Optical beam shaping and diffraction free waves: A variational approach

John A. Gemmer, Shankar C. Venkataramani, Charles G. Durfee, Jerome V. Moloney

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 L2 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.

Original languageEnglish (US)
Pages (from-to)15-28
Number of pages14
JournalPhysica D: Nonlinear Phenomena
StatePublished - Aug 15 2014


  • Beam shaping
  • Fresnel approximation
  • Localized waves
  • Paraxial wave equation
  • Phase retrieval

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


Dive into the research topics of 'Optical beam shaping and diffraction free waves: A variational approach'. Together they form a unique fingerprint.

Cite this