skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on May 22, 2020

Title: Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain

Abstract

An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. Here, this phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses.

Authors:
 [1];  [1]; ORCiD logo [1]
  1. Univ. of Nebraska, Lincoln, NE (United States)
Publication Date:
Research Org.:
Univ. of Nebraska, Lincoln, NE (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1595962
Alternate Identifier(s):
OSTI ID: 1515101
Grant/Contract Number:  
[FG02-96ER14646]
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
[ Journal Volume: 99; Journal Issue: 5]; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Angular momentum of light; Lasers; Optics & lasers; Perturbative methods

Citation Formats

Vikartofsky, Andrew, Jahns, Ethan C., and Starace, Anthony F. Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain. United States: N. p., 2019. Web. doi:10.1103/PhysRevA.99.053832.
Vikartofsky, Andrew, Jahns, Ethan C., & Starace, Anthony F. Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain. United States. doi:10.1103/PhysRevA.99.053832.
Vikartofsky, Andrew, Jahns, Ethan C., and Starace, Anthony F. Wed . "Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain". United States. doi:10.1103/PhysRevA.99.053832.
@article{osti_1595962,
title = {Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain},
author = {Vikartofsky, Andrew and Jahns, Ethan C. and Starace, Anthony F.},
abstractNote = {An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. Here, this phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses.},
doi = {10.1103/PhysRevA.99.053832},
journal = {Physical Review A},
number = [5],
volume = [99],
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on May 22, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Twisted photons
journal, May 2007

  • Molina-Terriza, Gabriel; Torres, Juan P.; Torner, Lluis
  • Nature Physics, Vol. 3, Issue 5
  • DOI: 10.1038/nphys607

The Formula of Faa Di Bruno
journal, December 1980


Generation and Applications of Extreme-Ultraviolet Vortices
journal, April 2017


Creating High-Harmonic Beams with Controlled Orbital Angular Momentum
journal, October 2014


From Ford to Faà
journal, June 2001


Gaussian beam propagation beyond the paraxial approximation
journal, January 1979

  • Agrawal, G. P.; Pattanayak, D. N.
  • Journal of the Optical Society of America, Vol. 69, Issue 4
  • DOI: 10.1364/JOSA.69.000575

Faà di Bruno's formula, lattices, and partitions
journal, June 2005

  • Encinas, L. Hernández; del Rey, A. Martín; Masqué, J. Muñoz
  • Discrete Applied Mathematics, Vol. 148, Issue 3
  • DOI: 10.1016/j.dam.2005.02.009

Perturbative representation of ultrashort nonparaxial elegant Laguerre-Gaussian fields
journal, October 2018


Space-time profiles of an ultrashort pulsed Gaussian beam
journal, April 1997

  • Zhongyang Wang,
  • IEEE Journal of Quantum Electronics, Vol. 33, Issue 4
  • DOI: 10.1109/3.563385

Virtual source for a Laguerre–Gauss beam
journal, January 2002


Higher-order complex source for elegant Laguerre–Gaussian waves
journal, January 2004

  • Bandres, Miguel A.; Gutiérrez-Vega, Julio C.
  • Optics Letters, Vol. 29, Issue 19
  • DOI: 10.1364/OL.29.002213

Beam modes beyond the paraxial approximation: A scalar treatment
journal, April 1998


Fields of a Gaussian beam beyond the paraxial approximation
journal, September 2006


Orbital angular momentum: origins, behavior and applications
journal, January 2011

  • Yao, Alison M.; Padgett, Miles J.
  • Advances in Optics and Photonics, Vol. 3, Issue 2
  • DOI: 10.1364/AOP.3.000161

Fifth‐order corrected electromagnetic field components for a fundamental Gaussian beam
journal, October 1989

  • Barton, J. P.; Alexander, D. R.
  • Journal of Applied Physics, Vol. 66, Issue 7
  • DOI: 10.1063/1.344207

Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses
journal, January 2000


Theory of electromagnetic beams
journal, March 1979


The Curious History of Faà di Bruno's Formula
journal, March 2002


From Maxwell to paraxial wave optics
journal, April 1975

  • Lax, Melvin; Louisell, William H.; McKnight, William B.
  • Physical Review A, Vol. 11, Issue 4
  • DOI: 10.1103/PhysRevA.11.1365

Nonperturbative Twist in the Generation of Extreme-Ultraviolet Vortex Beams
journal, October 2016


Free-space propagation of ultrashort pulses: Space-time couplings in Gaussian pulse beams
journal, November 1999