Self-hybridization within non-Hermitian localized plasmonic systems

Abstract

The orthogonal eigenmodes are well-defined solutions of Hermitian equations describing many physical situations from quantum mechanics to acoustics. However, a large variety of non-Hermitian problems, including gravitational waves close to black holes or leaky electromagnetic cavities, require the use of a bi-orthogonal eigenbasis with consequences challenging our physical understanding [1][2][3][4] . The need to compensate for energy losses made the few successful attempts 5-8 to experimentally probe non-Hermiticity extremely complicated. We overcome this problem by considering localized plasmonic systems. As the non-Hermiticity in these systems does not stem from temporal invariance breaking but from spatial symmetry breaking, its consequences can be observed more easily. We report on the theoretical and experimental evidence for non-Hermiticity-induced strong coupling between surface plasmon modes of different orders within silver nanodaggers. The symmetry conditions for triggering this counter-intuitive self-hybridization phenomenon are provided. Similar observable effects are expected to exist in any system exhibiting bi-orthogonal eigenmodes.In any situation described by a Hermitian equation (such as mechanics, acoustics, quantum mechanics and electromagnetism), the usual approach in linear physics is to apply the concept of eigenmodes. Examples are endless: the vibrations of a guitar string are best understood as a superposition of the string eigenmodes and the properties of an atom can be simply deduced from its orbitals' properties. It is thus tempting to adapt this concept to systems in which eigenmodes are harder to define, namely for nonHermitian systems.One class of non-Hermitian systems consists of open systems that span a wide range of physical situations, from gravity waves close to black holes to lasers cavities or propagating surface plasmons [9][10][11][12] . In those cases, quasi-normal modes (QNMs) are specially constructed so that time-reversal symmetry breaking does not prevent the establishment of a complete basis, especially when parity-time symmetry is preserved. Another class is represented by localized surface plasmons (LSPs). In this case, the structure of the constituting equation is non-symmetric.In the two cases, a bi-orthogonal rather than orthogonal basis must be used. A full quantum theory of bi-orthogonal modes has been developed 1,3 . Bi-orthogonality has a few famous and exciting consequences, including the existence of 'exceptional points' where both the energy and wavefunctions coalesce 2,13-15 . Exceptional points are usually associated with the apparition of non-trivial physical effects, such as asymmetric mode switching 14 . Such effects have only very recently been studied experimentally 5,7,8,16 because manipulating QNMs in open systems requires to exactly balance dissipation 2,17 . Surprisingly, using LSPs to explore nonHermitian physics has not been reported, although dissipation balancing is not required in this case. Moreover, describing LSP physics with bi-orthog...

Probing nonorthogonality of eigenfunctions and its impact on transport through open systems

“…In photonic systems, it leads to the existence of exceptional points in systems that incorporate both gain and loss but in which parity-time symmetry is preserved [24,25] and to the enhancement of the linewidth and spontaneous emission rates in laser resonators [26][27][28]. Its impact has also been explored in localized plasmonic surfaces [29], dielectric microcavities [30,31] and chaotic systems with small perturbations [32,33]. Thus the impact of non-Hermiticity on wave functions is critical to the deposition and evolution of energy in open linear and nonlinear systems, communications, imaging, spectral analysis, and resource exploration.…”

Dispersion characteristics of face modes in ionic-crystal and plasmonic-metal nanoparticles

“…The ω − -like coupling of the high energy branch modes resembles shifts toward increasingly "anti-bonding" states, to adopt terminology from hybridization theory, 37 consistent with self-hybridization of coupled modes in the particle geometry. 24 These results also suggest an additional effect on the photonic states and spectra of these particles, for both ionic crystals where the dielectric function is bounded by transverse optical (TO) and…”

“…Similar approaches using the n-lowest energy modes have been used for the demonstration of the effect of biorthogonality of the eigenvectors associated with the surface charges in such systems. 24 However, it has been well-known since early work on the infrared response of ionic crystal cubes that some high energy modes, specifically modes above the surface mode energy ω S , contribute significantly to the optical spectrum. 25,26 These modes are described here as 'face' modes based on the distribution of surface charges across the faces of prismatic nanoparticles as well as the previous descriptions of these modes observed in EELS experiments on cubes and other prismatic particles.…”

Electron energy analysis by phase-space shaping with THz field cycles

“…17 for a review) is therefore a widespread method to obtain fundamental chemical and structural information from complex materials. For example, plasmonic 18 or vibrational excitations 19 can be probed with spectral and spatial resolution of ∼10 meV and $<1\hspace{0.17em}$ nm at the same time 19 . Recently, the capabilities of EELS have also been extended to the femtosecond domain 20 .…”