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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 18 — Sep. 8, 2014
  • pp: 21347–21353

On the frequency-doubled conically-refracted Gaussian beam

Stephen D. Grant, Svetlana A. Zolotovskaya, Todor K. Kalkandjiev, W. Allan Gillespie, and Amin Abdolvand  »View Author Affiliations

Optics Express, Vol. 22, Issue 18, pp. 21347-21353 (2014)

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A Potassium Titanyl Phosphate (KTP) crystal has been used in conjunction with a 10-ps pulsed laser to produce a frequency-doubled conically-refracted Gaussian beam. The ‘free’ and ‘forced’ beams that make up the scheme for nonlinear conical refraction were readily observable in non-phase-matched conditions. The dependency of the frequency-doubled beam patterns on the incident beam polarization, which until now has remained unexplored, was examined in detail. We have also revealed the existence of two orthogonally polarized ‘free’ rays for particular orientations of the incident beam polarization.

© 2014 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization

ToC Category:
Nonlinear Optics

Original Manuscript: July 2, 2014
Revised Manuscript: August 7, 2014
Manuscript Accepted: August 13, 2014
Published: August 26, 2014

Stephen D. Grant, Svetlana A. Zolotovskaya, Todor K. Kalkandjiev, W. Allan Gillespie, and Amin Abdolvand, "On the frequency-doubled conically-refracted Gaussian beam," Opt. Express 22, 21347-21353 (2014)

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  1. W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).
  2. H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1, 112–120 (1833).
  3. J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann. 48, 461–462 (1839).
  4. C. V. Raman and T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942). [CrossRef]
  5. M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010). [CrossRef]
  6. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “The creation and annihilation of optical vortices using cascade conical diffraction,” Opt. Express 19(3), 2580–2588 (2011). [CrossRef] [PubMed]
  7. A. Abdolvand, “Conical diffraction from a multi-crystal cascade: experimental observations,” Appl. Phys. B 103(2), 281–283 (2011). [CrossRef]
  8. C. F. Phelan, K. E. Ballantine, P. R. Eastham, J. F. Donegan, and J. G. Lunney, “Conical diffraction of a Gaussian beam with a two crystal cascade,” Opt. Express 20(12), 13201–13207 (2012). [CrossRef] [PubMed]
  9. S. D. Grant and A. Abdolvand, “Left- and right-circularly polarized light in cascade conical diffraction,” Opt. Lett. 37(24), 5226–5228 (2012). [CrossRef] [PubMed]
  10. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Multiple rings formation in cascaded conical refraction,” Opt. Lett. 38(9), 1455–1457 (2013). [CrossRef] [PubMed]
  11. H. Shih and N. Bloembergen, “Conical Refraction in Second-Harmonic Generation,” Phys. Rev. 184(3), 895–904 (1969). [CrossRef]
  12. A. J. Schell and N. Bloembergen, “Second harmonic conical refraction,” Opt. Commun. 21(1), 150–153 (1977). [CrossRef]
  13. A. J. Schell and N. Bloembergen, “Laser studies of internal conical refraction. III. Second-harmonic conical refraction in α-iodic acid,” Phys. Rev. A 18(6), 2592–2602 (1978). [CrossRef]
  14. A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 436–439 (1978).
  15. M. V. Berry, “Conical refraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004). [CrossRef]
  16. J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006). [CrossRef]
  17. M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8(12), 1043–1051 (2006). [CrossRef]
  18. M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007). [CrossRef]
  19. M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical refraction: Observation and theory,” Proc. R. Soc. A, 462, 1629–1642 (2007).
  20. V. Peet and D. Zolotukhin, “Free-space evolution of focused Gaussian beams transformed by conical diffraction in a biaxial crystal,” Opt. Commun. 283(15), 3011–3016 (2010). [CrossRef]
  21. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, H. Tomizawa, and J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21(4), 4503–4511 (2013). [CrossRef] [PubMed]
  22. G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: New observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013). [CrossRef] [PubMed]
  23. C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009). [CrossRef] [PubMed]
  24. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010). [CrossRef]
  25. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010). [CrossRef] [PubMed]
  26. V. Peet, “Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams,” Opt. Lett. 36(15), 2913–2915 (2011). [CrossRef] [PubMed]
  27. A. Turpin, Y. Loiko, T. K. Kalkandjiev, and J. Mompart, “Free-space optical polarization demultiplexing and multiplexing by means of conical refraction,” Opt. Lett. 37(20), 4197–4199 (2012). [CrossRef] [PubMed]
  28. S. D. Grant, S. A. Zolotovskaya, W. A. Gillespie, T. K. Kalkandjiev, and A. Abdolvand, “Azimuthally and radially polarized light in conical diffraction,” Opt. Lett. 39(7), 1988–1991 (2014). [CrossRef] [PubMed]
  29. S. D. Grant and A. Abdolvand, “Evolution of conically diffracted Gaussian beams in free space,” Opt. Express 22(4), 3880–3886 (2014). [CrossRef] [PubMed]
  30. V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980). [CrossRef]
  31. A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002). [CrossRef]
  32. M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical refraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005). [CrossRef]
  33. R. A. Indik and A. C. Newell, “Conical refraction and nonlinearity,” Opt. Express 14(22), 10614–10620 (2006). [CrossRef] [PubMed]
  34. J. Kroupa, “Second-harmonic conical refraction in GUHP,” J. Opt. 12(4), 045706 (2010). [CrossRef]
  35. S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011). [CrossRef]
  36. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, J. Trull, C. Cojocaru, and J. Mompart, “Type I and type II second harmonic generation of conically refracted beams,” Opt. Lett. 38(14), 2484–2486 (2013). [CrossRef] [PubMed]
  37. T. K. Kalkandjiev and M. Bursukova, “Conical Refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008). [CrossRef]
  38. A. Turpin, V. Shvedov, C. Hnatovsky, Y. V. Loiko, J. Mompart, and W. Krolikowski, “Optical vault: A reconfigurable bottle beam based on conical refraction of light,” Opt. Express 21(22), 26335–26340 (2013). [CrossRef] [PubMed]
  39. R. T. Darcy, D. McCloskey, K. E. Ballantine, B. D. Jennings, J. G. Lunney, P. R. Eastham, and J. F. Donegan, “White Light Conical Diffraction,” Opt. Express 21(17), 20394–20403 (2013). [CrossRef] [PubMed]

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