PRODUCTION OF FREE ELECTRON BEAMS WITH HELICAL WAVEFRONTS AND QUANTIZED ANGULAR MOMENTUM

 

Benjamin J. McMorran1, Amit Agrawal1, Ian M. Anderson2, Andrew Herzing2, Henri J. Lezec1, Jabez J. McClelland1, John Unguris1

1Center for Nanoscale Science and Technology, NIST, Gaithersburg, MD 20899, USA

2Surface and Microanalysis Science Division, NIST, Gaithersburg, MD 20899, USA

 

We generated beams of electrons that carry quantized orbital angular momentum using nanofabricated diffraction holograms1. These electron vortex beams, analogous to optical vortices such as Laguerre-Gaussian light beams, are composed of free electrons with helical wavefunctions and quantized orbital angular momentum in free space. Electron vortex beams offer fundamental insights into quantum behavior and electromagnetism, and can be applied to image magnetic and biological materials at the nanoscale.

 

The nanoscale diffraction holograms used to generate the beams consist of forked grating patterns with 20 nm feature sizes milled through a 30 nm suspended silicon nitride membrane using a focused ion beam (FIB). The forked grating pattern simulates the interference between helical waves and a reference plane wave. In a transmission electron microscope (TEM), this pattern is imprinted upon the de Broglie wavefronts of a spatially coherent beam of 300 keV electrons transmitted through the hologram. The electrons then diffract into multiple vortex beams that are each composed of electrons with helical wavefronts and quantized orbital angular momentum. By fabricating a more severely forked grating with multiple “tines”, one can impart arbitrary amounts of quantized orbital angular momentum to free electrons.

 

We demonstrated beams carrying up to 100 h quanta of angular momentum per electron. In these beams, each electron wavefunction is described by a set of steep, intertwined helices. The electron wavefunction has zero amplitude along the axis of the vortex core due to destructive interference. As a result, such electron vortex beams are hollow, and when projected onto an imaging detector they appear as a thin annulus surrounding a dark vortex core. Using the imaging optics of the TEM, we observed how these beams evolve in free space and found that the orbital states expand in time. This means that the electron vortex beam can be approximated by a superposition of straight line trajectories.

 

Free electron beams carrying orbital angular momentum, enabled by diffractive optics for electrons, provide a promising new tool for electron microscopy. They can be used to image magnetic materials using an exchange of quantized angular momentum from the beam to magnetic atoms in a sample. Electron vortex beams can also be used for phase contrast enhancement of electron-transparent objects in a TEM such as biological materials, by implementing a spiral phase microscopy technique2 recently developed in optical microscopy. Such beams could also be used to manipulate matter, such as inducing torque and eddy currents or applying effective magnetic fields at the nanoscale. Many of these applications will require electron beams with large angular momentum per electron, similar to those demonstrated here.

 

[1] B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, Science in press, (2011).

2 S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).