A Newtonian Approach to Negative Index Metamaterials
Authors: Hosang Yoon and Donhee Ham
School of Engineering and Applied Sciences, Harvard University, USA
Link to Donhee Ham Research Group >>
Negative index metamaterials have been celebrated due to their unusual ability to manipulate electromagnetic waves, such as bending light in the ‘wrong’ direction  and focusing light below the diffraction limit , which may prove technologically useful. To achieve negative refraction, a variety of material systems with engineered electric and/or magnetic properties have been developed. Reporting in Nature , we have demonstrated a ‘kinetic’ route to negative refraction, where exploitation of acceleration of electrons in a two-dimensional (2D) conductor leads to extraordinarily strong negative refraction with refractive index as large as -700.
Electrons in a conductor subjected to an electric field collectively accelerate according to Newton’s 2nd law of motion, creating a current that lags the electric field by 90°, as in a magnetic inductor. The conductor may then be considered as an inductor, but with its inductance being of kinetic origin . This kinetic inductance is usually not much appreciable in ordinary three-dimensional conductors, but in a 2D conductor, it is orders-of-magnitude larger than magnetic inductance, which is what we exploit to create the dramatically strong negative refraction.
The acceleration of electrons is continually interrupted by their collisions with vibrations, impurities, or defects of the crystal lattice. Imagine a time-varying sinusoidal electric field at a given frequency, which accelerates/decelerates electrons into an oscillation motion. If the mean scattering rate is too high to accommodate an appreciable fraction of an oscillation period, the acceleration effect is hard to observe, and the conductor acts as an Ohmic resistor. This can be avoided in two ways: one is to cool the conductor to lower the scattering rate as in our work ; the other is to increase the frequency at room temperature, as currently pursued in our lab.
Figure 1. Optical micrograph (left) and schematic (right) of the metamaterial. The 2DEG strip array is connected to electromagnetic waveguides to the left and right. (Image reproduced from the paper published in Nature )
We employ a GaAs/AlGaAs 2D electron gas (2DEG) as a demonstrational 2D conductor. Our metamaterial designed in the GHz frequency range is an array of 2DEG strips (Fig. 1). Signal (S) lines flanked by ground (G) lines on the left and right of the strip array are coplanar waveguides (CPWs) that guide electromagnetic waves to and from the metamaterial. As an electromagnetic wave arrives from the left CPW, its electric field between the S and G lines accelerates electrons in/along the leftmost few strips. This inductive movement of electrons is capacitively coupled to the strip on the right, accelerating electrons there. This dynamics repeats to propagate an ‘electro-kinetic’ wave from left to right, perpendicular to the strips acting as kinetic inductors. It is this electro-kinetic wave that is negatively refracting. The negative refractive index is large due to the large kinetic inductance of the GaAs/AlGaAs 2DEG strip.
Figure 2. (Click on the image to see high resolution version) Dispersion relation (left) and refractive index (middle) of a 13-strip metamaterial with strip length 112 μm and periodicity 1.25 μm measured at different cryogenic temperatures. (right) Refractive index measured for metamaterials with various strip length (l) and periodicity (a). (Image reproduced from the paper published in Nature)
Microwave scattering experiments over 1~50 GHz confirms negative refraction; the measured dispersion of the electro-kinetic wave (Fig. 2, left) shows opposite signs for the phase and group velocities above a cutoff frequency. The corresponding negative refractive index is hundreds in magnitude, two orders of magnitude larger than typical negative refractive indices (Fig. 2, middle). With varying geometric parameters, an index as large as -700 is obtained (Fig. 2, right).
The very large negative index brings the science of negative refraction into drastically miniaturized scale, enabling ultra-subwavelength manipulation of electromagnetic waves. We expect to see the similar result at room temperatures by increasing the frequency towards the THz range, which is the direction our lab is now taking.
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