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Unified Approach towards the Dynamics of Optical and Electron Vortex Beams
Pratul Bandyopadhyay1, Banasri Basu1, Debashree Chowdhury1
1Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, Barrackpore Trunk Road, Kolkata 700 108, India.
Physical Review Letters
|April 23, 2016
Summary
This study unifies optical vortex beams (OVBs) and electron vortex beams (EVBs) using geometric phase and Hall effects. It reveals how beam properties, like paraxiality and tilt, dictate OAM and spin Hall effects in various fields and media.
Area of Science:
- Quantum optics
- Particle physics
- Condensed matter physics
Background:
- Vortex beams, including optical vortex beams (OVBs) and electron vortex beams (EVBs), carry orbital angular momentum (OAM).
- Hall effects describe particle deflection in response to fields, with OAM and spin Hall effects being specific manifestations.
- Understanding the interplay between beam dynamics, geometric phase, and Hall effects is crucial for advanced applications.
Purpose of the Study:
- To propose a unified framework for understanding the dynamics of OVBs and EVBs.
- To connect the behavior of these beams to geometric phase and associated Hall effects.
- To explore the generation of arbitrary fractional orbital angular momentum states.
Main Methods:
- Formulation in cylindrical coordinates to describe local vortex structure and OAM.
- Analysis of electron vortex beams (EVBs) in external electric fields.
- Analysis of optical vortex beams (OVBs) in inhomogeneous media.
Main Results:
- Paraxial EVBs in electric fields exhibit an OAM Hall effect.
- Nonparaxial EVBs with tilted vortices show a spin Hall effect.
- Paraxial OVBs in inhomogeneous media induce an OAM Hall effect.
- Nonparaxial OVBs with tilted vortices exhibit a spin Hall effect.
- Both OVBs and EVBs with tilted vortices can generate OAM states with arbitrary fractional values.
Conclusions:
- A unified framework based on geometric phase successfully describes the dynamics of both OVBs and EVBs.
- The Hall effects (OAM and spin) are dependent on beam paraxiality, vortex tilt, and the surrounding environment (fields or media).
- The framework provides a pathway for controlling and generating fractional OAM states in both optical and electron vortex beams.
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