Development of New Nonlinear Optical Crystals in the Borate Series

Chapter 24

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Development of New Nonlinear Optical Crystals in the Borate Series Chuangtian Chen Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, 350002 China

This review gives a brief presentation of the basic concepts and calculation methods of the "anionic group theory" for the NLO effect in borate crystals. On this basis, boron-oxygen groups of various known borate structure types have been classified and systematic calculations were carried out for microscopic second -order susceptibilities of the groups. Through these calculations, a series of structural criteria serving as useful guidelines for finding and developing new NLO crystals in the borate series were found: (1) The planar six-membered ring (B O ) and the planar trigonal (BO ) group, each possessing a conjugated π-orbital system, are far more favourable for producing larger second-order susceptibilities' and anisotropy of linear susceptibilities than the non -planar tetrahedral (BO ) group. (2) On the other hand, the ultraviolet absorption edges of non-planar groups, such as (ΒΟ ) (B O ) - are shifted to shorter wavelengths than those of the (B O ) and (BO ) groups. (3) The SHG coefficients and birefringences of borate crystals can be adjusted to a certain extent by suitable arrangement of the 3- and 4coordinated Β atoms, e.g. (BO ) and (BO ) (Β O ) vs (B O ) and ( B O ) · On the basis of these structural criteria, we have been successful in developing some excellent new NLO materials, including LiB O (LBO). 3-

3-

3

6

3

6

3

5-

4

5-,

5

4

3

7

3-

3-

3

3-

3

5-

3

7

5-,

4

3-

3

6

7 -

3

8

3

5

The rapid development of laser science and technology which occurred after 1960 included the elucidation of the theoretical principles for designing

0097-6156/91/0455-0360$06.00/0 © 1991 American Chemical Society In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


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Nonlinear Optical Crystak in the Borate Series

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nonlinear o p t i c a l (NLO) d e v i c e s . The major remaining problem that severly r e s t r i c t s progress i n t h i s f i e l d is the scarcity of appropriate NLO m a t e r i a l s . As a r e s u l t , the search for new NLO m a t e r i a l s , p a r t i c u l a r l y in the UV and FAR-IR regions, i s s t i l l very a c t i v e , even though intensive e f f o r t s in this f i e l d have been made for about 20 y e a r s f l ] . S c i e n t i s t s searching for new NLO materials r e a l i s e the importance of a thorough e l u c i d a t i o n of the s t r u c t u r e - p r o p e r t y r e l a t i o n s h i p between NLO e f f e c t s and m i c r o s t r u c t u r e . Many attempts have already been made i n t h i s d i r e c t i o n . Among them i n p a r t i c u l a r we may c i t e the bond parameter methods, exemplified by the work of Bloembergen[2]; the anharmonic o s c i l l a t o r models of Kurtz and Robinson[3] and Garrett and Robinson[4]; the bond parameter methods of Jeggo and Boyd[5] and Bergman and Crane[6]; and the bond charge model of Levine[7] before the 1970s. Among these, the Levine [7, 8,] model i s the most successful, and has been shown to be particularly useful in elucidating the structureproperty r e l a t i o n s h i p for NLO e f f e c t s i n A-B type semiconductor materials., the basic s t r u c t u r e u n i t of which c o n s i s t s of S P - h y b r i d t e t r a h e d r a l l y coordinated atoms. However, t h i s method has not been so successful for other types of NLO c r y s t a l s i n which the basic structural u n i t does not belong to the category of simple σ - t y p e bonds. For example, i f such a bond charge model should be extended to ferroelectric crystals c o n s i s t i n g of oxygen octahedra with t r a n s i t i o n metal atoms as the centres, one must introduce new parameters that have some kinds of u n c e r t a i n t y [9, 10]. As a result, it would be d i f f i c u l t to use the model to understand the s t r u c t u r e - p r o p e r t y r e l a t i o n between NLO p r o p e r t i e s and microstructures of the c r y s t a l s except the above A-B type semiconductor m a t e r i a l s . Since the 1970s, Several research groups have discovered that n o n - l i n e a r s u s c e p t i b i l i t i e s of c r y s t a l s arise from basic structural units with d e l o c a l i z e d valence electron orbitals belonging to more than two atoms, rather than with those l o c a l i z e d around two atoms connected by a simple σ - t y p e bond. Davydov et a l [11] showed that n o n - l i n e a r s u s c e p t i b i l i t i e s of organic c r y s t a l s a r i s e from molecules as t h e i r basic structural units, and proposed that conjugated organic molecules with donor-acceptor radicals w i l l exhibit large non-linear susceptibilities. This idea was further developed by Chemla et al. [12], Oudar and Chemla [13] and Oudar and Leperson [14], enabling them and others to discover a series of new organic NLO crystals exhibiting very large second-order s u s c e p t i b i l i t i e s , such as POM [ 1 δ ] , NPP [16] ABP [17] as well as DAN [18]. Furthermore i t helped to e s t a b l i s h 3

In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


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MATERIALS FOR NONLINEAR OPTICS: CHEMICAL PERSPECTIVES

the s c i e n t i f i c basis of a new approach i n the f i e l d of organic NLO materials, known as 'molecular engineering'. During 1968 - 1970, DiDomenico & Wemple [19] found that the non-linear s u s c e p t i b i l i t i e s of perovskite and tungsten-bronze type materials are l a r g e l y due to the d i s t o r t i o n i n ΒΟβ oxygen-octahedra. Thus, the l a t t e r i s considered as the basic s t r u c t u r a l u n i t for the production of n o n - l i n e a r s u s c e p t i b i l i t y i n these c r y s t a l s . But because they only used a parametric method, known as the p o l a r i z a t i o n p o t e n t i a l tensor ioi j , i t i s impossible to a s c e r t a i n the r e l a t i o n s h i p between the electronic structure of ΒΟβ oxygen-octahedra and t h e i r macroscopic second-order s u s c e p t i b i l i t i e s . As e a r l y as 1967, during a very d i f f i c u l t p e r i o d i n China, we i n i t i a t e d an extensive study to develop a general quantum- chemical NLO-active group theory i n order to make a systematic e x p l o r a t i o n of the s t r u c t u r e - p r o p e r t y r e l a t i o n s h i p for NLO e f f e c t s i n some typical inorganic NLO c r y s t a l s then known. This work has l e d to the establishment of the s o - c a l l e d "anionic group" theory [20,21] and an approximate method of c a l c u l a t i o n based on the second-order pertubation theory for NLO s u s c e p t i b i l i t i e s of c r y s t a l s [ 2 2 , 2 3 ] . On the basis of this theoretical model, Chen's group succeeded i n a systematic e l u c i d a t i o n of the s t r u c t u r e property r e l a t i o n s h i p for the NLO e f f e c t for almost a l l the p r i n c i p a l types of inorganic NLO c r y s t a l s , namely the perovskite and tungsten-bronze[24], phosphate [25], iodate[26], n i t r i t e c r y s t a l s [22] e t c . Since 1979 Chen's group has turned i t s a t t e n t i o n to borates. They recognized that borate compounds have numerous s t r u c t u r a l types since borate atoms may have e i t h e r three or f o u r - f o l d c o o r d i n a t i o n . This complex s t r u c t u r a l nature of borate compounds leads to a great variation i n the selection of s t r u c t u r a l types favorable for the NLO e f f e c t , and the anionic group theory can be used to systematically e l u c i d a t e which structural unit is most likely to exhibit large n o n - l i n e a r i t i e s [ 2 7 ] . This a c t i v e theoretical analysis and systematic experimental work lead our group to discover BBO (barium metaborate, fl-BaB2 04), which i s a h i g h - q u a l i t y UV NLO borate c r y s t a i [ 2 8 ] . Following the discovery of BBO, much broader theoretical activities were conducted to extend structure-property relations from NLO phenomena to linear optical (LO) p r o p e r t i e s of the c r y s t a l s as well[29]. C e r t a i n LO p r o p e r t i e s of c r y s t a l s , such as transparency range and phase-matching range are important for s o p h i s t i c a t e d t e c h n i c a l a p p l i c a t i o n s i n o p t i c - e l e c t r o n i c f i e l d s . Extensive t h e o r e t i c a l analyses made by our group i n the past year involve c a l c u l a t i o n s of the UV absorption edges and the b i r e f r i n g e n c e of



24.

CHEN

Nonlinear Optical Crystals in the Borate Series

363

c r y s t a l s . It was shown t h a t u s i n g t h e D v - S C M - Χ α method the a b s o r p t i o n edges o f c r y s t a l s in UV range may be e v a l u a t e d i n terms o f the components t h a t a r e the basic s t r u c t u r a l u n i t s o f the c r y s t a l s . T h i s t h e o r e t i c a l work e n a b l e d our group to appraise in a sophisticated way the UV properties of borate NLO crystals at a microstructure level. This led directly to the d i s c o v e r y o f a n o t h e r new UV NLO c r y s t a l — LiB305(LBO) [ 3 0 ] , w h i c h p o s s e s s e s some b e t t e r NLO and LO p r o p e r t i e s than BBO. All these theoretical and experimental advances have encouraged us to try to set up a s c i e n t i f i c basis for molecular engineering suitable for inorganic NLO materials as s c i e n t i s t s have done f o r o r g a n i c NLO materials. In the following part we will give a brief d e s c r i p t i o n of the " a n i o n i c group t h e o r y " f o r the NLO effects in crystals, including the b a s i c c o n c e p t s and calculation methods adopted. In the n e x t s e c t i o n we w i l l discuss how to use this theoretical model t o develop new UV NLO crystals in the b o r a t e s e r i e s . F i n a l l y , the measurements and c h a r a c t e r i s t i c features o f t h e NLO p r o p e r t i e s o f t h e s e new b o r a t e c r y s t a l s w i l l be d i s c u s s e d .

I.

The A n i o n i c Group T h e o r y and t h e Methods o f A p p r o x i m a t e Quantum-Chemical MO T h e o r y A d o p t e d f o r the C a l c u l a t i o n o f t h e NLO Susceptibilities of C r y s t a l s

Here we give only a b r i e f d e s c r i p t i o n of t h i s t h e o r y and the method o f c a l c u l a t i o n used. For d e t a i l s the r e a d e r i s r e f e r r e d t o the l i t e r a t u r e [ 2 1 , 2 2 , 2 3 ] . In modern laser technology , second-order NLO e f f e c t s such as SHG ( ) , sum or d i f f e r e n c f r e q u e n c y g e n e r a t i o n [SFG ( ^ C ^ i ^ ) o r DFG ( yj^ï^ ) ] and p a r a m e t r i c o s c i l l a t i o n and*' c L m p l i f i c a t i o n almost commonly used. In t h i s r e v i e w , however, b e s i d e s some l i n e a r o p t i c a l (LO) p r o p e r t i e s , we c o n f i n e o u r s e l v e s t o the d i s c u s s i o n of o n l y the SHG c o e f f i c i e n t s f o r most NLO c r y s t a l s , s i n c e t h e r e i s no significant difference between SHG and SFG, DFG, etc, i f the d i s p e r s i o n s o f the s e c o n d - o r d e r s u s c e p t i b i l i t i e s a r e not c o n s i d e r e d . Physical properties related to the electron motion in crystals fall essentially into two categories. Some, s u c h as t h e e l e c t r i c a l p r o p e r t i e s o f crystals, arise from long-range i n t e r a c t i o n s i n the lattice; here long-range forces from the electron-electron or the electron-core i n t e r a c t i o n s p l a y an i m p o r t a n t r o l e . In t h e s e c a s e s , the use o f e n e r g y band theory i s e s s e n t i a l . On t h e o t h e r hand, i n NLO effects the p r o c e s s o f e l e c t r o n i c e x c i t a t i o n by t h e incident



364


r a d i a t i o n does not make any important c o n t r i b u t i o n . They e s s e n t i a l l y a r i s e from the process of s c a t t e r i n g , where the a c t i o n of the incident photons on the electrons i n the crystal serves only as a kind of perturbation. In other words, the e l e c t r o n s confined to t h e i r ground state are only slightly disturbed by the incident photons. Hence the NLO e f f e c t s should be c l a s s i f i e d into the second category where short-range forces play a d e c i s i v e role. We therefore make the assumption that, i n the NLO e f f e c t s , the e l e c t r o n motion may be regarded as confined to small regions. In other words, any NLO s u s c e p t i b i l i t y (or second-order susceptibility) in crystals is a localized effect a r i s i n g from the a c t i o n of incident photons on the electrons i n c e r t a i n o r b i t a l s of atomic c l u s t e r s . Therefore, what we need to do i s to define at f i r s t the region of the l o c a l i z e d motion of valence electrons i n order to make reasonable estimates of the bulk second-order s u s c e p t i b i l i t y of the c r y s t a l . For this purpose we have analyzed almost a l l p r i n c i p a l types of NLO m a t e r i a l s known, such as p e r o v s k i t e , tungsten-bronze type, i o d a t e , phosphate and molybdate, nitrite and organic c r y s t a l s containing s u b s t i t u t e d benzene as major NLO-active molecules. Much to our s u r p r i s e , we found that i n any type of the m a t e r i a l with large NLO e f f e c t s , the basic structure unit without exception i s b u i l t up from anionic groups (or molecules) which are capable of producing large microscopic NLO effects, such as the (ΜΟβ) " coodination octahedron i n perovskite and tungstenbronze type m a t e r i a l s ; the (IO3 )" group i n iodates; the (PO4 ) " and (M0O4 ) ~ groups i n phosphates and molybdates; the (NO2)" group in nitrites; the s u b s t i t u t e d benzen molecules i n most organic molecular c r y s t a l s . On t h i s basis we proposed a t h e o r e t i c a l model called the "anionic group theory " for NLO s u s c e p t i b i l i t i e s , with the following two assumptions as basic premises: ( i ) The o v e r a l l SHG c o e f f i c i e n t of the crystal is the geometrical superposition of the microscopic second-order susceptibility tensors of the relevant i o n i c groups,and has nothing to do with the essentially s p h e r i c a l c a t i o n s . The former can be expressed as t* \\ η

3

2

tt

Where V i s the volume of a unit c e l l , Ν i s the number of basic s t r u c t u r a l groups i n t h i s u n i t c e l l , a i i » , a j j » , akk' are the d i r e c t i o n cosines between the macroscopic coordinates of the c r y s t a l and the microscopic coordinates of the pth group and ?(}?}yJU CpJ i s the microscopic second-order s u s c e p t i b i l i t y of* t n i s



24. CHEN


365

pth group. (ii) The microscopic second-order susceptibility of the basic anionic groups ( or molecular s t r u c t u r a l u n i t s ) can be c a l c u l a t e d from the l o c a l i z e d molecular o r b i t a l s of these groups (or molecules) by terms of the second-order p e r t u r b a t i o n theory of the SHG c o e f f i c i e n t given by the ABDP theory of Armstrong and co- workers [31] and i n Ref. [22]. The next step to reach to our aims i s to determine the l o c a l i z e d molecular o r b i t a l s of the anionic group. Of course, there are many methods available for the c a l c u l a t i o n s of molecular o r b i t a l s i n our theory, such as the various approximation methods and even the recently developed Dv-Χα method discussed i n quantum chemistry. But, i n view of the nature of the basic assumptions i n our theory, the CNDO approximation seems to be s u i t a b l e for c a l c u l a t i o n s of SHG c o e f f i c i e n t s when the anionic groups c o n s i s t of elements from the f i r s t , second and t h i r d f a m i l i e s i n the p e r i o d i c t a b l e . EHMO type approximations are suitable for other elements, particularly if t r a n s i t i o n metal elements take part i n the i o n i c groups or molecules. It i s not necessary to use higher approximations. Based upon the method of c a l c u l a t i o n adopted, a complete computer programme c o n s i s t i n g of three main parts can e a s i l y be w r i t t e n for support of such calculations. The three parts are as follows: (a) the CNDO part or EHMO part with Madelung c o r r e c t i o n for c a l c u l a t i o n of the l o c a l i z e d e l e c t r o n o r b i t a l s i n the anionic group; (b) the t r a n s i t i o n matrix element calculation part; and (c) the second-order susceptibility part for the calculation of the microscopic susceptibility of the anionic group followed by the c a l c u l a t i o n of the macroscopic SHG c o e f f i c i e n t s of the c r y s t a l . It i s obvious that our ' a n i o n i c group theory' can be generalized into an 'NLO-active group t h e o r y ' , thus permitting a straightforward extention to the c o n s i d e r a t i o n of discrete uncharged groups (such as urea or s u b s t i t u t e d benzene) and even c a t i o n i c groups as basic NLO-active s t r u c t u r a l u n i t s .

I I . The Development of New Borates: from BBO to LBO We now proceed to apply our a n i o n i c group theory to a systematic d i s c u s s i o n of the NLO e f f e c t s i n borate c r y s t a l s . The extension of our i n v e s t i g a t i o n i n t o the NLO e f f e c t s of borate crystals has great p r a c t i c a l significance i n two r e s p e c t s . On the one hand, most borate crystals are transparent far into the intermediate UV region and o c c a s i o n a l l y even f a r t h e r because of the large difference i n the electro-



366


n e g t i v i t i e s of the boron and the oxygen atom on the B-0 bond. This i s one of the most interesting spectral regions i n which l a s e r m a t e r i a l s c i e n t i s t s are looking for new NLO applications. The intrinsic damage threshold of most borate crystals is very high on account of the wide band gaps and the d i f f i c u l t y of ion and e l e c t r o n transport i n these compact l a t t i c e s , even under very intense laser irradiation. On the other hand, most borate crystals can be grown from high temperature melts by top seeding methods, g e n e r a l l y resulting i n good y i e l d s of high o p t i c a l quality c r y s t a l s for making NLO d e v i c e s . According to the anionic group theory, the second-order s u s c e p t i b i l i t i e s i n borate c r y s t a l s should be mainly determined by boron-oxygen anionic groups and their alignment i n space. The s p h e r i c a l cations c o n t r i b u t e l i t t l e to the NLO e f f e c t s . Therefore, before considering the alignment, i n order for a borate c r y s t a l to have large o p t i c a l n o n l i n e a r i t i e s , at l e a s t the basic s t r u c t u r a l u n i t s or boron-oxygen groups i n the crystals must be capable of exhibiting large microscopic second-order susceptibilities. From t h i s point of view i t i s l o g i c a l t h a t , i n order to i d e n t i f y and develop new UV NLO c r y s t a l s among the borate compounds, a very important step i s to carry out a systematic classification of the structures of the various kinds of boron-oxygen a n i o n i c groups found i n borate c r y s t a l s , and then to c a l c u l a t e the second-order s u s c e p t i b i l i t i e s for each of those groups. This step i s essential to identify the s t r u c t u r a l u n i t s that are favorable for larger microscopic nonlinearities. Indeed, the s t r u c t u r e c l a s s i f i c a t i o n and c a l c u l a t i o n s have helped us to understand why deff of K35 i s so small and whether there are other boron-oxygen groups that may e x h i b i t larger microscopic second-order susceptibilities. From 1979 to 19S4, the classification and c a l c u l a t i o n s for various known boron-oxygen groups were performed i n our research group[27]. Several major boron-oxygen groups, i n c l u d i n g t r i g o n a l group (ΒΟ3) "· tetrahedral anionic group ( B O 4 ) " » planar six-memberr i n g anionic group ( B 3 O 6 ) " ' non-planar six-member-ring anionic group ( B 3 O 7 ) - ' (B30s) "» ( B 3 O 9 ) - ' and Siamese-twinned double six-member-ring a n i o n i c group ( B 5 O i 0 ) " and { B 4 O 9 ) " are shown i n F i g . 1-3. Some of the c a l c u l a t e d r e s u l t s [ 2 7 ] f o r the n o n l i n e a r i t i e s of these anionic groups are l i s t e d i n Table 1. T h e i r relative orders of microscopic second-order s u s c e p t i b i l i t i e s are: 3

5

3

7

5

5

9

6

y.(B 0 )^ X(B 0 )^'X(BO ) 3

6

/

3

7

}

>X(BCV)

The calculated microscopic second-order s u s c e p t i b i l i t i e s l i s t e d i n table 1 c l e a r l y show that


24. CHEN

(a) φ


367


(b) Boron

® oxygen o r hydroxy i o n 3

5

Fig. 1. The molecular configurations of (a) (B0 ) ", (b) (B0 ) ' groups. (Reprinted with permission from ref. 27. Copyright 1985.) 3

4

(c)

Boron

(d)

oxygen

oxygen o r hydroxy i o n 3

5

7

Fig. 2. The molecular configurations of (a) (B~0 ) ', (b) (BLC^) ", (C) (B O ) ", and (d) ( B 0 ) " groups. (Reprinted with permission from ref. 27. Copyright 1985.) 6

3

G

9

3

9

(a)

(b)

•

Ο

Boron

®

oxygen

oxygen o r hydrogen i o n 5

Fig. 3. The molecular configurations of the Siamese-twinned double 6-ring [B O ] " (or [B 0 (OH) ]') and [ B ^ ] " (or [B 0 (OH) ] ') groups. (Reprinted with permission from ref. 27. Copyright 1985.) 5

6

5

6

4

2

4

5

4


10


l

2

l

1 2

x

3

0.641 -0.641

3

(B0 ) -

Table

123 113 223

4

3 1

5 -

,

and

2

2

133

1

1H

3

3

2.9323 "2.9323 0.0000

6

(Β 0 ) "

5

(B5O10) ""

2

2

133

1

H!

-2.9308 0.8212 -0.6288

5

groups

3

of (Βθ3) ~,

(B3O7) -

anionic

susceptibilities

e s u , ^=1.064 μπι)

(B307)

10~

- 0 . 1578 0. 0335 - 0 . 0329*

(B0 ) 5-

(units:

(B306) ",

3

1. T h e m i c r o s c o p i c s e c o n d - o r d e r


2

2

1

3

3

3

333

2

1

1

5

-1.335 0.01732 0.0458 -0.0614

(B5O10) "

5

(BO4) -,

24. CHEN



3

369

the planar (B3O6) " anionic group with a s i x - r i n g conjugated π - o r b i t a l system i s an i d e a l s t r u c t u r a l u n i t for large NLO e f f e c t s , provided that the borate crystals would not be crystallographically centrosymmetric. This possibility is particularly a t t r a c t i v e i n view of the fact that a l l B-0 bonds are capable of t r a n s m i t t i n g UV l i g h t due to the large d i f f e r e n c e i n e l e c t r o n e g a t i v i t y between Β and Ο atoms. These t h e o r e t i c a l analyses and the other extensive e f f o r t s , i n c l u d i n g the synthesis of metaborate c r y s t a l s with (B3Οδ ) " groups as basic s t r u c t u r a l u n i t s , some powder SHG t e s t s , phase e q u i l i b r i u m s t u d i e s , c r y s t a l growth, c r y s t a l s t r u c t u r e determination, and a s e r i e s of measurements of various p h y s i c a l p r o p e r t i e s , have led to the discovery and the establishment of BBO as a high q u a l i t y NLO m a t e r i a l [ 2 8 ] . While BBO c r y s t a l s have been widely used as good UV NLO c r y s t a l s for various NLO devices, three disadvantages of t h i s c r y s t a l have been recognized i n recent years: (1) The absorption edge of BBO i s only at 190 nm. Therefore, even though BBO has a large b i r e f r i n g e n c e , and may be phase-matched down to 200nm, the phase-matching range i s l i m i t e d by the absorption edge. (2) Its small angular acceptance (lmrad-.cm, for SHG, at λ.= 1.064 μιη) l i m i t s i t s a p p l i c a t i o n i n l a s e r systems possessing large divergence and i n cases where focussing i s needed to increase the power d e n s i t y . Its s e n s i t i v e angle tuning curve for o p t i c a l parametric oscillation also limits the spectral stabilityachievable i n that a p p l i c a t i o n . (3) The small Ζ component of i t s SHG c o e f f i c i e n t s severely restricts the use of the BBO c r y s t a l at wavelengths under 200 nm and for 90° n o n - c r i t i c a l phase-matching. If one uses the anionic group theory to analyze these d e f i c i e n c i e s i n view of the s t r u c t u r e of BBO, i t i s not d i f f i c u l t to understand that the o r i g i n of a l l these disadvantages i s the (B3Oe ) planar six-memberring group i t s e l f [ 2 9 , 3 0 ] . First, there are two structural factors responsible for the small Ζ component of SHG c o e f f i c i e n t s of BBO. One i s that (B3O6) " groups do not have any Ζ component, as shown i n the Table 1. The other i s that the normal d i r e c t i o n of the (B3O6) planes i s p a r a l l e l to the Ζ d i r e c t i o n of the BBO l a t t i c e , as shown i n F i g . 4. Therefore, i n order to increase the Ζ component of SHG c o e f f i c i e n t s i n borate c r y s t a l s , two p o s s i b i l i t i e s should be considered: (1) to t i l t (BsOe ) planar group r e l a t i v e to Ζ d i r e c t i o n of the l a t t i c e ; and (2) to s e l e c t other s t r u c t u r a l boron-oxygen groups which have large Ζ component while the planar 3

3


370


components are as large as (B306 ) " group. Unfortunately, the o r i e n t a t i o n of a molecular group i n the c r y s t a l l a t t i c e is not something we can c o n t r o l , and t h e r e f o r e , only the l a t t e r would be p r a c t i c a l . From Table I, the best candidate may be the (B30? ) ~ g r o u p [ 3 0 ] . In t h i s group, only one of the boron atoms in the (E3OG ) ~ planar group i s changed from t r i g o n a l to t e t r a h e d r a l c o o r d i n a t i o n . As the r e s u l t , while the and X-/2Z coefficients remain practically unchanged, the becomes numerically somewhat larger. Secondly, both experimental and c a l c u l a t e d r e s u l t s i n d i c a t e d that when c a t i o n s are e i t h e r a l k a l i metals or a l k a l i n e earth metals the p o s i t i o n s of the absorption edges of borate crystals are f u l l y dependent on the a nio nic groups. In other words, cations contribute l i t t l e to the band gap of c r y s t a l s . C a l c u l a t i o n s which utilize the DV-SCM-Χα method[32], one of the best methods for calculating the e l e c t r o n i c s t r u c t u r e of c l u s t e r s or a n i o n i c groups i n a l a t t i c e , show that the absorption edge of the planar six-member-ring ( B 3 O 6 ) " i s i n the 190-200 nm range. This is determined by the gap between dangling bond or π - c o n j u g a t e d o r b i t a l s and excited state anti-Tt-orbitals. However, the u l t r a v i o l e t absorption edges of non-planar groups such as the ί B 3 O 7 ) ~ group s h i f t to shorter wavelengths: nearly 160nm, 30nm shorter than that of ( B 3 O 6 ) " (see F i g . δ ) . This i s because the tetrahedral coordination of boron atoms i n non-planar groups destroys the π-conjugated electron system formed i n the planar groups. F i n a l l y , the a n i o n i c group of the c r y s t a l s i s a l s o found to be u s e f u l in evaluating the a n i s c t r o p y of linear susceptibility of the groups, and even of the c r y s t a l s as a whole, since the essentially spherically symmetrical cations in the crystals shall only contribute isotropic values for the linear s u s c e p t i b i l i t i e s of the c r y s t a l s , and the b i r e f r i n g e n c e or anisotropy of the crystals mainly come from c o n t r i b u t i o n of the a n i o n i c groups. In order to prove t h i s point of view we have p r e l i m i n a r y c a l c u l a t e d some b i r e f r i n g e n c e of c r y s t a l s , l i k e NaN02, B B O and L B O (see Table 2), using the l o c a l i z e d molecular o r b i t a l s of the a n i o n i c groups, and f i r s t order p e r t u r b a t i o n theory of quantum mechanics. The c a l c u l a t e d results show that although i t i s very d i f f i c u l t to reach a c c u r a t e l y the absolute values for r e f r a c t i v e indexes of the c r y s t a l s , we have obtained quite close values of the birefringence i n comparison with experimental data (also see Table 2). The reason i s that using l o c a l i z e d molecular orbitals to calculate microscopic linear s u s c e p t i b i l i t i e s of a n i o n i c groups or c a t i o n s , you must 3

3


3

3

5

3


24.

CHEN

371


Λ

. (B 0 ) 3-


3

Fig.

4.

6

Schematic drawing of BBO's L a t t i c e

net

σ*(Α ») 1

7Γ*(Α », Ε») 2

I "2000 Â

"880 À "1890

À dangling

bond

T(Oout)

I

I o(0

o u t

)

(a)

σ(Αχ) π* (B

A)

lf

"860 À

'

1

2

• "1800 - ι onnÀ A

"

,

1

L

-

L

dangling

bond

Tr(Oout) '

»

*(O

I N

)

(b) Fig.

5.

Schematic (Β3θβ) -« 3

picture of energy l e v e l s ( b ) (B3O7 ) " g r o u p s .

of

(a)

5



372


face an i n f i n i t e series, which u n l i k e second-order susceptibility converges very slowly, but the situation is entirely d i f f e r e n t , when concerning the c a l c u l a t i o n for b i r e f r i n g e n c e or anisotropy of l i n e a r susceptibility of the crystals, the l a t t e r i s only determined by the f r o n t i e r molecular o r b i t a l s of the anionic groups or molecules (for organic c r y s t a l s ) and the l o c a l o p t i c a l frequency e l e c t r i c field acted on. Therefore, it would be p o s s i b l e to use localized molecular o r b i t a l methods to evaluate anisotropy of linear susceptibility for d i f f e r e n t kinds of c r y s t a l s . For example, calculations for b i r e f r i n g e n c e of some inorganic NLO c r y s t a l s (see Table 2) p r e d i c t e d that the c r y s t a l s constructed from (B3O6; " or ( B O 3 ) ' groups should g e n e r a l l y possess a l a r g e r b i r e f r i n g e n c e than crystals where basic structural units are ( B O 4 ) " ' (B3O7) " group or other borate groups i n which one or more boron atoms are t e t r a h e d r a l l y coordinated. Based on t h i s t h e o r e t i c a l work, we p r e d i c t e d that the (Β3Ο7) · group i s another i d e a l basic s t r u c t u r a l u n i t f o r UV NLO c r y s t a l s which would improve upon the NLO and LO p r o p e r t i e s of BBO. It i s t h i s novel idea that motivated our research group to make extensive efforts which l e d to the discovery of a new" UV NLO c r y s t a l - L 1 B 3 O 5 (LBO)[30,34]. 3

3

5

5

5

III. Measurements and c a l c u l a t i o n s of the SHG coefficients for BBO, LBO and another borate crystals. In the l a s t s e c t i o n we b r i e f l y described how new NLO c r y s t a l s i n the borate were developed through a systematic classification and calculation of microscopic second-order susceptibilities and absorption edges for various kinds of B-O anionic groups. In t h i s section, we w i l l discuss how the anionic group theory i s used to c a l c u l a t e and e l u c i d a t e the NLO coefficients and p r o p e r t i e s for borate c r y s t a l s , p a r t i c u l a r l y for BBO and LBO. l.BBO c r y s t a l . Barium metaborate e x i s t s i n both α and β phases with the t r a n s i t i o n temperature at 9 2 5 ± 5 ° 0 The α phase is centrosymmetrical and therefore exhibits no NLO response at all. The J3 phase belongs to a noncentrosymmetric space group and i s very u s e f u l for UV NLO a p p l i c a t i o n s . In 1969, Hubner[35] reported that the space group of the low-temperature form of barium borate i s C 2 / C , a centrosymmetric s t r u c t u r e . However, i n 1979, by using a powder second-harmonic generation (SHG) t e s t , my group found that the low-temperature form of barium borate possesses a large NLO c o e f f i c i e n t , about six times



24. CHEN

373


l a r g e r than that of d e f f ( K D P ) . This r e s u l t implied that BBO had a noncentrosymmetric s t r u c t u r e . The r e s u l t s of work by various researchers [36,37,39] l a t e r on showed that R3C i s most l i k e l y the correct space group for BBO, with c e l l dimensions a=1.2532 nm, c=1.2712 nm. There are three non-vanishing SHG c o e f f i c i e n t s , d 3 3 , d 3 ι and d i ι , for R3c. By means of the Maker f r i n g e technique and the phase-matching method, Chen et a l . [28] determined the values of these SHG c o e f f i c i e n t s shown i n table 3. The very large anisotropy of the SHG e f f e c t i s j u s t as expected, with d 3 3 / d i i * 0.001. L i and Chen [23] made d e t a i l e d c a l c u l a t i o n s of the SHG c o e f f i c i e n t s of BBO and t h e i r r e s u l t s are also given i n table 3. It i s obvious that the agreement between the experimental and the c a l c u l a t e d values i s s a t i s f a c t o r y . Moreover, it confirms our p r e d i c t i o n that the planar ( B 3 O 6 ) " u n i t with the six-membered-ring conjugated o r b i t a l system i s mainly responsible for the l a r g e d i ι coefficient, whereas the very small d 3 ι and d 3 3 c o e f f i c i e n t s a r i s e mainly from the small deformation of the π - o r b i t a l system due to the presence of an oddordered crystal field along the 3 - f o l d a x i s , a r i s i n g from the spontaneous p o l a r i z a t i o n produced by the arrangement of the Ba cations around the (B3Oe) ~ a n i o n i c groups. 2. LiCdB03 and YAl3(B03)4 c r y s t a l s We have shown in section II that the (BO3 ) " anionic group i s a l s o favourable for the production of large second-order s u s c e p t i b i l i t i e s , although the NLO effect will be expected to be smaller than that of ( Β 3 Ο 6 ) " · Powdered samples and t i n y c r y s t a l s of LiCdB03 and Y A I 3 ( B O 3 ) 4 , with the ( B O 3 ) ~ anionic group as t h e i r s t r u c t u r a l u n i t , have been synthesized and grown i n our I n s t i t u t e . Powder SHG t e s t s have been c a r r i e d out on these samples. In the l i g h t of our anionic group model, with the help of the c r y s t a l s t r u c t u r e s determined by Lutz [39] and Leonyuk and Filmonov [40], i t i s simple to calculate their macroscopic SHG coefficients. Although powder t e s t s can only give rough r e l a t i v e values for the SHG c o e f f i c i e n t s , the data [27] i n table 4 show s a t i s f a c t o r y agreement between t h e o r e t i c a l and experimental r e s u l t s , leading to the f o l l o w i n g sequence of SHG c o e f f i c i e n t s ( d e f f ) f o r £ - B a B 2 0 4 , LiCdB03, and Y A I 3 ( B O 3 )4 : 13-BaB2 04 > LiCdBOs * Y A I 3 ( B O 3 U . 3. LBO (L1B3O5) c r y s t a l . In s e c t i o n 3, i t was shown that when one of the three t r i g o n a l l y coordinated Β atoms i n the planar (B3O6) " anionic group i s changed to tetrahedral coordination, thus forming a B30? group, the ζ components of the SHG c o e f f i c i e n t s , e . g . X/33 (which plays an important r o l e i n the NLO e f f e c t of the UV s p e c t r a l range for 90° n o n - c r i t i c a l phase matching) 3

3

3

3

3

3



6

3

ft,)

**).

2

o f /3-BaB 0

2

(N0 )

4

crystal

( units:

0.1100

0.1020

3J

-0.0038

37, 1378.

KDP p o w d e r .

0

1Ί

10

e . s . u . f o r SHG

d

e f f

d

eff

*

f o rthe

(KDP)

P r o c . IRE,

test

( 2 U

coefficient;

0.0457

Crystals,

« 5-6

p o w d e r SHG e f f e c t

(B3O7)

0.0538

LBO

a n d LBO

Relative value of I

6

o f NaNC>2, BBO

from S t a n d a r d s on P i e z o e l e c t r i c

= -(0.07+0.03)ά

-0.038

-0.038

±(4.60+0.30)

Experimental

3.78

/ e t c . ; data quoted

D

*„

Calculated

3

(B 0 )

structure

BBO

and a n i o n i c group

1.079 μιη f o r f u n d a m e n t a l w a v e l e n g t h )

S t a n d a r d sample:

1949,

*) · d n = ^-///

3

(B 0 ) -

group

X.=

3. SHG c o e f f i c i e n t s

Anionic

Table

0.2422

Experimental

2

0.1843

NaN0

Calculated

Crystal

T a b l e 2. B i r e f r i g e n c e


24.

CHEN

375


w i l l become l a r g e r , whereas X,u or %\2X more or l e s s r e t a i n the magnitudes found i n ( B 3 O 6 ) " ( c f . table 1). This important r e s u l t has been confirmed by our recent work on LBO[30]. L1B3O5 c r y s t a l l i z e s i n the space group P [41]. It is built up of a continuous network of endless (B3O5 ) s p i r a l chains (running p a r a l l e l to the ζ a x i s ) formed from B30? a n i o n i c groups with each of the four e x o - r i n g 0 atoms shared between the B3O7 groups i n the same chain or neighbouring c h a i n s , and L i c a t i o n s located i n the interstices. There are five nonvanishing SHG c o e f f i c i e n t s , d 3 3 , d 3 1 , d 3 2 , dis and d 2 4 , for the point group C 2 ν . Again with the help of the Maker f r i n g e and phase-matching methods, we have been able to measure a l l these SKG c o e f f i c i e n t s , with the results listed i n table 5. The macroscopic SHG coefficients of the L1B3O5 crystal have a l s o been calculated on the basis of the a n i o n i c group model without any adjustable parameters by using the structural data reported by Konig and A . R . H o p p e [ 4 1 ] . The r e s u l t s are a l s o shown i n table 5. The agreement between the c a l c u l a t e d and the experimental r e s u l t s i s s a t i s f a c t o r y . The discovery of t h i s new U V NLO c r y s t a l LBO adds convincing support to our c o n c l u s i o n that the a n i o n i c group model i s indeed a good working model f o r guiding the search f o r new NLO borate c r y s t a l s and c r y s t a l s of other s t r u c t u r e types. As pointed out by Chen et a l . [30], the f a c t that one of the three t r i g o n a l Β atoms i n the (B3Oe ) ~ anionic group has been changed to tetrahedral coordination to form the (B3O? ) " group i s bound to weaken the conjugated π-orbital system to an appreciable extent and tends to s h i f t the a b s o r p t i o n edge to a shorter wavelength i n the U V r e g i o n , i n fact down to 160 nm , c a . 30nm shorter than that of BBO, which i s u s e f u l for a p p l i c a t i o n s as a U V NLO m a t e r i a l . 4 . KB5 ( K B 5 O 8 4H2 0 or Κ[Β5θβ (0H)4 ]·2Η2θ The macroscopic SHG c o e f f i c i e n t s of the KB5 crystal have been calculated on the basis of our anionic group model [42], assuming that the [BsOeiOHU]" group is the primary a c t i v e group r e s p o n s i b l e for the production of SHG e f f e c t s ( c f . f i g u r e 3 a ) . The c a l c u l a t e d SHG c o e f f i c i e n t s of t h i s KB5 c r y s t a l are shown i n table 6. together with the experimental data. It has been pointed out that the largest component of the microscopic second-order susceptibility of B5 Οι 0 group i s » which, u n f o r t u n a t e l y , does not c o n t r i b u t e to the macroscopic SHG c o e f f i c i e n t s of KB5 since the point group of t h i s crystal is C 2 ν , and thus the macroscopic SHG c o e f f i c i e n t di 4 ( =2X. ) vanishes i d e n t i c a l l y . T h i s accounts p r i m a r i l y for the fact that the macroscopic 3


flû2|

3

5

i2J



3

3

YA1(B0 )

4

LiCd(B0 )

Crystal

l l 12

d

12 22

d

d

d

l l die

d

2.7039 4.2144 - 2.7093 - 4.2144 3.4000 - 3.4100

9

3

4

to 1.740 to 2.715 t o -1.742 t o -2.715 to 2.200 t o -2.200

C a l c u l a t e d SHG c o e f f i c i e n t (units:10~ e.s.u.)

3

and Y A 1 ( B 0 )

e

f

deff

d f

d

e f f

*).

d

3 6

(

K D p

9

e.s.u.

±0.15(1+0.1)

)=l.lxl(r

Experimental

0.61

*33

3

9

e.s.u.

(d

31

+2.75(1+0.12)

-2.24

d

32

2.69

d

9

=d

15

«d

d

3 1

3 1

e.s.u.,

9

1

e.s.u.)

~ 32

d

32

24

= d

d

X.=1.079 μπι ) *

( K D P ) i s t a k e n t o be l . l x l O "

(units:10~

3 6

±2.97(1+0.01)

o f LiB Os c r y s t a l

= 0.72xl0"

T a b l e 5. SHG c o e f f i c i e n t s

3 6

KDP p o w d e r .

( K D P ) = 0.66d (KDP)

S t a n d a r d sample:

Calculated

***)·

**).

deff(KDP)

deffCKDP)

of the strength

2.5

3.0

from test**

l( )

2u)

(X.=1.079um f o r t h e

Relative value of p o w d e r SHG e f f e c t

crystals

* ) . T h e r a n g e o f t h e c a l c u l a t e d SHG c o e f f i c i e n t s i s d e t e r m i n e d b y t h e r a n g e of the odd-ordered c r y s t a l l i n e f i e l d i n the c r y s t a l .

3

(B0 )-

A n i o n i c group

3

T a b l e 4. SHG c o e f f i c i e n t s o f L i C d ( B 0 ) fundamental wavelength )


24. CHEN

Nonlinear Optical Cryskds in the Borate Series 9

Table 6. The SHG coefficient of KB5 crystal (units: 10" esu for SHG coeff. ; χ.=1.064 μπι for fundamental wavelength) Anionic group [B 0 (OH) ]Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on September 1, 2015 | http://pubs.acs.org Publication Date: March 11, 1991 | doi: 10.1021/bk-1991-0455.ch024

5

6

4

1

d

ij 31

Calculated Experimental(1) Experimental(2)*

d

2.61

1.09

(- )2.53**

d

0.07

0.08

1.04

d

3.26

32 33

2.88

* The second set of experimental measurements was made by the Institute of Crystalline Materials, Shangdong University (private communications). ** It is supposed to be uncertain. SHG coefficients of KB5 amount only to one tenth that of KDP. In case there exists a crystal consisting of the same basic structural unit [Β5θδ(ΟΗ)4]" but crystallizing in point group either C2 or D2, the component PCpJ of the microscopic second-order susceptibility will make its contribution to the overall SHG effect of the crystal and exhibit as large an overall effect as half of that of KDP. This is left for further consideration.

Acknowledgments This work was supported by the Science Fund No. 1860823 of the national science fund committee. The author is very grateful to Wu Yicheng, Li Rukang and Lin Guomin for their assistance with the preparation of the manuscript. References [1] D.H. Auston, et al, Appl. Opt., 26 (1987), 211. [2] N. Bloembergen, "Nonlinear Optics", pp. 5-8 (Benjamin, New York, 1965). [3] S.K. Kurtz and F.Ν.Η.Robinson, Appl. Phys. Lett, 10 (1967), 62. [4] C.G.B.Garrett and F.Ν.Η.Robinson, IEEE J . Quant. Elect., 2 (1966),328; C.G.B. Garrett, IEEE J. Quant. Elect., 4 (1968), 70 [5] C.R.Jeggo and G.D. Boyd, J . Appl. Phys., 41 (1974), 2471. [6] J.G.Bergman and G.R.Crane, J . Chem. Phys., 60 (1974), 2470; B.C.Tofield, G.R.Crane and J.G. Bergman, Trans. Faraday Soc., 270 (1974), 1488. [7] B.F. Levine, Phys. Rev. Lett., 22 (1969), 787; 25 (1970), 440.



378


[8] B.F.Levine, Phys. Rev., B7 (1973), 2600. [9] Y. Fujii and T. Sakudo, ibid., Β13 (1976), 1161. [10] B.F.Levine, ibid., B13 (1976), 5102. [11] B.L.Davydov, L.D.DerKacheva, V.V.Duna, M.E.Zhabotinskii, V.F.Zolin, et a l . , Sov. Phys. JETP Lett., 12 (1970), 16. [12] D.S.Chemla, D.J.L.Oudar, and J.Jerphagnon, Phys.Rev., B12 (1975), 4534. [13] J.L.Oudar and D.S.Chemla, Opt. Commun, 13 (1975), 164. [14] J.L.Oudar and H.Leperson, ibid., 15 (1975),256. [15] J.Zyss, D.S.Chemla, and J.F.Nicoud, J.Chem. Phys., 74 (1981), 4800. [16] J.Zyss, J.F.Nicoud and M.Coquillay J.Chem. Phys. 81 (1984), 4160. [17] C.C.Frazier, Μ.Ρ.Cockererham, Ε.A.Chauchard and C.H.Lee J. Opt. Soc. Am. B4 (1977), 1899. [18] J.C.Baumert, R.J.Twieg, G.C.Βjorklund, J.A.Logan, and C.W.Dirk Appl. Phys. Lett. 51 (1987), 1484. [19] M.DiDomenico J r . , S.H.Wemple J.Appl. Phys. 40 (1969), 720. S.H.Wemple, M.DiDomenico Jr. J. Appl. Phys. 40 (1969), 735. S.H.Wemple, M.DiDomenico J r . , I. Camlibel, Appl. Phys. Lett. 12 (1968), 209. [20] C.T.Chen Acta Phys. Sin., 25 (1976), 146. (in Chinese). [21] C.T.Chen Scientica Sin., 22 (1979), 756. [22] C.T.Chen, Z.P.Liu and H.S.Shen Acta Phys. Sin. 30 (1981), 715 (in Chinese ). [23] R.K.Li, and C.T.Chen Acta Phys. Sin., 34 (1985), 823 (in Chinese). [24] C.T.Chen

Acta Phys. Sin.

26 (1977), 486 (in Chinese).

[25] C.T.Chen Commun. Fujian Inst. Struct. Matter. No. 2 (1979), 1. (in Chinese). [26] C.T.Chen Acta Phys. Sin. 26 (1977), 124 (in Chinese). [27] C.T.Chen, Y.C.Wu, and R.K.Li, Chinese Phys.Lett. 2 (1985), 389 [28] C.T.Chen, Β.C.Wu, A.Jiang and G.M.You Scientia Sin. Β18 (1985), 235. [29] C.T.Chen Laser Focus World Nov.(1989 ),129 [30] C.T.Chen, Y.C.Wu, A.Jiang, Β.C.Wu, G.M.You and R.K.Li, S.J.Lin J. Opt. Soc. Am. B6 (1989), 616.



24.

CHEN


379

[31] J.A.Armstrong, Ν.Blombergen, J.Ducuing and P.S.Pershan Phys. Rev. 127 (1962), 1918 [32] H.Sambe and R.H.Felton J. Chem. Phys. 62 (3) (1975), 1122 B.Delley and D.E.Ellis J.Chem. Phys. 76 (4) (1982), 1949 [33] J.Huang "Calculations of birefringences of the crystals using anionic group theory", M.S.Treatise, Sep. 1987, Fujian Institute of Research on the Structure of Matter (in Chinese) [34] S.J.Lin, Z.Y.Sun, B.C.Wu and C.T.Chen J. Appl. Phys. 67 (1990) 634. [35] K.H.Hubner, Neues Jahrb. Mineral, Monatsh, (1969), 335. [36] S.F.Lu, M.Y.Ho and J.L.Huang, Acta Phys. Sci. 31 (1982), 948 [37] J.Liebertz and S.Stahr, Ζ.Kristallogr., 165 (1983), 91. [38] R.Frohlich, Ζ.Kristallogr., 168 (1984 ), 109. [39] F.Lutz, Recent Dev. Condens. Matter Phys. Ist., 3 (1983), 339 [40] N.I.Leonyuk and A.A.Flimonov Krist. Tech., 9 (1974), 63. [41] H.Konig and A.Hoppe, Z. anorg. allg. chem. 439 (1978), 71. [42] Y.C.Wu and C.T.Chen Acta Phys. Sin. 35 (1986), 1 (in Chinese) RECEIVED August 13, 1990


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