Local Density of States for Nanoplasmonics

Abstract

We obtain the local density of states (LDOS) for any nanoplasmonic system in the frequency range dominated by a localized surface plasmon. By including the Ohmic losses in a consistent way, we show that the plasmon LDOS is proportional to the local field intensity normalized by the absorbed power. We obtain explicit formulas for the energy transfer (ET) between quantum emitters and plasmons as well as between donors and acceptors situated near a plasmonic structure. In the latter case, we find that the plasmon-assisted ET rate is proportional to the LDOS product at the donor and acceptor positions, obtain, in a general form, the plasmon ET enhancement factor, and establish the transition onset between Förster-dominated and plasmon-dominated ET regimes.The rapid advances in nanoplasmonics of the past decade opened up possibilities for energy concentration and transfer at length scales well below the diffraction limit [1]. Optical interactions between dye molecules or semiconductor quantum dots, hereafter referred to as quantum emitters (QEs), and localized plasmons in metal-dielectric composite nanostructures underpin major phenomena in plasmon-enhanced spectroscopy, including surface-enhanced Raman scattering [2], plasmonassisted fluorescence [3][4][5] and energy transfer [6][7][8], strong QE-plasmon coupling [9][10][11], and the plasmonic laser (spaser) [12][13][14]. The interaction of a QE, located at r, with electromagnetic modes is characterized by the local density of states (LDOS) ρ(ω, r) = (2ω/πc 2 )Im[TrḠ(ω; r, r)], whereḠ(ω; r, r ′ ) is the electromagnetic Green dyadic and c and ω are speed and frequency of light, which represents the number of modes in unit volume and frequency interval [15]. In particular, the LDOS quantifies the Purcell enhancement of spontaneous emission by a QE in a photonic environment [16], e.g., near metal surfaces [17][18][19][20], metamaterials [21,22], or plasmonic nanostructures [23][24][25][26]. A closely related quantity, the cross density of states (CDOS) ρ(ω; r, r ′ ) = (2ω/πc 2 )Im[TrḠ(ω; r, r ′ )], describes spatial correlations, e.g., due to indirect coupling between QEs [27]. While for high-symmetry systems, such as flat surfaces or spherical particles, the electromagnetic LDOS is known, its evaluation for general-shape systems presents a rather challenging task. A photon emission by a QE involves all system eigenmodes that define the continuum of final states [28,29], so that, in open systems, the calculations of the LDOS and CDOS rely on carefully defined quasinormal modes [30,31].At the same time, nanoplasmonic systems support a host of phenomena that are underpinned by nonradiative plasmon-assisted transitions. For example, energy transfer (ET) between QEs and plasmons, whose frequencies are tuned to resonance, is the key process in many plasmonics applications [32,33]. The magnitude and range of the Förster ET between a donor and an acceptor near a plasmonic structure is strongly enhanced by the plasmonmediated ET channel [34][35][36][37], while the role of the ...

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

“…The Green dyadic (6) is valid for a well-defined plasmon mode (ω pl τ pl ≫ 1) in any nanoplasmonic system, and its consistency is ensured by the optical theorem [37]. With the plasmon Green dyadic (6), the system (5) takes the form…”

“…The LDOS of a single plasmon mode is related to the plasmon Green dyadic (6) as ρ(ω, r) = −(2π 2 ω pl ) −1 Im TrD(ω; r, r), and has the Lorentzian form [37],…”

“…For QE frequencies ω 21 close to the plasmon frequency ω pl , we can adopt the single mode approximation for the Green dyadic [37] …”

“…Whereas the energy flow between individual QEs and plasmon can go in either direction depending on the QE quantum state, the net gain-plasmon ET rate is determined by population inversion N 21 and, importantly, distribution of plasmon states in the gain region. Since individual QE-plasmon ET rates are proportional to the plasmon local density of states (LDOS), which can vary in a wide range depending on QEs' positions and system geometry [37], the net ET rate is obtained by averaging the plasmon LDOS over the gain region. Therefore, the plasmon mode volume should relate, in terms of average system characteristics, the laser condition (1) to the microscopic gain-plasmon ET picture.…”

Landau damping of surface plasmons in metal nanostructures

“…For brevity, we omit the mode index l hereafter. The general expression for plasmon decay rate Γ has the form [69] …”