Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation

Abstract

We propose an exactly solvable electrodynamical model for surface plasmon amplification by stimulated emission of radiation (spaser). The gain medium is described in terms of the nonlinear permittivity with negative losses. The model demonstrates the main feature of a spaser: a self-oscillating state (spasing) arising without an external driving field if the pumping exceeds some threshold value. In addition, it properly describes synchronization of a spaser by an external field within the Arnold tongue and the possibility of compensating for Joule losses when the pumping is below threshold. The model also gives correct qualitative dependencies of spaser characteristics on pumping.

Loss compensation by spasers in plasmonic systems

“…On this basis, concerns of possibility of loss compensation spasers were raised. As we discussed in [40], for dye-based spasers pumped optically, which we consider in the current paper, the situation is different. For our system, both the pump power and the electric field strength for the pumping wave have reasonable values of 5 10 W − and 100 V/m, respectively.…”

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

“…Furthermore, defining the plasmon mode volume in terms of field intensity at a specific point [25,30] seems impractical due to very large local field variations near the metal surface caused by particulars of system geometry, for example, sharp edges or surface imperfections: strong field fluctuations would grossly underestimate the mode volume that determines spasing threshold for gain distributed in an extended region. At the same time, while spasing was theoretically studied for several specific systems [3,[20][21][22][23][24], the general spaser condition was derived, in terms of system parameters such as permittivities and optical constants, only for two-component systems [15,36] without apparent relation to the mode volume in Eq. (1).…”

Spaser quenching by off-resonant plasmon modes

“…Even though a metal nanostructure possesses discrete spectrum of localized plasmon modes, e.g., characterized by angular momentum l for spherical systems, the QE coupling to off-resonant modes well separated in frequency from QE (and from resonant mode) is usually considered sufficiently weak and, hence, neglected [3,[20][21][22][23][24]. However, while this is a good approximation for high-quality cavity modes, the plasmon resonances are characterized by much broader bands due to large Ohmic losses in metal, so that a significant fraction of excited QE energy is transferred to off-resonant modes, especially for small QE distances to the metal surface and, correspondingly, large QE-plasmon coupling [25][26][27][28].…”