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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26852–26867

Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration

Damian N. Schimpf, Jan Schulte, William P. Putnam, and Franz X. Kärtner  »View Author Affiliations

Optics Express, Vol. 20, Issue 24, pp. 26852-26867 (2012)

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We report on a novel class of higher-order Bessel-Gauss beams in which the well-known Bessel-Gauss beam is the fundamental mode and the azimuthally symmetric Laguerre-Gaussian beams are special cases. We find these higher-order Bessel-Gauss beams by superimposing decentered Hermite-Gaussian beams. We show analytically and experimentally that these higher-order Bessel-Gauss beams resemble higher-order eigenmodes of optical resonators consisting of aspheric mirrors. This work is relevant for the many applications of Bessel-Gauss beams in particular the more recently proposed high-intensity Bessel-Gauss enhancement cavities for strong-field physics applications.

© 2012 OSA

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3410) Lasers and laser optics : Laser resonators

ToC Category:
Physical Optics

Original Manuscript: October 1, 2012
Revised Manuscript: November 4, 2012
Manuscript Accepted: November 7, 2012
Published: November 14, 2012

Damian N. Schimpf, Jan Schulte, William P. Putnam, and Franz X. Kärtner, "Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration," Opt. Express 20, 26852-26867 (2012)

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  1. C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEEE J. Microw. Opt. Acoust.2, 105–112 (1978). [CrossRef]
  2. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491– 495 (1987). [CrossRef]
  3. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010). [CrossRef]
  4. T. A Planchon, L. Gao, D. E Milkie, M. W Davidson, J. A Galbraith, C. G Galbraith, and Eric Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods8, 417–423 (2011). [CrossRef] [PubMed]
  5. M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photon. Rev.6, 607–621 (2012). [CrossRef]
  6. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419, 145–147 (2002). [CrossRef] [PubMed]
  7. D. Li and K. Imasaki, “Vacuum laser-driven acceleration by two slits-truncated Bessel beams,” Appl. Phys. Lett.87, 091106 (2005). [CrossRef]
  8. J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, “Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis,” J. Opt. Soc. Am. A20, 2113–2122 (2003). [CrossRef]
  9. A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, “Axicon-based Bessel resonator: analytical description and experiment,” J. Opt. Soc. Am. A18, 1986–1992 (2001). [CrossRef]
  10. B. Ma, F. Wu, W. Lu, and J. Pu, “Nanosecond zero-order pulsed Bessel beam generated from unstable resonator based on an axicon,” Opt. Laser Technol.42, 941–944 (2010). [CrossRef]
  11. W. P. Putnam, D. N. Schimpf, G. Abram, and F. X. Kärtner, “Bessel-Gauss beam enhancement cavities for high-intensity applications,” Opt. Express20, 24429–24443 (2012). [CrossRef]
  12. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Spagnolo Schirripa, “Generalized Bessel-Gauss beams,” J. Mod. Opt.43(6), 1155–1166 (1996).
  13. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higherorder Bessel beams,” Opt. Express17, 23389–23395 (2009). [CrossRef]
  14. C. Palma, “Decentered Gaussian beams, ray bundles, and Bessel-Gauss beams,” Appl. Opt.36, 1116–1120 (1997). [CrossRef] [PubMed]
  15. A. R. Al-Rashed and B. E. A. Saleh, “Decentered Gaussian beams,” Appl. Opt.34, 6819–6825 (1995). [CrossRef] [PubMed]
  16. A. R. Al-Rashed, “Spatial and temporal modes of resonators with dispersive phase-conjugate mirrors,” PhD Thesis (1997).
  17. S. A. Collins, “Lens-System Diffraction Integral Written in Terms of Matrix Optics,” J. Opt. Soc. Am.60, 1168–1177 (1970). [CrossRef]
  18. G. Ryshik, Tables of Series, Products and Integrals (Verlag Harri Deutsch, 1981).
  19. H. F. Johnson, “An improved method for computing a discrete hankel transform,” Comp. Phys. Comm.43, 181–202 (1987). [CrossRef]
  20. L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett.23, 409–411 (1998). [CrossRef]
  21. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A21, 53–58 (2004). [CrossRef]
  22. A. Fox and T. Li, “Computation of optical resonator modes by the method of resonance excitation,” IEEE J. Quantum Electron.4, 460–465 (1968). [CrossRef]
  23. A. E. Siegman, Lasers (University Science Books, 1986).
  24. O. Brzobohaty, T. Cizmar, and P. Zemanek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express16, 12688–12700 (2008). [CrossRef] [PubMed]

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