New nonlinear-optical crystal: LiB 3 05

Transcription

1 616 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989 Chen et al. New nonlinear-optical crystal: LiB 3 05 Chuangtian Chen Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, , China Yicheng Wu Department of Applied Chemistry, University of Science and Technology of China, Hefei, Anhui, China Aidong Jiang, Bochang Wu, Guiming You, Rukang Li, and Shujie Lin Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, , China Received May 26, 1988; accepted December 6, 1988 The boron-oxygen compound LiB is recognized as a new nonlinear-optical crystal. This follows theoretical calculations of the second-harmonic generation (SHG) coefficients using the anionic group theory and the complete neglect of differential overlap approximation to obtain the localized wave functions of component groups. An optically perfect single crystal with space group P, 2021, grown at the Fujian Institute of Research on the Structure of Matter by the high-temperature flux method, is found to be transparent from 160 nm to 2.6 rim. It has a SHG coefficient comparable with that of P-BaB as well as two other outstanding advantages: a high damage threshold of 25 GW/cm 2 (at um, 0.1 nsec) and a wide acceptance angle of 25 mrad for 0 $ 900 and 95 mrad for 0 = 900 with a 6-mm-long crystal. INTRODUCTION There are numerous structural types of boron-oxygen compounds, since the boron atoms may have either three or four coordinations. This gives great potential for theoretically choosing structural types favorable for new nonlinear-optical (NLO) crystals. Also, crystals of such compounds grown by the high-temperature flux method generally have high optical quality, a high damage threshold, chemical stability, and transparency far into the ultraviolet. These particular properties led us to search for new ultraviolet NLO crystals among the borates. As early as 1979, we suggested a theoretical model called the anionic group theory' for the NLO susceptibility of the crystals. The model pointed out systematically the relationship between the structure of the component groups of atoms of a crystal and facility of second-harmonic generation (SHG), and it gave an approximate method for calculating the crystal's macroscopic NLO susceptibilities from the microscopic NLO susceptibilities of the groups. This allowed us to propose some structural criteria for searching for NLO crystals among the borates. 2 In particular, we pointed out that the (B ) 3 - planar group is more likely to produce a larger second-harmonic susceptibility than other nonplanar groups in the borate series. This led to the discovery by us and our co-workers of the new NLO crystal, f-bab 2 04 (BBO). 3 Theoretical calculations of the SHG coefficients for this and other crystals, 4 ' 5 notably KB (OH) 4-2H 2 0 (KB5) were made in terms of the anionic group theory, using the complete neglect of differential overlap (CNDO) approximations 6 to calculate the localized electronic structure of the particular component groups. The calculated SHG coefficients for the BBO crystal were found to be in good agreement with the experimental data. 4 These theoretical and experimental results indicated that although the (B ) 3 - group of BBO has some important advantages for ultraviolet NLO applications, it has two deficiencies, which are not present for nonplanar groups such as the B0 4 and B structural units of KB5. 2, 7 First, because of the 7r-electron system, the ultraviolet absorption edge of the B group is at a longer wavelength than that of the nonplanar groups such as B0 4 and B For example, the ultraviolet absorption edge of BBO is at 190 nm, nearly 30 nm longer than that of KB5. 8 Obviously this restricts the use of the BBO crystal at wavelengths below 200 nm. Second, owing to the symmetry of the B30 6 planar group and the arrangement of B groups within the BBO crystal, 4 all z components of the SHG coefficients of the crystal are small or even zero. Obviously, if the SHG coefficients possess small z components, the effective SHG coefficients (deff) will be reduced essentially to zero because of the cos Opm factor, when the phase-matching angle pm changes from a small angle to 90. Once again, this restricts the use of the BBO crystal at wavelengths under 200 nm. Since these deficiencies are not present for nonplanar groups, we sought to find a compromise between planar and nonplanar groups. Indeed, it was demonstrated 2 that if one of the boron atoms in the B planar group is changed from triagonal to tetrahedral coordination, thereby forming a B group, the z components of the microscopic NLO susceptibilities, for example, X133, become larger, while xi,, and X122 remain the same. At the same time, the ultraviolet /89/ $ Optical Society of America

2 Chen et al. absorption edge moves to a shorter wavelength, as the tetrahedral coordination of the boron atom in the B group partially destroys the 7r-conjugated electron system. In this paper we first present calculations of the SHG coefficients for two crystals with the B group, CsB 3 05 and LBO. Next, we discuss the growth of LBO crystals of useful size and optical quality, and finally we present the results of measurements of the linear-optical and NLO properties, including the powder SHG test, and measurements of the damage threshold. From these considerations, it is found that LBO is a promising new NLO crystal. THEORETICAL BACKGROUND According to the anionic group theory,' the NLO susceptibility in crystals is a localized effect arising from the action of incident photons on the electrons in certain clusters of orbitals. The appropriate grouping of orbitals may be an anionic group for inorganic crystals (or a molecule for molecular crystals), and this grouping is thought of as the basic structural unit and primary source of the NLO susceptibilities. Therefore, to calculate the bulk SHG coefficient of the crystals, we made two basic assumptions in the theoretical model. First, the overall SHG coefficient of the crystal is the geometric superposition of all the microscopic SHG coefficients of the relevant groups (or molecules) and has nothing to do with the spherical cation. The former can be expressed as n Xijk( 2 w) = N E aii X ajj X akk'x X P)A,,(2w), (1) p=l i'j'k' where N is the number of cells per unit volume, n is the number of groups in the unit cell, aji', ajj,, and cakk' are the direction cosines of the group Cartesian axes with the crys- Table 1. Microscopic SHG Coefficients of the B Group in CsB and LBOa a Units: Xijk CsB LBO esu. Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 617 tallographic axes, and x(ov(20) is the microscopic SHG coefficient of the pth group in the unit cell. Second, the microscopic SHG coefficients of the basic anionic groups (or molecular structural units) can be calculated from the localized wave functions of the groups (or molecules) by means of the second-order perturbation theory of the SHG coefficient given by the ABDP theory of Armstrong and co-workers 9 and in Ref. 10. Now, there are many methods available for the calculation of this localized wave function, such as the various approximation methods and even the recently developed Dv-Xa method discussed in quantum chemistry. But, in view of the nature of the basic assumptions of our theory, the CNDO approximation seems to serve our purpose here, and it is not necessary to use higher approximations. There are three known noncentric crystals, CsB 3 0 5, TIB 3 0 5, and LBO, with the B group as the structural unit for the borate. CsB and TIB are isomorphous orthorhombic crystals belonging to the space group P , while LBO is also orthorhombic, although it belongs to Pna 21 On the basis of the assumptions of our theoretical model, it is obvious that CsB and TIB should have almost the same SHG coefficients. The structures of CsB and LiB have been determined by Krogh-Moe" and Konig and Hoppe. 1 2 The unit cell dimensions of CsB30 5 are a = ± 0.001, b = ± 0.001, c = ± A, and z = 2. Those of LiB are a = ± , b = ± , c = ± A, and z = 2. Both crystals are built up of a continuous network of B groups with cesium and lithium cations, respectively, located in the interstices. Two B groups share one oxygen atom and are connected to form endless chains running parallel to one axis. These chains are then interlinked by B-O bonds. Using the crystal structure data, we have calculated the microscopic SHG coefficients of the B group in CsB 3 05 and LBO crystals with the CNDO-type approximation to calculate the electronic wave function of the group. The results are listed in Table 1. There are three nonzero SHG coefficients, i.e., X333, X311, and X322, for the ideal B group with C 2, symmetry 13 and the Kleinman symmetry condition. But the B groups in both CsB and LiB crystals have 10 nonzero microscopic SHG coefficients. This is due to the distortion and spatial arrangement of the B groups in the actual crystals. Because of the restrictions of the crystal symmetry, there are few microscopic coefficients that can contribute to the macroscopic ones. For CsB 3 0 5, all coefficients except d 14 vanish, and for LBO only d 33, d 3 l, and d 32 are nonzero. Using Eq. (1) and the results listed in Table 1, we calculat- Table 2. SHG Coefficients of LBO and CsB Crystalsa Crystal d 33 d 32 d 3 l d14 LBO Calculated Experimental ( ) ( ) '2.75 ( ) CsB Calculated 2.06 a Units: 10-9 esu, X = 1.079jgin. d 36 (KDP) = 1.1 X 109esu.

3 618 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989 Chen et al. I c.41) C: CC Co 0-L c a c ~~D O CD CDO E c'j '-.r 10 r M~ C 4 C'4 4 i CNJ C`J C Fig. 1. Ultraviolet transmission spectrum of th lelb( ) crystal at wavelengths between 110 and 280 nm. ed the macroscopic SHG coefficients of the two crystals, and they are listed in Table 2. These calculated results indicate two important facts that are useful when one is searching for new NLO crystals in the B-O compounds with the B group as a structural unit: (1) The LBO crystal will produce rather large z components of the SHG coefficients, which are useful in generating coherent light in the ultraviolet range and for noncritical phase maching (90 phase matching). In addition, since the tetra-coordinated B atom destroys the 7rconjugated electron system in the B-O ring, the absorption edge of the crystal consisting of B groups will move toward a shorter wavelength in the ultraviolet region than that of the BBO crystal. 3 (2) The microscopic SHG components X222 of both the LBO and CsB crystals are three to five times higher than that of other components. Unfortunately, however, in both crystals X222 is canceled by that of other equivalent B groups. It might be expected that a crystal with isolated B groups could produce a much larger SHG effect than that of LiB30 5, if the spatial arrangement of the groups were more favorable for a constructive superposition of this large component. CRYSTAL GROWTH The phase diagram of the pseudobinary system Li 2 O-B was first studied by Sastry and Hummel,1 4 who pointed out that there is a new compound, Li 2 O:3B (LiB30 5 ), the melting point of which is near 8340C. Then, in 1978, Konig and Hoppe prepared a single crystal of LiB by the solidreaction method and determined its space group as Pna2,. Furthermore, in 1980, a 1 mm X 1 mm X 4 mm single crystal with the same space structure as that of Konig was grown by Ihara and Yuge,1 2 who used vapor deposition. Now even larger perfect single crystals of LiB 3 0 5, with an approximate size of 30 m X 30 m X 15 mm, have been grown at our institution by using the high-temperature solution top-seeding method. The experimental setup and processing are as follows: A platinum crucible 40 mm in height and 40 mm in diameter is charged with a homogeneous mixture of Li 2 O and H 3 BO 3 and then placed into a furnace with an ambient material made of A and aluminum to stabilize the temperature. The furnace is then sealed with a cover that has a hole for insertion of the seed. The furnace is heated rapidly to a temperature of 9500C with a nickel-chromium heating wire and after 5 h cooled rapidly to 8480C. A seed crystal of LBO oriented along the C 2 axis is inserted slowly into the crucible and kept in contact with the surface of the melt, while a temperature of 8480C is maintained for half an hour. The melt is then cooled rapidly to C, and then the temperature is slowly reduced to C at a rate of C/ day until the end of the growth. The crystal thus obtained is pulled from the melt and then cooled to room temperature at a rate of 400C/h. Owing to the small interstices of the LBO lattice, which consist of endless (B ),- helices, it is not easy for cations other than Li+ to enter the interstices of the lattice. As a result, the crystal tends to be inclusion free, even though the crystals are grown from flux. Therefore all the crystals grown by the high-temperature solution top- Table 3. Principal Refractive Indices of LBO X (um) nx ny( 2 1)a n ny is the principal refractive index along the 21 axis of LBO.

4 Chen et al. Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 619 (0 than that of the BBO crystal. Figure 1 shows the transmission spectrum of the LBO crystal from 110 to 280 nm. The transparent range of the crystal is 160 nm to 2.6 Am. Obvi- I W ously, this is useful for applications in the ultraviolet range. 20I ( REFRACTIVE INDICES Using the method of the least angle of deflection, we mea-.50]0 sured the three principal refractive indices of LBO at 16 wavelengths from X = Am to X = gm as listed in 40i Table 3; Eqs. (2) are their Sellmeier equations. The values 400 calculated from them are exactly consistent with experiment00 tal ones to four significant digits: n,2= , ' ny2= _ X 2 i I I I I I I I J I(0) Fig. 2. Stereographic plot of the phase-matching loci of both Type I and Type II for SHG from im in LBO. (mv 20- n,2 = _ X2, (2) o( He t 8 Type I, 9S=10.73 B~~~~6=9( pm=6mm m~~~p -60 i i =95mrad l s (sec) 0 Fig. 4. Units: Angle-tuned curve of SHG for a Nd:YAP laser at 1.079,um. 2 /60 sec sn (0) Fig. 3. Stereographic plot of the phase-matching loci of both Type I and Type II for THG from gm in LBO. >4 c(2i) seeding method have high optical quality and transmission in the ultraviolet range. ABSORPTION SPECTRA As was pointed out in Ref. 2, because one of the boron atoms in the B30 7 group becomes tetra coordinated, the specific 7rconjugated electron system of the original B30 6 planar group has been destroyed, thereby moving the absorption edge of crystals, consisting of the B group, to a shorter wavelength. The ultraviolet absorption edge of the LBO crystal is thus lowered to a wavelength of 160 nm,' 5-30 nm shorter C'U) Temperature (C) Fig. 5. Temperature-tuned curve of noncritical phase matching for Nd:YAP laser at 1.079,um.

5 620 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989 Chen et al. (mv)l NA Fig. 6. Units: (mv) As the crystal lattice of LBO is built up of endless helices of (1307)n-, the interstices between helices are so small that only the Li+ cation can enter them. This ensures that the crystals are inclusion free, even though they are grown from flux. It is well known that a crystal that contains inclusions will have a greatly reduced damage threshold, as happens for the BBO crystal. The inclusion-free nature of LBO is thus favorable for increasing the damage threshold of this crystal. In addition, since the band gap of LBO is as wide as 7.75 ev, and the crystal lattice of LBO is so compact, production and transportation of ions and electrons along the lattice do not occur easily, even with intense laser irradiation, thereby favoring a high damage threshold. Using a Q-switched Nd:YAG laser with a pulse energy of 2.3 J, a pulse duration of 0.1 nsec, and X = gm, the damage thresholds of LBO, BBO, and KDP crystals were measured and compared. The results shows that the surface damage threshold of LBO is as high as 25 GW/cm 2,1 7 that is, 3.57 times higher than that of KDP and 1.6 times higher than that of BBO. To our knowl _8-0 Fig. 7. LBO. i. : i :.. V :.. ::... :.~ Maker fringe of the 2 /60 sec.. :i ' d,3 2 coefficient at Calculated Maker fringe of the d3 2 coefficient Units: 2/60 sec. where the wavelength, X, is in micrometers. Phase-matching conditions for SHG and third-harmonic generation of a YAG laser at m have been calculated and are shown in Figs. 2 and 3. The measurements of the phase-matching angles for 0 = 900 in one principal plane are exactly in agreement with the calculated ones. The preliminary measurements show that the acceptance angles of a 6-mm-long LBO crystal are 95 mrad for 0 = 900 and 25 mrad for Figure 4 shows a typical angletuned curve for SHG of a YAG laser at gm with 0 = 900. The phase-matching angles for type I SHG, which give the angles between the propagation direction of the laser beam and the a and b axes of the crystal, are 0 = and 0 = 900 respectively, so the coherence length is as long as 266 gm for a wavelength of A = m. Therefore it should be possible to achieve noncritical phase matching by adjusting the temperature of the crystal. This was confirmed by our experimental results. Figure 5 shows the temperature-tuning curve for SHG from the LBO crystal cut along the a, b, and c axes with the a axis as the propagation direction of the fundamental wave, as shown in the insert. The noncritical phase-matching temperature of the crystal is T = 112'C. We will give a more detailed discussion of this experimental result in a later paper. NONLINEAR-OPTICAL PROPERTIES It is known that the LBO crystal, with point group C 2,, has five NLO coefficients, namely, d3l, d3 2, d33, d1 5, and d 24. All these NLO coefficients were measured by the Maker fringe method, using a homemade rotating-mirror Nd:YAP laser at X = gm and a Princeton Applied Research Model 4420/ 4402 boxcar averager, with the d3 6 Maker fringe of KDP as a standard. Figure 6 shows the measurement of the d3 2 coefficient, which agrees well with the theoretical curve shown in 2000 (sec) Fig. 7, which was calculated by our formula and that of Ref. im in LBO. 16. Table 2 lists the results of all five NLO coefficients of the LBO crystal as calculated from the Maker fringe measurements. To verify these results, the d3 2 coefficient was also determined by the phase-matching method, using a Nd:YAG laser at 1.064,gm. For type I phase matching with 0 = 900, 0 = 10.73, as represented in Fig. 2, the effective NLO coefficient for LiB30 5 is deff d, cos (3) In the measurement, deff of the BBO crystal with a type I phase-matching condition is used as a standard. The result obtained, d32 = ( )d3 6 KDP, is consistent with the d 2 value given by the Maker fringe method in Table 2. The above SHG measurements show that the agreement between the calculated and experimental values is satisfactory (cf. Table 2). All these measurements, including noncritical phase-matching achieved by adjusting the tempera (sec) ture of the crystal, have verified the results of our calculations. tt im in DAMAGE THRESHOLD

6 Chen et al. edge, the surface-damage threshold of the LBO crystal is the highest of any NLO crystal measured so far. MISCELLANEOUS CHARACTERISTICS OF THE CRYSTAL The crystal is chemically stable and is not hydroscopic. It has good mechanical properties for easy cutting and polishing. Its hardness is close to that of silica glass. ACKNOWLEDGMENTS This research is supported by the Science Fund of the Chinese Academy of Sciences, and the authors thank Lloyd Davis and Qi-xian Chen for their assistance in the preparation of this manuscript. The following colleagues of the authors participated in some phases of this work: Lin-hua Yu, Nong Chen, Chaoyang Sun, and Lin Qi. REFERENCES AND NOTES 1. C. T. Chen, Sci. Sin. 22, 756 (1979). 2. C. T. Chen, Y. C. Wu, and R. K. Li, Chin. Phys. Lett. 2, 389 (1985). Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B C. T. Chen, B. Wu, A. Jiang, and G. You, Sci. Sin. B 28, 235 (1985). 4. R. K. Li and C. T. Chen, Acta Phys. Sin. 34, 823 (1985). 5. Y. C. Wu and C. T. Chen, Acta Phys. Sin. 35, 1 (1986). 6. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory (McGraw-Hill, New York, 1970). 7. C. T. Chen, Y. C. Wu, and R. K. Li, Int. Rev. Phys. Chem. (to be published). 8. R. E. Stickel, Jr., and F. B. Dunning, Appl. Opt. 17, 981 (1978). 9. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962). 10. C. T. Chen, Z. P. Liu, and H. S. Shen, Acta Phys. Sin. 30, 715 (1981). 11. J. Krogh-Moe, Acta Crystal. 13, 889 (1960); B 30, 1178 (1974). 12. H. Konig and A. Hoppe, Z. Anorg. Allg. Chem. 439,71 (1978); M. Ihara, M. Yuge, and J. Krogh-Moe, Yogyo Koyokai Shi 88, 179 (1980). 13. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1985). 14. B. S. R. Sastry and F. A. Hummel, J. Am. Ceram. Soc. 41, 7 (1958). 15. The transmission of the LiB30 5 crystal in the ultraviolet range was measured by R. H. French, Central Research and Development Department, E. I. DuPont de Nemours and Company. 16. J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970). 17. The damage threshold of the LiB305 crystal was measured by Dianyuan Fan, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences.