There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Metamaterials, artificial electromagnetic media that are structured on the subwavelength scale, were initially suggested for the negative-index 'superlens'. Later metamaterials became a paradigm for engineering electromagnetic space and controlling propagation of waves: the field of transformation optics was born. The research agenda is now shifting towards achieving tunable, switchable, nonlinear and sensing functionalities. It is therefore timely to discuss the emerging field of metadevices where we define the devices as having unique and useful functionalities that are realized by structuring of functional matter on the subwavelength scale. In this Review we summarize research on photonic, terahertz and microwave electromagnetic metamaterials and metadevices with functionalities attained through the exploitation of phase-change media, semiconductors, graphene, carbon nanotubes and liquid crystals. The Review also encompasses microelectromechanical metadevices, metadevices engaging the nonlinear and quantum response of superconductors, electrostatic and optomechanical forces and nonlinear metadevices incorporating lumped nonlinear components.

/pdf/from-metamaterials-to-metadevices-4vgaose515.pdf

From metamaterials to metadevices.

Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam-Berry phase and Huygens' metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.

A review of metasurfaces: physics and applications.

Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response, mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam-Berry phase and Huygens' metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.

A review of metasurfaces: physics and applications

We study the properties of plasmonic excitations localized at 2D and 3D nanoscale perturbations of a flat metal surface within the general method of surface integral equations. The resonant values of the optical permittivity ej and the plasmonic eigenfunctions—distributions of the surface charge density σj(r)—are investigated. General symmetry properties linking the cases of convex and concave perturbations (bumps and mirror-reflected pits) are established. The impact of the height-to-width perturbation ratio h0/r0 on the localized surface plasmons is twofold: while the resonant permittivities ej drop linearly with h0/r0 leading to strong redshifts of the resonances, the scale of localization stays constant (≈r0). The presence of sharp shape features (tips and corners) with the curvature radius ρ0≪r0 leads to superlocalization of charge density on the scale of ρ0 and, simultaneously, to an additional strong drop of ej.

Plasmons localized at nanoscale perturbations of flat metal surface

The general density functional approach is used to develop a molecular-statistical theory of rod-coil diblock copolymers which is valid in the case of both weak and strong segregation. The free energy of the rod-coil copolymer is expressed as a functional of the number densities of rod and coil monomers which depend on the translational and orientational degrees of freedom. The equilibrium densities are determined by minimization of the free energy functional and depend on the orientational and translational order parameters of the monomers. The order parameters are calculated numerically by minimization of the free energy taking into account the incompressibility condition within the formalism of Lagrange multipliers. Phase diagrams are obtained and the profiles of orientational and translational order parameters are presented as functions of temperature and the fraction of coil fragments. It is shown that the lamellar phase possesses strong orientational order and the stability of the phase is increasing with the increasing fraction of rod monomers.

Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers

The realization of lossless metasurfaces with true chirality crucially requires the fabrication of three-dimensional structures, constraining their feasibility for experiments and hampering practical implementations. Even though the three-dimensional assembly of metallic nanostructures has been demonstrated previously, the resulting plasmonic resonances suffer from high intrinsic and radiative losses. The concept of photonic bound states in the continuum (BICs) is instrumental for tailoring radiative losses in diverse geometries, especially when implemented using lossless dielectrics, but applications have so far been limited to planar and intrinsically achiral structures. Here, we introduce a novel nanofabrication approach to unlock the height of generally flat all-dielectric metasurfaces as an accessible parameter for efficient resonance and functionality control. In particular, we realize out-of-plane symmetry breaking in quasi-BIC metasurfaces and leverage this design degree of freedom to demonstrate, for the first time, an optical all-dielectric quasi-BIC metasurface with maximum intrinsic chirality that responds selectively to light of a particular circular polarization depending on the structural handedness. Our experimental results not only open a new paradigm for all-dielectric BICs and chiral nanophotonics but also promise advances in the realization of efficient generation of optical angular momentum, holographic metasurfaces, and parity-time symmetry-broken systems. symmetry-broken qBIC metasurfaces via the height difference of the meta-unit resonators. We have revealed how to employ this degree of freedom for the simultaneous tailoring of the qBIC chirality and Q factor, thus opening vast prospects for multi-functional and lossless metasurfaces impacting nonlinear chiral optics and lasing, chirality sensing and, prospectively, enantiomer-selective photochemistry.

Unlocking the out-of-plane dimension for photonic bound states in the continuum to achieve maximum optical chirality

In the framework of the model of short pitch modes (SPM) developed for antiferroelectric liquid crystals, the sets of various relaxation modes related to ferro-, antiferro- and ferrielectric phases are explained. The 'soft-like' modes describe the amplitude perturbations of short pitch modes, while the Goldstone modes describe the azimuthal perturbations of the molecular packings related to short pitch modes. The frequencies of the Goldstone modes are mainly determined by the chirality parameter, depending on the number of short pitch modes. The relaxation modes described correspond to the observed phase diagrams in liquid crystal materials for which the measurements of dielectric spectra are presented.

The semi-phenomenological model of antiferroelectricity in chiral smectic liquid crystals. iii. dielectric spectroscopy

It is shown that when approaching the spatial subharmonics generation threshold in fast photorefractive crystals (the sillenites, CdTe), a practically unlimited (singular) amplification of the nonlinear photorefractive response is possible, which results in a drastic increase in the spatial amplification of weak signals. A theory of critical spatial amplification is developed. This theory takes into account real attributes of fast photorefractive crystals such as the vectorial nature of wave coupling and nonuniform broadening of resonances owing to light absorption. The theory is applied to the analysis of the observable characteristics of critical enhancement and to optimization of the conditions of experiments aimed at the detection and investigation of this phenomenon.

Maxim V. Gorkunov

Papers

Plasmons localized at nanoscale perturbations of flat metal surface

Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers

Unlocking the out-of-plane dimension for photonic bound states in the continuum to achieve maximum optical chirality

The semi-phenomenological model of antiferroelectricity in chiral smectic liquid crystals. iii. dielectric spectroscopy

Critical Enhancement of Nonlinear Response in Fast Photorefractive Crystals