Negative permeability and negative refraction in composite systems with finite-size inclusions

It is shown that the spatial dispersion in composite systems formed by inclusion of finite size spheres may lead to negative group velocity and, subsequently, to negative refraction. Longitudinal and transverse electromagnetic modes exhibiting negative dispersion are found in the system of finite size charged clouds. It is also shown that similar mechanism due to the electric quadrupole coupling leads to excitation of longitudinal and transverse eigenmodes with negative dispersion in a random set of nonmagnetic metal spheres embedded in a dielectric host. It is shown that the negative refraction related to the spatial dispersion effects may alternatively be viewed as a result of simultaneously negative permittivity and permeability.

Figure 1

The two-dimensional spatial distribution of the transverse magnetic field $B_z(x,y)$ (the top picture) and longitudinal electric field $E_x(x,y)$ (the bottom picture) obtained from PIC simulations. The incident laser pulse carryer frequency is ${\omega }_0=7.85\times {10}^{14}$ s${}^{-1}$, and the slab's plasma frequency ${\omega }_p=8.05\times {10}^{14}$ s${}^{-1}$. The Debye wavelength is ${\lambda }_D\approx 0.47\times {10}^{-7}$ m and the particle radius $a\approx 4.486\times {10}^{-7}$ m. The spatial coordinates $X$ and $Y$ are normalized to the grid spacing $\Delta \approx 6.3\times {10}^{-7}$ m.

Figure 2

(a) Transverse modes with electric quadrupole and magnetic dipole corrections. The negative-dispersion branch is seen in the gap region; $n_s{a}^3=0.2$, $a=3c/{\omega }_p$, where ${\omega }_p$ is the plasma frequency of the metal sphere, $\omega$ is normalized to the plasma frequency, and $k$ is in units of $c/{\omega }_p$. (b) Longitudinal modes with electric quadrupole corrections.

Figure 3

Effective dielectric function $\varepsilon \left(\omega \right)$ (solid line) and magnetic permeability $\mu \left(\omega \right)$ (dashed line) for a system of spheres in vacuum versus normalized frequency; $n_s{a}^3=0.2$, $a=3c/{\omega }_p$. The dielectric permittivity and magnetic permeability are negative for $0.6023<\omega <0.6325$, where $\omega$ is normalized to the plasma frequency ${\omega }_p$.