We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the incident constituent plane wave fields to obtain the reflected and transmitted constituent plane wave fields. We derive these matrices and describe the complete formalism by implementing these matrices. This formalism, though physically equivalent to Fresnel formalism, has greater mathematical elegance and computational efficiency as compared to the latter. We utilize exact 3D expressions of the constituent plane wavevectors and electric fields of the incident, reflected and transmitted waves, which enable us to seamlessly analyse plane waves, paraxial and non-paraxial beams, highly diverging and tightly focused beam-fields as well as waves of miscellaneous wavefront-shapes and properties using the single formalism. The exact electric field expressions automatically include the geometric phase information; while we retain the wavefront curvature information by using appropriate multiplicative factors. We demonstrate our formalism by obtaining the reflected and transmitted fields in a simulated Gaussian beam model. Finally, we briefly discuss how our generalized formalism is capable of analysing the reflection-transmission problem of a very large class of complex optical waves -- by referring to some novel works from the current literature as exemplary cases.
We present the results of numerical analysis of Gauss-Bessel beam reflection from a dielectric film under different angles of incidence. A transverse shift of the beam under the orbital momentum sign change is observed. The value of the shift is independent of the polarization state of the incident beam.
Group delay for a reflected light pulse from a weakly absorbing dielectric slab is theoretically investigated, and large negative group delay is found for weak absorption near a resonance of the slab ($Re(kd)=mπ$). The group delays for both the reflected and transmitted pulses will be saturated with the increase of the absorption.
Utilizing the underlying physics of evanescent wave amplification by a negative-refractive-index slab, it is shown that evanescent waves with specific spatial frequencies can also be amplified without any reflection simply by two dielectric planar waveguides. The simple configuration allows one to take advantage of the high resolution limit of a high-refractive-index material without contact with the object.
We study reflection of TE Laguerre-Gaussian light beam by dielectric slab and show that the Goos-Hänchen and the Imbert-Federov shifts show resonant behavior following to the behavior of the reflection. Moreover the Imbert-Federov linear and the Goos-Hänchen angular shifts strongly depend on the orbital angular momentum m. Due to destructive interference of two beams reflected from upper and down interfaces of the slab profile of the reflected light beam acquires structure which distinctively displays an amount of m.
Under the sub-wavelength condition ($w<λ/2$), an analytical model of light transmission and reflection through $1$D metallo-dielectric gratings of real metals has been developed. It has been shown that the transmission intensity associated with the Fabry-Perot (FP) resonance of a $1$D metallo-dielectric grating of a real metal decreases with the increasing grating thickness and the dielectric constant of the ridge material. Further, it has also been demonstrated that the intensity of the FP resonance increases with the increasing slit width while it is independent of the grating period ($P$) a…
We demonstrate the appearance of unexpected reflection resonances in corrugated dielectric waveguides. These are due to the curvature of the boundary. The effect is as strong as the ordinary Bragg resonances, and reduces the transmission through our waveguide by 20%. It is thus of high relevance for the design of optimized waveguiding structures. We validate our analytical predictions based on coupled mode theory by a comparison to numerical simulations.
Very weak left/right asymmetry in reflection and transmission is offered by a layer of a topological insulator on top of a layer of an anisotropic dielectric material, but it can be enhanced very significantly by using a periodic multilayer of both types of materials. This is an attractive prospect for realizing one-way terahertz devices, because both types of materials can be grown using standard physical-vapor-deposition techniques.
A photonic jet (terajet at THz frequencies) commonly denotes a specific spatially localized region in the near-field at the front side of a dielectric particle with diameter comparable with wavelength illuminated with a plane wave from its backside (i.e., the jet emerges from the shadow surface of a dielectric particle). In this paper the formation of photonic is demonstrated using the recently proposed 3D dielectric cuboids working in reflection mode when the specific spatially localized region is localized towards the direction of incidence wavefront. The results of simulations based on Fini…
In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric permittivity are related by spatial Kramers-Kronig (KK) relations, are one-way reflectionless, whatever the angle of incidence. Such a fascinating property, besides of extending our comprehension of the fundamental phenomenon of reflection, may offer new ways for the design of antireflection surfaces and thin materials with efficient light absorption. However, KK dielectric media are generally describ…
The oblique incidence of a Bessel beam on a dielectric slab with refractive index n1 surrounded by a medium of a refractive index n>n1 may be studied simply by expanding the Bessel beam into a set of plane waves forming the same angle with the axis of the beam. In the present paper we examine a Bessel beam that impinges at oblique incidence onto a layer in such a way that each plane-wave component impinges with an angle larger than the critical angle.
The stationary states of a microlaser are related to the decaying quasibound states of the corresponding passive cavity. These are interpreted classically as originating from sequential escape attempts of an ensemble of rays obeying a curvature-corrected Fresnel formula. Polarization-dependent predictions of this model, and its limitations for stable orbits in partially chaotic systems are discussed.
We present a significantly different reflection process from an optically thin flat metallic or dielectric layer and propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse. Unipolar pulses in reflection arise due to specifics of effectively one-dimensional pulse propagation. Namely, we show that in considered system the field emitted by a flat medium layer is proportional to the velocity of oscillating medium charges instead of their acceleration as it is usually the case. When the single-cycle pulse interacts …
The fundamental optical effects that are at basis of giant reflection band and anomalous negative transmission in a self-sustained rectangular dielectric grating slab in P polarization and for incidence angle not very far from the Brewster's angle of the equivalent slab, are investigated. Notice, that the self sustained dielectric grating slab is the simplest system that, due to the Bragg diffraction, can show both the former optical effects. A systematic study of its optical response is performed by an analytical exact solution of the Maxwell equations for a general incidence geometry. At var…
The possibility of overcoming the critical condition for localized photonic nanojet upon plane optical wave diffraction at mesoscale dielectric particle, which is commonly known as "the refractive index contrast is less than two", was recently reported in our works. To this end, the novel geometrical scheme of photonic nanojet generation in "reflection mode" was proposed based on a super-contrast microparticle (n~2) placed near a flat mirror. In this paper, through the numerical FDTD calculations of optical near-field structure of 2D and 3D dielectric microparticles (cylinder, sphere) we exten…
Radiative emission from an open-ended unflanged planar dielectric waveguide is studied for the case of TM polarization on the basis of an iterative scheme. The first step of the scheme leads to approximate values for the reflection coefficients and electromagnetic fields inside and outside the waveguide. It is shown that for the related problems of reflection from a step potential in one-dimensional quantum mechanics and of Fresnel reflection of an electromagnetic plane wave from a half-space the iterative scheme is in accordance with the exact solution.
Exerting well-defined control over the reflection $(R)$, absorption $(A)$, and transmission $(T)$ of electromagnetic waves is a key objective in quantum optics. To this end, one often utilizes hybrid structures comprised of elements with different optical properties in order to achieve features such as high $R$ or high $A$ for incident light. A desirable goal would be the possibility to tune between all three regimes of nearly perfect reflection, absorption, and transmission within the same device, thus swapping between the cases $R\to 1$, $A\to1$, and $T\to1$ dynamically. We here show that a …
We present an initial study of the angular spectrum of a bianisotropic refractive metasurface at an interface between two dielectric media. In this study, we report on the existence of three distinct angular regions: a)~a rotated transmission cone, b)~a modified total internal reflection region, and c)~a new total retro-reflection region.
Radiative emission from a semi-infinite unflanged circular cylindrical dielectric waveguide or optical fiber is studied for the case of axisymmetric modes of TM polarization on the basis of an iterative scheme. The first step of the scheme leads to approximate values for the reflection coefficients and the electromagnetic fields inside and outside the waveguide. In a numerical example the reflection back into the waveguide is appreciable. Correspondingly the radiation pattern of the outgoing radiation differs appreciably from the lowest order approximation in which reflection is neglected.
The Goos-Hanchen effect of light reflected from sandwich (three-layered) structures composed of a superconducting YBa2Cu3O7 film and two different dielectric films is investigated theoretically. It has been shown that optical anisotropy of YBa2Cu3O7 film, as well as its positions in the three-layer specimen, strongly effects on the lateral shift values. We have shown that, for all positions of the superconducting film in the three-layered structure, variation of temperature makes possible to control the values of the lateral shift of TE-polarized light at the incidence angles close to pseudo-B…
A single paraxial beam reflection at a plane dielectric interface, configured appropriately, can lead to the formation of a polarization singularity in the inhomogeneously polarized output beam-field for any central angle of incidence. In this paper we derive the necessary condition to realize this effect. We explore the phase singularity characteristics associated to this polarization-singular field; and explore the dynamics of the singularities due to controlled variations of the input polarization. The simulation-generated exact field information lead to the exploration of the unique Goos-H…
Phase-space procedure based on coherent state representation is proposed for investigation of reflection and transmission of light beams at a curved dielectric boundary. Numerical simulations of reflection and transmission of light at various boundaries separating two different dielectrics are carried out. Significant influence of wave-front curvature and polarization of incident beam on the reflectance and transmittance is shown.
We discuss curvature corrections to Fresnel's laws for the reflection and transmission of light at a non-planar refractive-index boundary. The reflection coefficients are obtained from the resonances of a dielectric disk within a sequential-reflection model. The Goos-Hänchen effect for curved light fronts at a planar interface can be adapted to provide a qualitative and quantitative extension of the ray model which explains the observed deviations from Fresnel's laws.
Controlling thin film formation is technologically challenging. The knowledge of physical properties of the film and of the atoms in the surface vicinity can help improve control over the film growth. We investigate the use of the well-established selective reflection technique to probe the thin film during its growth, simultaneously monitoring the film thickness, the atom-surface van der Waals interaction and the vapor properties in the surface vicinity.
A comparative study of unloaded Q-factor measurements of a TE011 mode sapphire dielectric resonator with unloaded Q-factor value of 731,000 at a frequency of 10 GHz and temperature of 65 K using two best Q-factor measurement methods are presented. The Transmission (TMQF) and Reflection methods are based on relevant multi-frequency S-parameter measurements and circle fitting procedures to compute the unloaded Q-factor of the resonator. For accurate comparison of the methods a delay compensation procedure (introduced in the TMQF technique to remove delay due to non-calibrated cables) has been ap…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Osipyan Institute of Solid State Physics RAS（奥西皮扬固体物理研究所）；PN Lebedev Physical Institute of RAS（列别捷夫物理研究所）
We describe a novel artificial dielectric material which has applications at millimetre and submillimetre wavelengths. The material is manufactured from layers of metal mesh patterned onto thin polypropylene sheets which are then bonded together using a hot pressing process to provide planar rugged discs which can be reliably cycled to cryogenic temperatures. The refractive index of this material can be tuned by adjusting the geometry and spacing of the metal-mesh layers. We demonstrate its usage by designing and characterising a broadband anti-reflection coating for a Z-cut crystalline Quartz…
Reflection and transmission of narrow beams at a dielectric interface is analysed. It is confirmed that for arbitrary incidence two types of beams - Elegant Hermite-Gaussians of linear polarization and Elegant Laguerre-Gaussians of circular polarization, both defined in the interface plane - can be treated as vector normal modes of the interface. Excitation of higher-order modes by cross-polarization coupling is described by changes of mode indices induced by generalised transmission and reflection matrices. It is explicitly shown that, off-axis in general, spectral placements of the excited o…
The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the comp…
Grazing incidence waves incident onto a surface will almost always be completely reflected. Here, we focus on removing reflection at grazing incidence, adopting the factorisation method from quantum mechanics and applying it to the Helmholtz equation that governs a single electromagnetic polarisation. We show that there are two approaches, the first is to require real dielectric profiles that support a half-bound state at grazing incidence. The second is to allow non-Hermitian dielectric profiles that exhibit PT symmetry, supporting waves with constant intensity throughout the profile.
Metadevices based on dielectric nanostructured surfaces with both electric and magnetic Mie-type resonances have resulted in the best efficiency to date for functional flat optics with only one disadvantage: a narrow operational bandwidth. Here we experimentally demonstrate broadband transparent all-dielectric metasurfaces for highly efficient polarization manipulation. We utilize the generalized Huygens principle, with a superposition of the scattering contributions from several electric and magnetic multipolar modes of the constituent meta-atoms, to achieve destructive interference in reflec…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and th…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity being an arbitrary continuous function of the coordinate. We have shown that the problem of plane wave scattering by an inhomogeneous layer is reduced to a system of first order differential equations that contain the derivative of the refractive index or dielectric permittivity of the layer, which can be used, for example, when searching for an analytical sol…
By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.
The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the investigation of the near-zone optical response of dielectrics. The laws of reflection and refraction for discrete structures in the case of a regular atomic distribution are studied and the structure of evanescent harmonics induced by an external plane wave near the surface is investigated in details. It is shown by means of analytical and numerical calculat…
All-dielectric nanostructures have recently emerged as a promising alternative to plasmonic devices, as they also possess pronounced electric and magnetic resonances and allow effective light manipulation. In this work, we study optical properties of a composite structure that consists of a silicon nanoparticle array (metasurface) and high-index substrate aiming at clarifying the role of substrate on reflective properties of the nanoparticles. We develop a simple semi-analytical model that describes interference of separate contributions from nanoparticle array and the bare substrate to the to…
The degenerate case of normal incidence and reflection of an optical beam (both paraxial and non-paraxial) at a plane isotropic dielectric interface, which is azimuthally symmetric in terms of the momentum-spatial variation of Fresnel coefficients but not in terms of the fundamental polarization inhomogeneity of the incident field, requires in-depth analyses. In this paper, we use the reflection and transmission coefficient matrix formalism to derive an exact field expression of a normal-reflected diverging beam. The availability of the exact field information allows controlled variations of t…
We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic, absorbing or non-absorbing materials and is free of discontinous solutions. We calculate the reflection and transmission coefficients and derive equations for the electric field distribution for any number of layers. The algorithm is easily comprehensible and can be straight forwardly implemented in a computer program. To demonstrate the capabilities of the appro…
In this paper, we propose an effective model including a macroscopic Hamiltonian to describe the interactions between a two-level atom and scattered light in a 1-D dielectric waveguide. The proposed formalism allows us to incorporate the effect of changing optical media inside the continuum while demonstrating a non-classical derivation of Fresnel Law. We obtain the transport characteristics of the two-level system, explore its high-Q bandreject filter property and discuss the implications of radiative and non-radiative dissipation. In addition, we apply our formalism to a modified Fabry-Pérot…
Conventional transparent materials at optical frequencies have refractive index values (n) greater than unity -- most commonly between about 1 and 4. This paper explores optical phenomena made possible by using materials with refractive indices less than unity. We focus primarily on fused silica (SiO2), a polar dielectric with strong phonon resonances in the mid infrared that result in a spectral region in which n < 1 with modest optical loss. Using this ubiquitous easy-to-deposit material, we demonstrate infrared-frequency external reflection, frustrated external reflection, and direct coupli…
The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials being coupled to form dimers. The Bruggeman and Maxwell Garnett formalisms were developed to estimate the permittivity dyadic of the homogenized composite material (HCM), under the quasi-electrostatic approximation. Both randomly oriented and identically oriented dimers were accommodated; in the former case the HCM is isotropic, whereas in the latter case the HC…
The study of high-index dielectric nanoparticles currently attracts a lot of attention. They do not suffer from absorption but promise to provide control on the properties of light comparable to plasmonic nanoparticles. To further advance the field, it is important to identify versatile dielectric nanoparticles with unconventional properties. Here, we show that breaking the symmetry of an all-dielectric nanoparticle leads to a geometrically tunable magneto-electric coupling, i.e. an omega-type bianisotropy. The suggested nanoparticle exhibits different backscatterings and, as an interesting co…
The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-Hänchen and transverse Imbert-Federov shifts of the centroid of a reflected optical beam. The centroid shift is related to the centre of the constellation, whose geometry otherwise depends on higher-order terms in an expansion of the reflection matrix. We present an approximation of the field around the constellation of increasing order as an Appell sequence of complex polynom…
Transmission and reflection of an electromagnetic pulse through a dielectric slab doped with the quantum dot molecules is investigated. It is shown that the transmitted and reflected pulses depend on the inter-dot tunneling effect and can be controlled by applying a gate voltage.
Polarizers are essential in diverse photonics applications including display [1], microscopy [2], polarimetric astrophysical observation [3], laser machining [4], and quantum information processing [5]. Whereas conventional polarizers based on natural crystals and multilayer thin films are commonplace, nanostructured polarizers offer compact integrability [6,7], thermal stability in high-power systems [4,8], and space-variant vector beam generation [9,10]. Here, we introduce a new class of reflectors and polarizers fashioned with dielectric nanowire grids that are mostly empty space. It is fun…
We demonstrate a novel and simple approach to cloaking a scatterer on a ground plane. We use an extremely thin dielectric metasurface (λ/12) to reshape the wavefronts distorted by a scatterer in order to mimic the reflection pattern of a flat ground plane. To achieve such carpet cloaking, the reflection angle has to be equal to the incident angle everywhere on the scatterer. We use a graded metasurface and calculate the required phase gradient to achieve cloaking. Our metasurface locally provides additional phase to the wavefronts to compensate for the phase difference amongst light paths indu…
Describing the phenomenon of total internal reflection in terms of a reflection coefficient of unit magnitude, we found that, not only can propagating plane waves be total internally reflected at the planar interface of two dissimilar, homogeneous, isotropic dielectric-magnetic mediums, but evanescent plane waves can also be. The refracting medium must be the optically denser of the two mediums for total internal reflection of an evanescent plane wave to occur.
The Brewster's law predicts zero reflection of p-polarization on a dielectric surface at a particular angle. However, when loss is introduced into the permittivity of the dielectric, the Brewster condition breaks down and reflection unavoidably appears. In this work, we found an exception to this long-standing dilemma by creating a class of nonmagnetic anisotropic metamaterials, where an anomalous Brewster effects with independently tunable absorption and refraction emerges. This loss-independent Brewster effect is bestowed by the extra degrees of freedoms introduced by anisotropy and strictly…
Symmetry and reciprocity constraints on polarization state of the field diffracted by gratings of quasi-planar particles are considered. It is shown that the optical activity effects observed recently in arrays of quasi-planar plasmonic particles on a dielectric substrate are due to the reflection of the field at the air-dielectric slab interface and are proportional to this reflection coefficient.
We introduce a practical dielectric metasurface design for microwave frequencies. The metasurface is made of an array of dielectric resonators held together by dielectric connections thus avoiding the need of a mechanical support in the form of a dielectric slab and the spurious multiple reflections that such a slab would generate. The proposed design can be used either for broadband metasurface applications or monochromatic wave transformations. The capabilities of the concept to manipulate the transmission phase and amplitude of the metasurface are supported by numerical and experimental res…
