The optical properties of slab waveguides made of indefinite permittivity ($\vep$) materials (IEM) are considered. In this medium the transverse permittivity is negative while the longitudinal permittivity is positive. At any given frequency the waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward-wave. The rest of them are backward waves which can have very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity. Above the critical thickness, the waveguide supports complex-conjugate decay modes instead of propagating modes. The presence of loss in IEMs will lift the degeneracy, resulting in modes with finite group velocity. Feasible realization is proposed. The performance of IEM waveguide is analyzed and possible applications are discussed which are supported by numerical calculations. These slab waveguides can be used to make optical delay lines in optical buffers to slow down and trap light, to form open cavities, to generate strong longitudinal electric fields, and as phase shifters in optical integrated circuits.
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 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 theoretically predict efficient optical second-harmonic generation (SHG) from a few hundred nanometer thick slab consisting of a quadratic nonlinear anisotropic medium whose linear principal permittivities are, at the fundamental wavelength, very small and have different signs (indefinite medium). We show that, by illuminating the slab with a p-polarized fundamental wave (with intensity of a few MW/cm^2), a highly efficient scattering of the second-harmonic field occurs when the conditions of linear complete slab transparency for the fundamental wave are met. The high efficiency of the SHG …
We show that resonant tunneling of electromagnetic fields can occur through a three-layer structure composed of a single-negative (i.e., either negative-permittivity or negative-permeability) slab paired with bi-layer made of double-positive (i.e., positive permittivity and permeability) media. In particular, one of the two double-positive media can be chosen arbitrarily (even vacuum), while the other may exhibit extreme (either near-zero or very high) permittivity/permeability values. Our results on this counterintuitive tunneling phenomenon also demonstrate the possibility of synthesizing do…
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…
It is shown that the transparency of opaque material with negative permittivity exhibits resonant behavior. The resonance occurs as a result of the excitation of the surface waves at slab boundaries. Dramatic field amplification of the incident evanescent fields at the resonance improves the resolution of the the sub-wavelength imaging system (superlens). A finite thickness slab can be totally transparent to a \textit{p}-polarized obliquely incident electromagnetic wave for certain values of the incidence angle and wave frequency corresponding to the excitation of the surface modes. At the res…
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…
Anisotropic materials with different signs of components of the permittivity tensor are called indefinite materials. Known realizations of indefinite media suffer of high absorption losses. We show that periodic arrays of parallel carbon nanotubes (CNTs) can behave as a low-loss indefinite medium in the infrared range. We show that a finite-thickness slab of CNTs supports the propagation of backward waves with small attenuation in an ultra-broad frequency band. In prospective, CNT arrays can be used for subwavelength focusing and detection, enhancing the radiation efficiency of small sources.
We predict that a liquid crystal/silver nanoparticles mixture can be designed so that, in a frequency range, its effective ordinary and extraordinary permittivities have real parts of different signs. We exploit this result to design a nano-photonic device obtained by sandwiching a few hundred nanometer thick slab of the proposed mixture between two silica layers. By resorting to full-wave simulations, we show that, by varying the direction of an externally applied electric field, the device can be used as an optical modulator since its transmissivity can be switched between 0.02 and 0.4 at a …
An ambichiral structure comprising sheets of an anisotropic dielectric material rejects normally incident plane waves of one circular polarization (CP) state but not of the other CP state, in its fundamental Bragg regime. However, if the same structure is made of an dielectric--magnetic material with indefinite permittivity and permeability dyadics, it may function as a polarization--universal rejection filter because two of the four planewave components of the electromagnetic field phasors in each sheet are of the positive--phase--velocity type and two are of the negative--phase--velocity typ…
Using complex plane analysis we show that left-handed slab may support either leaky slab waves, which are backward because of negative refraction, or leaky surface waves, which are backward or forward depending on the propagation direction of the surface wave itself. Moreover, there is a general connection between the reflection coefficient of the left-handed slab and the one of the corresponding right-handed slab (with opposite permittivity and permeability) so that leaky slab modes are excited for the same angle of incidence of the impinging beam for both structures. Many negative giant late…
The resolution of conventional optical lenses is limited by the wavelength. Materials with negative refractive index have been shown to enable the generation of an enhanced resolution image where both propagating and non-propagating waves are employed. We analyze such a Veselago lens by exploiting some exact one dimensional integral expressions for the quasi-static electric potential of a point charge in that system. Those were recently obtained by expanding that potential in the quasi-static eigenfunctions of a three-flat-slabs composite structure. Numerical evaluations of those integrals, us…
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…
Optical modes in anisotropic slab waveguides with topological and chiral magnetoelectric effects are investigated analytically, by deriving the closed-form characteristic equations of the modes and hence computing the dispersion-diagrams. In order to compute the characteristic equations, a vector-potential approach is introduced by incorporating a generalized Lorentz gauge, and the corresponding Helmholtz equations are derived correspondingly. It will be shown that the formation of the complex modes and hybridization of the optical modes in such slab waveguides is inevitable. Moreover, when th…
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…
Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus the nonpropagating near-fields, thereby achieving a subdiffraction image. In this work we discuss the sensitivity of the subwavelength focus to various slab parameters, pointing out the connection to slab plasmon modes. We also note and resolve a paradox associated with the perfect imaging of a point source. We conclude that subwavelength resolution is achieva…
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 paramete…
The materials having negative permittivity and negative permeability, which are labeled as double-negative (DNG) materials, have attracted much attention because of their unusual physical properties, which are different from those of conventional double-positive (DPS) materials. Animations obtained by the finite-difference time-domain method (FDTD) are provided showing how a transient sinusoidal signal that starts at t=0 propagates in the DPS and DNG waveguides. Three types of waveguides are considered: a slab or grounded slab inside the cladding medium and a parallel-plate waveguide filled wi…
A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physica…
We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. …
A slab with relative permittivity $ε= - 1 + iδ$ and permeability $μ= - 1 + iδ$ has a critical distance away from the slab where a small particle will either be cloaked or imaged depending on whether it is located inside or outside that critical distance. We find that the optical force acting on a small cylinder under plane wave illumination reaches a maximum value at this critical distance. Contrary to the usual observation that superlens systems should be highly loss-sensitive, this maximum optical force remains a constant when loss is changed within a certain range. For a fixed particle-slab…
We give a solution to the fundamental problem of restoring optical resonances in deep subwavelength structures by resorting to indefinite metamaterials. We prove that a nanometric thick hyperbolic slab with very small permittivities exhibits etalon resonances and provides high-contrast optical angular filtering. This is possible since the hyperbolic dispersion allows the vacuum radiation to couple with medium plane waves with longitudinal wavenumbers large enough to yield optical standing waves within the nanometric slab thickness. Our findings can form the basis of a novel way for shrinking o…
We show that the finite-difference frequency-domain method is well-suited to study subwavelength lensing effects in left-handed materials (LHM's) and related problems. The method is efficient and works in the frequency domain, eliminating the need for specifying dispersion models for the permeability and permittivity as required by the popular finite-difference time-domain method. We show that "superlensing" in a LHM slab with refractive index n = -1 can be approached by introducing an arbitrarily small loss term. We also study a thin silver slab, which can exhibit subwavelength imaging in the…
The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefr…
Non-radiative coupling between conductive coils is a candidate mechanism for wireless energy transfer applications. In this paper, we propose a power relay system based on a near-field metamaterial superlens, and present a thorough theoretical analysis of this system. We use time-harmonic circuit formalism to describe all interactions between two coils attached to external circuits and a slab of anisotropic medium with homogeneous permittivity and permeability. The fields of the coils are found in the point-dipole approximation using Sommerfeld integrals, which are reduced to standard special …
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…
We show that a thin superconductor slab illuminated by a desired pattern of light behaves as a completely controllable two-dimensional photonic media that could be applied in a wide range of optical devices. In this case, the permittivity spatial variation, which is fundamentally required in many photonic devices, is achieved by means of selective variation of cooper-pair density under patterned irradiation. The process of photo-effect in superconductors is the proposed mechanism for deformation of spatial distribution of cooper pair density and consequently non-uniform permittivity. In this p…
We analyze spectrum of waveguide modes of an arbitrary uniaxial anisotropic metamaterial slab with non-local electromagnetic response whose permittivity tensor could be described within Drude approximation. Spatial dispersion was introduced within the hydrodynamical model. Both anisotropy and spatial dispersion were considered as perturbations. This helps to distinguish their effect on the spectrum of the slab and to analyze lifting of the degeneracy of eigenmodes at plasma frequency in detail. Spatial dispersion is shown to result in break of the singularity in the den- sity of optical states…
We consider bound states in the continuum (BICs) in low-contrast dielectric gratings (DGs). It is demonstrated that the BICs originate from the reduced guided modes on the effective dielectric slab with the permittivity equal to the average permittivity of the DG. In case of isolated resonances the positions of BICs can be found from two-wave dispersion relationships for guided leaky modes. In the case of the degeneracy between the two families of leaky modes the system exhibits an avoided crossing of resonances. In the spectral vicinity of the avoided crossing the transmittance as well as the…
We examine some of the optical properties of a metamaterial consisting of thin layers of alternating metal and dielectric. We can model this material as a homogeneous effective medium with anisotropic dielectric permittivity. When the components of this permittivity have different signs, the behavior of the system becomes very interesting: the normally evanescent parts of a P-polarized incident field are now transmitted, and there is a preferred direction of propagation. We show that a slab of this material can form an image with sub-wavelength details, at a position which depends on the frequ…
In this report, we achieved total transmission and reflection in a slab of zero index materials with defect(s). By controlling the defect's radius and dielectric constant, we can obtain total transmission and reflection of EM wave. The zero index materials, in this report, stand for materials with permittivity and permeability which are simultaneously equal to zero or so called matched impedance zero index materials. Along with theoretical calculations and simulation demonstrations, we also discuss about some possible applications for the proposed structure such as shielding or cloaking an obj…
In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave-matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static-like regime where the electromagnetic field is spatially slowly-varying over a physically large region. The so-called epsilon-near-zero metamaterials thus offer an ideal platform where to manipulate the inner details of the "stretched" field. Here we theoretically prove that a standard nonlinearity is abl…
We study the mode conversion and resonant absorption phenomena occurring in a slab of a stratified anisotropic medium, optical axes of which are tilted with respect to the direction of inhomogeneity, using the invariant imbedding theory of wave propagation. When the tilt angle is zero, mode conversion occurs if the longitudinal component of the permittivity tensor, which is the one in the direction of inhomogeneity in the non-tilted case, varies from positive to negative values within the medium, while the transverse component plays no role. When the tilt angle is nonzero, the wave transmissio…
Metamaterials with simultaneous negative permittivity and negative permeability (also called left-handed materials) open new avenues to achieving unprecedented physical properties and functionality unattainable with naturally occurring materials. It has been predicted that a metamaterial slab waveguide can slow down light significantly (even to zero velocity) as the thickness of the core layer approaches a critical thickness. Here we show that coupling between the forward and backward modes becomes significant near the critical thickness due to the good matching of the wavevectors and modal pr…
We demonstrate that arrays of split ring resonators (SRR) can have negative refractive index at optical frequencies (~1.4 eV). Our calculations reveal that the electric fields of radiation interact strongly with even symmetric SRR at optical frequencies as the size of the SRR becomes of the order of the wavelength (~lambda /3) for practicably realizable structures. We also demonstrate by calculations the focussing of a line source by a flat slab of a (2D) SRR medium. The negative refractive index here is related to the plasmonic excitations of the SRR and cannot be directly explained by the us…
The evidence that double negative media, with an effective negative permittivity, and an effective negative permeability, can be manufactured to operate at frequencies ranging from microwave to optical is ushering in a new era of metamaterials. They are referred to here as 'left-handed', even though a variety of names is evident from the literature. In anticipation of a demand for highly structured integrated practical waveguides, this paper addresses the impact of this type of medium upon waveguides that can be also nonlinear. After an interesting historical overview and an exposure of some s…
Optical imaging beyond the diffraction limit was one of the primary motivations for negative-index metamaterials, resulting in Pendry's perfect lens and the more attainable superlens. While these approaches offer sub-diffractional resolution, they do not provide a mechanism for magnification of the image. Hyperbolic (or indefinite-permittivity) metamaterials have been theoretically considered and experimentally demonstrated to provide simultaneously subdiffractive imaging and magnification; however, they are plagued with low efficiency and complex fabrication. In this work, we present theoreti…
