Resonance amplification of left-handed transmission at optical frequencies by stimulated emission of radiation in active metamaterials

We demonstrate that left-handed resonance transmission from metallic metamaterial, composed of periodically arranged double rings, can be extended to visible spectrum by introducing an active medium layer as the substrate. The severe ohmic loss inside metals at optical frequencies is compensated by stimulated emission of radiation in this active system. Due to the resonance amplification mechanism of recently proposed lasing spaser, the left-handed transmission band can be restored up to 610 nm wavelength, in dependence on the gain coefficient of the active layer. Additionally, threshold gains for different scaling levels of the double-ring unit are investigated to evaluate the gain requirement of left-handed transmission restoration at different frequency ranges.


Introduction
Surface plasmon amplification by stimulated emission of radiation, shortened as spaser [1], was proposed to explore the potential applications in nanoplasmonics.
More recently, as an analogy of the localized surface plasmon amplification, a lasing spaser [2], by combining the metallic metamaterial and gain medium, can achieve transmission amplification or lasing effect with coherent stimulated emission. As it is different from the dark mode of a spaser, a lasing spaser with metallic metamaterial as the resonant inclusion can radiate to the far field and generate transmission amplification with orders of magnitude enhancement at resonance frequency.
On the other hand, metamaterials have attracted wide interest because of their important applications in negative refraction [3][4][5][6][7], superlens [8] and invisible cloak [9]. However, electromagnetic resonance is usually required for the metallic metamaterials to obtain these extraordinary properties [10][11][12][13], such as the left-handed transmission, which unavoidably results in severe resonance loss, especially at optical frequencies where metals can not be regarded as perfect conductor. Therefore, how to compensate the intrinsic ohmic loss in metallic metamaterials is very important in order to obtain lossless negative refraction behavior and optical left-handed transmission, because metal attenuation progressively dominates the resonant response at optical frequencies. As a matter of fact, Sarychev and Tartakovsky have demonstrated theoretically that a plasmoic metamaterial comprising metallic horseshoe-shaped nanotennas, if filled with highly efficient gain medium, can serve as a very compact source of electromagnetic radiation [14]. In this paper, inspired by the concept of the lasing spaser mechanism [2] as well as the other works reported earlier, we investigate numerically the amplification of the left-handed resonant transmission at terahertz frequencies, and even visible spectrum, with the aim to compensate the severe intrinsic ohmic loss by stimulated emission of radiation.

Numerical model
According to the work of Zheludev et al., the active medium, such as a semiconductor pumped by optical or electrical signal, is characterized by a gain coefficient α with the value of ε are the real and imaginary part of the electric permittivity of the active medium, respectively [2]. In this work, such an active medium is used as the substrate of the metallic structure composed of concentric double rings, which was demonstrated to be efficient on generating the left-handed resonance in microwave regime [15]. Figure 1 shows

Simulation results
As demonstrated in our previous work [15], the double-ring metamaterial with the millimeter sizes specified earlier can exhibit the left-handed behavior with high transmission magnitude. However, by scaling the structure simultaneously down to the micrometer sizes (with a scaling factor 3 Fig. 4(a) is larger than the threshold gain of 70 1 cm − from the asymmetric split-ring metamaterial at 35 THz [2]. The reason for these two aspects may be that the asymmetric split-ring metamaterial has a resonance with higher Q-factor than the double-ring one does. In addition, the dependence of the left-handed bandwidth on the gain coefficient can be estimated from Fig. 4(b). The simulation result seems that transmission amplification does not lead to obvious change in the transmission bandwidth, which is attributed to the relatively low Q-factor of the double-ring metamaterial.  Fig. 1) into the visible spectrum will lead to the unrealistic case of gap g and metal thickness smaller than 20 nm. Thus, this case is calculated with a different geometric configuration: edge length of the out ring a is 185 nm, gap g is 20 nm, metal cross section is 20×20 nm 2 , and unit cell is in 210×100×210 nm 3 . Figure 5(  α .

Conclusions
Resonance Amplification method similar to the active left-handed materials could also be extended to other metamaterials, such as superlens and cloaking structures.