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

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.

[1]  W. Jiyang,et al.  Anisotropy of Nonlinear-Optical Property of RCOB (R= Gd, Y) Crystal , 2001 .

[2]  Zheshuai Lin,et al.  Mechanism for linear and nonlinear optical effects in monoclinic bismuth borate (BiB3O6) crystal , 2001 .

[3]  Xiufeng Cheng,et al.  Crystal growth, thermal and optical performance of BiB3O6 , 2001 .

[4]  D. Lammers,et al.  Nonlinear optical properties of borate crystals , 2000 .

[5]  Subsolidus phase equilibria of the CaO-B2O3-BaO system , 1995 .

[6]  Zheshuai Lin,et al.  The development of new borate-based UV nonlinear optical crystals , 2005 .

[7]  Shengxia Zhang,et al.  Structural analysis of nonlinearities of Ca4ReO(BO3)3 (Re = La, Nd, Sm, Gd, Er, Y) , 1999 .

[8]  Jing-Pei Cao,et al.  Synthesis and characterization of a novel non-linear optical material La2SrB10O19 , 2000 .

[9]  David N. Nikogosyan,et al.  Effective nonlinearity coefficients for three-wave interactions in biaxial crystal of mm2 point group symmetry , 1993 .

[10]  A. Mosset,et al.  Crystal engineering strategy for quadratic nonlinear optics. Part II: Hg(IO3)2 , 2003 .

[11]  Masood Ghotbi,et al.  Optical second harmonic generation properties of BiB3O6. , 2004, Optics express.

[12]  Y. Mori,et al.  90° Phase-Matching Properties of YCa4O(BO3)3 and GdxY1-xCa4O(BO3)3 , 2001 .

[13]  P. Halasyamani,et al.  Combining second-order Jahn-Teller distorted cations to create highly efficient SHG materials: synthesis, characterization, and NLO properties of BaTeM2O9 (M = Mo6+ or W6+). , 2003, Journal of the American Chemical Society.

[14]  M. V. Hobden.  Phase‐Matched Second‐Harmonic Generation in Biaxial Crystals , 1967 .

[15]  Hiromasa Ito,et al.  Generalized study on angular dependence of induced second‐order nonlinear optical polarizations and phase matching in biaxial crystals , 1975 .

[16]  S. Payne,et al.  Nonlinear optical properties of LaCa(4)O(BO(3))(3). , 2001, Optics letters.

[17]  Gerard Aka,et al.  Nonlinear optical borate crystal Ba2B10O17 , 2001, SPIE LASE.

[18]  X. Long,et al.  Growth of nonlinear optical calcium pyroniobate crystal , 2005 .

[19]  Ladislav Bohatý,et al.  Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO) , 1998 .

[20]  Shaojun Zhang,et al.  Growth and noncritical phase-matching third-harmonic-generation of GdxY1−xCa4O(BO3)3 crystal , 2000 .

[21]  P. Halasyamani,et al.  Synthesis, Structure, and Characterization of a New Second-Harmonic-Generating Tellurite: Na2TeW2O9 , 2002 .

[22]  D. A. Roberts,et al.  Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions , 1992 .

[23]  Guibao Xu,et al.  Noncollinear second-harmonic generation in BiB 3 O 6 , 2004 .

[24]  Improved second-harmonic generation by selective Yb ion doping in a new nonlinear optical crystal YCa/sub 4/O(BO/sub 3/)/sub 3/ , 1999 .

[25]  Huaidong Jiang,et al.  The second-harmonic-generation property of GdCa4O(BO3)3 crystal with various phase-matching directions , 2001 .

[26]  B. Chai,et al.  The nonlinear optical properties of the XYB2O6 family of compounds , 2001 .

[27]  G. Montemezzani,et al.  Refractive indices of Sn2P2S6 at visible and infrared wavelengths. , 2005, Optics express.

[28]  R. Smith,et al.  Synthesis, Structure, and Properties of the Noncentrosymmetric Pyroborate BaCuB2O5 , 1997 .

[29]  V. Sirutkaitis,et al.  Optical, vibrational, thermal, electrical, damage, and phase-matching properties of lithium thioindate , 2004 .

[30]  Huaidong Jiang,et al.  Growth and investigation of a new nonlinear optical crystal: bismuth borate BiB3O6 ☆ , 2001 .

[31]  D. Cui,et al.  Efficient second harmonic generation in a new nonlinear La2CaB10O19 crystal , 2002 .

[32]  D. F. Eaton,et al.  Nonlinear Optical Materials , 1991, Science.

[33]  S. Xie,et al.  PHASE-RELATIONS IN THE SYSTEM AL2O3-B2O3-ND2O3 , 1991 .

[35]  J. Gavaldà,et al.  Crystal Growth, Structural Characterization, and Linear Thermal Evolution of KGd(PO3)4 , 2005 .

[36]  Hiroyuki Furuya,et al.  Crystal Growth and Optical Characterization of Rare-Earth (Re) Calcium Oxyborate ReCa4O(BO3)3 (Re=Y or Gd) as New Nonlinear Optical Material , 1997 .

[37]  Shoutian Zheng,et al.  K2[Ge(B4O9)].2H2O: a unique 3D alternating linkage mode of a B4O9 cluster and GeO4 unit in borogermanate with two pairs of interweaving double helical channels. , 2004, Inorganic chemistry.

[38]  David Eimerl,et al.  Deuterated L-arginine phosphate: a new efficient nonlinear crystal , 1988 .

[39]  M. Kanatzidis,et al.  α- and β-A2Hg3M2S8 (A = K, Rb; M = Ge, Sn): Polar quaternary chalcogenides with strong nonlinear optical response , 2003 .

[40]  M. Yoshimura,et al.  Crystal growth and characterization of GdxY1-xCa4O(BO3)3 crystal , 1999 .

[41]  Jiao Y. Y. Lin,et al.  Determination of the nonlinear optical coefficients of YCa 4 O(BO 3 ) 3 crystal , 2000 .

[43]  T. Fahlen,et al.  Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4 , 1984 .

[44]  J. Gavaldà,et al.  Crystallization Region, Crystal Growth, and Phase Transitions of KNd(PO3)4 , 2003 .

[45]  François Salin,et al.  Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca 4 GdO(BO 3 ) 3 , 1997 .

[46]  Y. Mori,et al.  Design and growth of new NLO crystals for UV light generation , 2005 .

[47]  V. A. D'yakov,et al.  Optical and nonlinear optical properties of LiNaCO3 single crystals , 1999, Other Conferences.

[48]  B. Boulanger,et al.  Linear and nonlinear optical properties of the monoclinic Ca 4 YO(BO 3 ) 3 crystal , 2004 .

[49]  Ladislav Bohatý,et al.  Linear optical properties of the monoclinic bismuth borate BiB3O6 , 2000 .

[50]  Petra Becker,et al.  Borate Materials in Nonlinear Optics , 1998 .

[51]  Gerard Aka,et al.  Crystal growth and optical properties of rare earth calcium oxoborates , 2002 .

[52]  Huaidong Jiang,et al.  Optical and thermal properties of nonlinear optical crystal LaCa4O(BO3)3 , 2003 .

[53]  Bruce H. T. Chai,et al.  Crystal growth of YCa4O(BO3)3 and its orientation , 1999 .

[54]  K. Friese,et al.  Characterization of the room-temperature phase of Tl2MoO4: crystal structure, symmetry mode analysis and second-harmonic generation measurements. , 2001, Acta crystallographica. Section B, Structural science.

[55]  Martin Richardson,et al.  Second harmonic generation in Yb doped YCa4O(BO3)3 , 1998 .

[56]  P. Halasyamani,et al.  Synthesis and characterization of Te2SeO7 : A powder second-harmonic-generating study of TeO2, Te2SeO7, Te2O5, and TeSeO4 , 2001 .

[57]  Yicheng Wu,et al.  Growth of a nonlinear optical crystal La2CaB10O19 (LCB) , 2003 .

[58]  Z. Shao,et al.  Studies on the effective nonlinear coefficient of GdCa4O(BO3)3 crystal , 1999 .

[59]  Ning Ye,et al.  Computer-Assisted Search for Nonlinear Optical Crystals , 1999 .

[60]  Jian-fu Li,et al.  Crystal growth and spectroscopic characterizations of pure and Nd3+-doped Cd3Y(BO3)3 crystals , 2004 .

[61]  Chuangtian Chen,et al.  A New Lanthanum and Calcium Borate La2CaB10O19 , 2001 .

[62]  D. Armstrong,et al.  Measurement of the chi^(^2^) tensor of GdCa~4O(BO~3)~3 and YCa~4O(BO~3)~3 crystals , 2005 .

[63]  P. Halasyamani,et al.  Hydrothermal preparation, structures, and NLO properties of the rare earth molybdenyl iodates, RE(MoO2)(IO3)4(OH) [RE = Nd, Sm, Eu]. , 2003, Inorganic chemistry.