Scattering-Free Plasmonic Optics with Anisotropic Metamaterials

We develop an approach to utilize anisotropic metamaterials to solve one of the fundamental problems of modern plasmonics—parasitic scattering of surface waves into free-space modes, opening the road to truly two-dimensional plasmonic optics. We illustrate the developed formalism on the examples of plasmonic refractor and plasmonic crystal, and discuss limitations of the developed technique and its possible applications for sensing and imaging structures, high-performance mode couplers, optical cloaking structures, and dynamically reconfigurable electroplasmonic circuits.

Figure 1

(a) Fraction of energy of incident SPP scattered into plane waves from the interface between two SPP-supporting media with different SPP refractive indices; ${ϵ}_{1+}=2$; ${ϵ}_{2+}={ϵ}_{2-}=-10$ (b) normalized field structure corresponding to ${ϵ}_{1-}=1$ in (a).

Figure 2

(a) Truly plasmonic optics: no free-space modes are excited in SPP refraction; (b) Fresnel relations for transmitted (blue, dashed) and reflected (red, solid) SPPs. Dots and lines correspond to numerical solution of Maxwell equations and analytical Eqs. (7) respectively; ${ϵ}_{1-}^x=2.7$; ${ϵ}_{1-}^{yz}={ϵ}_{1+}^{yz}={ϵ}_{1+}^x=1$; ${ϵ}_{2-}^x={ϵ}_{2-}^{yz}={ϵ}_{2+}^{yz}=-10$; ${ϵ}_{2+}^x=-3.7$; (c) refraction of SPPs; arrows correspond to Eq. (6); $H_y$ component of the field across $x=50\mathrm{nm}$ plane is shown; (d) normalized field distribution along $y=0$ axis. Note that SPPs have constant $x$ profile despite change in refractive index (wavelength) at $z=0$ [compare to Fig. 1b].

Figure 3

(a) Geometry of the plasmonic Bragg reflector (b) the dependence of Bragg vector on the SPP incidence angle at $\lambda =500\mathrm{nm}$; dashed and dash-dotted lines correspond to panels (c) and (d); (c) the regime of “surface mirror”; $H_y$ component of the field at $x=50\mathrm{nm}$. (d) transparency band of the same plasmonic crystal; ${ϵ}_{11}^x=2.7$; ${ϵ}_{11}^{yz}={ϵ}_{12}^{yz}={ϵ}_{12}^x=1$; ${ϵ}_{21}^x={ϵ}_{21}^{yz}={ϵ}_{22}^{yz}=-10$; ${ϵ}_{22}^x=-3.71$.

Figure 4

Scattering at the interface between two SPP structures (a) ${ϵ}_{2+}^x=-3.71$, ${ϵ}_{1-}^x$ is varied; (b) ${ϵ}_{1-}^x=2.7$, ${ϵ}_{2+}^x$ is varied; remaining parameters in (a),(b) ${ϵ}_{1-}^{yz}={ϵ}_{1+}^x={ϵ}_{1+}^{yz}=1$; ${ϵ}_2={ϵ}_{2-}^x={ϵ}_{2-}^{yz}={ϵ}_{2+}^{yz}=-10$ (c) scattering in the system with common metal substrate ${ϵ}_{1-}^{yz}={ϵ}_{1+}^x={ϵ}_{1+}^{yz}=2$; ${ϵ}_{2-}^x={ϵ}_{2-}^{yz}={ϵ}_{2+}^x={ϵ}_{2+}^{yz}=-10$ as a function of ${ϵ}_{1-}^x$; (d) effect of losses in the structure in (c) on scattering; red dashed line: ${ϵ}_{1-}^x=3(1+i{ϵ}^{\prime \prime })$; ${ϵ}_{1-}^{yz}=2(1+i{ϵ}^{\prime \prime })$; blue solid line: ${ϵ}_2=-10(1-i{ϵ}^{\prime \prime })$. (e) Scattering of $m=0$ TM mode in layered structure proposed in Ref. 12 (inset); normalized energy flux is shown; ${ϵ}_2=-3.5+2.8i$; ${ϵ}_{\mathrm{PMMA}}=2.25$; ${\lambda }_0=0.51\mu \mathrm{m}$ (f) same as (e), but the polymer is anisotropic with ${ϵ}^z=2.62$, ${ϵ}^{r\varphi }=1$.