Topological Transitions in Metamaterials

Abstract

Here, we present the optical equivalent of the Lifshitz transition in strongly anisotropic metamaterials. When one of the components of the dielectric permittivity tensor of such a composite changes sign, the corresponding isofrequency surface transforms from an ellipsoid to a hyperboloid. Since the photonic density of states can be related to the volume enclosed by the isofrequency surface, such a topological transition in a metamaterial leads to a dramatic change in the photonic density of states, with a resulting effect on every single physical parameter related to the metamaterial -from thermodynamic quantities such as its equilibrium electromagnetic energy to the nonlinear optical response to quantumelectrodynamic effects such as spontaneous emission. In the present paper, we demonstrate the modification of spontaneous light emission from quantum dots placed near the surface of the metamaterial undergoing the topological Lifshitz transition, and present the theoretical description of the effect.

Dual-channel spontaneous emission of quantum dots in magnetic metamaterials

“…In contrast to previous work investigating PL enhancement in single nanoparticles and nanoantennas 3,40,41 or in Fano-type 30,42,43 and hyperbolic metamaterials 31,32 , our SRR metamaterial supports both electric and magnetic modes that are spectrally matched to the emission of semiconductor QDs at around l QD ¼ 800 nm wavelength. Since both modes in our metamaterial can be engineered independently from each other, our QD metamaterial offers new opportunities to tailor the spontaneous emission of quantum emitters into two independent radiative decay channels.…”

“…In such structures, the hybridization of QDs with electric resonances of a metamaterial can lead to photoluminescence (PL) enhancement and modification of the PL properties that can be controlled by the metamaterial design 30,31 . Topological transitions in hyperbolic metamaterials 32 have also shown an important avenue to alter the photonic density of states by changing the isofrequency surfaces via plasmonic resonances.…”

Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial

“…These materials offer an efficient way to manipulate the propagation of light to yield a number of novel and exotic phenomena, such as, negative refraction [19][20][21][22][23] , super-resolution imaging [24][25][26] , enhanced optical absorption 27,28 and spontaneous emission 29,30 . In this work, we leverage a visible-frequency hyperbolic metamaterial to implement a planar device of wavelength-scale thickness able to enforce highly asymmetric, broadband transmission of transverse-magnetic (TM) polarized visible-frequency light under illumination at normal incidence.…”

Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes

“…In particular, when circularly polarized light interacts with specifically designed nanostructured metasurfaces that break spatial inversion symmetry, photons of different polarizations (optical spin) may take different trajectories, in close analogy to the spin Hall effect for electrons [7][8][9][10][11] . In terms of manipulation of emission properties, anisotropic metamaterials with hyperbolic isofrequency surfaces have been proposed for nonresonant enhancement of the spontaneous emission rate 13 , which are fundamentally limited only by the basic dimensionality of an artificial unit cell 14 and nonlocal effects 15 . Such anisotropic metamaterials have different signs of the longitudinal (e 8 ) and transverse (e > ) components of the effective permittivity tensor and have been realized as nanowire arrays 16 or layered metaldielectric structures 13 ( Fig.…”

“…In terms of manipulation of emission properties, anisotropic metamaterials with hyperbolic isofrequency surfaces have been proposed for nonresonant enhancement of the spontaneous emission rate 13 , which are fundamentally limited only by the basic dimensionality of an artificial unit cell 14 and nonlocal effects 15 . Such anisotropic metamaterials have different signs of the longitudinal (e 8 ) and transverse (e > ) components of the effective permittivity tensor and have been realized as nanowire arrays 16 or layered metaldielectric structures 13 ( Fig. 1).…”