Nonreciprocal response of electrically biased graphene-coated fiber.

Here, we theoretically investigate the nonreciprocal response of an electrically biased graphene-coated dielectric fiber. By electrically biasing the graphene coating along the fiber axis, the dynamic conductivity of graphene exhibits a nonsymmetric response with respect to the longitudinal component of guided-mode wave vectors. Consequently, the guided waves propagating in two opposite directions may encounter distinct propagation features. In this work, the electromagnetic properties, such as modal dispersion and some field distributions, are presented, and the strength of nonreciprocity is discussed for different parameters of graphene, such as its chemical potential and material loss. Furthermore, the influence of the radius of the fiber on the nonreciprocal response is investigated. We envision that such nonreciprocal optical fibers may find various potential applications in the THz regime.

Feature issue introduction: temporal and spatiotemporal metamaterials.

Temporal modulation of material parameters provides a new degree of freedom for metamaterials, metasurfaces and wave-matter interactions as a whole. In time-varying media the electromagnetic energy may not be conserved, and the time reversal symmetry may be broken, which may lead to novel physical effects with potential applications. Currently, theoretical and experimental aspects of this field are rapidly advancing, expanding our understanding of wave propagation in such complex spatiotemporal platforms. This field promises novel possibilities and directions in research, innovation and exploration.

Effect of Epsilon-Near-Zero Modes on the Casimir Interaction between Ultrathin Films.

Vacuum fluctuation-induced interactions between macroscopic metallic objects result in an attractive force between them, a phenomenon known as the Casimir effect. This force is the result of both plasmonic and photonic modes. For very thin films, field penetration through the films will modify the allowed modes. Here, we theoretically investigate the Casimir interaction between ultrathin films from the perspective of force distribution over real frequencies for the first time. Pronounced repulsive contributions to the force are found due to the highly confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only exist in ultrathin films. These contributions persistently occur around the ENZ frequency of the film irrespective of the interfilm separation. We further associate the ENZ modes with a striking thickness dependence of a proposed figure of merit (FOM) for conductive thin films, suggesting that the motion of objects induced by Casimir interactions is boosted for deeply nanoscale sizes. Our results shed light on the correlation between special electromagnetic modes and the vacuum fluctuation-induced force as well as the resulting mechanical properties of ultrathin ENZ materials, which may create new opportunities for engineering the motion of ultrasmall objects in nanomechanical systems.

Possibility for inhibited spontaneous emission in electromagnetically open parity-time-symmetric guiding structures.

Remote sensing and manipulation of quantum emitters are functionalities of significant practical importance in quantum optics. Unfortunately, these abilities are considered as fundamentally challenging in systems of inhibited spontaneous emission. The reason is intimately related to the common perception that, in order to nullify the spontaneous emission decay rate, the system has to be electromagnetically closed, meaning that all loss channels should be avoided, including radiation. However, since radiation is prohibited in these systems, far-field sensing and by reciprocity, also far-field manipulation are considered impossible. Here, we suggest a possible solution to this challenge and theoretically propose an electromagnetically open system that may exhibit a complete inhibition of spontaneous emission while supporting guiding waves. This peculiar functionality is achieved through a feedback wave mechanism that is found in parity-time-symmetric structure. The analysis is based on an exact Green's function derivation as well as full wave simulations involving a realistic design for the sake of future experimental validation.

Near-zero-index media as electromagnetic ideal fluids.

Near-zero-index (NZI) supercoupling, the transmission of electromagnetic waves inside a waveguide irrespective of its shape, is a counterintuitive wave effect that finds applications in optical interconnects and engineering light-matter interactions. However, there is a limited knowledge on the local properties of the electromagnetic power flow associated with supercoupling phenomena. Here, we theoretically demonstrate that the power flow in two-dimensional (2D) NZI media is fully analogous to that of an ideal fluid. This result opens an interesting connection between NZI electrodynamics and fluid dynamics. This connection is used to explain the robustness of supercoupling against any geometrical deformation, to enable the analysis of the electromagnetic power flow around complex geometries, and to examine the power flow when the medium is doped with dielectric particles. Finally, electromagnetic ideal fluids where the turbulence is intrinsically inhibited might offer interesting technological possibilities, e.g., in the design of optical forces and for optical systems operating under extreme mechanical conditions.

Non-Hermitian doping of epsilon-near-zero media.

In solid-state physics, "doping" is a pivotal concept that allows controlling and engineering of the macroscopic electronic and optical properties of materials such as semiconductors by judiciously introducing small concentrations of impurities. Recently, this concept has been translated to two-dimensional photonic scenarios in connection with host media characterized by vanishingly small relative permittivity ("epsilon near zero"), showing that it is possible to obtain broadly tunable effective magnetic responses by introducing a single, nonmagnetic doping particle at an arbitrary position. So far, this phenomenon has been studied mostly for lossless configurations. In principle, the inevitable presence of material losses can be compensated via optical gain. However, taking inspiration from quantum (e.g., parity-time) symmetries that are eliciting growing attention in the emerging fields of non-Hermitian optics and photonics, this suggests considering more general gain-loss interactions. Here, we theoretically show that the photonic doping concept can be extended to non-Hermitian scenarios characterized by tailored distributions of gain and loss in either the doping particles or the host medium. In these scenarios, the effective permeability can be modeled as a complex-valued quantity (with the imaginary part accounting for the gain or loss), which can be tailored over broad regions of the complex plane. This enables a variety of unconventional optical responses and waveguiding mechanisms, which can be, in principle, reconfigured by varying the optical gain (e.g., via optical pumping). We envision several possible applications of this concept, including reconfigurable nanophotonics platforms and optical sensing, which motivate further studies for their experimental validation.

Tunable radiation enhancement and suppression using a pair of photonically doped epsilon-near-zero (ENZ) slabs.

Manipulation of the radiation efficiency and pattern of quantum emitters by engineering the electromagnetic properties of the surrounding medium is crucial for designing various light sources. Here, we theoretically demonstrate the possibility of designing a compact and tunable resonator using a pair of photonically doped epsilon-near-zero (ENZ) slabs that are separated by a deeply subwavelength air gap. Such resonators are shown to be capable of switching between completely transparent and opaque states, for a TM-polarized normally incident plane wave, by slightly changing the permittivity of the dielectric dopants. We exploit this behavior for tunable radiation enhancement and suppression for a quantum emitter placed inside the air gap.

Manipulating thermal emission with spatially static fluctuating fields in arbitrarily shaped epsilon-near-zero bodies.

The control and manipulation of thermal fields is a key scientific and technological challenge, usually addressed with nanophotonic structures with a carefully designed geometry. Here, we theoretically investigate a different strategy based on epsilon-near-zero (ENZ) media. We demonstrate that thermal emission from ENZ bodies is characterized by the excitation of spatially static fluctuating fields, which can be resonantly enhanced with the addition of dielectric particles. The "spatially static" character of these temporally dynamic fields leads to enhanced spatial coherence on the surface of the body, resulting in directive thermal emission. By contrast with other approaches, this property is intrinsic to ENZ media and it is not tied to its geometry. This point is illustrated with effects such as geometry-invariant resonant emission, beamforming by boundary deformation, and independence with respect to the position of internal particles. We numerically investigate a practical implementation based on a silicon carbide body containing a germanium rod.

Soft surfaces and enhanced nonlinearity enabled via epsilon-near-zero media doped with zero-area perfect electric conductor inclusions.

Introducing a dielectric inclusion inside an epsilon-near-zero (ENZ) host has been shown to dramatically affect the effective permeability of the host for a TM-polarized incident wave, a concept coined as photonic doping [Science355, 1058 (2017)SCIEAS0036-807510.1126/science.aal2672]. Here, we theoretically study the prospect of doping the ENZ host with infinitesimally thin perfect electric conductor (PEC) inclusions, which we call "zero-area" PEC dopants. First, we theoretically demonstrate that zero-area PEC dopants enable the design of soft surfaces with an arbitrary cross-sectional geometry. Second, we illustrate the possibility of engineering the PEC dopants with the goal of transforming the electric field distribution inside the ENZ while maintaining a spatially invariant magnetic field. We exploit this property to enhance the effective nonlinearity of the ENZ host.

Electromagnetic Funnel: Reflectionless Transmission and Guiding of Waves through Subwavelength Apertures.

Confining and controlling electromagnetic energy typically involves a highly resonant phenomenon, especially when subwavelength confinement is desired. Here, we present a class of nonresonant, self-dual planar metastructures capable of protected energy transmission from one side to the other, through arbitrarily narrow apertures. It is shown that the transmission is in the form of matched propagating modes and is independent of the thickness and specific composition of the surface. We analytically prove that the self-dual condition is sufficient to guarantee 100% transmission that is robust to the presence of discontinuities along the propagation path. The results are confirmed numerically through study of various scenarios. The operation is broadband and subject only to the bandwidth of the constituent materials. The polarization of the internal field can also be independently controlled with respect to the incident one. Our structures are promising for applications in sensing, particle trapping, near-field imaging, and wide scan antenna arrays.

Zero-index structures as an alternative platform for quantum optics.

Vacuum fluctuations are one of the most distinctive aspects of quantum optics, being the trigger of multiple nonclassical phenomena. Thus, platforms like resonant cavities and photonic crystals that enable the inhibition and manipulation of vacuum fluctuations have been key to our ability to control light-matter interactions (e.g., the decay of quantum emitters). Here, we theoretically demonstrate that vacuum fluctuations may be naturally inhibited within bodies immersed in epsilon-and-mu-near-zero (EMNZ) media, while they can also be selectively excited via bound eigenmodes. Therefore, zero-index structures are proposed as an alternative platform to manipulate the decay of quantum emitters, possibly leading to the exploration of qualitatively different dynamics. For example, a direct modulation of the vacuum Rabi frequency is obtained by deforming the EMNZ region without detuning a bound eigenmode. Ideas for the possible implementation of these concepts using synthetic implementations based on structural dispersion are also proposed.

Polaritonic Hybrid-Epsilon-near-Zero Modes: Beating the Plasmonic Confinement vs Propagation-Length Trade-Off with Doped Cadmium Oxide Bilayers.

Polaritonic materials that support epsilon-near-zero (ENZ) modes offer the opportunity to design light-matter interactions at the nanoscale through extreme subwavelength light confinement, producing phenomena like resonant perfect absorption. However, the utility of ENZ modes in nanophotonic applications has been limited by a flat spectral dispersion, which leads to small group velocities and extremely short propagation lengths. Here, we overcome this constraint by hybridizing ENZ and surface plasmon polariton (SPP) modes in doped cadmium oxide epitaxial bilayers. This results in strongly coupled hybrid modes that are characterized by an anticrossing in the polariton dispersion and a large spectral splitting on the order of 1/3 of the mode frequency. These hybrid modes simultaneously achieve modal propagation and ENZ mode-like interior field confinement, adding propagation character to ENZ mode properties. We subsequently tune the resonant frequencies, dispersion, and coupling of these polaritonic-hybrid-epsilon-near-zero (PH-ENZ) modes by tailoring the modal oscillator strength and the ENZ-SPP spectral overlap. PH-ENZ modes ultimately leverage the most desirable characteristics of both ENZ and SPP modes, allowing us to overcome the canonical plasmonic trade-off between confinement and propagation length.

Nanoimprinted Chiral Plasmonic Substrates with Three-Dimensional Nanostructures.

We report a large-area fabrication method to prepare chiral substrates patterned with arrays of multilayer, three-dimensional nanostructures using a combination of nanoimprint lithography and glancing angle deposition. Several structures are successfully fabricated using this method, including L-shaped, twisted arc and trilayer twisted Au nanorod structures, demonstrating its generality. As one typical example, arrays of L-shaped nanostructures, consisting of two layers of orthogonally oriented Au nanorods separated by a Ge dielectric layer in the thickness direction, exhibit giant optical chirality in the infrared region with an experimentally achieved g-factor as high as 0.38. Electromagnetic simulations show that the optical chirality results from plasmon hybridization between the two orthogonal Au segments. To demonstrate scalability, a 1 cm2 chiral substrate is fabricated with uniform chiral optical property. This method combines both high throughput and precise geometrical control and is therefore promising for applications of chiral metamaterials.

Extremely small wavevector regime in a one-dimensional photonic crystal heterostructure for angular transmission filtering.

One-dimensional photonic crystals (PCs), when operating near the band edge in the dispersion diagram, inherently possess nearly polarization-independent angular selectivity-an angular transmission window around the normal direction with reflection for other angles. However, the incident light is mostly reflected at the PC-air interface due to large impedance mismatch. We show that the reflection may be sufficiently suppressed by utilizing a specially designed antireflection structure consisting of a PC having a different pitch from that of the host PC. The underlying mechanism is that the interfaces of the antireflection PC with the host PC and the air structure are selected such that the transverse impedance has a real value, which is positioned at the center of the thickness of a material film. Moreover, our structure provides a high-throughput wide angular transmission window, including the normal direction in both s and p polarizations. We develop an analytical model that captures the angular selectivity observed in numerical results.

Digital metamaterials.

Balancing complexity and simplicity has played an important role in the development of many fields in science and engineering. One of the well-known and powerful examples of such balance can be found in Boolean algebra and its impact on the birth of digital electronics and the digital information age. The simplicity of using only two numbers, '0' and '1', in a binary system for describing an arbitrary quantity made the fields of digital electronics and digital signal processing powerful and ubiquitous. Here, inspired by the binary concept, we propose to develop the notion of digital metamaterials. Specifically, we investigate how one can synthesize an electromagnetic metamaterial with a desired permittivity, using as building blocks only two elemental materials, which we call 'metamaterial bits', with two distinct permittivity functions. We demonstrate, analytically and numerically, how proper spatial mixtures of such metamaterial bits lead to elemental 'metamaterial bytes' with effective material parameters that are different from the parameters of the metamaterial bits. We then apply this methodology to several design examples of optical elements, such as digital convex lenses, flat graded-index digital lenses, digital constructs for epsilon-near-zero (ENZ) supercoupling and digital hyperlenses, thus highlighting the power and simplicity of the methodology.

Modeling vanadium dioxide phase transition due to continuous-wave optical signals.

Vanadium dioxide (VO(2)) is a material that undergoes thermal phase transition resulting in drastic changes in its material properties. The phase change can also be brought on by optical pumping. Several experimental results have been presented in the literature dealing with such phase transitions brought on by optical pumping. In this manuscript we present a theoretical framework, which addresses this problem by self consistently solving the electromagnetic problem and the thermodynamic problem using a multiphysics approach when such transitions are thermally mediated, as is the case with continuous-wave optical pumps. Such an analysis provides us with insights into the transition process and also helps explain the conditions under which some of the observed experimental results like bistability takes place. Such optically induced phase transition materials also present the intriguing possibility of ultrahigh nonlinearity where the input optical signal essentially converts a dielectric into a plasmonic material. These materials can find significant applications in nonlinear metatronics.

Modal interference in spiky nanoshells.

Near-field enhancement of the electric field by metallic nanostructures is important in non-linear optical applications such as surface enhanced Raman scattering. One approach to producing strong localization of the electric field is to couple a dark, non-radiating plasmonic mode with a broad dipolar resonator that is detectable in the far-field. However, characterizing or predicting the degree of the coupling between these modes for a complicated nanostructure can be quite challenging. Here we develop a robust method to solve the T-matrix, the matrix that predicts the scattered electric fields of the incident light, based on finite-difference time-domain (FDTD) simulations and least square fitting algorithms. This method allows us to simultaneously calculate the T-matrix for a broad spectral range. Using this method, the coupling between the electric dipole and quadrupole modes of spiky nanoshells is evaluated. It is shown that the built-in disorder in the structure of these nanoshells allows for coupling between the dipole modes of various orientations as well as coupling between the dipole and the quadrupole modes. A coupling strength of about 5% between these modes can explain the apparent interference features observed in the single particle scattering spectrum. This effect is experimentally verified by single particle backscattering measurements of spiky nanoshells. The modal interference in disordered spiky nanoshells can explain the origin of the spectrally broad quadrupole resonances that result in strong Quadrupole Enhanced Raman Scattering (QERS) in these nanoparticles.

Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers.

We experimentally demonstrate enhanced third-harmonic generation from indium tin oxide nanolayers at telecommunication wavelengths with an efficiency that is approximately 600 times larger than crystalline silicon (Si). The increased optical nonlinearity of the fabricated nanolayers is driven by their epsilon-near-zero response, which can be tailored on-demand in the near-infrared region. The present material platform is obtained without any specialized nanofabrication process and is fully compatible with the standard Si-planar technology. The proposed approach can lead to largely scalable and highly integrated optical nonlinearities in Si-integrated devices for information processing and optical sensing applications.

Two cases of spatial transformations.

Here, we give an overview of our work on two topics related to the theme of spatial transformations in wave theory, namely the concepts of transformation electronics and 'digital' metamaterials. In the first topic, we show that the notion of transformation optics can be extended to other physical phenomena such as tailoring the effective mass of charged carriers, e.g. electrons, in specially designed semiconductor superlattices. We discuss how the combination of thin layers of electronic materials with different effective mass of electrons may lead to bulk composite structures in which the effective mass of electrons may exhibit extreme anisotropy. For the second case, we show that any desired electromagnetic permittivity can, in principle, be engineered with proper combinations of two deeply subwavelength building blocks with relative permittivity values whose real parts have opposite signs. Owing to the presence of a plasmonic resonance between the two building blocks with oppositely signed dielectric constants, the achieved effective relative permittivity for the bulk composite may have values outside the range defined by the two permittivity values of the building blocks. We discuss some of the salient features of these two spatial transformation phenomena.

Roles of epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials in optical metatronic circuit networks.

The concept of metamaterial-inspired nanocircuits, dubbed metatronics, was introduced in [Science 317, 1698 (2007); Phys. Rev. Lett. 95, 095504 (2005)]. It was suggested how optical lumped elements (nanoelements) can be made using subwavelength plasmonic or non-plasmonic particles. As a result, the optical metatronic equivalents of a number of electronic circuits, such as frequency mixers and filters, were suggested. In this work we further expand the concept of electronic lumped element networks into optical metatronic circuits and suggest a conceptual model applicable to various metatronic passive networks. In particular, we differentiate between the series and parallel networks using epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials. We employ layered structures with subwavelength thicknesses for the nanoelements as the building blocks of collections of metatronic networks. Furthermore, we explore how by choosing the non-zero constitutive parameters of the materials with specific dispersions, either Drude or Lorentzian dispersion with suitable parameters, capacitive and inductive responses can be achieved in both series and parallel networks. Next, we proceed with the one-to-one analogy between electronic circuits and optical metatronic filter layered networks and justify our analogies by comparing the frequency response of the two paradigms. Finally, we examine the material dispersion of near-zero relative permittivity as well as other physically important material considerations such as losses.