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Frontiers in Optics

Metamaterials with Gain and Interpretation of Transmission in Pump-Probe Experiments

Costas M. Soukoulis, Thomas Koschny

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We numerically investigate loss compensation and transmission in pump-probe experiments in resonant metamaterials with gain using an FDTD algorithm coupled to semiclassical rate equations. We observe differential transmittance signals from the coupled system that are a factor of four to five larger than for the bare quantum well. We observe a more rapid temporal decay of the differential transmittance signal for the coupled system compared to the bare quantum well. The effective metamaterial gain beyond the bare quantum-well gain, leading to a significant reduction of the metamaterial’s losses, but no complete compensation of the losses. We explain experimentally observed negative differential transmission by gain-dependent impedance. Article not available.

DOI
10.1364/ls.2011.lwa2

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We numerically investigate loss compensation and transmission in pump-probe experiments in resonant metamaterials with gain using an FDTD algorithm coupled to semiclassical rate equations. We observe differential transmittance signals from the coupled system that are a factor of four to five larger than for the bare quantum well. We observe a more rapid temporal decay of the differential transmittance signal for the coupled system compared to the bare quantum well. The effective metamaterial gain beyond the bare quantum-well gain, leading to a significant reduction of the metamaterial’s losses, but no complete compensation of the losses. We explain experimentally observed negative differential transmission by gain-dependent impedance. Article not available.
We establish a new approach for pump-probe simulations of metallic metamaterials coupled to the gain materials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, we have studied light amplification of arrays of metallic split-ring resonators with a gain layer underneath. We find that the differential transmittance ΔT/T can be negative for split-ring resonators on the top of the gain substrate, which is not expected, and ΔT/T is positive for the gain substrate alone. These simulations agree with pump-probe experiments and can help to design new experiments to compensate for the losses of metamaterials.
We present evidence of strong coupling between the gain material and the metallic metamaterials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, the numerical pump-probe experiments are performed in several configurations (split-ring resonators (SRRs), inverse SRRs and fishnets) of metamaterials, demonstrating reduction of the resonator damping in all cases and hence the possibility for loss compensation. We find that the differential transmittance ΔT/T can be negative in different SRR configurations, such as SRRs on the top of the gain substrate, gain in the SRR gap and gain covering the SRR structure, while in the fishnet metamaterial with gain ΔT/T is positive.
We present a general theory of gain-modified emission dynamics between two quantum emitters (two level systems) in a linear gain medium, demonstrating how gain modifies the usual radiative decay rates and inter-emitter coupling and decay rates, that are well known from purely lossy systems. We derive a Born-Markov master equation that shows explicitly how gain modifies the usual rates appearing for two emitters in a loss only medium, and introduces new gain terms. We then present Bloch equations in the bare state basis as well as a dressed-state basis (using superradiant and subradiant states). As an application of the theory, we show calculations for a fully three-dimensional metal dimer in a gain-compensated medium, containing two quantum emitters, and show explicit solutions in terms of the quasinormal modes, which easily allows one to obtain all the relevant decay rates. We study the modified decay dynamics, gain excited pumping, as well as the entanglement entropy and spectral emission. We also demonstrate how a breakdown of the weak excitation approximation in the presence of gain requires a careful treatment beyond a linear response, which yields non-trivial incoherent coupling terms that typically are not included in dipole-dipole coupling models or heuristic gain pumping models.
Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
Electromagnetically induced transparency (EIT) in metamaterials is studied experimentally in a waveguide system with tunable intrinsic loss. There is a window in the transmission spectrum with nearly unchanged maximum transmittance, which is the result of simultaneous suppression of reflection and absorption. Group delay measurements demonstrate the transmission-delay product is almost independent of the intrinsic loss while the bandwidth-delay product is affected. Dynamic evolution of EIT in metamaterials is also investigated and we observe parameter-controllable excitation transfer from the bright resonator to the dark resonator during the process of EIT buildup.