The design and simulated performance of a coated nano-particle laser

Abstract

The optical properties of a concentric nanometer-sized spherical shell comprised of an (active) 3-level gain medium core and a surrounding plasmonic metal shell are investigated. Current research in optical metamaterials has demonstrated that including lossless plasmonic materials to achieve a negative permittivity in a nano-sized coated spherical particle can lead to novel optical properties such as resonant scattering as well as transparency or invisibility. However, in practice, plasmonic materials have high losses at optical frequencies. It is observed that with the introduction of active materials, the intrinsic absorption in the plasmonic shell can be overcome and new optical properties can be observed in the scattering and absorption cross-sections of these coated nano-sized spherical shell particles. In addition, a "super" resonance is observed with a magnitude that is10(3) greater than that for a tuned, resonant passive nanosized coated spherical shell. This observation suggests the possibility of realizing a highly sub-wavelength laser with dimensions more than an order of magnitude below the traditional half-wavelength cavity length criteria. The operating characteristics of this coated nano-particle (CNP) laser are obtained numerically for a variety of configurations.

Directive properties of active coated nano-particles

“…These resonances were exploited in [6] and [7], where efficient MTM-based ESAs were proposed, and in [8] where MTM-inspired electrically small near-field parasitic resonators were used as impedance transformers to realize matching of the overall antenna system to its source and to the wave impedance of the medium in which it radiates. While the above works focused on radio and microwave frequencies, similar highly resonant properties, for potential use in nano-sensing, -amplifying and -antenna applications, were reported for passive plasmonic-based configurations at optical frequencies, see e.g., [9], [10] and the works referenced therein, as well as active plasmonic-based configurations, see e.g., [11] and the works referenced therein, as well as [12] and [13]. In particular, interesting enhancements of directivity patterns for higher order mode sub-wavelength radiators made of DPS materials in conjunction with passive MTMs or plasmonic materials, were reported in [10], this providing an alternate route towards sub-wavelength radiators with high directivities.…”

“…Previous results [11]- [14] have demonstrated that highly resonant sub-wavelength CNPs can be designed by including gain, e.g., inside their nano-cores. Such active configurations were found to lead to scattering crosssections that are orders of magnitude larger than the values predicted by their geometrical sizes, see e.g., [11] and the works referenced therein, as well as to the enormous radiated powers for localized excitation sources [12]- [14].…”

“…Such active configurations were found to lead to scattering crosssections that are orders of magnitude larger than the values predicted by their geometrical sizes, see e.g., [11] and the works referenced therein, as well as to the enormous radiated powers for localized excitation sources [12]- [14]. In those works, significant attention has been devoted to a CNP consisting of a silica (SiO 2 ) nano-core of radius 24 nm, coated with a 6 nm thick silver (Ag) nano-shell for which the frequency and size-dependency of the permittivity was taken into account.…”

“…2  n is the refractive index of the silica nano-core in the frequency region of interest, and the parameter  determines the nature of the nano-core and thus of the CNP. In particular, it becomes lossless (and passive) for 0   , it is lossy and passive for 0   (in which case  is referred to as the absorption coefficient [15] or optical loss constant [11]) and it is active for 0   (in which case it is referred to as the optical gain constant [11]). We note that both of the parameters, n and  , are contained in the expression for the wave number of the silica nano-core in the following manner:…”

“…For the active CNPs (consisting of a silica nano-core covered with a silver nano-shell) studied in [11]- [14], presently referred to simply as Ag-based CNPs, the so- Figure 2 displays notable differences between the cylindrical and spherical active CNP designs. All of the results in Figure 2 have been thoroughly accounted for via extensive near-field investigations for cylindrical [13] and spherical [12,14] active Ag-based CNPs.…”