We propose a coherent optical method for creating negative refractive index (NRI) for a gaseous ensemble of ground-state polar molecules possessing both permanent electric and magnetic moments. Exploiting the pure rotational transition between the two lowest rotational levels of the ground vibrational state one can generate two dressed states of mixed parity using a microwave laser. These dressed states are then used as the two lower states of a Λ-type three-level scheme using two infrared lasers to couple them to another ro-vibrational level in the ground-state manifold. One of the infrared lasers is used as a weak probe and the other as a control field with a fixed detuning. We take into account local-field effects on the dielectric response of the medium at the probe frequency in terms of Clausius-Mossoti relation. We extract magnetic response out of purely dielectric response and calculate the magnetic permeability of the medium in terms of dielectric susceptibility. Our results show that there is a small frequency window near the two-photon resonance where both electric permittivity and magnetic permeability are negative with vanishingly small absorption. The figure of merit for the medium is shown to exceed unity. We interpret our results in terms of the proximity of EIT and quantum interference. We discuss the possible realization of our method using cold polar molecules that are recently experimentally produced.
A fundamental building block for nanophotonics is the ability to achieve negative refraction of polaritons, because this could enable the demonstration of many unique nanoscale applications such as deep-subwavelength imaging, superlens, and novel guiding. However, to achieve negative refraction of highly squeezed polaritons, such as plasmon polaritons in graphene and phonon polaritons in boron nitride (BN) with their wavelengths squeezed by a factor over 100, requires the ability to flip the sign of their group velocity at will, which is challenging. Here we reveal that the strong coupling bet…
Negative refraction provides an attractive platform to manipulate mid-infrared and terahertz radiation for molecular sensing and thermal radiation applications. However, its implementation based on available metamaterials and plasmonic media presents challenges associated with optical losses, limited spatial confinement, and lack of active tunability in this spectral range. Here, we demonstrate gate-tunable negative refraction at mid-infrared frequencies using hybrid topological polaritons in van der Waals heterostructures with high spatial confinement. We experimentally visualize wide-angle n…
Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction o…
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 …
The in-plane negative refraction of high-momentum (i.e., high-k) photonic modes could enable many applications such as imaging and hyperlensing in a planar platform at deep-subwavelength scales. However, its practical implementation in experiments remains elusive so far. Here we propose a class of hyperbolic metasurfaces, which is characterized by an anisotropic magnetic sheet conductivity and can support the in-plane ultrahigh-k magnetic designer polaritons. Based on such metasurfaces, we report the first experimental observation of the all-angle negative refraction of designer polaritons at …
Negative refraction plays an important role in acoustic wave manipulation and imaging. However, conventional systems based on acoustic metamaterials suffer from the limits induced by loss-related and resolution issues. In this work, a parity-time (PT)-symmetric system is introduced to realize loss-free bidirectional acoustic negative refraction. The system is composed of a pair of locally PT-symmetric multi-layer metasurfaces sandwiching a region of free space, which also forms a global PT-symmetry. The property of bidirectional negative refraction, which is rare for regular PT-symmetric struc…
We develop a theory to compute and interpret the photonic band structure of a periodic array of metallic helices for the first time. Interesting features of band structure include the ingenuous longitudinal and circularly polarized eigenmodes, the wide polarization gap [Science 325, 1513 (2009)], and the helical symmetry guarantees the existence of negative group velocity bands at both sides of the polarization gap and band crossings pinned at the zone boundary with fixed frequencies. A direct proof of negative refraction via a chiral route [Science 306, 1353 (2004)] is achieved for the first …
The refraction of linearly polarized plane waves into a half-space occupied by a material moving at constant velocity was studied by directly implementing the Lorentz transformations of electric and magnetic fields. From the perspective of a co-moving observer, the moving material was a spatially local, pseudochiral omega material. Numerical studies revealed that whether or not negative refraction occurrs in the moving material depends upon the speed of movement as well as the angle of incidence and the polarization state of the incident plane wave. Furthermore, the phenomenons of negative pha…
A plasmonic nanoantenna probed by a plane-polarized optical field in a medium with no gain materials can show zero absorption or even amplification, while exhibiting maximal polarizability. This occurs through coupling to an adjacent nanoantenna in a specially designed metamolecule, which is pumped by an orthogonal optical field with phase shift. The introduced scheme is a classical counterpart of an effect known in quantum optics as enhancement of the index of refraction (EIR). In contrary to electromagnetically induced transparency (EIT), where the medium is rendered highly dispersive at the…
The energy flux patterns of inverse Goos-Hanchen (GH) shift around the interface between air and negatively refractive photonic crystal (NRPhC) with different surface terminations is investigated. Results show that NRPhC exhibits inverse GH shift in TM and TE polarization, and the localization and pattern of energy flux differ in TM and TE polarizations and are strongly affected by surface termination. This is different to the condition of negative permittivity materials (i.e., metal), which only presents inverse GH shift in TM polarization. In the case of TE polarization, the energy flux patt…
We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magneto-dielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bi-cubic lattice of dielectric and magnetic dipoles for a lattice constant small compared to the resonance wavelength $λ$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a selfconsistent way by a proper incorporation of the singular self-interaction terms…
This letter proposes a quasi-planar chiral resonator suitable for the design of negative refractive index matamaterial. It is presented an analytical model for the determination of its polarizabilities, and the viability of negative refraction in chiral and racemic arrangements with the proposed inclusions is analyzed. The present analysis is expected to pave the way to the design of negative refractive index matamaterials made of a single kind of inclusions feasible from standard photo-etching techniques.
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
Crystal quartz is a well-known anisotropic medium with optically active phonons in the THz region where hyperbolic phonon-polaritons can be excited. Here, we use this material to illustrate how the behavior of bulk and surface hyperbolic polaritons can be drastically modified by changing the orientation of the crystal's anisotropy axis with respect to its surface. We demonstrate, both theoretically and experimentally, phenomena associated with the orientation of hyperbolic media. We show the consequences of slight changes in the crystal's orientation in various ways, from the creation of hyper…
The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wavevectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that: (i) negative (positive) refraction can arise even though the phase velocity is positive (negative); (ii) counterposition can arise in ins…
We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, however, in general, do not satisfy the conservation laws for individual photons in consequence of the lack of the ``which path'' information in a two-channel wave scattering. The field structure for the reflected/refracted beam is analyzed. In the scattering of a linearly-polarized beam, photons of opposite helic…
We extend designs of perfect lenses to the focussing of surface plasmon polaritons (SPPs) propagating at the interface between two anisotropic media of opposite permittivity sign. We identify the role played by the components of anisotropic and heterogeneous tensors of permittivity and permeability, deduced from a coordinate transformation, in the dispersion relation governing propagation of SPPs. We illustrate our theory with three-dimensional finite element computations for focussing of SPPs by perfect flat and cylindrical lenses.
From the fundamental requirement of causality, we derive a rigorous criterion of negative refraction (left-handedness). This criterion imposes the lower limits on the electric and magnetic losses in the region of the negative refraction. If these losses are eliminated or significantly reduced by any means, including the compensation by active (gain) media, then the negative refraction will disappear. This theory can be particularly useful in designing new left-handed materials: testing the expected polarizabilities of a medium against this criterion would check the compliance with the causalit…
Nonlinear response in a material increases with its index of refraction as $n^4$. Commonly, $n \sim$ 1 so that diffraction, dispersion, and chromatic walk-off limit nonlinear scattering. Ferroelectric crystals with a periodic 3D polarization structure overcome some of these constraints through versatile Cherenkov and quasi-phase-matching mechanisms. Three-dimensional self-structuring can also lead to a giant optical refraction. Here, we perform second-harmonic-generation experiments in KTN:Li in conditions of giant broadband refraction. Enhanced response causes wavelength conversion to occur i…
The propagation of electromagnetic waves in the anisotropic medium with a single-sheeted hyperboloid dispersion relation is investigated. It is found that in such an anisotropic medium E- and H-polarized waves have the same dispersion relation, while E- and H-polarized waves exhibit opposite amphoteric refraction characteristics. E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted at the interface associated with the anisotropic medium. By suitably using the properties of anomalous refraction in the anisotropic medium it is possible t…
Theoretical and computational study of reflection and refraction of electromagnetic waves with $p$-polarized and normal incidence electric wave amplitude vector on anisotropic, inhomogeneous and linear medium has been done. The medium used in this study is a model of susceptibility in the form of rank-2 tensor which its value depends on the frequency, position and time. Theoretical and computational formulation of transmittance and reflectance are then tested using vacuum and FeF$_2$ magnetic material.
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through…
We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and \textit{metamaterials}, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normaly and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For n…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane electromagnetic waves in ordinary dielectrics, the kinematical and dynamical aspects of these phenomena are studied, such as the intensity of the various wave components and the change in the polarization of the wave as it crosses the boundary. As a prerequisite of this, we show that the plane wave solution must be written as a suitable superposition of the cir…
Time-varying metasurfaces are emerging as a powerful instrument for the dynamical control of the electromagnetic properties of a propagating wave. Here we demonstrate an efficient time-varying metasurface based on plasmonic nano-antennas strongly coupled to an epsilon-near-zero (ENZ) deeply sub-wavelength film. The plasmonic resonance of the metal resonators strongly interacts with the optical ENZ modes, providing a Rabi level spitting of ~30%. Optical pumping at frequency ω induces a nonlinear polarisation oscillating at 2ω responsible for an efficient generation of a phase conjugate and a ne…
We inspect the optical properties of dissipative double-negative metamaterials (DNMM) and find explicit expression for the total reflection angle and the correct Fresnel formulae describing the reflection and refraction for the DNMM at the oblique incident of the electromagnetic wave on the interface for \textit{TE} as well as \textit{TM} electromagnetic wave polarization. The reflectivity and transmissivity of DNMM film embedded in a positive refraction index (PIM) surrounding are presented and discussed.
Research on photonics and metamaterials constantly challenges our intuitive understanding of the behaviour of light. In recent years we have seen negative refraction, focusing of light by a flat slab, a ``perfect'' prism, and an ``invisibility cloak'' [1-6]. It is generally understood that the cause of this unusual behaviour is the strong (anomalous) dispersion, i.e., dependence of the material properties on the frequency of light. Dispersion can be either due to a natural microscopic resonance of the material as with surface plasmons-polaritons, or due to an effective resonance (band-gap) of …
Recently discovered valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional gapped valleytronic materials such as bilayer graphene or MoS2. Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states at the internal domain wall between two VPCs with spectrally overlapping bandgap zones and opposite half-integer valley-Chern indices. We experimentally demonstrate the robustness of the kink states in VPCs that support degenerate transverse-electric-like (TE) and transverse-magnetic-like (TM) topolo…
We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having resonant atomic transitions to excited states with different angular momentum. We employ a computational method based on the recently proposed Dirichlet-to-Neumann (DtN) map technique which accurately models non-Markovian dynamics as well as interactions involving higher-order electric and magnetic multipole transitions. We design topologically robust edge states…
The specific optical nonlinearities inherent in aggregates of metal nanoparticles under pico- and nanosecond pulsed laser irradiation are studied in nanoparticle aggregates formed in silver hydrosols. The results of experimental studies of the correlation between the degree of aggregation of silver hydrosols and their nonlinear refraction index at the wavelengths 0.532 and 1.064 microns are discussed. The experiments revealed that nonlinear refraction index changes its sign at 1.064 microns as the degree of the hydrosol aggregation grows. The role of various processes occurring in resonant dom…
We develop a new approach to build a material with negative refraction index. In contrast to conventional designs which make use of a resonant behavior to achieve a non-zero magnetic response, our material is intrinsically non-magnetic and relies on an anisotropic dielectric constant to provide a left-handed response in waveguide geometry. We demonstrate that the proposed material can support surface (polariton) waves, and show the connection between polaritons and the enhancement of evanescent fields, also referred to as super-lensing.
Light transfer in gradient-index media generally follows curved ray trajectories, which will cause light beam to converge or diverge during transfer and induce the rotation of polarization ellipse even when the medium is transparent. Furthermore, the combined process of scattering and transfer along curved ray path makes the problem more complex. In this paper, a Monte Carlo method is presented to simulate polarized radiative transfer in gradient-index media that only support planar ray trajectories. The ray equation is solved to the second order to address the effect induced by curved ray tra…
We propose a semi-analytical modeling of smoothed laser beams deviation induced by plasma flows. Based on a Gaussian description of speckles, the model includes spatial, temporal and polarization smoothing techniques,through fits issued from hydrodynamic simulations with a paraxial description of electromagnetic waves. This beam bending model is then included in a ray tracing algorithm, and carefully validated. When applied as a post-process to the propagation of the inner cone in a full-scale simulation of a NIF experiment,the beam bending along the path of the laser affects the refraction co…
We uncover and identify the regime for a magnetically and ferroelectrically controllable negative refraction of light traversing multiferroic, oxide-based metastructure consisting of alternating nanoscopic ferroelectric (SrTiO$_2$) and ferromagnetic (Y$_3$Fe$_2$(FeO$_4$)$_3$, YIG) layers. We perform analytical and numerical simulations based on discretized, coupled equations for the self-consistent Maxwell/ferroelectric/ferromagnetic dynamics and obtain a biquadratic relation for the refractive index. Various scenarios of ordinary and negative refraction in different frequency ranges are analy…
We study perspectives of nanowire metamaterials for negative-refraction waveguides, high-performance polarizers, and polarization-sensitive biosensors. We demonstrate that the behavior of these composites is strongly influenced by the concentration, distribution, and geometry of the nanowires, derive an analytical description of electromagnetism in anisotropic nanowire-based metamaterials, and explore the limitations of our approach via three-dimensional numerical simulations. Finally, we illustrate the developed approach on the examples of nanowire-based high energy-density waveguides and non…
