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Topological Nanospaser a Rapid Progress Nanophotonics 2020; 9(4): 865–874 Research article Rupesh Ghimire*, Jhih-Sheng Wu*, Vadym Apalkov* and Mark I. Stockman* Topological nanospaser https://doi.org/10.1515/nanoph-2019-0496 a rapid progress. Theoretical developments [1–4] were fol- Received December 5, 2019; revised February 11, 2020; accepted lowed by the first experimental observations of the spaser February 12, 2020 [5, 6] and then by an avalanche of new developments, designs, and applications. Currently, there are spasers Abstract: We propose a nanospaser made of an achiral whose generation spans the entire optical spectrum, from plasmonic–metal nanodisk and a two-dimensional chiral the near-infrared to the near-ultraviolet [7–15]. gain medium – a monolayer nanoflake of a transition- Several types of spasers, which are synonymously metal dichalcogenide (TMDC). When one valley of the called also nanolasers, have so far been well developed. TMDC is selectively pumped (e.g. by a circular-polarized Historically, the first is a nanoshell spaser [5] that con- radiation), the spaser (surface plasmon amplification by tains a metal nanosphere as the plasmonic core that is stimulated emission of radiation) generates a mode car- surrounded by a dielectric shell containing gain material, rying a topological chiral charge that matches that of typically dye molecules [5, 16]. Such spasers are the small- the gain valley. There is another, chirally mismatched, est coherent generators produced so far, with sizes on time-reversed mode with exactly the same frequency but the order of 10 nm. Almost simultaneously, another type the opposite topological charge; it is actively suppressed of nanolasers was demonstrated [6] that was built from by the gain saturation and never generates, leading to a a semiconductor gain nanorod situated over a surface of strong topological protection for the generating matched a plasmonic metal. It has a micrometer-scale size along mode. This topological spaser is promising for use in the nanorod. Its modes are surface plasmon (SP) polari- nano-optics and nanospectroscopy in the near field espe- tons with nanometer-scale transverse size. Given that cially in applications to biomolecules that are typically the spasers of this type are relatively efficient sources chiral. Another potential application is a chiral nanolabel of far-field light, they are traditionally called nanolas- for biomedical applications emitting in the far field an ers, although an appropriate name would be polari- intense circularly polarized coherent radiation. tonic spasers. Later, this type of nanolasers (polaritonic Keywords: near-field optics; spaser; optical pumping; spasers) was widely developed and perfected [7, 12, 17–20]. plasmonics; symmetry protected topological states; topo- There are also spasers that are similar in design to the logical materials; valleytronics. polaritonic nanolasers but are true nanospasers whose dimensions are all on the nanoscale. Such a spaser con- sists of a monocrystal nanorod of a semiconductor gain material deposited atop of a monocrystal nanofilm of 1 Introduction a plasmonic metal [21]. These spasers possess very low thresholds and are tunable in all visible spectra by chang- Spaser (surface plasmon amplification by stimulated ing the gain semiconductor composition, while the geom- emission of radiation) was originally introduced in 2003 etry remains fixed [11, 14, 22]. There are also other types as a nanoscopic phenomenon and device: a generator and of demonstrated spasers. Among them, we mention sem- amplifier of coherent nanolocalized optical fields. Since iconductor-metal nanolasers [23] and polaritonic spasers then, the science and technology of spasers experienced with plasmonic cavities and quantum dot gain media [24]. A fundamentally different type of quantum genera- *Corresponding authors: Rupesh Ghimire, Jhih-Sheng Wu, tors is the lasing spaser [4, 25, 26]. A lasing spaser is a Vadym Apalkov and Mark I. Stockman, Center for Nano-Optics periodic array of individual spasers that interact in the (CeNO) and Department of Physics and Astronomy, Georgia State near field and form a coherent collective mode. Such University, Atlanta, GA 30303, USA, e-mail: rghimire1@student. lasing spasers have been built of plasmonic crystals that gsu.edu. https://orcid.org/0000-0001-5729-6402 (R. Ghimire); [email protected] (J.-S. Wu); [email protected] (V. Apalkov); incorporate gain media. One type of lasing spasers is a [email protected]. https://orcid.org/0000-0002-6996-0806 periodic array of holes in a plasmonic metal film depos- (M.I. Stockman) ited on a semiconductor gain medium [10]; another type Open Access. © 2020 Rupesh Ghimire, Jhih-Sheng Wu Vadym Apalkov Mark I. Stockman et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. 866 R. Ghimire et al.: Topological nanospaser is a periodic array of metal nanoparticles surrounded by charge, which is (in units of π) 1 at the K point and −1 at the a dye molecules solution [27]. We have recently proposed K′ point. The corresponding electron states at these two a topological lasing spaser that is built of a honeycomb points are chiral, as completely determined by their topol- plasmonic crystal of silver nanoshells containing a gain ogy, with opposite chiralities, which is protected by the T medium inside [28]. The generating modes of such a symmetry. spaser are chiral SPs with topological charges of m = ± 1, While for the gapless graphene the topological charge which topologically protects them against mixing. Only at the K or K′ point is quantized, in two-dimensional one of the m = ± 1 topologically charged modes can gener- semiconductors such as transition-metal dichalcoge- ate at a time selected by a spontaneous breaking of the nide (TMDC) materials, which have the same honeycomb time-reversal (T ) symmetry. crystal structure as graphene but broken inversion sym- The spasers not only are of a significant fundamental metry and, consequently, a finite bandgap, there is no interest but also are promising for applications based on quantization of the topological charges at the two valleys, their nanoscale-size modes and high local fields. Among K or K′. In the TMDCs, the Berry curvature has a maximum such demonstrated applications are those to sensing of at the K points, but it is not singular. It monotonically minute amounts of chemical and biological agents in decreases away from the K points, and the corresponding the environment [18, 19, 29]. Another class of the demon- Berry flux is nonuniversal and, by modulus (in units of π), strated applications of the spasers is that in cancer thera- is always less than 1. Despite this, the chiral nature of the nostics (therapeutics and diagnostics) [16]. An important electron states at the K points is preserved. Namely, the perspective application of spasers is on-chip communica- state are chiral with opposite chiralities at two valleys, K tions in optoelectronic information processing [30]. and K′, as protected by T -reversal symmetry. This prop- It is of a great interest to explore intersections of the erty is crucial for our analysis below, where the interaction spaser technology and topological physics. In our recently of the TMDC material with plasmon modes is considered. proposed topological lasing spaser [28], the topologically In this article, we propose a topological nanospaser charged eigenmodes stem from the Berry curvature [31, 32] that also generates a pair of mutually time-reversed chiral of the plasmonic Bloch bands of a honeycomb plasmonic SP eigenmodes with topological charges of ±1, whose crystal of silver nanoshells. In contrast, the gain medium fields are rotating in time in the opposite directions. In inside these nanoshells is completely achiral. This topo- a contrast to the findings of Wu et al. [28], this proposed logical lasing spaser is predicted to generate a pair of spaser is truly nanoscopic, with a radius ~10 nm. The top- mutually time-reversed eigenmodes carrying topological ological charges (chiralities) of its eigenmodes originate charges of ±1, which strongly compete with each other, so from the Berry curvature of the gain-medium Bloch bands. only one of them can be generated at a time. This gain medium is a two-dimensional honeycomb Topology plays an important role in all fields of nanocrystal of a TMDC [33–35]. The plasmonic subsystem physics, from condensed matter physics to cosmology. In is an achiral nanodisk of a plasmonic metal. Note that solids, the topological properties are determined by the previously the TMDCs have been used as the gain media change of the phase of an electron wave function and are of microlasers where the cavities were formed by micro- quantified by the Berry connection and the correspond- disk resonators [36, 37] or a photonic crystal microcavity ing Berry curvature. The Berry curvature acts as a mag- [38]. None of these lasers generated a chiral, topologically netic field in the reciprocal space, and the flux of the Berry charged mode. curvature through the first Brillouin zone determines the total topological charge that is quantized and is called the Chern number. Although for the systems with the T symmetry the 2 Spaser structure and main total topological charge is zero, it can have nonzero values equations and even quantized within some regions of the reciprocal space called valleys. An example of such systems is gra- The geometry and the fundamentals of functioning of phene, which is semimetal with two inequivalent points, the proposed topological nanospaser are illustrated in K and K′, in the reciprocal space, where the electron Figure 1. This spaser consists of a thin silver nanosphe- energy dispersion is of a relativistic Dirac type. The Berry roid placed atop of the two-dimensional gain medium (a curvature at these two points is singular and zero else- nanodisk of a monolayer TMDC) (Figure 1A). As Figure where. The total flux of the Berry curvature through any 1B illustrates, the gain medium is pumped with cir- surface that encloses K or K′ point is quantized topological cularly polarized light, which is known to selectively R.
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