We show that Parity-time symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective Parity operator involving both mirror symmetry and coupling between electric and magnetic fields. This approach extends the discussion of Parity-time symmetry to the situation with more than one material potential. We show that the band structure of a one-dimensional photonic crystal with alternating purely dielectric and purely magnetic slabs can undergo a phase transition between propagation modes and evanescent modes when the balanced gain/loss parameter is varied. The cross-matching between different material potentials also allows exceptional points of the constitutive matrix to appear in the long wavelength limit where they can be used to construct ultrathin metamaterials with unidirectional reflection.
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.
Epsilon-near-zero (ENZ) metamaterial slabs at visible frequencies based on metal-dielectric multilayers are experimentally realized. Transmission, reflection and absorption spectra are measured and used to determine the complex refractive indices and the effective permittivities of the ENZ slabs, which agree with the results obtained from both the numerical simulations and the optical nonlocalities analysis. Furthermore, light propagation in ENZ slabs and directional emission from ENZ prisms are also analyzed. The accurate determination of the ENZ wavelength for metal-dielectric multilayer met…
Motivated by the recent progress in analog computing [Science 343, 160 (2014)], a new approach to perform spatial integration is presented using a dielectric slab waveguide. Our approach is indeed based on the fact that the transmission coefficient of a simple dielectric slab waveguide at its mode excitation angle matches the Green's function of first order integration. Inspired by the mentioned dielectric-based integrator, we further demonstrate its graphene-based counterpart. The latter is not only reconfigurable but also highly miniaturized in contrast to the previously reported designs [Op…
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.
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 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.
Photonic components based on structured metallic elements show great potential for device applications where field enhancement and confinement of the radiation on a subwavelength scale is required. In this paper we report a detailed study of a prototypical metallo-dielectric photonic structure, where features well known in the world of dielectric photonic crystals, like band gaps and defect modes, are exported to the metallic counterpart, with interesting applications to infrared science and technology, as for instance in quantum well infrared photodetectors, narrow-band spectral filters, and …
We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method, while the propagation and scattering of the electromagnetic waves are calculated by the multiple scattering theory. It is shown that within partial bandgaps, the waves tend to bend away from the forbidden directions. Such a property may render novel applications in manipulating optical flows. In addition, the relevance with the imaging by flat photonic crys…
What we believe to be a new type of resonant coupling of an incident bulk wave into guided modes of a slab with a thick holographic grating is shown to occur in the presence of strong frequency detunings of the Bragg condition. This happens through the reflection of the strongly noneigen +1 diffracted order with the slab-grating boundaries, the resultant reflected waves forming a guided slab mode. Rigorous coupled-wave analysis is used for the numerical analysis of the predicted resonant effects. Possible applications include enhanced options for the design of multiplexing and demultiplexing s…
Symmetry principles and theorems are of crucial importance in optics. Indeed, from one side they allow to get direct insights into phenomena by eliminating unphysical interpretations; from the other side, they guide the designer of photonic components by narrowing down the parameter space of design variables. In this Letter we illustrate a significant departure from the Babinet spectral complementarity in a very common and technologically relevant situation: that of a patterned conducting screen placed on a subwavelength dielectric slab. The symmetry property predicted by Babinet theorem is co…
A composite plasmonic slab based on double-layer metallic gratings and a dielectric film is experimentally and numerically demonstrated in terahertz (THz) regions, which can support two resonance modes and then form a broad bandgap (40%). As compared to the double-layer metal grating, the dielectric film in composite THz slabs significantly enhances the transmission of the transverse magnetic (TM) mode. Electric field vector proved that the low-frequency resonance mode originates from the symmetric plasmonic mode and the high-frequency resonance mode is induced by the hybrid mode of plasmonic …
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.
Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially important applications. It is relatively easy to find a few EPs for a structure with parameters, but isolated EPs provide no information about their formation and variation in parameter space, and it is always difficult to ensure that all EPs in a domain of…
A configuration to excite the Uller-Zenneck surface electromagnetic waves at the planar interfaces of homogeneous and isotropic dielectric materials is proposed and theoretically analyzed. The Uller-Zenneck waves are surface waves that can exist at the planar interface of two dissimilar dielectric materials of which at least one is a lossy dielectric material. In this work, a slab of a lossy dielectric material was taken with lossless dielectric materials on both sides. A canonical boundary-value problem was set up and solved to find the possible Uller-Zenneck waves and waveguide modes. The Ul…
We consider propagation of transverse magnetic electromagnetic waves through a nonlinear metamaterial slab, of subwavelength thickness and very small average dielectric permittivity, made up of alternating metal and dielectric nonlinear layers. Exploiting the effective-medium approach, we prove that the output field intensity is a multi-valued function of both the input field intensity and incidence angle so that the transmissivity exhibits a novel kind of multi-stability and a pronounced two-parameter hysteresis behavior. The predicted two-parameter hysteresis physically stems from the fact t…
A special kind of degeneracies known as the exceptional points (EPs), for resonant states on a dielectric periodic slab, are investigated. Due to their unique properties, EPs have found important applications in lasing, sensing, unidirectional operations, etc. In general, EPs may appear in non-Hermitian eigenvalue problems, including those related to PT-symmetric systems and those for open dielectric structures (due to the existence of radiation loss). In this paper, we study EPs on a simple periodic structure: a slab with a periodic array of gaps. Using an efficient numerical method, we calcu…
Light confinement induced by resonant states in aperiodic photonic structures are interesting for many applications. A particular case of these resonances can be found in 2D quasi-crystalline arrangements of dielectric cylinders. These systems present a rather isotropic band gap as well as isolated in-gap photonic states (as a result of spatially localized resonances). These states are built by high symmetry polygonal clusters that can be regarded as photonic molecules. In this paper we study the transmission properties of a slab of glass cylinders arranged in approximants of decagonal quasi-c…
We investigate the diffraction of guided modes of a dielectric slab waveguide on a simple integrated structure consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic rigorous coupled-wave analysis demonstrate the existence of sharp resonant features and bound states in the continuum (BICs) in the reflectance and the transmittance spectra occurring at oblique incidence of a TE-polarized guided mode on the ridge. Using the effective index method, we explain the resonances by the excitation of the cross-polarized modes of the ridge. The f…
We explored the effects of relative motion on the excitation of surface-plasmon-polariton (SPP) waves guided by the planar interface of a metal film and a dielectric slab, both materials being isotropic and homogeneous. Electromagnetic phasors in moving and non-moving reference frames were related directly using the corresponding Lorentz transformations. Our numerical studies revealed that, in the case of a uniformly moving dielectric slab, the angle of incidence for SPP-wave excitation is highly sensitive to (i) the ratio $β$ of the speed of motion to speed of light in free space and (ii) the…
We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial differentiation and integration of the profile of optical beams propagating in the waveguide. The differentiation and integration operations are performed in transmission and in reflection, respectively, at oblique incidence of the beam impinging on the ridge. The implementation of these operations is associated with the resonant excitation of a cross-polarized eigenmode of the ridge. At the considered parameters of the structure and incidence geometry, …
In this paper, we examine the modification of specific nonclassical properties of the nonlinear coherent state on sphere upon perpendicular propagation through an absorptive and dispersive dielectric slab at finite temperature. For this purpose, by describing the dielectric dispersion of the slab by Lorentz model, the quadrature squeezing and the Mandel parameter are evaluated for the transmitted state. A generalization of single-mode nonlinear coherent state to the continuum-mode is considered. The degree of second-order coherence is instead calculated for a continuum nonlinear coherent state…
We investigate propagation of a transverse magnetic field through a nonlinear metamaterial slab of sub-wavelength thickness and with a very small and negative linear dielectric permittivity. We prove that, for a given input intensity, the output intensity is a multi-valued function of the field incidence angle so that the transmissivity exhibits angular multi-stability and a pronounced directional hysteresis behavior. The predicted directional hysteresis is a consequence of the fact that the linear and nonlinear contributions to the overall dielectric response can be comparable so that the ele…
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…
A rigorous coupled-wave analysis of birefringent holographic gratings with periodically-modulated dielectric tensor along an in-plane direction and tensor variations in the thickness direction
In this letter we discuss a phase transition-like anomalous behavior of Faraday rotation angles in a simple parity-time ($\mathcal{P}\mathcal{T}$) symmetric model with two complex $δ$-potential placed at both boundaries of a regular dielectric slab. In anomalous phase, the value of one of Faraday rotation angles may turn negative, and both angles suffer spectral singularities and yield strong enhancement near singularities.
Traditionally, photonic crystal slabs can support resonances that are strongly confined to the slab but also couple to external radiation. However, when a photonic crystal slab is placed on a substrate, the resonance modes become less confined, and as the index contrast between slab and substrate decreases, they eventually disappear. Using the scale structure of the Dione juno butterfly wing as an inspiration, we present a low-index zigzag surface structure that supports resonance modes even without index contrast with the substrate. The zigzag structure supports resonances that are contained …
Coherent Virtual Absorption in Dielectric Slabs: A Temporal Analysis of Symmetric and Asymmetric Geometries
Fowler School of Engineering, Chapman University（查普曼大学福勒工程学院）；Schmid College of Science and Technology, Chapman University（查普曼大学施密德科学与技术学院）；Institute for Quantum Studies, Chapman University（查普曼大学量子研究所）
We numerically investigate the propagation of a spatially localized and quasi-monochromatic electromagnetic pulse through a slab with Lorentz dielectric response in the epsilon-near-zero regime, where the real part of the permittivity vanishes at the pulse carrier frequency. We show that the pulse is able to excite a set of virtual polariton modes supported by the slab, the excitation undergoing a generally slow damping due to absorption and radiation leakage. Our numerical and analytical approaches indicate that in its transient dynamics the electromagnetic field displays the very same enhanc…
We show that a nonlinear metallo-dielectric layered slab of subwavelength thickness and very small average dielectric permittivity displays optical multistable behavior at arbitrary low optical intensities. This is due to the fact that, in the presence of the small linear permittivity, one of the multiple electromagnetic slab states exists no matter how small is the transmitted optical intensity. We prove that multiple states at ultra-low optical intensities can be reached only by simultaneously operating on the incident optical intensity and incidence angle. By performing full wave simulation…
We closely study the local amplifications of visible light on a thin dielectric slab presenting a sub-wavelength array of small, rectangular, bottom-closed holes. The high-quality Fabry-Perot resonances of eigen modes which vertically oscillate, and their corresponding near-field maps, especially inside the voids, are numerically quantified with RCWA and analytically interpreted through a quasi-exact modal expansion. This last method gives explicit opto-geometrical rules allowing to finely understand the general trends in 1D and 2D. In more advanced examples, we show that multi-cavity and/or s…
We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged ether on top or on the both sides of the slab. Based on the Fourier modal approach we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-side grating possesses either mirror or glide symmetry the Bloch bound states are stable to variation of parameters as far as the above symme…
Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is normal to the slab plane. If dielectric permittivity of the waveguide core is more than extraordinary permittivity of the hyperbolic medium each TM mode has two cut-off frequencies. The dispersion relations for these modes are found and numerically solved for cases of focusing and defocussing medium of the core. Number of possible modes at given frequency depends…
We present the experimental observation of the superlensing effect in a slab of a one-dimensional photonic crystal made of tilted dielectric elements. We show that this flat lens can achieve subwavelength resolution in different frequency bands. We also demonstrate that the introduction of a proper corrugation on the lens surface can dramatically improve both the transmission and the resolution of the imaged signal.
We analyse van der Waals interactions between a pair of dielectrically anisotropic plane-layered media interacting across a dielectrically isotropic solvent medium. We develop a general formalism based on transfer matrices to investigate the van der Waals torque and force in the limit of weak birefringence and dielectric matching between the ordinary axes of the anisotropic layers and the solvent. We apply this formalism to study the following systems: (i) a pair of single anisotropic layers, (ii) a single anisotropic layer interacting with a multilayered slab consisting of alternating anisotr…
Functional tunability, environmental adaptability, and easy fabrication are highly desired properties in metasurfaces. Here we provide a tunable bilayer metasurface composed of two stacked identical dielectric magnetic mirrors, which are excited by the dominant electric dipole and other magnetic multipoles, exhibiting nonlocal electric field enhancement near the interface and high reflection. Differ from the tunability through the direct superposition of two structures with different functionalities, we achieve the reversible conversion between high reflection and high transmission by manipula…
Recently reported large values of exciton-polariton nonlinearity of transition metal dichalcogenide (TMD) monolayers coupled to optically resonant structures approach the values characteristic for GaAs-based systems in the regime of strong light-matter coupling. Contrary to the latter, TMD-based polaritonic devices remain operational at ambient conditions and therefore have greater potential for practical nanophotonic applications. Here we present the study of the nonlinear properties of Ta$_2$O$_5$ slab waveguide coupled to a WSe$_2$ monolayer. We first confirm that the hybridization between …
The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance d…
We investigate a short (~1.5μm) partially-corrugated tapered waveguide structure for mode coupling from a silicon micro-slab to a plasmonic nano-gap waveguide at the optical communication frequency. More than 80% transmission efficiency is reported numerically for the first time. The result indicates that the corrugated waveguide structure should not only be helpful for realizing full on-chip silicon plasmonic devices but also a good choice for mode coupling enhancement from dielectric waveguides to plasmonic waveguides. Meanwhile, we point out that the coupling mechanism reported here is diff…
We show that anisotropic negative effective dispersion relation can be achieved in pure dielectric rod-type metamaterials by turning from the symmetry of a square lattice to that of a rectangular one, i.e. by breaking the rotation symmetry of effective homogeneous medium. Theoretical predictions and conclusions are verified by both numerical calculations and computer based simulations. The proposed anisotropic metamaterial, is used to construct a refocusing slab-lens and a subdiffraction hyperlens. The all-dielectric origin makes it more straightforward to address loss and scaling, two major i…
We present a way of exciting surface plasmon polaritons along non-patterned metallic surfaces by means of a flat squeezing slab designed with transformation optics. The slab changes the dispersion relation of incident light, enabling evanescent coupling to propagating surface plasmons. Unlike prism couplers, the proposed device does not introduce reflections at its input interface. Moreover, its compact geometry is suitable for integration. A feasible dielectric implementation of the coupler is suggested. Finally, we show that the angular response of the device can be engineered by using a non…
Two results about the planewave response of an isotropic, dielectric--magnetic, homogeneous, planar slab are deduced when the real parts of both the permittivity and the permeability are altered from positive to negative. First, the reflection and the transmission coefficients suffer phase reversals without change in their respective magnitudes. Second, the Goos-Haenchen shifts experienced by beams on total reflection reverse their directions.
We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics whic…
In terahertz (THz) photonics, there is an ongoing effort to develop thin, compact devices such as dielectric photonic crystal (PhC) slabs with desirable light matter interactions. However, previous works in THz PhC slabs are limited to rigid substrates with thicknesses $\sim$ 100s of micrometers. Dielectric PhC slabs have been shown to possess in-plane modes that are excited by external radiation to produce sharp guided mode resonances with minimal absorption for applications in sensors, optics and lasers. Here, we confirm the existence of guided resonances in a membrane-type THz PhC slab with…
When a guided mode is excited in a dielectric slab coupled to a backward surface wave at the interface between a dielectric and a left-handed medium, light is confined in the structure : this is a light wheel. Complex plane analysis of the dispersion relation and coupled-mode formalism give a deep insight into the physics of this phenomenon (lateral confinement and the presence of a dark zone).
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 study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode wit…
The valleys of two-dimensional transition metal dichalcogenides (TMDCs) offer a new degree of freedom for information processing. To take advantage of this valley degree of freedom, on one hand, it is feasible to control valleys by utilizing different external stimuli like optical and electric fields. On the other hand, nanostructures are also used to separate the valleys by near field coupling. However, for both above methods, either required low-temperature environment or low degree of coherence properties limit their further applications. Here, we demonstrate all-dielectric photonic crystal…
The traversal times for an electromagnetic pulse traversing a slab of dispersive and dissipative material with negative dielectric permittivity ($ε$) and magnetic permeability ($μ$) have been calculated by using the average flow of electromagnetic energy in the medium. The effects of bandwidth of the pulse and dissipation in the medium have been investigated. While both large bandwidth and large dissipation have similar effects in smoothening out the resonant features that appear due to Fabry-Pérot resonances, large dissipation can result in very small or even negative traversal times near the…
