Graphene Metamaterials for Intense, Tunable, and Compact Extreme Ultraviolet and X-Ray Sources

Abstract

The interaction of electrons with strong electromagnetic fields is fundamental to the ability to design high-quality radiation sources. At the core of all such sources is a tradeoff between compactness and higher output radiation intensities. Conventional photonic devices are limited in size by their operating wavelength, which helps compactness at the cost of a small interaction area. Here, plasmonic modes supported by multilayer graphene metamaterials are shown to provide a larger interaction area with the electron beam, while also tapping into the extreme confinement of graphene plasmons to generate high-frequency photons with relatively low-energy electrons available from tabletop sources. For 5 MeV electrons, a metamaterial of 50 layers and length 50 µm, and a beam current of 1.7 µA, it is, for instance, possible to generate X-rays of intensity 1.5 × 10⁷ photons sr^-1 s^-1 1%BW, 580 times more than for a single-layer design. The frequency of the driving laser dynamically tunes the photon emission spectrum. This work demonstrates a unique free-electron light source, wherein the electron mean free path in a given material is longer than the device length, relaxing the requirements of complex electron beam systems and potentially paving the way to high-yield, compact, and tunable X-ray sources.

Keywords: X‐ray sources; free‐electrons; graphene; metamaterials; nanophotonics; plasmons.

Figure 1

Graphene metamaterial plasmon‐driven free‐electron source of short‐wavelength light. a) 2D schematic of the setup. The driving laser excites MRPs by means of a grating structure; the free electrons in the beam (with trajectories as dashed black lines) oscillate due to the MRP field (E_x in red and blue), emitting EUV to X‐ray radiation. b) The emission is shown to be highly directional and nearly monochromatic by plotting the emitted radiation intensity in arbitrary units (for N _G = 50 graphene layers, N _P = 100 grating periods and at driving laser wavelength of λ₀ = 7.086 µm). c) We show how the emission intensity can be scaled up by increasing the number N _G of graphene sheets in the metamaterial, increasing the interaction area, both in the case of suspended graphene (SG) and dielectric spacing (DS). Depending mainly on the mobility µ of the electrons in the graphene, we find an optimum N _G ^* at which the output intensity is maximized (for N _P = 500). We consider a maximum electric field magnitude in the structure E _max = 3 GV m⁻¹, grating periodicity p = 100 nm, groove depth d = 50 nm, grooves' width w = 50 nm, dielectric spacings' thickness s = 25 nm.

Figure 2

Tunable radiation emission: higher orders (n) MRPs. The MRPs are shown plotting in red and blue the transverse component of the electric field for MRPs with a) n = 2, m = 22, λ₀ = 2.628 µm, E ₀ = 329 MV m⁻¹ and b) n = 3, m = 14, λ₀ = 2.251 µm, E ₀ = 810 MV m⁻¹. c,d) The corresponding emitted radiation spectra are shown, respectively, for an electron beam with the characteristics specified in ref. 44. In each structure, a different nth emission harmonic is brightest: c) the second harmonic for structure (a), and d) the third harmonic for structure (b). In these simulations, we consider N _G = 30 graphene sheets and N _P = 50 grating periods (total length is L = 5 µm).

Figure 3

Mode dispersion of the graphene multilayer structure showing the MRPs numbered by the integers n, m. The map shows the absorption A computed and plotted within the nonlocal random phase approximation for the graphene conductivity σ_g = σ_g(ω₀, q = 2π/p) as a function of the normalized inverse periodicity and frequency. For n = 1, we find multiple absorption peaks that correspond to different MRPs and that we enumerate with an integer m. Other higher energy absorption lines correspond instead to MRPs of order n > 1 that is possessing larger longitudinal momenta. Note that here the electron mobility has been artificially reduced to increase the visibility of the absorption lines that would otherwise (for higher values of µ) be even narrower. We choose electron mobility µ = 10 × 10³ cm² V⁻¹ s⁻¹, denote the Fermi wavevector with k _F, and consider N _G = 5 graphene layers with spacing s = p/4. Note that since the longitudinal momentum for nth order MRPs is q = 2πn/p, we expect stronger nonlocal effects to occur for n > 1 (the effects of nonlocalities here are nevertheless negligible and are addressed more in detail in Section S4, Supporting Information).