Optical beam shaping and diffraction free waves: a variational approach

We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty pr...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-05
Main Authors: Gemmer, John A, Venkataramani, Shankar C, Durfee, Charles G, Moloney, Jerome V
Format: Article
Language:English
Subjects:
Algorithms
Beams (radiation)
Lower bounds
Phase retrieval
Physical properties
Wave diffraction
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove rigorous lower bounds on the functional that capture how the various physical parameters in the problem determine the accuracy of the beam shaping. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg-Saxton algorithm to beam shaping problems arising in remote delivery of beams and pulses.
ISSN:2331-8422
DOI:10.48550/arxiv.1307.6289