Limitations of Particle-Based Spasers

Abstract

We present a semi-classical analytic model for spherical core-shell surface plasmon lasers. Within this model, we drop the widely used one-mode approximations in favor of fully electromagnetic Mie theory. This allows for incorporation of realistic gain relaxation rates that so far have been massively underestimated. Especially, higher order modes can undermine and even reverse the beneficial effects of the strong Purcell effect in such systems. Our model gives a clear view on gainand resonator-requirements, as well as on the output characteristics that will help experimenters to design more efficient particle-based spasers.Nanoscopic sources of coherent electromagnetic fields are essential elements for different fields in nanooptics, such as nanoplasmonics [1], metamaterials [2], and quantum plasmonics [3]. A surface plasmon laser (spaser) might be such a nanoscopic source [4,5].As compared to a laser, the obvious difference of a spaser is the use of plasmons instead of photons. Plasmons are inherently localized excitations and generally exhibit much smaller (mode) volumes than photonic cavity modes [6]. From an electromagnetic perspective, there is no reason to expect any further principle deviations from well-known (semi-classical) laser physics. For instance, Mie theory [7] completely describes the electromagnetic field for a spherical particle irrespective of the constituent material, i.e., whispering gallery modes of dielectric spheres and localized plasmon modes of metallic spheres are all included. However, as we will detail below, there are certain issues that have to be treated with care.Recently, a number of spaser devices [8][9][10][11][12][13][14] have been characterized and extensive theoretical work has addressed fundamental and device-specific spaser properties [15][16][17][18][19][20]. However, several questions, even of a fundamental nature, remain to be answered. Perhaps the most important of these is related to the rather low spaser efficiency. For instance, previous experiments placed very high demands on the pump (e.g., high laser pulse intensities [10]), the synthesis of the spaser's gain medium (e.g., dense incorporation of fluorophores [8]), and, quite generally, very high demands regarding the material quality [14]. Accordingly, these issues are reflected by the rather small number of publications that address spaser action in fully nanoscopic systems and systems working with organic gain media [8][9][10].Analytic theoretical descriptions have mainly focused on quasi-static analysis, so far [4,[16][17][18][19][20]. Within this framework only a nanoparticle's dipolar resonance or generic numbers of the gain medium's relaxation rate have been considered to describe the spaser. Rather numerical cold cavity analysis of actual devices has been used in order to show (i) correspondence with observed far-field patterns and measured spectra etc. [11][12][13][14], (ii) that the resonator under observation is unable to support ordinary purely optical modes [11][12][13][14], and (iii) to estimate th...

Nanolasers Enabled by Metallic Nanoparticles: From Spasers to Random Lasers

“…On the other hand, recent theoretical studies suggest that an extremely high level of optical gain would be required to achieve spasing resonance in single nanoparticle resonators. This level of gain may not have been supplied in previous experiments . In addition, the existence of high‐order plasmonic modes introduce quenching effects in dye molecules which further increases the necessary gain to reach the spasing region .…”

“…This level of gain may not have been supplied in previous experiments. [41,55,72] In addition, the existence of high-order plasmonic modes introduce quenching effects in dye molecules which further increases the necessary gain to reach the spasing region. [55] To settle this ambiguity, a direct optical characterization of the lasing characteristics of single nanoparticles are thus required.…”

Active Nanophotonics

“…The  -factor is typically small in macroscopic lasers because of their multimode operation, resulting in a well pronounced amplified spontaneous emission (ASE) kink in the inputoutput characteristic [144]. For metal particle-based nanolasers (spaser), the value of  -factor significantly drops from units of ~10 -1 to ~10 -4 as a luminescent molecule gets closer to the particle surface [105]. This effect is known as quenching and it consists in the excitation of highly dissipative higher-order modes in the nanoparticle [145], [146].…”

Theoretical study of plasmonic lasing in junctions with many molecules

“…inhomogeneous broadening [19]. As a result, the energy transfer from the quantum emitters to the MNP plasmon becomes inefficient, and the coupling to other plasmon modes may occur, which further complicates the situation [16].…”

“…The rapid damping of plasmon excitations impedes the achievement of plasmonic lasing [16] unless many quantum emitters concertedly transfer their energy to the MNP. These quantum emitters should, in turn be excited, e.g., by optical pumping [3][4][5][6][7][8][9][10][11][12] or by electrical injection [13,14].…”