We revisit the mechanisms governing the sub-wavelength spatial localization of light in surface plasmon polariton (SPP) modes by investigating both local and global features in optical powerflow at SPP frequencies. Close inspection of the instantaneous Poynting vector reveals formation of optical vortices - localized areas of cyclic powerflow - at the metal-dielectric interface. As a result, optical energy circulates through a subwavelength-thick 'conveyor belt' between the metal and dielectric where it creates a high density of optical states (DOS), tight optical energy localization, and low group velocity associated with SPP waves. The formation of bonding and anti-bonding SPP modes in metal-dielectric-metal waveguides can also be conveniently explained in terms of different spatial arrangements of localized powerflow vortices between two metal interfaces. Finally, we investigate the underlying mechanisms of global topological transitions in metamaterials composed of multiple metal and dielectric films, i.e., transitions of their iso-frequency surfaces from ellipsoids to hyperboloids, which are not accompanied by the breaking of lattice symmetry. Our analysis reveals that such global topological transitions are governed by the dynamic local re-arrangement of local topological features of the optical interference field, such as vortices and saddle points, which reconfigures global optical powerflow within the metamaterial. These new insights into plasmonic light localization and DOS manipulation not only help to explain the well-known properties of SPP waves but also provide useful guidelines for the design of plasmonic components and materials for a variety of practical applications.
Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tuneability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete …
The local electric field distribution has been investigated in a core-shell cylindrical metamaterial structure under the illumination of a uniform incident optical field. The structure consists of a homogeneous dielectric core, a shell of graded metal-dielectric metamaterial, embedded in a uniform matrix. In the quasi-static limit, the permittivity of the metamaterial is given by the graded Drude model. The local electric potentials and hence the electric fields have been derived exactly and analytically in terms of hyper-geometric functions. Our results showed that the peak of the electric fi…
We present the first study of disorder in planar metamaterials consisting of strongly interacting metamolecules, where coupled electric dipole and magnetic dipole modes give rise to a Fano-type resonant response and show that positional disorder leads to light localization inherently linked to collective magnetic dipole excitations. We demonstrate that the magnetic excitation persists in disordered arrays and results in the formation of "magnetic hot-spots".
Light propagation through 1D disordered structures composed of alternating layers, with random thicknesses, of air and a dispersive metamaterial is theoretically investigated. Both normal and oblique incidences are considered. By means of numerical simulations and an analytical theory, we have established that Anderson localization of light may be suppressed: (i) in the long wavelength limit, for a finite angle of incidence which depends on the parameters of the dispersive metamaterial; (ii) for isolated frequencies and for specific angles of incidence, corresponding to Brewster anomalies in b…
A detailed theoretical and numerical analysis of the localization length in alternating metamaterial-birefringent random layered stacks, under uncorrelated thickness-disorder, has been performed. Similar structures have recently been reported to suppress the Brewster delocalization for $\it{p}$-polarized light, when "standard" isotropic layers (with positive index of refraction) are considered instead of metamaterial layers, providing a generic means to produce polarization-insensitive, broadband reflections. However, this enhancement of localization is valid for short wavelengths $λ$ compared…
Precise control and manipulation of optical fields on a nanoscale is one of the most important and challenging problems in "nanophotonics". Since optical wavelength is on a much larger microscale, it is impossible to employ conventional focusing for that purpose. We show the strong optically-induced interactions between discrete meta-molecules in a metamaterial system and coherent monochromatic continuous light beam with a spatially-tailored phase profile can be used to prepare a sub-wavelength scale energy localization. Well isolated energy hot-spots as small as $λ/10$ can be created and posi…
We predict the existence of a novel class of multidimensional light localizations in out-of-equilibrium ferroelectric crystals. In two dimensions, the non-diffracting beams form at arbitrary low power level and propagate even when their width is well below the optical wavelength. In three dimensions, a novel form of subwavelength light bullets is found. The effects emerge when compositionally disordered crystals are brought to their metastable glassy state, and can have a profound impact on super-resolved imaging and ultra-dense optical storage, while resembling many features of the so-called …
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vici…
We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it was numerically discovered that in such structures with weak fluctuations of refraction indices, the localization length $L_{loc}$ can be enormously large for small wave frequencies $ω$. Within the fourth order of perturbation theory in disorder, $σ^2 \ll 1$, we derive the expression for $L_{loc}$ valid for any $ω$. In the limit $ω\rightarrow 0$ one gets a q…
We summarize the results of our comprehensive analytical and numerical studies of the effects of polarization on the Anderson localization of classical waves in one-dimensional random stacks. We consider homogeneous stacks composed entirely of normal materials or metamaterials, and also mixed stacks composed of alternating layers of a normal material and metamaterial. We extend the theoretical study developed earlier for the case of normal incidence [A. A. Asatryan et al, Phys. Rev. B 81, 075124 (2010)] to the case of off-axis incidence. For the general case where both the refractive indices a…
We investigate numerically and experimentally the near-field response of disordered arrays comprising asymmetrically split ring resonators that exhibit strong cooperative response. Our simulations treat the unit cell split ring resonators as discrete pointlike oscillators with associated electric and magnetic point dipole radiation, while the strong cooperative radiative coupling between the different split rings is fully included at all orders. The methods allow to calculate local field and Purcell factor enhancement arising from the collective electric and magnetic excitations. We find subst…
We have analyzed numerically the localization length of light $ξ$ for nearly periodic arrangements of homogeneous stacks (formed exclusively by right-handed materials) and mixed stacks (with alternating right and left-handed metamaterials). Layers with index of refraction $n_1$ and thickness $L_1$ alternate with layers of index of refraction $n_2$ and thickness $L_2$. Positional disorder has been considered by shifting randomly the positions of the layer boundaries with respect to periodic values. For homogeneous stacks, we have shown that the localization length is modulated by the correspond…
We review the basic physics behind light interaction with plasmonic nanoparticles. The theoretical foundations of light scattering on one metallic particle (a plasmonic monomer) and two interacting particles (a plasmonic dimer) are systematically investigated. Expressions for effective particle susceptibility (polarizability) are derived, and applications of these results to plasmonic nanoantennas are outlined. In the long-wavelength limit, the effective macroscopic parameters of an array of plasmonic dimers are calculated. These parameters are attributable to an effective medium corresponding…
In this paper we reveal the physics behind the formation of tri- and tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric coupling and describe the anti-crossing splitting phenomenon in the hyperbolic dispersion which arises due to the hybridization of the plasmonic and magnetic Bloch high-k polaritons. This considerably deepens the understanding of the high-k polaritons and the topology of the optical iso-frequency surfaces in k-space and will find applications in optical nano-resolution imaging and emission rate and directivity control. To accomplish this, we develop …
A numerical study of the features of the scattering of incident radiation at a periodically modulated hyperbolic metamaterial boundary was carried out. We have found optimal - sawtooth-shaped profile of the interface which provides minimal reflection. It is shown that at a certain orientation of the optical axes of the metamaterial, a subwave localization of the field occurs at the saw-tooth interface. An approximate analytical expression for the eigenmode was found. A generalization of the numerical method is implemented for calculating fields, based on the application of the Green's second i…
There has been a surge of interest in the subwavelength confinement of the electromagnetic fields. It is well known that in optics the subwavelength confinement can be obtained due to surface plasmon (quasielectrostatic) oscillations. In this paper we propose to realize the subwavelength confinement in microwaves due to dipolar-mode (quasimagnetostatic) magnon oscillations in ferrite particles. Our studies of interactions between microwave electromagnetic fields and small ferrite particles with magnetic-dipolar-mode (MDM) oscillations show strong localization of electromagnetic energy. MDM osc…
In the past two decades, artificial structures known as metamaterials have been found to exhibit extraordinary material properties that enable the unprecedented manipulation of electromagnetic waves, elastic waves, molecules, and particles. Phenomena such as negative refraction, bandgaps, near perfect wave absorption, wave focusing, negative Poissons ratio, negative thermal conductivity, etc., all are possible with these materials. Metamaterials were originally theorized and fabricated in electrodynamics, but research into their applications has expanded into acoustics, thermodynamics, seismol…
Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band - where the magnetic permeability $μ(ω)$ is positive and the dielectric permittivity $ε(ω)$ is negative - is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the rol…
The ability to engineer metamaterials with tunable nonlinear optical properties is crucial for nonlinear optics. Traditionally, metals have been employed to enhance nonlinear optical interactions through field localization. Here, inspired by the electronic properties of materials, we introduce and demonstrate experimentally an asymmetric metal-semiconductor-metal (MSM) metamaterial that exhibits a large and electronically tunable effective second-order optical susceptibility (\c{hi}(2)). The induced \c{hi}(2) originates from the interaction between the third-order optical susceptibility of the…
Optomechanical manipulation of micro and nano-scale objects with laser beams finds use in a large span of multidisciplinary applications. Auxiliary nanostructuring could substantially improve performances of classical optical tweezers by means of spatial localization of objects and intensity required for trapping. Here we investigate a three-dimensional nanorod metamaterial platform, serving as an auxiliary tool for the optical manipulation, able to support and control near-field interactions and generate both steep and flat optical potential profiles. It was shown that the 'topological transi…
Carefully designed nanostructures can inspire new type of optomechanical interactions and allow surpassing limitations set by classical diffractive optical elements. Apart from strong near-field localization, nanostructured environment allows controlling scattering channels and might tailor many-body interactions. Here we investigate an effect of optical binding, where several particles demonstrate a collective mechanical behaviour of bunching together in a light field. In contrary to classical binding, where separation distances between particles are diffraction limited, an auxiliary hyperbol…
Nonreciprocal transmission is the fundamental process behind unidirectional wave propagation phenomena. In our work, a compact and practical parity-time (PT) symmetric metamaterial is designed based on two Silicon Carbide (SiC) media separated by an air gap and photonically doped with gain and loss defects. We demonstrate that an exceptional point (EP) is formed in this PT-symmetric system when SiC operates as a practical epsilon-near-zero (ENZ) material and by taking into account its moderate optical loss. Furthermore and even more importantly, strong self-induced nonreciprocal transmission i…
For dielectric multilayered metamaterials, the effective-parameter representation is known to be insensitive to geometrical features occurring at deeply subwavelength scales. However, recent studies on periodic and aperiodically ordered geometries have shown the existence of certain critical parameter regimes where this conventional wisdom is upended, as the optical response of finite-size samples may depart considerably from the predictions of standard effective-medium theory. In these regimes, characterized by a mixed evanescent/propagating light transport, different classes of spatial (dis)…
We study the dynamics of a pair of nonlinear split-ring resonators (a `metadimer') excited by an alternating magnetic field and coupled magnetically. Linear metadimers of this kind have been recently used as the elementary components for three-dimensional metamaterials or 'stereometamaterials' [N. Liu {\em et al}, Nature Photon. {\bf 3}, 157 (2009)]. We demonstrate that nonlinearity offers more possibilities with respect to real-time tunability and a multiplicity of states which can be reached by varying the external field. Moreover, we demonstrate almost total localization of the energy in on…
Surface Plasmon Resonance sensors are a well-established class of sensors which includes a very large variety of materials and detection schemes. However, the development of portable devices is still challenging as due to the intrinsic complexity of the optical excitation/detection schemes. In this work we show that Nanoporous gold (NPG) films may overcome these limitations by providing excellent sensitivity without the need of sophisticated fabrication approaches and/or optical setup. The sensing mechanism is related the co-localization of optical energy and analytes into the pores that promo…
One of the most significant breakthroughs in physics of the last decade has been the discovery that materials with non-trivial topological properties for electronic, electromagnetic, acoustic and mechanical responses can be designed and manufactured at our will through engineered metamaterials (MMs). Here, we review the foundation and the state-of-the-art advances of topological photonics, acoustics and mechanical MMs. We discuss how topological MMs enable nontrivial wave phenomena in physics, engineering, of great interest for a broad range of interdisciplinary science disciplines such as cla…
The Purcell effect is defined as the modification of spontaneous decay in the presence of a resonator, and in plasmonics it is usually associated with the large local-field enhancement in "hot spots" due to surface plasmon polaritons. Here we propose a novel strategy for enhancing the Purcell effect through engineering the radiation directivity without a strict requirement of the local field enhancement. Employing this approach, we demonstrate how to enhance the Purcell effect by two orders of magnitude in all-dielectric nanostructures recently suggested as building blocks of low-loss nanophot…
We provide detailed comparisons between experimental findings and numerical simulations of large cooperatively interacting, spatially disordered metamaterial arrays, consisting of asymmetrically split rings. Simulation methods fully incorporate strong field-mediated inter-meta-atom interactions between discrete resonators and statistical properties of disorder, while approximating the resonators' internal structure. Despite the large system size, we find a qualitative agreement between the simulations and experiments, and characterize the microscopic origins of the observed disorder response. …
Different optical nanostructures containing both loss and gain components attract ever-increasing attention as novel advanced materials and building blocks for a variety of nanophotonic and plasmonic applications. Unique tunable optical signatures of the so-called active metamaterials support their utilizing for sensing, imaging, and signal processing on micro- and nanoscales. However, this tunability requires flexible control over the metamaterials parameters, which could be provided by involving a set of nonlinear interactions. In this paper, we propose a method of governing ultrashort pulse…
