Related Experiment Video
Updated: May 8, 2026

X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells
Published on: August 20, 2019
Incomplete Airy beams: finite energy from a sharp spectral cutoff
James D Ring1, Christopher J Howls, Mark R Dennis
1H H Wills Physics Laboratory, University of Bristol, Bristol, UK. james.ring@bristol.ac.uk
Abstract:
We present a mathematical analysis of the finite-energy Airy beam with a sharply truncated spectrum, which can be generated by a uniformly illuminated, finite-sized spatial light modulator, or windowed cubic phase mask. The resulting "incomplete Airy beam" is tractable mathematically, and differs from an infinite-energy Airy beam by an additional oscillating modulation and the decay of its fringes. Its propagation can be described explicitly using an incomplete Airy function, from which we derive simple expressions for the beam's total power and mean position. Asymptotic analysis reveals a simple connection between the cutoff and the region of the beam with Airy-like behavior.
Related Concept Videos
Interference and Diffraction
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Emission Spectra
Improper Integrals: Infinite Intervals
Deflection of a Beam
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Beams
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...

