# Research Highlights

## Graphene: Low-mass terahertz cavtiy optomechanics

In addition to its unique optical response, graphene exhibits many unusual elastic properties that make it an intriguing material for mechanical measurement and actuation at the quantum limit. In this work we demonstrate that graphene is capable of supporting a large optomechanical coupling coefficient, on the same order of those observed in state-of-the-art 3D optomechanical materials. With an operating frequency around 100 THz, the dispersive coupling coefficient reaches $g_{om}$ = 180 MHz/nm and $g_{om}$ = 500 MHz/nm in the resolved and unresolved sideband regimes, respectively. We find that predominantly dispersive coupling requires a high graphene Fermi level and mid-infrared excitation, while predominantly dissipative coupling favors a moderate graphene Fermi level and near-infrared excitation. The significance of this work is that the field of cavity optomechanics can benefit from the combination of large in-plane stiffness and low mass and the strong light-matter interaction of single- and few-layer graphene membranes.

1. I. A. D. Williamson, S. H. Mousavi, and Z. Wang, “Large Cavity-Optomechanical Coupling with Graphene at Infrared and Terahertz Frequencies,” ACS Photonics, vol. 3, no. 12, pp. 2353–2361, Dec. 2016. (pdf, web)

## Graphene: A platform for engineered signal dispersion and periodic media

These results consider the unusual dispersion and attenuation of chip-scale graphene and copper transmission lines in the terahertz spectrum. Our results, when viewed across a wide range of frequencies and geometric sizes reveals that the conductor kinetic inductance provides a means for realizing a broad bandwidth of constant signal attenuation and linear phase dispersion with a size-independent low-frequency cutoff. In a way, this response is the counterpart of the LC response realized in the Gridded Fiber, but is achieved through an entirely different underlying physical mechanism.

The significance of these results is that on-chip transmission lines are conventionally thought to be limited by a large RC time constant resulting from the increased resistance of sub-micron conductors. Additionally, the interplay between the kinetic inductance, the magnetic inductance, and the resistance has never been considered in the context of transmission line signaling performance over a large parameter space. We conduct a comprehensive comparison of the dispersion of copper and graphene transmission line performance through the RC, LC, and multi-mode plasmonic regimes. Furthermore, the higher-order frequency-dependent losses that adversely affect signaling performance are characterized. Our results demonstrate that the low frequency cutoff of a kinetic LC regime is defined by the phenomenological free carrier scattering rate in nanoscale lines and opens up the possibility of realizing a large bandwidth of flat signal attenuation. Moreover, up to 40$\times$ wavelength reduction is observed in the transverse electric-magnetic (TEM) mode of graphene transmission lines operating in the terahertz spectrum.

We demonstrate that the kinetic inductance from two single-layer graphene sheets, effectively a graphene parallel plate waveguide, allow silicon photonic crystal slabs with sub-micron periodicity to operate in the terahertz regime (corresponding to a 100$\times$ wavelength reduction). Photonic crystals are the backbone for a number of important integrated photonic systems for light confinement, dispersion engineering, nonlinearity enhancement, and other unusual effects arising from their structural periodicity.

The photonic band structure that arises from the merger of the silicon photonic crystal and the graphene parallel plate waveguide is uniformly scaled from the corresponding 2D crystal, opening up the opportunity to realize many of the unique features of purely 2D optical systems. For example, the demonstrated system supports a large photonic band gap (approximately 27%) and can confine light along in-plane line defect waveguides.

1. I. A. D. Williamson, S. H. Mousavi, and Z. Wang, “Extraordinary wavelength reduction in terahertz graphene-cladded photonic crystal slabs,” Scientific Reports, vol. 6, p. 25301, May 2016. (pdf, web)
2. S. H. Mousavi, I. A. D. Williamson, and Z. Wang, “Kinetic inductance driven nanoscale 2D and 3D THz transmission lines,” Scientific Reports, vol. 6, p. 25303, May 2016. (pdf, web)

## High performance signaling in radio frequency fiber transmission lines

The skin and proximity effects fundamentally limit the bandwidth and reach of conventional (two-conductor) off-chip transmission lines and interconnects. In this work we present a design and fabricated prototype of a radio frequency transmission line that mitigates the skin and proximity effects. The device is made of a grid of micron-scale electrodes embedded in an insulating polymer cladding that can be readily fabricated using a thermal fiber-draw fabrication process. The fabrication procedure can produce meter to kilometer long fibers with well defined sub-micron features in its cross section. The performance of this so-called Gridded Fiber is characterized by an unprecedented signal bandwidth (approximately 2 GHz) of frequency-flat attenuation and linear phase dispersion which is enabled by an optimized current phasing scheme across the grid of electrodes.

The signifcance of this design is in mitigating the square root frequency-dependence of signal attenuation arising from constricted electrical current flow. This low pass response limits the resolution of time domain transmission line sensors and creates a trade off between the maximum length and maximum data rate in transmission lines that are used as communication channels. The Gridded Fiber, through the degrees of freedom from its grid of electrodes, provides a platform that can be readily fabricated to overcome these issues that have long-plagued passive high-frequency transmission lines.

1. I. A. D. Williamson, T.-A. N. Nguyen, and Z. Wang, “Suppression of the skin effect in radio frequency transmission lines via gridded conductor fibers,” Applied Physics Letters, vol. 108, no. 8, p. 083502, Feb. 2016. (pdf, web)