Metamaterials are artificially engineered materials that possess properties not found in nature. Over the years, they have enjoyed a great deal of fascination because they are said to bend light in an unexpected way. Their most fascinating application is, arguably, the “invisibility cloak”, which is not only theoretically possible but practically possible. Apart from that there are several more applications such as wireless power transfer (WPT), ultrafast data processing, high-speed fiber optic telecommunication networks, smartphone camera lenses and efficient solar cells.
One of the applications of metamaterials is in WPT. Metamaterials can be used as a means of “channeling” the energy from transmitter to receiver.
As this illustration suggests, a slab of metamaterial may facilitate the process of wirelessly charging the electric vehicle.
However, one may still ask a question if the metamaterials are really ideal for such charging. In this article we will take a critical look the metamaterials by analyzing the physics behind them.
How do metamaterials work?
The properties that are usually implied are electric permittivity ε and magnetic permeability μ; they are related to propagation of electromagnetic waves. These properties are also related to WPT. One of the most common types of metamaterials consists of inductors arranged on a plane in a regularized manner. The inductors have self-resonance at a certain frequency. Also, each of these inductors is coupled to all the rest of inductors, most strongly, to its immediate neighbors. This arrangement of inductors can be viewed as an equivalent to a slab (of metamaterial) having certain values of permittivity and permeability. Depending on frequency, the values of permittivity and permeability can be below zero, for example, -1.
When illuminated by an incident electromagnetic wave, metamaterials refract the wave and change the direction of propagation as normally happens with visible light traveling from air to water. However, with permittivity and permeability below zero, the bending occurs in a “negative” direction.
For WPT we are primarily interested in changing the direction of the magnetic field to “focus” magnetic field toward receiver coil. If at the frequency of transfer the magnetic permeability is less than zero, then the slab of metamaterial acts as magnetic lens (Ref. 1, 2).
A slab of metamaterial can, therefore, be placed between transmit and receive coils in order to improve the efficiency of the power transfer. A large amount of research was done to study the effect of metamaterials for WPT and it has been shown, both in simulations and experimentally, that metamaterials can indeed be used to enhance the power transfer.
Metamaterial or repeater coil?
To visualize the effect of metamaterials on power transfer, we first simulate power transfer with transmit and receive coils only. We apply RF voltage to the transmit coil, solve for currents in both coils. We then plot absolute value and streamlines of magnetic field at several consecutive time moments.
WPT without metamaterials.
We then create a metamaterial having 25 inductors and place it between transmit and receive coils. Again, we apply RF voltage to the transmit coil and solve for currents in all 27 coils (transmit coil, receive coil and metamaterial coils).
WPT with metamaterials.
We observe that presence of metamaterial coils helps focus magnetic field lines towards the receive coil, which increases the efficiency of the power transfer. We now take a closer look at the currents flowing in the metamaterial coils. The magnitudes of the currents slightly different, however, their phases are about the same. This means that at a particular instant of time, the currents flow in the same direction. Looking at figure below, one can come to conclusion that currents of neighboring coils are roughly equivalent to one bigger loop of current.
From this perspective, a 5×5 array of coils is approximately equivalent to one bigger coil (repeater coil) having roughly the size of the 5×5 array of coils.
We now do a simulation for a single repeater coil and compare the results with those for 5×5 array of coils.
WPT with single large repeater coil.
We observe that the magnetic field of the single repeater coil is quite similar to the field of the metamaterial having 5×5 array of coils.
Speaking about efficiency of the power transfer, the efficiency greatly depends on losses in the metamaterial (or in the repeater coil). First of all, there are ohmic losses in conductor due to conductor resistances. Secondly, there are eddy (induced) currents that arise because of currents in the neighboring coils. As we know metamaterials consist of large number of individual inductors and, therefore, they will have more losses in them. The simple design such as large repeater coil is potentially less lossy and, therefore, more efficient. This conclusion is also confirmed in the paper of Chabalko et al. (Ref 3), where the authors showed that a single repeater coil is more efficient than a slab of metamaterial.
Are metamaterials optimal for WPT?
Metamaterials are often thought to serve as an intermediate layer between the transmit coil and receive coil.
First of all, it seems that the slab of metamaterial can be replaced by an appropriately sized repeater coil, which will likely have better performance. The single repeater coil is much cheaper to manufacture and it is easier to tune.
Secondly, it is often assumed that it is necessary to have air gaps both between transmit coil – repeater coil (or metamaterial) and also between repeater coil (or metamaterial) and receive coil.
(a) Focusing with metamaterial, (b) focusing with repeater coil, (c) transmit coil only.
However, looking at the example of an electric car being charged, we do not need to have a gap between transmit coil and repeater coil (or metamaterial). It would be beneficial in terms of efficiency if the repeater coil (or metamaterial) is removed altogether and the transmitter coil is moved closer to the receive coil.
Arguably, we arrive at the following conclusion. Advantages of using metamaterial for WPT are not obvious: focusing of the magnetic field can more efficiently be done with a repeater coil.
 V. Veselago, Phys. Usp, 10, 509, 1968
 J. Pendry, Phys. Rev. Lett. 85, 3966, 2000
 M.J. Chabalko, J. Besnoff, D.S. Ricketts, IEEE Antennas and Wireless Communication Letters,” vol. 15, 2016.