Ultrafast optical-field-induced photoelectron emission in a vacuum nanoscale gap: An exact analytical formulation

Abstract

By exactly solving the one-dimensional time-dependent Schrödinger equation, we construct an analytical solution for nonlinear photoelectron emission in a nanoscale metal–vacuum–metal junction driven by a single-frequency laser field, where the impact of image and space charges is neglected. Based on the analytical formulation, we examine the photoelectron energy spectra and emission current under various laser fields and vacuum gap distances. Our calculation shows the transition from direct tunneling to multiphoton induced electron emission as gap distance increases. In the multiphoton regime, the photoemission current density oscillatorily varies with the gap distance, due to the interference of electron waves inside the gap. Our model reveals the energy redistribution of photoelectrons across the two interfaces between the gap and the metals. Additionally, we find that decreasing the gap distance (before entering the direct tunneling regime) tends to extend the multiphoton regime to higher laser intensity. This work provides clear insights into the underlying photoemission mechanisms and spatiotemporal electron dynamics of ultrafast electron transport in nanogaps and may guide the future design of advanced ultrafast nanodevices, such as photoelectron emitters, photodetectors, and quantum plasmonic nanoantennas.