Nanoscale Femtosecond Coherent Radiation and Spatiotemporally Shaped free electron Wavefunction

Abstract

We study tunable nanoscale femtosecond coherent radiation based on a coupled nanowire pair (CNP) structure that is excited by a strong laser. The structure functions as a nanoscale undulator (NU): the electrons moving through the nanogap are driven by a spatially periodic, transverse optical near-field. We show that the transverse near-field can actively shape the electron wavefunction by inducing both a periodic oscillation and a quantum squeezing of its width. We then validate this theoretical framework by numerically solving the relativistically corrected time-dependent Schrödinger equation (RC-TDSE). The generated femtosecond pulse trains can be spectrally, temporally, and spatially controlled. This framework establishes the transverse optical near-field interaction as a novel mechanism to spatiotemporally shape electron wavefunctions, which illuminates a path to versatile platform for on-chip femtosecond coherent light source and the application in free-electron quantum optics.

Figures (4)

• Figure 1: NU based on a CNP for coherent radiation generation. (a) Schematic of the proposed set-up. An electron propagates through the nanogap (10 nm width) between two parallel hexagonal nanowires ($L=5\mu m$). The inset illustrates the electron's transverse oscillation trajectory within the gap, driven by the gap mode. (b) Simulated $E_x$ field distribution in the $x-z$ cross-section of the CNP gap with $y=0$, excited by an 800 nm linearly polarized laser with the amplitude of $1.5\times10^9$ V/m along $x$. The black solid lines indicate the nanowire boundaries. (c) the $E_x$ field distribution in the $y-z$ cross-section with $x=0$. (d) The field intensity within CNP gap. The sampled line is $y=0$ in the cross-section shown in (e). (e) The electric field distribution in the $x-y$ cross-section with $z=0$. The arrows represent the directions and amplitudes of the electric field.
• Figure 2: Electron wavefunction evolution and EELS for different incident kinetic energies (1 keV, 10 keV, and 30 keV) in the NU. (a)-(c) Snapshots of the real-space electron probability density $|\psi (x,z,t)|^2$ during interaction (the time evolutions of the wave packets are provided in Supplemental Material movie). (d)-(f) Corresponding EELS spectra $P(\Delta E)$ after interaction. Discrete peaks separated by a single photon energy are observed. Insets: Final probability density in the momentum-space $|\tilde{\psi}(k_x, k_z)|^2$.
• Figure 3: Spectrum and spatial distribution of the radiation from actively shaped electrons. (a), (c) Radiation spectra for electrons with energies of $1keV$ and $10keV$, respectively. (b), (d) Corresponding normalized spatial distributions of the radiation intensity. The polar ($\theta$) and azimuthal ($\phi$) angles are defined in Fig. 1. Forward and backward radiation are distinguished by color and dashed line box.
• Figure 4: Farfield power of forward and backward radiation for a free electron with an energy of (a) $1keV$ and (b) $10keV$.