Funneling Light through a Subwavelength Aperture with Epsilon-Near-Zero Materials

We present a comprehensive study of enhanced light funneling through a subwavelength aperture with realistic (lossy) epsilon-near-zero (ENZ) materials. We realize experimentally an inclusion-free ENZ material layer operating at optical frequencies and characterize its performance. An analytical expression describing light funneling through several structures involving ENZ coupling layers is developed, validated with numerical solutions of Maxwell equations, and utilized to relate the performance of the ENZ coupling systems to their main limiting factor, material losses.

Figure 1

(a) Schematic of the as-grown ENZ-material optical measurements (inset) and the transmission and reflection data from these measurements; symbols show experimental reflection (red circles) and transmission (blue diamonds); lines represent theoretical fits. (b) Retrieved permittivity spectra from the data in (a).

Figure 2

(a) Scanning electron microscope image of a representative ENZ-coupled subwavelength aperture used in experiments (length of the yellow scale bar is $6\mu \mathrm{m}$). (b) Schematic drawing of the structure geometry. The total thickness of the ENZ material, $n$-doped InAsSb, is $d_1+d_g\simeq 1.15\mu \mathrm{m}$. The thickness of both the gold and slit is $d_g\simeq 300\mathrm{nm}$. Slit widths ($w$), between $0.9$ and $1.8\mu \mathrm{m}$, were investigated experimentally.

Figure 3

Transmission for TM- (red curve) and TE- (magenta curve) polarized light, for systems with (a) $w=1\mu \mathrm{m}$ and (b) $w=1.4\mu \mathrm{m}$. (c) Transmission through the GaAs control structure with $w=1\mu \mathrm{m}$ (main figure) and $w=1.4\mu \mathrm{m}$ (inset). (d) Transmission at the ENZ-enhanced transmission peak as a function of slit width $w$. In all panels, symbols and solid lines correspond to experimental data and dashed lines to analytical results. Analytical results accurately predict off-resonant behavior of relatively small slits ($\sqrt{{ϵ}_g}w/\lambda \lesssim 0.5$) while slightly overestimating on-resonant transmission [18]. For thicker slits, higher-mode transmission becomes important.

Figure 4

(a) Comparison between transmitted power at the ENZ wavelength in three ENZ-assisted structures: (i) the system realized in our experiments (red), when ENZ material fills the substrate and in-slit regions, (ii) the system where the ENZ material is deposited as a thin substrate layer, but air fills both the slit region and the region above the slit (green), and finally, (iii) the design originally suggested in Ref. 14 where ENZ fills substrate, slit, and superstrate regions of the geometry shown in Fig. 2 (black). (b)–(d) illustrate field distribution in the three systems [(i)–(iii), respectively] for $\mathrm{imag}(ϵ)=0.1$. The dashed line in (a) represents material loss realized in our experiments.