Abstract
We theoretically investigate the amplification of extraordinary optical transmission (EOT) phenomena in periodic arrays of subwavelength apertures incorporating gain media. In particular, we consider a realistic structure consisting of an opaque silver film perforated by a periodic array of slits and clad on each side by an optically pumped dielectric thin film containing rhodamine dye molecules. By solving the semiclassical electronic rate equations coupled to rigorous finite-element simulations of the electromagnetic fields, we show how the resonant electric-field enhancement associated with EOT properties enables complete ohmic loss compensation at moderate pump intensity levels. Furthermore, our calculations show that, as a consequence of the strong spatial hole-burning effects displayed by the considered structures, three separate regimes of operation arise: the system can behave as an absorber, an optical amplifier or a laser, depending on the value of the pump intensity. A discussion on the feasibility of reaching the lasing regime in the considered class of structures is also presented.
Highlights
Applied in this paper consists essentially in extending the traditional frequency-domain analysis of gain amplification and lasing action [22, 23] to structures displaying a highly non-uniform gain distribution at the subwavelength scale
In order to do that, we generalize recent works in this context [7, 11, 14] and solve the electronic rate equations of a four-level model of the active medium coupled to rigorous electrodynamical calculations of both the pump and probe obtained by means of the finite-element method (FEM)
For values of the pump field magnitude larger than those corresponding to complete ohmic loss compensation, the action of the gain medium induces the considered system to effectively behave as an optical amplifier [23]
Summary
We consider the active structure shown in figure 1. To describe the electronic dynamics of the rhodamine dye molecules, we assume that their corresponding electronic energy levels and transition rates can be accounted for by a four-level system (see schematics in the inset of figure 1) This approximation has shown its accuracy to model optical gain induced by the considered class of active dyes [24]. Under this assumption, the whole EM response of the structure under continuous-wave (cw) excitations can be obtained by solving the following set of linearly coupled partial differential equations, which govern the spatio-temporal dynamics of the electronic population densities (Ni (r, t), i = 0, 1, 2, 3) of each of the energy levels displayed in the inset of figure 1 [22]:. By applying this condition to equation (8), it is straightforward to conclude that the effect of the probe beam on the population inversion N (r) is negligible, and that, the two-step approach considered here gives virtually the same results as those obtained by using a full self-consistent calculation
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