Trapping Light in Plain Sight:  Embedded Eigenstates in Open 3D Nanostructures Being able to confine and localize light in small volumes is of paramount importance in several scenarios, e.g., for sensing, data storage and processing. In finite-size open systems, however, any optical state is known to gradually lose its energy by coupling with radiation modes in the surrounding environment, resulting in finite oscillation lifetime. For this reason, light confinement is conventionally achieved by suppressing these radiation channels, “closing” the source region with reflectors or photonic band-gap materials. It has recently been pointed out that ideal optical bound states with infinite lifetime may also interestingly exist within the continuum of radiation modes in open unbounded 2D structures (photonic crystal slabs) [1], in analogy with so-called “embedded eigenstates” in quantum systems [2]. These setups however require infinitely large apertures. In recent works [3]-[4], Silveirinha and our group independently showed that ideal light confinement can be surprisingly achieved also in finite-size three-dimensional open structures, even in the presence of symmetry-compatible radiation channels. Notably, we have theoretically demonstrated ideal light trapping with infinite lifetime in open metallo-dielectric nanocavities in the limit of vanishing material loss. It was previously shown that composite multi-layered nanoparticles may exhibit Fano scattering resonances, arising from the interference of different plasmon modes [5]. Interestingly, we observed that, by varying the composition of plasmonic and dielectric materials, the resonance lifetime of these resonances can diverge at specific singular frequencies (a), as the coupling to free-space radiation is suppressed. This feature represents the fingerprint of an optical bound state with zero radiation loss – and therefore infinite lifetime – remarkably realized in an open system without altering the photonic density of states of the surrounding environment. Our investigations shed light on the generation and dynamics of these embedded scattering eigenstates existing within the radiation continuum (b). This phenomenon may lead to extreme light localization and enhancement (see animations), as the impinging energy is trapped in a self-sustained power flow within the open cavity (c-d). These findings demonstrate a fundamental mechanism for light confinement in open systems, enabled by plasmonic materials, with exciting possibilities for enhanced nonlinearities, thermal ablation, nanolasing, data storage and sensing. [1] C.W. Hsu et al. Nature 499, 188 (2013). [2] F.Capasso et al. Nature 358, 565 (1992). [3] M.G. Silveirinha, Phys. Rev. A 89, 023813 (2014). [4] F.Monticone and A.Alù, Phys. Rev. Lett. 112, 213903 (2014). [5] F.Monticone et al. Phys. Rev. Lett. 110, 113901 (2013). (Adapted from [4]) (a) Scattering cross section for the composite nanosphere in the inset, as a function of wavelength and aspect ratio. Numbers denote disappearing Fano features, as their lifetime diverges. (b) Evolution of the complex eigenfrequency of the nanoparticle eigenmode 4, for different aspect ratios (insets: corresponding scattering spectra). An ideally bound state arises when its eigenfrequency becomes real. (c) Power distribution under plane-wave illumination, at the embedded eigenstate frequency (right) and slightly off-resonance (left); (d) power flow distribution.

Embedded   eigen-state:    Time   animation   of   the   magnetic   field   (top)   and electric    field    (bottom)    for    a    composite    nanosphere,    under    plane    wave illumination,   at   the   frequency   of   the   embedded   eigenstate   supported   by the    scatterer.    The    fields    are    highly    enhanced    and    localized    inside    the particle,   which   acts   as   an   open   magnetic   cavity,   supporting   an   optical bound   state   very   weakly   coupled   to   the   outside   radiation.   Different   from conventional   plasmonic   resonances,   here   the   external   scattering   is   weak, while    the    impinging    energy    is    trapped    in    a    self-sustained    power    flow within the open cavity.

Right   off-resonance:    Time   animation   of   the   magnetic   field   (top)   and electric   field   (bottom)   for   a   composite   nanosphere,   under   plane   wave illumination,   at   a   frequency   slightly   detuned   from   the   eigenfrequency of   the   embedded   eigenstate   supported   by   the   scatterer.   The   impinging power   simply   flows   through   the   particle   as   one   would   expect   in   a weakly scattering nanostructure.