Magnetism from Conductors, and Enhanced Non-Linear Phenomena

Abstract

We show that microstructures built from non-magnetic conducting sheets exhibit an effective magnetic permeability, /mu_meff, which can be tuned to values not accessible in naturally occurring materials, including large imaginary components of /mu_meff. The microstructure is on a scale much less than the wavelength of radiation, is not resolved by incident microwaves, and uses a very low density of metal so that structures can be extremely lightweight. Most of the structures are resonant due to internal capacitance and inductance, and resonant enhancement combined with compression of electrical energy into a very small volume greatly enhances the energy density at critical locations in the structure, easily by factors of a million and possibly by much more. Weakly non-linear materials placed at these critical locations will show greatly enhanced effects raising the possibility of manufacturing active structures whose properties can be switched at will between many states

Figures (17)

• Figure 1: Unit cell of a periodic structure. We assume that the unit cell dimensions are much smaller that the wavelength of radiation, and average over local variations of the fields. In the case of the$\mathbf{B}$ - field we average over the faces of the cell and in the case of the $\mathbf{H}$ - field, over one of the edges.
• Figure 2: Model A consists of a square array of metallic cylinders designed to have magnetic properties in the direction parallel to the axes of the cylinders.
• Figure 3: Model$B$ consists of a square array of cylinders as for model $A$ but with the difference that the cylinders now have internal structure The sheets are divided into a 'split ring' structure and separated from each other by a distance $d$. In any one sheet there is a gap which prevents current from flowing around that ring.
• Figure 4: When a magnetic field parallel to the cylinder is switched on it induces currents in the 'split rings' as shown in the figure. The greater the capacitance between the sheets, the greater the current.
• Figure 5: The effective magnetic permeability for model$B$ shows a resonant structure dictated by the capacitance between the sheets and the magnetic inductance of the cylinder. We sketch the typical form for a highly conducting sample, $\sigma \approx 0$. Below the resonant frequency $\mu_{e f f}$ is enhanced, but above resonance $\mu_{\text{eff }}$ is less than unity and may be negative close to the resonance.