may be used in radio communication and imaging underwater. Similar surface waves may also be guided by various tissue boundaries inside a human body. For example, such surface wave solutions may exist at planar interfaces between skull bones and grey matter inside a human h…
A conventional general electromagnetic force definition has been widely used to analyze radiation forces in dielectric media in published research works. However in this paper, we would like to indicate that this conventional force definition is flawed.
The discovery of topological insulators has rapidly been followed by the advent of their photonic analogues, motivated by the prospect of backscattering-immune light propagation. So far, however, implementations have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two-dimensional systems, which closely mimic their electronic counterparts. In addition, metamaterials-based implementations subject to electromagnetic duality and bianisotropy conditions suffer from intricate designs and narrow operating bandwidths. Here, it is shown that symmetry-protected topol…
Guided by the planar interface of two dissimilar linear, homogeneous mediums, a Voigt surface wave arises due to an exceptional point of either of the two matrixes necessary to describe the spatial characteristics in the direction normal to the planar interface. There is no requirement for either or both partnering mediums to be dissipative, unlike a Voigt plane wave which can propagate only in a dissipative medium.
Propagation of the TE electromagnetic waves in self-focusing medium is governed by the nonlinear Schroedinger equation. In this paper the stationary solutions of this equation have been systematically presented. The phase-plane method, qualitative analysis, and mechanical interpretation of the differential equations are widely used. It is well known that TE waves can be guided by the single interface between two semi-infinite media, providing that one of the media has a self-focusing (Kerr type) nonlinearity. This special solution is called a spatial soliton. In this paper our interests are no…
The idea of working with a near-critical phase-separated liquid mixture whereby the surface tension becomes weak, has recently made the field of laser manipulation of liquid interfaces a much more convenient tool in practice. The deformation of interfaces may become as large as several tenths of micrometers, even with the use of conventional laser power. This circumstance necessitates the use of nonlinear geometrical theory for the description of surface deformations. The present paper works out such a theory, for the surface deformation under conditions of axial symmetry and stationarity. Goo…
The dynamical characteristics of electromagnetic fields include energy, momentum, angular momentum (spin) and helicity. We analyze their spatial distributions near the planar interface between two transparent and non-dispersive media, when the incident monochromatic plane wave with arbitrary polarization is totally reflected, and an evanescent wave is formed in the medium with lower optical density. Based on the recent arguments in favor of the Minkowski definition of the electromagnetic momentum in a material medium [Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); Phys. Rev. Lett. 119, 073…
Classical electromagnetic boundary conditions (EMBCs) fail to describe quantum interface phenomena at nanoscale. Here, we construct the interface model with a transition layer describing the electromagnetic field inhomogeneity across the interface. Generalized nanoscale EMBCs are derived by introducing the magnetic interfacial response functions (IRFs) and are rewritten as three different forms based on Maxwell's equations in first order approximation. The corresponding Fresnel formula are further used to analyze the interfacial photonic phenomenon, demonstrating interesting behaviors of Brews…
I compute from first principles the local heating rate $q$ (the amount of electromagnetic energy converted to heat per unit time per unit volume) for electromagnetic waves propagating in magnetically and electrically polarizable media. I find that, in magnetic media, this rate has two separate contributions, $q^{(V)}$ and $q^{(S)}$, the first coming from the volume of the medium and the second from its surface. I argue that the second law of thermodynamics requires that the volume contribution be positive and that this requirement, in turn, prohibits negative refraction. This result holds for …
We unveil the generation of universal morphologies of fluid interfaces by radiation pressure whatever is the nature of the wave, acoustic or optical. Experimental observations reveal interface deformations endowed with step-like features that are shown to result from the interplay between the wave propagation and the shape of the interface. The results are supported by numerical simulations and a quantitative interpretation based on the waveguiding properties of the field is provided.
The propagation of electromagnetic surface waves guided by the planar interface of two isotropic chiral materials, namely materials $\calA$ and $\calB$, was investigated by numerically solving the associated canonical boundary-value problem. Isotropic chiral material $\calB$ was modeled as a homogenized composite material, arising from the homogenization of an isotropic chiral component material and an isotropic achiral, nonmagnetic, component material characterized by the relative permittivity $\eps_a^\calB$. Changes in the nature of the surface waves were explored as the volume fraction $f_a…
The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random medium and the rough boundaries, and the second one which corresponds to the unperturbed Green functions describes the scattering by an homogeneous layer with the rough boundaries. As these equations are formally similar to classical equations used in scattering theory by an infinite random medium, we will be able to apply standard procedures to calculate the …
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realise coatings to achieve exotic effects like optical illusions and anomalous diffraction behaviour. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the nex…
The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by $ PT $ symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features s…
Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media, the Brillouin energy density, as well as with the recently-introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and m…
Solutions of the boundary-value problem for electromagnetic waves guided by a layer of a homogeneous and isotropic (metal or dielectric) material sandwiched between a structurally chiral material (SCM) and a periodically multi-layered isotropic dielectric (PMLID) material were numerically obtained and analyzed. If the sandwiched layer is sufficiently thick, the two bimaterial interfaces decouple from each other, and each interface may guide one or more electromagnetic surface waves (ESWs) by itself. Depending on the constitution of the two materials that partner to form an interface, the ESWs …
Surface scattering of free electrons strongly modifies the electromagnetic response near the interface. Due to the inherent anisotropy of the surface scattering that necessarily reverses the normal the interface component of the electron velocity while its tangential component may remain the same, a thin layer near a high-quality interface shows strong dielectric anisotropy. The formation of the resulting hyperbolic dispersion layers near the metal-dielectric interface strongly modifies the local density of states, and leads to orders of magnitude changes in all associated phenomena.
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical repartition is described by a pair-distribution function. The boundary contribution is included in the Green functions with the help of scattering operators which can represent any existing theory of scattering by rough surfaces. By using a standard procedure, we derive the integral Bethe-Salpeter equation under the ladder approximation and, by differentiation, …
Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where electromagnetic material parameters play the roles of `mass' and `energy' in an equivalent Dirac equation. The modes trapped between a gyrotropic medium and a mirror are then the counterpart of those at a `domain wall', where the mass of the Dirac particle changes sign. Considering the general case of arbitrary electromagnetic media, we provide an analytical proof relatin…
It is known that the near-field spectrum of the local density of states of the electromagnetic field above a SiC/air interface displays an intense narrow peak due to the presence of a surface polariton. It has been recently shown that this surface wave can be strongly coupled with the sheet plasmon of graphene in graphene-SiC heterosystems. Here, we explore the interplay between these two phenomena and demonstrate that the spectrum of the electromagnetic local density of states in these systems presents two peaks whose position depends dramatically both on the distance to the interface and on …
We present a general methodology for electromagnetic homogenization and characterization of bianisotropic metasurfaces formed by regular or random arrangements of small arbitrary inclusions at the interface of two different isotropic media. These topologies can provide the most general electric and magnetic surface-bound dipolar responses to incident electromagnetic waves. The approach unites and generalizes the earlier theories developed independently by two research groups: the joint group of profs. Holloway and Kuester and the joint group of profs. Simovski and Tretyakov. We demonstrate the…
Extraordinary rays in a hyperbolic metamaterial behave as particle world lines in a three dimensional (2+1) Minkowski spacetime. We analyze electromagnetic field behavior at the boundaries of this effective spacetime depending on the boundary orientation. If the boundary is perpendicular to the space-like direction in the metamaterial, an effective Rindler horizon may be observed which produces Hawking radiation. On the other hand, if the boundary is perpendicular to the time-like direction an unusual physics situation is created, which can be called "the end of time". It appears that in the l…
The discovery of photonic hyperbolic dispersion surfaces in certain van der Waals bonded solids, such as hexagonal boron nitride and bismuth selenide (a topological insulator), offers intriguing possibilities for creating strongly modified light-matter interactions. However, open problems exist in quantifying electromagnetic field fluctuations in these media, complicating typical approaches for modeling photonic characteristics. Here, we address this issue by linking the identifying traits of hyperbolic response to a coupling between longitudinal and transverse fields that can not occur in iso…
We extend a previous analysis of spatial correlation functions for classical electromagnetic vector fields near a perfectly conducting boundary [PRE, vol. 73, 036604 (2006)] to the case of an isotropic semi-infinite medium with planar interface and characterized by a first-order impedance boundary condition. The analytical results are illustrated with calculations for the case of point separations in the direction perpendicular to the interface. For the incident plus reflected field, the dependence of the complex-valued and inhomogeneous spatial correlation function on the permittivity, permea…
In this paper we propose a new paradigm to create superlenses inspired by n-p-n junctions of graphene. We show that by adjoining a n-type region and a p-type region with a crystal dislocation, it is possible to mimic the interaction of complementary Hamiltonians and achieve subwavelength imaging. We introduce an effective model of the system, and show that it predicts perfect lensing for both propagating and evanescent waves due to the excitation of a resonant mode at the interface between each region. This phenomenon is the consequence of a nontrivial boundary condition at the n-p interfaces …
SMUTHI is a python package for the efficient and accurate simulation of electromagnetic scattering by one or multiple wavelength-scale objects in a planarly layered medium. The software combines the T-matrix method for individual particle scattering with the scattering matrix formalism for the propagation of the electromagnetic field through the planar interfaces. In this article, we briefly introduce the relevant theoretical concepts and present the main features of SMUTHI. Simulation results obtained for several benchmark configurations are validated against commercial software solutions. Ow…
An important issue in phenomenological macroscopic electrodynamics of moving media is the definition of the energy and momentum of the electromagnetic field in matter. Rather surprisingly, this topic has demonstrated a remarkable longevity, and the problem of the electromagnetic energy and momentum in matter remained open, despite numerous theoretical and experimental investigations. We overview the definition of the momentum of light in matter and demonstrate that, for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled e…
Temporal metamaterials have been recently exploited as a novel platform for conceiving several electromagnetic and optical devices based on the anomalous scattering response arising at a single or multiple sudden changes of the material properties. However, they are difficult to implement in realistic scenarios by switching the permittivity of a material in time, and new strategies to achieve time interfaces in a feasible manner must be identified. In this paper, we investigate the possibility to realize a temporal metamaterial without acting on the material properties, but rather on the effec…
