OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Glenn D. Boreman
  • Vol. 44, Iss. 32 — Nov. 10, 2005
  • pp: 6971–6985

Effective second-order nonlinearity in acentric optical crystals with low symmetry

Pancho Tzankov and Valentin Petrov  »View Author Affiliations

Applied Optics, Vol. 44, Issue 32, pp. 6971-6985 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (490 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We derive explicit expressions in the frame of the optical indicatrix for the second-order effective nonlinearity in biaxial crystals with point groups 2, m, and 1, governing the conversion efficiency in three-wave nonlinear optical interactions. The tabulated expressions for the monoclinic symmetry classes 2 and m are valid for all possible orientations of the optical indicatrix relative to the crystallographic frame and for propagation along an arbitrary direction outside the principal planes. They can be used for direct estimation of the effective nonlinearity in the same frame where the phase-matching loci are calculated. The relevant properties and conventions used for the newly emerging acentric monoclinic crystals belonging to the borate family are summarized and tabulated. The derivations are expected to help establish adherence to uniform nomenclature and conventions for these novel inorganic nonlinear crystals, and to eliminate ambiguity and increasing confusion in the literature and in the industrial specifications. The general expressions for the effective nonlinearity are reduced for triclinic crystals of point group 1 to simplified forms in the principal planes.

© 2005 Optical Society of America

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Nonlinear Optics

Original Manuscript: March 18, 2005
Manuscript Accepted: May 9, 2005
Published: November 10, 2005

Pancho Tzankov and Valentin Petrov, "Effective second-order nonlinearity in acentric optical crystals with low symmetry," Appl. Opt. 44, 6971-6985 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, 1973).
  2. M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967). [CrossRef]
  3. J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984). [CrossRef]
  4. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992). [CrossRef]
  5. V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd rev. ed. (Springer, 1999). [CrossRef]
  6. V. G. Dmitriev, D. N. Nikogosyan, “Effective nonlinearity coefficients for three-wave interactions in biaxial crystals of mm2 point group symmetry,” Opt. Commun. 95, 173–182 (1993). [CrossRef]
  7. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  8. H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second-order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975). [CrossRef]
  9. O. I. Lavrovskaya, N. I. Pavlova, A. V. Tarasov, “Second harmonic generation of light from an AIG:Nd3+laser in an optically biaxial crystal of KTiOPO4,” Sov. Phys. Crystallogr. 31, 678–681 (1986)[transl. from Kristallografiya 31, 1145–1151 (1986)].
  10. IEEE Standard on Piezoelectricity, (IEEE, 1988).
  11. D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, G. Kennedy, “Deuterated L-arginine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989). [CrossRef]
  12. P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1991).
  13. S. Singh, “Nonlinear optical materials,” in Handbook of Laser Science and Technology, M. J. Weber, ed., Vol. III of Optical Materials (CRC Press, 1986), Section 1.1.
  14. M. Born, E. Wolf, Principles of Optics, 6th ed. (reprinted with corrections), (Pergamon, 1993).
  15. R. L. Sutherland, Handbook of Nonlinear Optics2nd rev. ed. (Marcel Dekker, 2003).
  16. S. Fossier, S. Salaün, J. Mangin, O. Bidault, I. Thénot, J.-J. Zondy, W. Chen, F. Rotermund, V. Petrov, P. Petrov, J. Henningsen, A. Yelisseyev, L. Isaenko, S. Lobanov, O. Balachninaite, G. Slekys, V. Sirutkaitis, “Optical vibrational, thermal, electrical, damage, and phase-matching properties of lithium thioindate,” J. Opt. Soc. Am. B 21, 1981–2007 (2004). [CrossRef]
  17. B. V. Bokut, “Optical mixing by biaxial crystals,” J. Appl. Spectrosc. 7, 425–429 (1967)[transl. from Z. Prikl. Spektrosk. 7, 621–624 (1967)]. [CrossRef]
  18. P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. 10, 979–992 (1998). [CrossRef]
  19. C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80, 1–25 (2005). [CrossRef]
  20. H. Hellwig, J. Liebertz, L. Bohaty, “Exceptional largenonlinear optical coefficients in the monoclinic bismuth borate BiB3O6(BIBO),” Solid State Commun. 109, 249–251 (1999). [CrossRef]
  21. H. Hellwig, J. Liebertz, L. Bohaty, “Linear optical properties of the monoclinic bismuth borate BiB3O6,” J. Appl. Phys. 88, 240–244 (2000). [CrossRef]
  22. B. Teng, J. Wang, Zh. Wang, H. Jiang, X. Hu, R. Song, H. Liu, Y. Liu, J. Wei, Z. Shao, “Growth and investigation of a new nonlinear optical crystal: bismuth borate BiB3O6,” J. Cryst. Growth 224, 280–283 (2001). [CrossRef]
  23. B. Teng, J. Wang, Zh. Wang, X. Hu, H. Jiang, H. Liu, X. Cheng, Sh. Dong, Y. Liu, Z. Shao, “Crystal growth, thermal and optical performance of BiB3O6,” J. Cryst. Growth 233, 282–286 (2001). [CrossRef]
  24. Zh. Wang, G. Xu, J. Liu, D. Hu, X. Xu, J. Wang, Z. Shao, “Noncollinear second-harmonic generation in BiB3O6,” Opt. Soc. Am. B 21, 1348–1353 (2004). [CrossRef]
  25. M. Ghotbi, M. Ebrahim-Zadeh, “Optical second harmonic generation properties of BiB3O6,” Opt. Express 12, 6002–6019 (2004). [CrossRef] [PubMed]
  26. L. Mei, Y. Wang, C. Chen, “Crystal structure of sodium beryllium borate fluoride,” Mater. Res. Bull. 29, 81–87 (1994). [CrossRef]
  27. Y. Wu, J. Liu, P. Fu, J. Wang, H. Zhou, G. Wang, C. Chen, “A new lanthanum and calcium borate La2CaB10O19,” Chem. Mater. 13, 753–755 (2001). [CrossRef]
  28. G. Wang, J. Lu, D. Gui, Z. Xu, Y. Wu, P. Fu, X. Guan, C. Chen, “Efficient second harmonic generation in a new nonlinear La2CaB10O19 crystal,” Opt. Commun. 209, 481–484 (2002). [CrossRef]
  29. X. W. Xu, T. C. Chong, G. Y. Zhang, S. D. Cheng, M. H. Li, C. C. Phua, “Growth and optical properties of a new nonlinear optical lanthanum calcium borate crystal,” J. Cryst. Growth 237–239, 649–653 (2002). [CrossRef]
  30. Y. Wu, P. Fu, F. Zheng, S. Wan, X. Guan, “Growth of a nonlinear optical crystal La2CaB10O19 (LCB),” Opt. Mater. 23, 373–375 (2003). [CrossRef]
  31. J. Cao, J. Wang, P. Fu, F. Guo, Zh. Yang, Y. Wu, “Synthesis and characterization of a novel non-linear optical material La2SrB10O19,” Prog. Cryst. Growth Charact. Mater. 40, 97–101 (2000). [CrossRef]
  32. M. Iwai, T. Kobayashi, H. Furuya, Y. Mori, T. Sasaki, “Crystal growth and optical characterization of rare-earth (Re) calcium oxyborate ReCa4O(BO3)3 (Re = Y or Gd) as new nonlinear optical material,”Jpn. J. Appl. Phys. 36, L276–L279 (1997). [CrossRef]
  33. Q. Ye, B. H. T. Chai, “Crystal growth of YCa4O(BO3)3 and its orientation,” J. Cryst. Growth 197, 228–235 (1999). [CrossRef]
  34. C. Chen, Z. Shao, J. Jiang, J. Wei, J. Lin, J. Wang, N. Ye, J. Lv, B. Wu, M. Jiang, M. Yoshimura, Y. Mori, T. Sasaki, “Determination of the nonlinear optical coefficients of YCa4O(BO3)3 crystal,” J. Opt. Soc. Am. B 17, 566–571 (2000). [CrossRef]
  35. P. Segonds, B. Boulanger, J.-P. Feve, B. Menaert, J. Zaccaro, G. Aka, D. Pelenc, “Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal,” J. Opt. Soc. Am. B 21, 765–769 (2004). [CrossRef]
  36. G. Aka, A. Kahn-Harari, F. Mougel, D. Vivien, F. Salin, P. Coquelin, P. Colin, D. Pelenc, J. P. Damelet, “Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca4GdO(BO3)3,” J. Opt. Soc. Am. B 14, 2238–2247 (1997). [CrossRef]
  37. S. Zhang, Z. Cheng, J. Lu, G. Li, J. Lu, Z. Shao, H. Chen, “Studies on the effective nonlinear coefficient of GdCa4O(BO3)3 crystal,” J. Cryst. Growth 205, 453–456 (1999). [CrossRef]
  38. Zh. Wang, J. Liu, R. Song, X. Xu, X. Sun, H. Jiang, K. Fu, J. Wang, Y. Liu, J. Wei, Z. Shao, “The second-harmonic-generation property of GdCa4O(BO3)3 crystal with various phase-matching directions,” Opt. Commun. 187, 401–405 (2001). [CrossRef]
  39. J. J. Adams, C. A. Ebbers, K. I. Schaffers, S. A. Payne, “Nonlinear optical properties of LaCa4O(BO3)3,” Opt. Lett. 26, 217–219 (2001). [CrossRef]
  40. H. Jiang, D. Li, K. Zhang, H. Liu, J. Wang, “Optical and thermal properties of nonlinear optical crystal LaCa4O(BO3)3,” Chem. Phys. Lett. 372, 788–793 (2003). [CrossRef]
  41. H. Furuya, M. Yoshimura, T. Kobayashi, K. Murase, Y. Mori, T. Sasaki, “Crystal growth and characterization of GdxY1−xCa4O(BO3)3 crystal,” J. Cryst. Growth 198–199, 560–563 (1999). [CrossRef]
  42. Sh. Zhang, Zh. Cheng, Sh. Zhang, J. Han, L. Sun, H. Chen, “Growth and noncritical phase-matching third-harmonic-generation of GdxY1−xCa4O(BO3)3 crystal,” J. Cryst. Growth 213, 415–418 (2000). [CrossRef]
  43. N. Umemura, H. Nakao, H. Furuya, M. Yoshimura, Y. Mori, T. Sasaki, K. Yoshida, K. Kato, “90° phase-matching properties of YCa4O(BO3)3 and GdxY1−xCa4O(BO3)3,” Jpn. J. Appl. Phys. 40, 596–600 (2001). [CrossRef]
  44. J. F. H. Nicholls, B. Henderson, B. H. T. Chai, “The nonlinear optical properties of the XYB2O6 family of compounds,” Opt. Mater. 16, 453–462 (2001). [CrossRef]
  45. Y. Ji, J. Liang, S. Xie, Y. Yu, “Subsolidus phase equilibria of the CaO-B2O3-BaO system,” J. Am. Ceram. Soc. 78, 765–768 (1995). [CrossRef]
  46. R. W. Smith, D. A. Keszler, “Synthesis, structure, and properties of the noncentrosymmetric pyroborate BaCuB2O5,” J. Solid State Chem. 129, 184–188 (1997). [CrossRef]
  47. Zh.-G. Hu, M. Yoshimura, Y. Mori, T. Sasaki, “Design and growth of new NLO crystals for UV light generation,” J. Cryst. Growth 275, 232–239 (2005). [CrossRef]
  48. S. Lei, Q. Huang, Y. Zheng, A. Jiang, C. Chen, “Structure of calcium fluoroborate, Ca5(BO3)3 F,” Acta Crystallogr. Sect. C 45, 1861–1863 (1989). [CrossRef]
  49. H.-X. Zhang, J. Zhang, Sh.-T. Zheng, G.-M. Wang, G.-Y. Yang, “K2[Ge(B4O9)] 2H2 O: a unique 3D alternating linkage mode of a B4O9 cluster and GeO4 unit in borogermanate with two pairs of interweaving double helical channels,” Inorg. Chem. 43, 6148–6150 (2004). [CrossRef] [PubMed]
  50. Y. Ji, J. Liang, Zh. Chen, S. Xie, “Phase relations in the system Al2O3-B2O3-Nd2O3,” J. Am. Ceram. Soc. 74, 444–446 (1991). [CrossRef]
  51. Zh. Zhu, Ch. Tu, J. Li, B. Wu, “Crystal growth and spectroscopic characterizations of pure and Nd3+-doped Cd3Y(BO3)3 crystals,” J. Cryst. Growth 263, 291–295 (2004). [CrossRef]
  52. X. Long, X. Han, “Growth of nonlinear optical calcium pyroniobate crystal,” J. Cryst. Growth 275, 492–495 (2005). [CrossRef]
  53. I. Parreu, R. Sole, J. Gavalda, J. Massons, F. Diaz, M. Aguilo, “Crystallization region, crystal growth, and phase transitions of KNd(PO3)4,” Chem. Mater. 15, 5059–5064 (2003). [CrossRef]
  54. I. Parreu, R. Sole, J. Gavalda, J. Massons, F. Diaz, M. Aguilo, “Crystal growth, structural characterization, and linear thermal evolution of KGd(PO3)4,” Chem. Mater. 17, 822–828 (2005). [CrossRef]
  55. B. Bentria, D. Benbertal, M. Bagieu-Beucher, A. Mosset, J. Zaccaro, “Crystal engineering strategy for quadratic nonlinear optics. Part II: Hg(IO3)2,” Solid State Sci. 5, 359–365 (2003). [CrossRef]
  56. Y. Porter, K. M. Ok, N. S. P. Bhuvanesh, P. Shiv Halasyamani, “Synthesis and characterization of Te2SeO7: a powder second-harmonic-generating study of TeO2, Te2SeO7, Te2O5, and TeSeO4,” Chem. Mater. 13, 1910–1915 (2001). [CrossRef]
  57. K. Friese, M. I. Aroyo, C. L. Folcia, G. Madariaga, T. Breczewski, “Characterization of the room-temperature phase of Tl2MoO4: crystal structure, symmetry mode analysis and second-harmonic generation measurements,” Acta Crystallogr. Sect. B 57, 142–150 (2001). [CrossRef]
  58. Th. C. Shehee, R. E. Sykora, K. M. Ok, P. S. Halasyamani, Th. E. Albrecht-Schmitt, “Hydrothermal preparation, structures, and NLO properties of the rare earth molybdenyl iodates, RE(MoO2)(IO3)4(OH) [RE=Nd, Sm, Eu],” Inorg. Chem. 42, 457–462 (2003). [CrossRef] [PubMed]
  59. J.-H. Liao, G. M. Marking, K. F. Hsu, Y. Matsushita, M. D. Ewbank, R. Borwick, P. Cunningham, M. J. Rosker, M. G. Kanatzidis, “α- and β-A2Hg3M2S8 (A=K, Rb; M=Ge, Sn): polar quaternary chalcogenides with strong nonlinear optical response,” J. Am. Chem. Soc. 125, 9484–9493 (2003). [CrossRef] [PubMed]
  60. H.-S. Ra, K. M. Ok, P. S. Halasyamani, “Combining second-order Jahn-Teller distorted cations to create highly efficient SHG materials: synthesis, characterization, and NLO properties of BaTeM2O9 (M=Mo6+or W6+),” J. Am. Chem. Soc. 125, 7764–7765 (2003). [CrossRef] [PubMed]
  61. J. Goodey, J. Broussard, P. S. Halasyamani, “Synthesis, structure, and characterization of a new second-harmonic-generating tellurite: Na2TeW2O9,” Chem. Mater. 14, 3174–3180 (2002). [CrossRef]
  62. K. M. Ok, P. S. Halasyamani, “New selenites: synthesis, structures, and characterizations of centrosymmetric Al2(Se2O5)3 and Ga2(Se2O5)3 and non-centrosymmetric In2(Se2O5)3,” Chem. Mater. 14, 2360–2364 (2002). [CrossRef]
  63. P. Ren, J. Qin, T. Liu, Y. Wu, C. Chen, “Characterization and properties of a nonlinear optical crystal in IR region: Rb-Cdl3H2O,” Opt. Mater. 23, 331–334 (2003). [CrossRef]
  64. W. K. Jang, Q. Ye, J. Eichenholz, M. C. Richardson, B. H. T. Chai, “Second harmonic generation in Yb doped YCa4O(BO3)3,” Opt. Commun. 155, 332–334 (1998). [CrossRef]
  65. W. K. Jang, Q. Ye, D. Hammons, J. Eichenholz, J. Lim, M. Richardson, B. H. T. Chai, E. W. Van Stryland, “Improved second-harmonic generation by selective Yb ion doping in a new nonlinear optical crystal YCa4O(BO3)3,” IEEE J. Quantum Electron. 35, 1826–1833 (1999). [CrossRef]
  66. Zh. Lin, Zh. Wang, C. Chen, M.-H. Lee, “Mechanism for linear and nonlinear optical effects in monoclinic bismuth borate (BiB3O6) crystal,” J. Appl. Phys. 90, 5585–5590 (2001). [CrossRef]
  67. D. Xue, K. Betzler, H. Hesse, D. Lammers, “Nonlinear optical properties of borate crystals,” Solid State Commun. 114, 21–25 (2000). [CrossRef]
  68. M. V. Pack, D. J. Armstrong, A. V. Smith, G. Aka, B. Ferrand, D. Pelenc, “Measurement of the χ(2) tensor of GdCa4O(BO3)3 and YCa4O(BO3)3 crystals,” J. Opt. Soc. Am. B 22, 417–425 (2005). [CrossRef]
  69. D. Vivien, G. Aka, A. Kahn-Harari, A. Aron, F. Mougel, J.-M. Benitez, B. Ferrand, R. Klein, G. Kugel, N. Le Nain, M. Jacquet, “Crystal growth and optical properties of rare earth calcium oxoborates,” J. Cryst. Growth 237–239, 621–628 (2002). [CrossRef]
  70. F. Mougel, G. Aka, F. Salin, D. Pelenc, B. Ferrand, A. Kahn-Harari, D. Vivien, “Accurate second harmonic generation phase matching angles prediction and nonlinear coefficients measurements of Ca4YO(BO3)3 (YCOB) crystal,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 709–714.
  71. G. Aka, F. Mougel, D. Vivien, R. Klein, G. Kugel, B. Ferrand, D. Pelenc, “Conversion efficiency and absolute effective nonlinear optical-coefficients of YCOB and GdCOB measured for different type I SHG phase matching configurations,” in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 548–553.
  72. C. Chen, N. Ye, J. Lin, J. Jiang, W. Zeng, B. Wu, “Computer-assisted search for nonlinear optical crystals,” Adv. Mater. 11, 1071–1078 (1999). [CrossRef]
  73. D. Xue, S. Zhang, “Structural analysis of nonlinearities of Ca4ReO(BO3)3 (Re=La, Nd, Sm, Gd, Er, Y),” Appl. Phys. A 68, 57–61 (1999). [CrossRef]
  74. Z.-P. Wang, J.-H. Liu, R.-B. Song, H.-D. Jiang, S.-J. Zhang, K. Fu, C.-Q. Wang, Y.-G. Liu, J.-Q. Wei, H.-C. Chen, Z.-S. Shao, “Anisotropy of nonlinear-optical property of RCOB (R=Gd, Y) crystal,” Chin. Phys. Lett. 18, 385–387 (2001). [CrossRef]
  75. J. L. Stone, D. A. Keszler, G. Aka, A. Kahn-Harari, Th. A. Reynolds, “Nonlinear optical borate crystal Ba2B10O17,” Proc. SPIE 4268, 175–179 (2001). [CrossRef]
  76. V. A. D’yakov, T. V. Laptinskaya, V. I. Pryalkin, “Optical and nonlinear optical properties of LiNaCO3 single crystal,” Proc. SPIE 3734, 415–419 (1999). [CrossRef]
  77. D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13, 2047–2057 (2005), and references therein. [CrossRef] [PubMed]

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