April 19, 2021.
The development of free-electron-based light sources has long been a subject of widespread interest owing to the fact that the wavelength of generated light can be tuned continuously from the long-wavelength range (microwaves and infrared) to the visible range and all the way to the short-wavelength range (ultraviolet and X-rays). However, the disadvantage of such a light source is its large size and high cost. For example, in free-electron lasers that generate light from microwaves down to X-ray wavelengths, high-energy electrons are passed through a periodic magnetostatic undulator (or magnetic wiggler field) which induces transverse electron oscillations. This results in the emission of light with a wavelength that depends on the energy of the electrons and the period of the wiggler field, which is typically in the cm scale. This increases the overall size requirement of the wiggler magnets to several tens of meters. Therefore, there have been continuous efforts to develop smaller light sources with several new ideas being proposed, such as the use of electromagnetic wigglers  produced by an intense laser. The period of these wigglers is in the μm scale and the short-wavelength light output is produced by Thompson or Compton scattering where the electrons are not required to have very high initial energies. Other ideas have also been proposed such as the replacement of magnetic wigglers with plasma wigglers  generated by density waves in the plasma and crystal wigglers  generated by periodically deformed crystals. In the past ten years, however, there have been efforts to develop compact light sources using “nanoscale” undulators. A few examples include dielectric-based undulators , light-wells , and plasmonic undulators based on either metallic naonogratings  or emerging 2D materials such as graphene .
Graphene, a material composed of a single layer of carbon atoms arranged in a honeycomb lattice has a number of remarkable properties, such as its excellent tensile strength, high optical transparency, extremely high electrical and thermal conductivity, and the ability to support surface plasmons. In particular, plasmons in graphene exhibit outstanding properties such as dynamic tunability, long lifetimes and strong field confinement. The latter is very important to the development of free-electron light sources since strongly confined graphene plasmons possess very high momentum which in turn results in the generation of short-wavelength radiation when electrons scatter off these plasmons. A novel advantage of this scheme is the ability to harness relatively low-energy electrons (< 10 MeV) for the generation of highly directional, monochromatic, high energy radiation in a compact design, circumventing the use of a large acceleration stage and the bulky and heavy neutron shielding that are necessary when electron energies above 10 MeV are used. Another attractive feature of such device is the possibility of tuning the generated light from infrared to X-ray frequencies by varying the electron energy, the frequency of surface plasmon, and Fermi energy of graphene which can be controlled by doping the graphene layer. This concept has been confirmed by theoretical and simulation results , but there have been no experimental results to date that corroborate the findings. Successful implementation of this concept is expected to have far reaching effects in both medicine, natural science and engineering applications.
Figure 1 A schematic for the proposal of a graphene-plasmon-based free-electron source of short-wavelength radiation. The dotted white lines represent free electrons that, on interaction with the graphene plasmons (red and blue), offer short-wavelength monochromatic photons (purple). Figure reproduced from .
This research project, sponsored by the Thailand Center of Excellence in Physics (ThEP), aims to develop a plasmonic device from graphene material. The main focus is on establishing sub-micron to nanoscale ribbon array structures on graphene sheets using electron-beam lithography (EBL) technique and plasma etching to achieve plasmon frequency in the range of THz. According to the analytical theory and numerical simulation , such a device could be realized as a compact light source that produces short-wavelength radiation in the ultraviolet and X-rays. So far, the research team has successfully synthesized large continuous sheets of graphene using chemical vapor deposition (CVD) technique. The graphene was initially grown on Cu foil and was transferred onto hBN/SiO2/Si substrates using the wet transfer method. The result from these steps is shown in Figure 2. We have also successfully patterned nanoribbon arrays with ribbon sizes of 2 μm, 1 μm and 500 nm (Figure 3). It is evident that the lithographically defined patterns have well-defined edges and the dimensions are consistent with the proposed design. A 200-nm ribbon fabrication is currently under progress.
Figure 2 Graphene synthesized by CVD technique after transfer onto hBN/SiO2/ Si substrate.
Figure 3 Schematic representation of a typical graphene nanoribbon array and optical micrographs of our fabricated nanoribbon structures with ribbon width of 2 μm, 1 μm and 500 nm.
In addition, we have used the wave optics module in COMSOL Multiphysics simulation platform to solve for the time-harmonic electromagnetic field distribution in graphene nanoribbon structure. The simulation employs the finite element method and Floquet periodic boundary conditions and the results are analyzed in terms of the transmittance, reflectance and absorptance. The simulation structure consists of graphene nanoribbon placed on top of SiO2 with = 3.9 and is surrounded on the top by an air atmosphere with air = 1. The graphene layer is modeled as a 2D layer with complex surface conductivity calculated from the Drude model, . The results obtained from the simulation are shown in Figure 4. Here, the graphene plasmon (GP) resonance peak was found to be dependent on the width of the ribbon. As the ribbon width is systematically reduced, the plasmon peak shifts to higher energies while the peak broadens and the intensity decreases. For example, when the width of the ribbon is 1.5 μm, the GP peak has an energy of 2 meV (0.5 THz) and the energy increases to 56 meV (13.5 THz) when the width of the ribbon is reduced to 100 nm. It was also found that the intensity of GP peak depends strongly on the number of ribbon layers, increasing approximately 5 times in magnitude when the number of graphene layers increases from 1 to 6. Also, the peak has shifted to higher energies and is now at 156 meV (37.5 THz), approximately a three-fold increase from its initial value.
Figure 4 Plasmonic resonance of graphene nanoribbon arrays. (Left) Width dependence of optical transmission through graphene nanoribbon arrays. Here the widths of the nanoribbons is varied from 100 – 1500 nm while the distance between each ribbon is fixed at 100 nm. (Right) Optical transmission of stacked devices with one, two, three, four, five and six layers of graphene nanoribbon arrays. These structures have identical width (100 nm) and distance between each ribbon (100 nm). The extinction is calculated as 1 - T/T0, where T and T0 are the transmission coefficients with and without graphene nanoribbon arrays, respectively.
 Esarey, E., Ride, S. K. & Sprangle, P. Phys. Rev. E 48, 3003–3021 (1993).
 Joshi, C., Katsouleas, T., Dawson, J. M., Yan, Y. T. & Slater, J. M. IEEE J. Quantum Electron. 23, 1571–1577 (1987).
 Bellucci, S. et al. Phys. Rev. Lett. 90, 034801 (2003).
 Plettner, T., & Byer, R. L. Phys. Rev. ST Accel. Beams 11, 030704 (2008).
 Adamo, G. et al. Phys. Rev. Lett. 104, 024801 (2010).
 Rosolen, G. et al. Light: Sci. Appl. 7, 64 (2018)
 Wong, L. J., Kaminer, I., Ilic, O., Joannopoulos, J .D. & Soljac¡ic´, M. Nat. Photonics 10, 46 (2016)
Ratchanok Somphonsane, Ph.D.
Department of Physics, Faculty of Science
King Mongkut’s Institute of Technology Ladkrabang