Simulations of Ferrite-Dielectric-Wire Composite Negative Index Materials

We perform extensive finite difference time domain simulations of ferrite based negative index of refraction composites. A wire grid is employed to provide negative permittivity. The ferrite and wire grid interact to provide both and index of refraction transmission peaks in the vicinity of the ferrite resonance. Notwithstanding the extreme anisotropy in the index of refraction of the composite, negative refraction is seen at the composite air interface allowing the construction of a focusing concave lens with a magnetically tunable focal length.

Figure 1

A sketch of the ferrite (black) and dielectric (gray) composite configuration with a square wire grid (black circles) centered in the dielectric and grid size $L$. The arrows indicate normal incident millimeter wave radiation. A 1 kOe external field is applied out of the figure to align the ferrite magnetization parallel to the wire axis and the wave polarization.

Figure 2

A series of transmission spectra through 39 unit thickness of the BaM-Mylar-wire composite varying the spacing of the square wire grid. As the spacing increases the high pass cutoff is reduced in frequency. As the cutoff approaches the BaM resonance a second peak appears below the FMR frequency (d). The complex relative permeability of BaM at 50% loading is shown for reference (a).

Figure 3

(a) The frequency dependence of the complex index for the case of a $648\mu \mathrm{m}$ grid spacing with a 1 kOe field bias. The transmission spectrum is seen in Fig. 2. (b) A plot of the index of refraction taken at the center of the transmission peaks as seen in Fig. 2. At larger grid spacings a peak with $n>0$ appears at frequencies below ferrimagnetic resonance. (c) The variation of the index of refraction at 40 GHz for the $648\mu \mathrm{m}$ composite with a small ($\pm 75\mathrm{Oe}$) modulation of the 1 kOe external field.

Figure 4

A two-dimensional FDTD simulation of the BaM-Mylar-wire composite studied in Figs. 2, 3. A 40 GHz line source is positioned close to the composite slab. The color intensity scale is saturated to better visualize the 40 GHz E field amplitude inside the composite. The index in the horizontal direction in the composite is $n=-1.06$. The inset plots the refracted angle versus the angle of incidence when plane waves are incident on the same composite. The refraction is limited to 41° consistent with the chevron angle observed when the line source is close to the material. The solid line shows the refraction expected for a homogeneous isotropic material of index $-1.06$.

Figure 5

The composite of Fig. 4 is cut to form a concave lens and the line source is moved away from the front surface. Negative refraction at the concave face results in the formation of a focus.