Light generation via quantum interaction of electrons with periodic nanostructures

Abstract

The Smith-Purcell effect is a hallmark of light-matter interactions in periodic structures, resulting in light emission with distinct spectral and angular distribution. We find yet undiscovered effects in Smith-Purcell radiation that arise due to the quantum nature of light and matter, through an approach based on exact energy and momentum conservation. The effects include emission cutoff, convergence of emission orders, and a possible second photoemission process, appearing predominantly in structures with nanoscale periodicities (a few tens of nanometers or less), accessible by recent nanofabrication advances. We further present ways to manipulate the effects by varying the geometry or by accounting for a refractive index. Our derivation emphasizes the fundamental relation between Smith-Purcell radiation andČerenkov radiation, and paves the way to alternative kinds of light sources wherein nonrelativistic electrons create Smith-Purcell radiation in nanoscale, on-chip devices. Finally, the path towards experimental realizations of these effects is discussed.

Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission

“…These include constructive interference [5], derivation of the reflected fields due to the electron evanescent field [18], as well as analyzing the induced currents on the grating's surface [19]. On the other end of the theoretical spectrum, QED analysis treated the electron as a plane wave in the transverse dimension [20][21][22][23][24][25][26], explained in quantum terms the Smith-Purcell dispersion relation [20,21], predicted quantum corrections [22], and analyzed the effect of the longitudinal size of the single electron on stimulated [24] and spontaneous [26] radiation. The radiation pattern in the point-particle limit of classical physics and the plane-wave solution of QED in the zero-recoil limit agree as a consequence of the correspondence principle, as ℏ is absent in both results.…”

“…Following Reimer and Kohl [27], we identify the electron current as J ¼ eðℏ=2m e iÞψ ⃗ ∇ψ þ c:c: ≅ evjψ T j 2 (where v ¼ẑℏk=m e with m e denoting the electron mass) resulting in the line currents employed in Refs. [20][21][22][23][24]. Following Jackson [34], we obtain a classical relation between the spectral radiant power of the wide current density and the point-particle result:…”

Near-field resonances in photon emission via interaction of electrons with coupled nanoparticles

“…Today we observe the burst of interest in the collective effects in the radiation processes of different nature and in different spectral ranges, from submillimeter (terahertz) to infrared, optical, UV, and x-ray ranges. Local field effects [1][2][3][4][5], including giant enhanced surface phenomena [1,6], excitation of plasmons in surface nanostructures [1,[7][8][9], new applications and ways of realization of the Smith-Purcell effect [5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], and many other interesting ideas including the strange, at first glance, ones like search for the new physics with atoms and molecules [23] rather than with collisions of superhighenergy charged particle beams at modern colliders--all these appeal to the attention of researchers all over the world. In a way, it is fair to say that today the interest in collective effects in radiation from complex systems, essentially dependent on the effects of coupling between their constituent elements, takes the lead over the existing theoretical background.…”

Smith–Purcell Radiation from Low-Energy Electrons

“…nanoscale devices 16 . A tunable light source integrated in an electron microscope would enable the development of novel electron-optical correlated spectroscopic techniques, with additional applications ranging from biological imaging to solid-state lighting 17 .…”