OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 1041–1047

Extreme high-intensity and ultrabroadband interactions in anisotropic β-BaB2O4 crystals

Matteo Conforti and Fabio Baronio  »View Author Affiliations

JOSA B, Vol. 30, Issue 4, pp. 1041-1047 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (516 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We derive unidirectional pulse propagation equations to describe extreme high-intensity and ultrabroadband optical interactions in uniaxial crystals, showing both second- and third-order nonlinear optical susceptivities. We focus our attention on the anisotropic nature of the quadratic and cubic nonlinear response of beta-barium-borate (β-BaB2O4, BBO) crystals. Two nonlinearly coupled first-order (in the propagation coordinate) equations describe the dynamics and interactions of the ordinary and extraordinary field polarizations, and are valid for arbitrarily wide pulse bandwidth. We exploit this model to predict harmonic and supercontinuum generation in BBO crystals under the strong and competing influence of quadratic and cubic susceptivities.

© 2013 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(320.2250) Ultrafast optics : Femtosecond phenomena
(190.4223) Nonlinear optics : Nonlinear wave mixing

ToC Category:
Nonlinear Optics

Original Manuscript: November 29, 2012
Manuscript Accepted: February 15, 2013
Published: March 27, 2013

Matteo Conforti and Fabio Baronio, "Extreme high-intensity and ultrabroadband interactions in anisotropic β-BaB2O4 crystals," J. Opt. Soc. Am. B 30, 1041-1047 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Mironov, V. Lozhkarev, V. Ginzburg, and E. Khazanov, “High-efficiency second-harmonic generation of superintense ultrashort laser pulses,” Appl. Opt. 48, 2051–2057 (2009). [CrossRef]
  2. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009). [CrossRef]
  3. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]
  4. M. Aoyama, K. Yamakawa, Y. Akahane, J. Ma, N. Inoue, H. Ueda, and H. Kiriyama, “0.85 PW, 33 fs Ti:sapphire laser,” Opt. Lett. 28, 1594–1596 (2003). [CrossRef]
  5. V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Malshakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KDP crystals,” Laser Phys. Lett. 4, 421–427 (2007). [CrossRef]
  6. C. Farrell, K. A. Serrels, T. R. Lundquist, P. Vedagarbha, and D. T. Reid, “Octave-spanning super-continuum from a silica photonic crystal fiber pumped by a 386 MHz Yb:fiber laser,” Opt. Lett. 37, 1778–1780 (2012). [CrossRef]
  7. X. Fang, M. Hu, L. Huang, L. Chai, N. Dai, J. Li, A. Tashchilina, A. M. Zheltikov, and C. Wang, “Multiwatt octave-spanning supercontinuum generation in multicore photonic-crystal fiber,” Opt. Lett. 37, 2292–2294 (2012). [CrossRef]
  8. J. Price, T. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Leong, P. Petropoulos, J. Flanagan, G. Brambilla, X. Feng, and D. Richardson, “Mid-IR supercontinuum generation from nonsilica microstructured optical fibers,” IEEE J. Sel. Top. Quantum Electron. 13, 738–749 (2007). [CrossRef]
  9. M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010). [CrossRef]
  10. C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and I. Hartl, “Supercontinuum generation in quasi-phase-matched LiNbO3 waveguide pumped by a Tm-doped fiber laser system,” Opt. Lett. 36, 3912–3914 (2011). [CrossRef]
  11. M. Conforti, F. Baronio, and C. De Angelis, “Ultra-broadband optical phenomena in quadratic nonlinear media,” IEEE Photon. J. 2, 600–610 (2010). [CrossRef]
  12. C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, I. Hartl, and M. E. Fermann, “Supercontinuum generation in quasi-phasematched waveguides,” Opt. Express 19, 18754–18773 (2011). [CrossRef]
  13. B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, “Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched quadratic interactions,” Phys. Rev. Lett. 109, 043902 (2012). [CrossRef]
  14. M. Levenius, M. Conforti, F. Baronio, V. Pasiskevicius, F. Laurell, C. De Angelis, and K. Gallo, “Multistep quadratic cascading in broadband optical parametric generation,” Opt. Lett. 37, 1727–1729 (2012). [CrossRef]
  15. J. Sung, S. Lee, T. Yu, T. Jeong, and J. Lee, “0.1 Hz 1.0 PW Ti:sapphire laser,” Opt. Lett. 35, 3021–3023 (2010). [CrossRef]
  16. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2005).
  17. M. Conforti, F. Baronio, and C. De Angelis, “Modeling of ultrabroadband and single-cycle phenomena in anisotropic quadratic crystals,” J. Opt. Soc. Am. B 28, 1231–1237 (2011). [CrossRef]
  18. A. V. Housakou and J. Herrmnann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef]
  19. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002). [CrossRef]
  20. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984).
  21. T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000). [CrossRef]
  22. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004). [CrossRef]
  23. G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382–5387 (2007). [CrossRef]
  24. P. Kinsler, S. B. P. Radnor, and G. H. C. New, “Theory of directional pulse propagation,” Phys. Rev. A 72, 063807 (2005). [CrossRef]
  25. P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010). [CrossRef]
  26. A. Kumar, “Ultrashort pulse propagation in a cubic medium including the Raman effect,” Phys. Rev. A 81, 013807 (2010). [CrossRef]
  27. M. Kolesik, P. T. Whalen, and J. V. Moloney, “Theory and simulation of ultrafast intense pulse propagation in extended media,” IEEE J. Sel. Top. Quantum Electron. 18, 494–506(2012). [CrossRef]
  28. J. E. Midwinter and J. Warner, “The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization,” Br. J. Appl. Phys. 16, 1135–1142 (1965). [CrossRef]
  29. J. E. Midwinter and J. Warner, “The effects of phase matching method and of crystal symmetry on the polar dependence of third-order non-linear optical polarization,” Br. J. Appl. Phys. 16, 1667 (1965). [CrossRef]
  30. P. S. Banks, M. D. Feit, and M. D. Perry, “High intensity third-harmonic generation,” J. Opt. Soc. Am. B 19, 102–118 (2002). [CrossRef]
  31. Note that the reported dm coefficients have reversed sign with respect to the ones usually reported in literature [16]. This is because the reference frames have been traditionally selected such that, for θ=0, ϕ=0, Ee ad Eo are directed in −x and −y direction, respectively [28]. In our reference frame we have Ee,o=Ex,y, i.e., simply the x and y electric field components. This change of sign is insignificant owing to the scaling properties of Eq. (23): E→−E, dm→−dm.
  32. M. Bache, H. Guo, B. Zhou, and X. Zheng, “The anisotropic Kerr nonlinear refractive index of β-BaB2O4,” arXiv: 1209.3158v1 (2012).
  33. F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, “Three-wave trapponic solitons for tunable high-repetition rate pulse train generation,” IEEE J. Quantum Electron. 44, 542–546 (2008). [CrossRef]
  34. F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthelemy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010). [CrossRef]
  35. M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. Wise, “Limits to compression with cascaded quadratic soliton compressors,” Opt. Express 16, 3273–3287 (2008). [CrossRef]
  36. M. Bache, O. Bang, B. Zhou, J. Moses, and F. Wise, “Optical Cherenkov radiation in ultrafast cascaded second-harmonic generation,” Phys. Rev. A 82, 063806 (2010). [CrossRef]
  37. M. Bache, O. Bang, B. Zhou, J. Moses, and F. Wise, “Optical Cherenkov radiation by cascaded nonlinear interaction: an efficient source of few-cycle energetic near- to mid-IR pulses,” Opt. Express 19, 22557–22562 (2011). [CrossRef]
  38. P. Wai, C. Menyuk, Y. Lee, and H. Chen, “Soliton at the zero-group-dispersion wavelength of a single-model fiber,” Opt. Lett. 12, 628–630 (1987). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited