Dynamically controllable anisotropic metamaterials with simultaneous attenuation and amplification

Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a metamaterial may be realized quite simply as a random mixture of electrically small (possibly nanoscale) spheroidal particles of at least two different isotropic dielectric materials, one of which must be dissipative but the other active. The dielectric properties of this metamaterial are influenced by the volume fraction, spatial distribution, particle shape and size, and the relative permittivities of the component materials. Similar metamaterials with more complicated linear as well as nonlinear constitutive properties are possible. Dynamic control of the active component material, for example, via stimulated Raman scattering, affords dynamic control of the metamaterial.

Figure 1

Real and imaginary parts of ${\epsilon }_{\text{Br}}^{\perp }$ (red, solid curves) and ${\epsilon }_{\text{Br}}^{\parallel }$ (blue, dashed curves) plotted against the volume fraction $f_a$, when ${\epsilon }_a=2-0.03i,{\epsilon }_b=3+0.05i$, and $U=5$. The yellow rectangle indicates the $f_a$ range where $\text{Im}\left\{{\epsilon }_{\text{Br}}^{\perp }\right\}<0$ but $\text{Im}\left\{{\epsilon }_{\text{Br}}^{\parallel }\right\}>0$.

Figure 2

Real and imaginary parts of ${\epsilon }_{\text{Br}}^{\perp }$ (red, solid curves) and ${\epsilon }_{\text{Br}}^{\parallel }$ (blue, dashed curves) plotted against the shape parameter $U$, when ${\epsilon }_a=2-0.03i,{\epsilon }_b=3+0.05i$, and $f_a=0.535$. The two yellow rectangles indicate the $U$ ranges where the product $\text{Im}\left\{{\epsilon }_{\text{Br}}^{\perp }\right\}\text{Im}\left\{{\epsilon }_{\text{Br}}^{\parallel }\right\}<0$.

Figure 3

Real and imaginary parts ${\epsilon }_{\text{Br}}^{\perp }$ and ${\epsilon }_{\text{Br}}^{\parallel }$, as well as the product $\text{Im}\left\{{\epsilon }_{\text{Br}}^{\perp }\right\}\text{Im}\left\{{\epsilon }_{\text{Br}}^{\parallel }\right\}$, plotted against the real and (negative) imaginary parts of the relative permittivity ${\epsilon }_a$, when ${\epsilon }_b=3+0.05i,f_a=0.25$, and $U=5$.

Figure 4

Real and imaginary parts of ${\epsilon }_{\text{SPFT}}^{\perp }$ (thick curves) and ${\epsilon }_{\text{SPFT}}^{\parallel }$ (thin curves) plotted against the normalized correlation length $k_{0}L$, when ${\epsilon }_a=2-0.03i,{\epsilon }_b=3+0.05i,f_a=0.535$, and $U=5$. The size parameter $\rho =0$ (red, solid curves), $0.5L$ (blue, dashed curves), and $L$ (green, broken dashed curves).

Figure 5

Real and imaginary parts ${\epsilon }_{\text{MG}}^{\perp }$ and ${\epsilon }_{\text{MG}}^{\parallel }$, as well as the product $\text{Im}\left\{{\epsilon }_{\text{MG}}^{\perp }\right\}\text{Im}\left\{{\epsilon }_{\text{MG}}^{\parallel }\right\}$, plotted against the real and (negative) imaginary parts of the relative permittivity ${\epsilon }_a$, when ${\epsilon }_b=3+0.05i,f_a=0.25$, and $U=5$. Particles of component material “a” are taken to be dispersed randomly in the component material “b,” and the shape parameter $U$ applies only to component material “a.”