Plasmon Injection to Compensate and Control Losses in Negative Index Metamaterials

Metamaterials have introduced a whole new world of unusual materials with functionalities that cannot be attained in naturally occurring material systems by mimicking and controlling the natural phenomena at subwavelength scales. However, the inherent absorption losses pose a fundamental challenge to the most fascinating applications of metamaterials. Based on a novel plasmon injection (PI or $\mathrm{\Pi }$) scheme, we propose a coherent optical amplification technique to compensate losses in metamaterials. Although the proof of concept device here operates under normal incidence only, our proposed scheme can be generalized to an arbitrary form of incident waves. The $\mathrm{\Pi }$ scheme is fundamentally different from major optical amplification schemes. It does not require a gain medium, interaction with phonons, or any nonlinear medium. The $\mathrm{\Pi }$ scheme allows for loss-free metamaterials. It is ideally suited for mitigating losses in metamaterials operating in the visible spectrum and is scalable to other optical frequencies. These findings open the possibility of reviving the early dreams of making “magical” metamaterials from scratch.

Figure 1

Conceptual structure for the $\mathrm{\Pi }$ scheme. The central superlattice constitutes the metamaterial. $P_1$ and $P_2$ are the input and output ports of the metamaterial, respectively. $P_3$ and $P_4$ are the auxiliary ports through which surface plasmons for amplification are excited externally. The red rectangular box illustrates the metamaterial unit cell consisting of gold grating and the gold thin film (in the center of the unit cell) embedded in polyimide. The thickness of the gold thin film and its distance from the strips are 5 and 8 nm, respectively. The thickness of the gold strips in the gratings is 11 nm. Grating period at the central superlattice (i.e., between the ports $P_1$ and $P_2$) is 80 and 86 nm at the side superlattices above the ports $P_3$ and $P_4$. There exist six periods in each of the side superlattices and 16 periods in the central superlattice. The structure is translationally invariant in the $z$ direction. SPPs propagate from the side superlattices to central superlattice and excite the metamaterial eigenmode (lower panel), which in turn amplifies the domestic SPPs in the central superlattice if an input field at port $P_1$ exists. Finally, the amplified SPPs couple to free-space modes. The surface plot corresponds to the $z$ component of the magnetic field ($\mathrm{A}/\mathrm{m}$) at magnetic resonance. The middle part of the central superlattice, indicated by a box, is enlarged and the field amplitude is multiplied by 4 to clearly illustrate the mode profile.

Figure 2

Effective parameters for a single functional layer at $\alpha =6$. (a) Real ($n^{\prime }$) and imaginary ($n^{\prime \prime }$) parts of the retrieved effective refractive index. Around 552 and 562 THz, the system behaves as an ultralow-loss NIM. (b) Real ($z^{\prime }$) and imaginary ($z^{\prime \prime }$) parts of the impedance.

Figure 3

Transmission spectra of the central superlattice. Transmittance through central superlattice increases with $\alpha$. The increase in the transmittance is significant in the negative refractive index region around 560 THz.

Figure 4

The figure of merit for the negative index material (${\mathrm{FOM}}_{-\mathbf{1}}$) as a function of $\alpha$. The blue data points show the ${\mathrm{FOM}}_{-1}$ for the simulated values of $\alpha$. The red solid line is the best-fit curve. ${\mathrm{FOM}}_{-1}$ diverges at $\alpha =7$ and the metamaterial becomes loss free. Beyond $\alpha =7$, the metamaterial becomes an amplifying medium.