Negative Magnetic Permeability in the Visible Light Region

Negative magnetic permeability of single split-ring resonators (SSRRs) is theoretically investigated in the visible light region. To describe the conduction characteristics of metal in the visible range, we develop the internal impedance formula completely. In our calculations, we determine the magnetic responses of the SSRR accurately. Based on our investigations, we also demonstrate the negative $\mu$ of the silver SSRR array in the visible light region.

Figure 1

Dispersion curves of the internal impedance of silver, gold, and copper; the curves labeled $a$ and $b$ are the surface resistivity $R_s$ calculated by using Eqs. (2, 3), respectively; the curves labeled $c$ and $d$ are the internal reactance $X_s$ calculated by using Eqs. (2, 3) respectively.

Figure 2

Models of SSRR used in our calculations. (a) The element of the SSRR, and (b) the array of the SSRR placed in the host material whose relative permittivity is ${\epsilon }_r$.

Figure 3

Real and imaginary parts of the effective permeability of the silver SSRRs in the host material (${\epsilon }_r=2.25$) as a function of the SSRRs’ dimensions. The labeling in each case indicates the unit-cell dimension $a$. The inset shows the corresponding dimensions of the SSRR in nanometers.

Figure 4

Frequency dependencies of the minimum ${\mu }_{\mathrm{Re}}$ of the SSRRs made of silver, gold, and copper. The ${\mu }_{\mathrm{Re}}$ minimum frequency dependence of the unit-cell dimension $a$ of the silver SSRRs is also shown.

Figure 5

Frequency dependencies of the minimum ${\mu }_{\mathrm{Re}}$ of the SSRRs made of (a) silver, (b) gold, and (c) copper according to the filling factor: $F=3\%$, 5%, 7%, 9%, and 11%. The ${\mu }_{\mathrm{Re}}$ minimum frequency dependencies of ${\mu }_{\mathrm{Im}}$ are also shown.