Figure 1

(a) A closed surface $\Sigma$ encloses a nonuniform region. (b) Extraction of the effective-medium parameters of a composite material based on the theory of Ref. 4.Reuse & Permissions

Figure 2

(a) Effective permittivity ${\varepsilon }_{\mathrm{eff}}$ (green curves) and permeability ${\mu }_{\mathrm{eff}}$ (blue curves) versus normalized frequency $\omega a/c$. The discrete symbols correspond to the full wave homogenization values (Ref. 13) and the solid lines are obtained using Clausius-Mossotti formulas. The inset shows the wave vector $k_x$ as a function of frequency. (b) $x$ component of the Poynting vector calculated using (i) averaged microscopic Poynting vector (solid blue) [Eq. (1)], (ii) nonlocal homogenization model (circles) [Eq. (2)], (iii) local effective parameters (diamonds) [Eq. (4)], and (iv) results based on the definition of Poynting vector of Ref. 7. (c) Stored energy calculated using (i) averaged microscopic stored energy (solid blue) [Eq. (6)], (ii) nonlocal homogenization model (circles) [Eq. (7)], and (iii) local effective parameters (diamonds) [Eq. (8)]. (d) Heating rate calculated using (i) averaged microscopic heating rate (solid blue) [Eq. (9)], (ii) nonlocal homogenization model (circles) [Eq. (10)], and (iii) local effective parameters (diamonds) [Eq. (11)]. The unit-cell geometry is shown in the inset.Reuse & Permissions

Figure 3

(a), (b) Similar to Fig. 2b, except that losses are taken into account: (a) $\Gamma /{\omega }_p=0.1$, (b) $\Gamma /{\omega }_p=2.0$. (c), (d) Similar to Fig. 2c, except that losses are taken into account: (c) $\Gamma /{\omega }_p=0.1$, (d) $\Gamma /{\omega }_p=0.5$.Reuse & Permissions

Figure 4

Time snapshot of $H_z$ for a Gaussian beam illuminating the metamaterial slab (${\theta }_i={33}^{°}$). (a) slab with dimensions $L_x=17.8a$ and $L_y=60.4a$ and plasmonic host with collision frequency $\Gamma /{\omega }_p=0.05$. (b) Similar to (a) but for the parameters $L_x=6a$, $L_y=60a$, and $\Gamma /{\omega }_p=0.9$.Reuse & Permissions