Embedded scattering eigenstates using resonant metasurfaces

Abstract

Optical embedded eigenstates are localized modes of an open structure that are compatible to radiation yet they have infinite lifetime and diverging quality factors. Their realization in nanostructures finite in all dimensions is inherently challenging, because they require materials with extreme electromagnetic properties. Here we develop a novel approach to realize these bound states in the continuum using ultrathin metasurfaces composed of arrays of nanoparticles. We first show that arrays of lossless nanoparticles can realize the condition for embedded eigenstates, and then explore the use of Ag nanoparticles coated with gain media shells to compensate material loss and revive the embedded eigenstate despite realistic loss in plasmonic materials. We discuss the possible experimental realization of the proposed structures and provide useful guidelines for practical implementation in nanophotonics systems with largely enhanced light-matter interactions. These metasurfaces may lead to highly efficient lasers, filters, frequency comb generation and sensors.

Anomalies in light scattering

“…By a Hermitian scatterer we denote a system without material gain/loss, thereby we use the fact that radiation to the propagating channels does not spoil the flux conservation of the stationary scattering process. However, one has to bear in mind that , which is an eigenmode of the scatterer with a real frequency in the continuum of unbounded radiation modes and can exist in lossless or -symmetrical [42][43][44] structures infinite in at least one direction [45] or for extreme values of parameters [46][47][48][49] (see Section 4).…”

“…With their genius of mathematical prediction, they constructed a 3D potential extending to infinity and oscillating in a way that the electron wavefunction is predicted to be localized with no radiation within an open system, atom or potential well, inside the continuum of unbounded states, i.e., when the energy of this state is positive. While in quantum mechanics this concept remains rather a mathematical curiosity [176,177], in recent years, the existence of EEs has been demonstrated in different areas of wave physics, including acoustics [178], hydrodynamics, and photonics [45,[179][180][181][182][183][184][185][186][187][188][189] revealing its general nature for wave physics. In this context, photonics has been demonstrated as a particularly attractive platform owing to the ability to tailor optical EEs due to modern extremely precise nanofabrication approaches.…”

Nonscattering Metasurface-Bound Cavities for Field Localization, Enhancement, and Suppression

“…In order to achieve high-Q invisible cavities in this range, one should use plasmonic metasurfaces with external energy pumping [32] or design invisible cavities based on highpermittivity dielectric metasurfaces (e.g., [50]). In the latter case, one can envisage realization of metasurfaces using arrays of subwavelength dielectric spheres or cylinders operating near the electric resonance.…”

Parallel-Plate Waveguides Formed by Penetrable Metasurfaces

“…The first and the second scenario correspond to the infinite and zero surface impedance of one of the sheets, respectively. Using the same method as we applied for the TM polarization, we assume that n is approaching infinity in (25). This gives rise to two solutions of ω:…”

“…In recent work [25], the bound mode in a double array of identical small lossless resonant particles was identified.…”