Abstract

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

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2005 (6)

C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80, 1–25 (2005).
[CrossRef]

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]

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]

X. Long, X. Han, “Growth of nonlinear optical calcium pyroniobate crystal,” J. Cryst. Growth 275, 492–495 (2005).
[CrossRef]

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]

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]

2004 (6)

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]

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]

M. Ghotbi, M. Ebrahim-Zadeh, “Optical second harmonic generation properties of BiB3O6,” Opt. Express 12, 6002–6019 (2004).
[CrossRef] [PubMed]

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]

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]

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]

2003 (8)

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]

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]

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]

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]

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]

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]

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]

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]

2002 (5)

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]

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]

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]

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]

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]

2001 (12)

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

2000 (5)

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]

D. Xue, K. Betzler, H. Hesse, D. Lammers, “Nonlinear optical properties of borate crystals,” Solid State Commun. 114, 21–25 (2000).
[CrossRef]

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]

H. Hellwig, J. Liebertz, L. Bohaty, “Linear optical properties of the monoclinic bismuth borate BiB3O6,” J. Appl. Phys. 88, 240–244 (2000).
[CrossRef]

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]

1999 (8)

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]

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]

Q. Ye, B. H. T. Chai, “Crystal growth of YCa4O(BO3)3 and its orientation,” J. Cryst. Growth 197, 228–235 (1999).
[CrossRef]

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]

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]

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]

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]

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]

1998 (2)

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]

P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. 10, 979–992 (1998).
[CrossRef]

1997 (3)

R. W. Smith, D. A. Keszler, “Synthesis, structure, and properties of the noncentrosymmetric pyroborate BaCuB2O5,” J. Solid State Chem. 129, 184–188 (1997).
[CrossRef]

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]

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]

1995 (1)

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]

1994 (1)

L. Mei, Y. Wang, C. Chen, “Crystal structure of sodium beryllium borate fluoride,” Mater. Res. Bull. 29, 81–87 (1994).
[CrossRef]

1993 (1)

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]

1992 (1)

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]

1991 (1)

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]

1989 (2)

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]

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]

1986 (1)

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)].

1984 (1)

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]

1975 (1)

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]

1967 (2)

M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
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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]

Adams, J. J.

Aguilo, M.

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]

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).
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Aka, G.

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).
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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).
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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]

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]

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]

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.

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.

Albrecht-Schmitt, Th. E.

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).
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Armstrong, D. J.

Aron, A.

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]

Aroyo, M. I.

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).
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Bagieu-Beucher, M.

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).
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Balachninaite, O.

Becker, P.

P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. 10, 979–992 (1998).
[CrossRef]

Benbertal, D.

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).
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Benitez, J.-M.

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).
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Bentria, B.

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).
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Betzler, K.

D. Xue, K. Betzler, H. Hesse, D. Lammers, “Nonlinear optical properties of borate crystals,” Solid State Commun. 114, 21–25 (2000).
[CrossRef]

Bhuvanesh, N. S. P.

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]

Bidault, O.

Bohaty, L.

H. Hellwig, J. Liebertz, L. Bohaty, “Linear optical properties of the monoclinic bismuth borate BiB3O6,” J. Appl. Phys. 88, 240–244 (2000).
[CrossRef]

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]

Bokut, B. V.

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]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (reprinted with corrections), (Pergamon, 1993).

Borwick, R.

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]

Boulanger, B.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Breczewski, T.

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]

Broussard, J.

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]

Butcher, P. N.

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1991).

Cao, J.

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]

Chai, B. H. T.

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]

Q. Ye, B. H. T. Chai, “Crystal growth of YCa4O(BO3)3 and its orientation,” J. Cryst. Growth 197, 228–235 (1999).
[CrossRef]

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]

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]

Chen, C.

C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80, 1–25 (2005).
[CrossRef]

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]

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]

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]

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]

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]

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]

L. Mei, Y. Wang, C. Chen, “Crystal structure of sodium beryllium borate fluoride,” Mater. Res. Bull. 29, 81–87 (1994).
[CrossRef]

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]

Chen, H.

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]

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]

Chen, H.-C.

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]

Chen, W.

Chen, Zh.

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]

Cheng, S. D.

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]

Cheng, X.

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]

Cheng, Z.

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]

Cheng, Zh.

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]

Chong, T. C.

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]

Colin, P.

Coquelin, P.

Cotter, D.

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1991).

Cunningham, P.

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]

D’yakov, V. A.

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]

Damelet, J. P.

Davis, L.

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]

Diaz, F.

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]

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]

Dmitriev, V. G.

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]

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd rev. ed. (Springer, 1999).
[CrossRef]

Dong, Sh.

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).
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Tables (8)

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Table 1 Forms of the dil Tensor in the Dielectric Frame xyza

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Table 2 Effective Nonlinearity for Symmetry Class 2 Crystals and Arbitrary Propagation Direction

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Table 3 Effective Nonlinearity for Symmetry Class 2 Crystals and Arbitrary Propagation Direction

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Table 4 Expressions for deff in the Principal Planes of Monoclonic Crystals with Symmetry Classes 2 and m

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Table 5 Optically Characterized Acentric Borate Crystals with a Monoclinic Structure

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Table 6 Acentric Monoclinic Inorganic Crystals with Stated Nonlinear Properties (Powder SHG Test Performed)

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Table 7 Nonlinear Coefficients of YCOB and GdCOB: Compilation of Experimental and Theoretical Resultsa

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Table 8 Expressions for deff in the Principal Planes of the Dielectric Frame xyz for Triclinic Acentric Crystals of Point Group 1

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

P i ( ω 3 ) = d i j k ( ω 3 , ω 2 , ω 1 ) E j ( ω 2 ) E k ( ω 1 ) .
P e s e s e f ( ω 3 ) = e i f d i j k e j s e k s E e s ( ω 2 ) E e s ( ω 1 ) = d eff I ( θ , φ ) E e s ( ω 2 ) E e s ( ω 1 ) ,
P e f e s e f ( ω 3 ) = e i f d i j k e j s e k f E e s ( ω 2 ) E e f ( ω 1 ) = d eff I I ( θ , φ ) E e s ( ω 2 ) E e f ( ω 1 ) ,
P e s e f e f ( ω 3 ) = e i f d i j k e j f e k s E e f ( ω 2 ) E e s ( ω 1 ) = d eff I I I ( θ , φ ) E e f ( ω 2 ) E e s ( ω 1 ) ,
e i s = [ cos θ cos φ cos δ sin φ sin δ cos θ sin φ cos δ + cos φ sin δ sin θ cos δ ] ,
e i f = [ cos θ cos φ sin δ sin φ cos δ cos θ sin φ sin δ + cos φ cos δ sin θ sin δ ] ,
cot 2 δ = cot 2 Ω sin 2 θ cos 2 θ cos 2 φ + sin 2 φ sin 2 φ cos θ
Ω = arcsin ( n z n y n y 2 n x 2 n z 2 n x 2 )
d eff s s f = ( d 11 cos 3 φ + 3 d 12 sin 2 φ cos φ + 3 d 16 sin φ cos 2 φ + d 22 sin 3 φ ) cos 3 θ sin δ cos 2 δ [ d 11 sin 2 φ cos φ + d 12 ( 3 cos 2 φ 2 ) cos φ + d 16 ( 3 sin 2 φ 2 ) sin φ + d 22 sin φ cos 2 φ ] cos θ sin 3 δ + 2 [ d 11 sin 2 φ cos φ d 12 ( 3 sin 2 φ 1 ) cos φ d 16 ( 3 cos 2 φ 1 ) sin φ + d 22 sin φ cos 2 φ ] cos φ sin δ cos 2 δ + 2 [ d 11 sin φ cos 2 φ d 12 ( 3 cos 2 φ 1 ) sin φ + d 16 ( 3 sin 2 φ 1 ) cos φ d 22 sin 2 φ cos φ ] cos 2 θ sin 2 δ cos δ [ d 11 sin φ cos 2 φ d 12 ( 3 cos 2 φ 1 ) sin φ + d 16 ( 3 sin 2 φ 1 ) cos φ d 22 sin 2 φ cos φ ] cos 2 θ cos 3 δ ( d 11 sin 3 φ + 3 d 12 sin φ cos 2 φ 3 d 16 sin 2 φ cos φ d 22 cos 3 φ ) sin 2 δ cos δ [ 3 ( d 13 cos φ + d 23 sin φ ) cos θ sin δ cos δ + ( d 13 sin φ d 23 cos φ ) ( 3 cos 2 δ 2 ) ] sin 2 θ cos δ d 14 [ sin 2 θ cos 2 φ cos δ ( 3 sin 2 δ 1 ) + sin θ sin 2 φ sin δ ( 3 cos 2 θ cos 2 δ + 3 cos 2 δ 1 ) ] + ½ ( d 15 d 24 ) sin 2 θ sin 2 φ ( 3 cos 2 δ 2 ) cos δ + ( d 15 sin 2 φ + d 24 cos 2 φ ) sin θ ( 3 sin 2 δ 2 ) sin δ + [ d 33 sin 2 θ + 3 ( d 15 cos 2 φ + d 24 sin 2 φ ) cos 2 θ ] sin θ sin δ cos 2 δ ,
d eff s f f = d eff f s f = + ( d 11 cos 3 φ + 3 d 12 sin 2 φ cos φ + 3 d 16 sin φ cos 2 φ + d 22 sin 3 φ ) cos 3 θ sin 2 δ cos δ + [ d 11 sin 2 φ cos φ + d 12 ( 3 cos 2 φ 2 ) cos φ + d 16 ( 3 sin 2 φ 2 ) sin φ + d 22 sin φ cos 2 φ ] cos θ cos 3 δ 2 [ d 11 sin 2 φ cos φ d 12 ( 3 sin 2 φ 1 ) cos φ d 16 ( 3 cos 2 φ 1 ) sin φ + d 22 sin φ cos 2 φ ] cos θ sin 2 δ cos δ + 2 [ d 11 sin φ cos 2 φ d 12 ( 3 cos 2 φ 1 ) sin φ + d 16 ( 3 sin 2 φ 1 ) cos φ d 22 sin 2 φ cos φ ] cos 2 θ sin δ cos 2 δ [ d 11 sin φ cos 2 φ d 12 ( 3 cos 2 φ 1 ) sin φ + d 16 ( 3 sin 2 φ 1 ) cos φ d 22 sin 2 φ cos φ ] cos 2 θ sin 3 δ ( d 11 sin 3 φ + 3 d 12 sin φ cos 2 φ 3 d 16 sin 2 φ cos φ d 22 cos 3 φ ) sin δ cos 2 δ + [ 3 ( d 13 cos φ + d 23 sin φ ) cos θ sin δ cos δ ( d 13 sin φ d 23 cos φ ) ( 3 sin 2 δ 2 ) ] sin 2 θ sin δ + d 14 [ sin 2 θ cos 2 φ sin δ ( 3 cos 2 δ 1 ) sin θ sin 2 φ cos δ ( 3 cos 2 θ sin 2 δ + 3 sin 2 δ 1 ) ] + ½ ( d 15 d 24 ) sin 2 θ sin 2 φ ( 3 sin 2 δ 2 ) sin δ ( d 15 sin 2 φ + d 24 cos 2 φ ) sin θ ( 3 cos 2 δ 2 ) cos δ [ d 33 sin 2 θ + 3 ( d 15 cos 2 φ + d 24 sin 2 φ ) cos 2 θ ] sin θ sin 2 δ cos δ ,
d i l = ( ± d 11 ± d 12 ± d 13 d 14 0 0 0 0 0 0 d 14 ± d 12 0 0 0 0 ± d 13 ± d 14 )
d i l = ( 0 0 0 0 ± d 15 d 16 d 16 d 22 d 23 ± d 24 0 0 ± d 15 ± d 24 ± d 33 d 23 0 0 )
d i l = ( 0 0 0 d 14 0 ± d 16 ± d 16 ± d 22 ± d 23 0 d 14 0 0 0 0 ± d 23 0 d 14 )
d i l = ( ± d 11 ± d 12 ± d 13 0 d 15 0 0 0 0 d 24 0 ± d 12 d 15 d 24 d 33 0 ± d 13 0 )
d i l = ( 0 0 0 d 14 ± d 15 0 0 0 0 ± d 24 d 14 0 ± d 15 ± d 24 ± d 33 0 0 d 14 )
d i l = ( d 11 d 12 d 13 0 0 ± d 16 ± d 16 ± d 22 ± d 23 0 0 d 12 0 0 0 ± d 23 d 13 0 )
d e f f s s f
d e f f f s f = d e f f s f f
d e f f s s f
d e f f f s f = d e f f s f f

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