Tunable IR to X-ray radiation sources based on
free-electrons interacting with graphene plasmons


Discovering a compact method of generating coherent X-rays is a long-standing holy grail in modern science and engineering. The wished-for device is commonly referred to as a “table-top X-ray laser”. Such a device would revolutionize many fields of science by making high-quality X-ray beams ubiquitous in academic and industrial laboratories . On the biomedical front, such a device would allow for incredibly sensitive, low-dosage imaging techniques with unprecedented resolution deep inside the human body. Today, high-quality X-ray beams can only be created in very  expensive and large national facilities that house  synchrotrons or free-electron lasers (e.g., the SLAC National Accelerator Laboratory).

We approach the challenge of high-quality X-ray sources from a novel direction by taking ideas from the rapidly developing field of graphene nanophotonics and using the recent discovery of graphene plasmons in particular. We demonstrate that graphene, with its ability to support strong electric fields and highly confined surface plasmon modes, is a promising platform upon which to realize chip-scale sources that generate efficient, highly-directional, and tunable X-ray radiation. Further work is still needed to explore the possibility of achieving coherent radiation from such a device, in order to have an actual laser. [see more details in the supplementary information of our paper]


The above process of high-frequency radiation generation can be explained through an electron-plasmon scattering theory that we develop through both analytical theory and ab initio simulations.

From a classical perspective, the process can be explained by the plasmon wiggling an electron beam: The graphene plasmons form a periodic electromagnetic grating that causes electrons (5eV to 5MeV) to oscillate and emit radiation from infrared to X-ray frequencies.

Graphene-plasmon-based free-electron source of short wavelength radiation. (left) A schematic showing the electon-plasmon interaction, in which (right) free-electrons (dotted white lines) interact with the graphene plasmon  field (glowing red and blue bars) to produce short-wavelength output radiation.

Our numerical simulation solves for the exact electron trajectories using the (relativistic) Newton-Lorentz  equation. The electromagnetic field experienced by each electron is the superposition of the plasmon field as well as the fields from other electrons in the beam. The emitted radiation is computed from the Liénard–Wiechert potentials (which are exact solutions of Maxwell equations).

We also derive an analytical theory for the electron-plasmon scattering process based on principles of electron-photon scattering (namely, Thomson scattering and inverse Compton scattering): The emitted photon frequency from an elastic collision of an electron and a plasmon is

                frequency of the emitted photon

                 angle of emission

         electron velocity

                 plasmon frequency

                 plasmon confinement factor (the ratio of the free-space wavelength to the plasmon wavelength at the same frequency; values ~200 have been experimentally achieved in graphene)

Regimes of Operation

In the terminology of the optics and photonics community, our scheme is a form of frequency up-conversion: Given a monochromatic light source that excites the graphene plasmon (typically at IR frequencies), the electron beam up-converts the frequency to the visible/UV/X-ray range. The use of this mechanism for  frequency down-conversion to the terahertz regime is also possible.

Regimes of frequency conversion for the graphene-plasmon-based free-electron radiation source. (a) Soft and hard X-ray generation using electron beams of energies achievable with lab-sized equipment, without extra acceleration stages. (b) Schemes for frequency up-conversion (continuous black lines) and down-conversion (dashed black lines) using a source of very non-relativistic electrons, which can be implemented in on-chip configurations. Notice that extreme down-conversion occurs at the point where the electron velocity matches the graphene plasmon phase velocity and electron-plasmon coupling is enhanced. The assumed free space wavelength is 1.5 microns for both panels (however, the vertical axes scale linearly when a different wavelength is used).

Further reading