8/8/2023 0 Comments Anomalies light phenomenaThey cannot by themselves become a laser, as there is no resonance to provide feedback, and furthermore, the assumed gain is by far insufficient to compensate the radiative loss. In contrast, our nanoparticles by themselves are only very weakly polarizable and operate in the Rayleigh limit, i.e., away from any intrinsic particle resonances. In these cases, extreme optical responses could be attributed to narrowing of the particle’s Mie resonances in the vicinity of their lasing thresholds, i.e., near the conditions of their radiative loss compensation. Previous studies on gain-doped spherical scatterers focused mainly on high- Δ n and/or high-gain scenarios, often predicting huge amplification at discrete wavelengths and incidence angles, already for single particles. (c) Optical cross sections σ of the same nanoparticle: scattering cross section – solid green, extinction cross section – dashed black. (b) Scalar polarizabilities α of a gain medium nanoparticle of radius ρ = 80 nm embedded in a dielectric environment of refractive index n d = 1.5: static polarizability – solid lines, dynamic polarizability – dashed lines, real part – red, imaginary part – blue. (a) Electric permittivity ε g of a gain medium with refractive index n g = 1.55, gain bandwidth ℏ γ g = 0.025 eV, and peak gain coefficient g max = 300 cm −1 at ℏ ω g = 2.25 eV: real part – red, imaginary part – blue. Due to periodicity, these are coupled to free space, leading to the observed singularities. Similar guided modes are supported by metasurfaces, even composed of weakly polarizable scatterers. This divergent coupling to amplified weakly guided slab modes provides an explanation for the metasurface behavior. We find that similar anomalies already occur in the reflectivity of a prism-coupled gain medium slab, where the incident light couples evanescently to guided modes in a traditional attenuated total reflection setup ( Figure 1, right). Furthermore, by considering the case of a resonant gain, we show that these anomalies must always emerge in pairs, and each of them is surrounded by a phase vortex, producing a scattered field of diverging amplitude and undefined phase, which makes them analogous to phase singularities observed in perfectly absorbing structures. In contrast to these reports, the anomalies discussed in this work result from interference effects caused by gain-induced phase alteration, leading to trapping of light inside the gain medium. These anomalies resemble sharp resonances associated with lasing thresholds, studied over the past decades in various gain-doped dielectric structures, ,, ,, ,, ,. While even with gain, each particle is a weak scatterer with response dominated by radiative loss, and their optical response is significantly modified in arrays, where the interplay of gain, loss, and interference gives rise to scattering anomalies. Contrary to our previous findings on arrays of plasmonic nanoparticles with a shell of gain, the scatterers considered here are not resonant by means of localized plasmon or Mie resonances but only due to a spectrally dependent gain medium. We study this system using a Green function method, ,, ,, which includes the coherent retarded electrodynamic coupling between all particles, and radiative damping as the essential ingredient. In this work, we theoretically demonstrate the existence of scattering anomalies embedded in the band structure of simple diffractive arrays of identical dielectric nanoparticles ( Figure 1, left) that are intrinsically weakly scattering, but imbued with a weak frequency-dependent gain. The interplay between gain and loss gives rise to many scattering anomalies, such as unidirectional invisibility, coherent perfect absorber-lasers, as well as manifestations of parity–time (PT) symmetry, ,, offering a platform for active control of light propagation, , and for enhanced light-matter interactions,. For instance, properly engineered gain and loss could overcome efficiency barriers of metasurfaces for wavefront transformation imposed by impedance mismatch, , mitigate constraints on electric and magnetic optical response of matter, , and control the scattering by small ensembles of nano-objects. Recent theoretical works suggest that, apart from lasing, the role of gain could be far more nontrivial. These studies largely relate to the notion of combining gain with surface lattice resonances, in which Rayleigh anomalies and plasmon particle resonances hybridize. Recently, extensive research has been devoted to combining metasurfaces with gain media, with the main focus on distributed feedback lasing and diffractive outcoupling in plasmonic and dielectric nanoparticle arrays. Electromagnetic metasurfaces are two-dimensional (2D) arrays of scatterers used to control amplitude, phase, and polarization of reflected, transmitted, and diffracted electromagnetic waves,.
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