# Electronics and Physics of Left-Handed Materials and Circuits

C.M. Krowne
Electronics Science and Technology Division

Introduction: The use of left-handed materials in the construction of components for physics instruments or electronic devices is an extremely new area to blossom. The materials display a different property of matter compared to ordinary matter in regard to the way in which electromagnetic waves propagate or travel through them. In ordinary matter, the energy flow or power goes in the same direction as the phase front or phase motion of the wave. This is not unlike what one would see if a pebble were dropped in a pond of water and the ripples observed. Power flow of the ripples or of an electromagnetic wave can be represented by a vector, called the Poynting vector P and the phase front by another vector k. At any given location we can say that Pk > 0, where the dot indicates the multiplication of two vectors, called the dot product.

Left-Handed Physics: Left-handed materials do not produce positive dot products between the power and phase vectors. Rather they have Pk < 0, in seeming contradiction to what we understand to be normal behavior. However, there is nothing fundamental that dictates, based on Maxwell's equations, that the product must always be positive. Since it is known that the Poynting vector is equal to the cross-product of the electric E and magnetic H fields, or E × H, in normal matter it can be demonstrated that E, H, and k form a right-handed system (Fig. 8(a)). Clearly, if k points oppositely to P, the triad E, H, and k must form a left-handed system (Fig. 8(b)). And this is how the term "left-handed materials" arose. Left-handed material is sometimes abbreviated as LHM. Similarly, for ordinary matter, or right-handed material, we can use RHM. Left-handed materials have also been variously referred to as negative index of refraction materials (NIM or NIRM), negative phase velocity materials (NPV or NPVM), backward wave materials (BWM), negative permittivity and permeability materials or double negative materials (DNM or NM).

FIGURE 8
Orientation of the Electric E, magnetic H, power P, and phase k vectors.

Prior Research: Interest in left-handed media (LHM) originally arose because of its purported ability, in combination with right-handed (RHM) or ordinary media, to allow unusual focusing of waves, with possible applications in subwavelength control of optical imaging and negative index of refraction (NIR) behavior leading to new radar uses. Definite proof of NIR has occurred in several laboratories in the last two years, and there is little question that focusing possibilities exist in the much lower frequency microwave/millimeter wavelength regimes compared to the optical regime.1 One of the unusual properties of the LHM in conjunction with RHM is the ability to take diverging or parallel rays of light and focus them with a flat plate of LHM. A convex lens will now cause rays of light hitting it from a source to diverge, but a concave lens will focus the light rays. These unusual behaviors of LHM were pointed out more than 35 years ago in the Russian physics literature.2 However, the possibility of backward wave behavior has been known since the 1950s and is available in both the American and British physics and electronics literature. So for nearly half a century, something has been known about LHM. The earliest work involved backward wave propagation in traveling wave tubes3 or microwave or millimeter wave devices and models using nonreciprocal materials or higher order modes.

Electronic Devices: In contrast to the imaging and radar applications stemming from LHM, potential electronic uses may also exist because new physics of propagation in left-handed media occur in structures compatible with integrated circuits,4 such as seen in Fig. 9. By treating the LHM as intrinsic with microscopic properties that may be described by constitutive relations relating the displacement field or electric flux density D and electric field intensity E, D = εE, and relating the magnetic flux density B to magnetic field intensity H, B = µH, the lectromagnetic fields within guided wave structures used in integrated circuits can be studied. Completely new dispersion diagrams (ω vs k) and electromagnetic field configurations have been found,5 as shown in Fig. 10 at 10 GHz.6 It has been proven that propagation in these structures enables regions of forward and backward waves to exist. Such new propagation behavior is in agreement with recent macroscopic realizations using lumped/distributed circuit elements to make backward wave circuits.7

FIGURE 9
Single microstrip structure using a DNM or LHM substrate. (a) Cross-sectional drawing with a DNM substrate having negative ε and µ to get the left-handed property, with a perfect conductor enclosing the device. (b) Perspective drawing without the encumbrance of the enclosing walls.
FIGURE 10
(a) Magnitude plot of the electric field E distribution, with an overlaid arrow plot giving the electric field vector E at 10 GHz.
(b)Magnitude plot of the magnetic field H distribution, with an overlaid arrow plot giving the magnetic field vector H at 10 GHz.

Microwave Applications: These circuits show that various transmission lines, couplers, and other circuit elements with different or improved characteristics can be made. It is expected that the same could be done for filters, producing devices with new properties or improved characteristics, taking advantage of the propagation and evanescent frequency bands existing in the dispersion diagram. Additionally, the new electromagnetic field distributions strongly imply that improved isolators and circulators could be constructed using LHM in combination with nonreciprocal materials based on carrier cyclotron motion or spin precession. New control components using reciprocal media are also possible, by teaming LHM with ferroelectric materials, for example.