Figure 1

(a) Isofrequency surface of type I HMM (${\epsilon }_{xx}>0,{\epsilon }_{zz}<0$) with Poynting vectors (orange arrows) shown normal to the surface. Note that the Poynting vector component $S_x$ is negative and points in a direction opposite to the wave-vector component. (b) The HMM response is achieved by using a multilayer realization of alternating subwavelength layers of metal and dielectric (shown above), or by using metal nanowires embedded in a dielectric host (shown below). (c) Real part of perpendicular and parallel components of dielectric permittivity predicted by EMT. The type I response occurs below 491 nm, while the type II response (${\epsilon }_{xx}<0,{\epsilon }_{zz}>0$) occurs in the longer wavelength region. We study a ${\text{Ag/TiO}}_2$ multilayer structure with unit-cell size $a$ $=$ 30 nm (15 nm/15 nm). (d) Real part of perpendicular and parallel components of dielectric permittivity predicted by EMT for a nanowire system. The type I response occurs for a broader range of wavelengths above 522 nm, while the type II response (${\epsilon }_{xx}<0,{\epsilon }_{zz}>0$) occurs in the short wavelength region. The system consists of silver nanowires embedded in an alumina matrix with a $\rho =0.22$ fill fraction.Reuse & Permissions

Figure 2

Local density of states (normalized to free space) at a distance $z_o=15$ nm away from the HMM slab predicted by EMT. An excellent agreement seen for the multilayer structure calculated via the transfer-matrix method. We show the type I HMM wavelength region only. Notice how the LDOS peaks occur at discrete wavelengths indicating that they must be fundamentally different from the usual broadband high-$k$ modes in HMMs.[9]Reuse & Permissions

Figure 3

Wave-vector-resolved local density of states (normalized to free space) of an emitter 15 nm away from HMM predicted by (a) the effective-medium theory. (b) Excellent agreement is seen for the practical multilayer structure. The highest LDOS occurs when the group velocity($\partial \omega /\partial k$), equal to the slope of the yellow regions, is nearly zero. These bright regions are the slow-light modes that are supported by the type I HMM.Reuse & Permissions

Figure 4

Complex-$k_x$ dispersion relation of slow-light modes predicted by EMT, calculated numerically (a) $\lambda$ vs $\text{Re}\left(k_x\right)$ and $\lambda$ vs $\text{Im}\left(k_x\right)$ (shown in the inset). Note that the waveguide mode solutions split into two branches: a forward traveling wave (black branch) and a backward traveling wave (red branch). A negative real part of the wave number has to be chosen for this backward branch so that $\text{Im}\left(k_x\right)>0$. (b) Energy velocity is calculated numerically using values from the dispersion relation. The arrows point toward the slow-light mode region before it becomes a highly leaky slow-light mode.Reuse & Permissions

Figure 5

Near-field variation of the spontaneous-emission lifetime of quantum emitters near the slow-light HMM waveguide. The distance of the quantum emitter is varied and normalized to the operating wavelength. (a) Numerical calculation of EMT and (b) practical multilayer system. The dark regions (color bar $<0.2$) corresponding to the lower lifetime of the slow-light modes extend much further, denoting excellent coupling of the emitters to slow-light modes as opposed to other radiative and nonradiative channels. (c) The refractive index of an 80 nm embedded layer between two 240 nm HMM slabs (shown in the inset) is varied to demonstrate the sensitivity of the slow-light mode, useful for optical biosensing. The inset shows the linear relation of the 450 nm slow-light mode as a function of the refractive index $n$ equal to 1.0, 1.2, 1.3, 1.5, and 1.6 (corresponding to the black arrows in the main plot).Reuse & Permissions