Optical beam shaping and diffraction free waves: A variational approach. Gemmer, J. A., Venkataramani, S. C., Durfee, C. G., & Moloney, J. V. Physica D: Nonlinear Phenomena, 283(0):15 - 28, 2014. ![Optical beam shaping and diffraction free waves: A variational approach [link]](https://bibbase.org/img/filetypes/link.svg "link")
Arxiv Journal doi abstract bibtex 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 various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. 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 the remote delivery of beams and pulses.
@article{GVDM2014,
abstract = {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 various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. 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 the remote delivery of beams and pulses.},
author = {John A. Gemmer and Shankar C. Venkataramani and Charles G. Durfee and Jerome V. Moloney},
date-added = {2017-01-29 16:04:45 +0000},
date-modified = {2017-01-29 20:11:00 +0000},
doi = {http://dx.doi.org/10.1016/j.physd.2014.06.003},
issn = {0167-2789},
journal = {Physica D: Nonlinear Phenomena},
keywords = {Fresnel approximation; pubs},
number = {0},
pages = {15 - 28},
title = {Optical beam shaping and diffraction free waves: A variational approach},
url_arxiv = {http://arxiv.org/abs/1307.6289},
url_journal = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},
volume = {283},
year = {2014},
Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2014.06.003}}
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