Ann. Rev. Mater. Sci. 1986. 16: 203-43 Copyright © 1986 by Annual Reviews Inc. All rights reserved

RECENT ADVANCES IN

NONLINEAR OPTICAL

AND ELECTRO-OPTICAL

MATERIALS

Chuang-tian Chen

Fujian Institute of Research on the Structure of Matter, Academia Sinica, Fuzhou, Fujian, China

Guang-zhao Liu

Shanghai Institute of Ceramics, Academia Sinica, Shanghai, China

INTRODUCTION

The discovery of optical second harmonic generation in crystals by Franken and his co-workers ( 1 ) in 1961 spurred rapid progress in nonlinear optics. Over the past two decades, this field has developed into a new branch of science (2). The rapid development was mainly due to simultaneous progress in laser technology. Only a laser can provide sufficiently strong, coherent radiation that can be efficiently converted in frequency and modulated in amplitude by nonlinear optical (NLO) and electro-optical (EO) effects. After the discovery of the NLO effect, scientists immediately recognized that any practical applications of NLO would depend on the development of new materials. Today some scientists are even inclined to think of NLO crystals as the future optical semiconductors, and the search for new materials is still very active. Historically, the development of NLO can be divided into three stages. The first stage was from 196 1 to the mid 1960s. During this period, the nonlinear response of matter was recognized in theory to be dependent upon susceptibilities X(n) and the applied optical electric field as shown in

203 0084-6600/86/0801-0203$02.00

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204 CHEN & LID

Equation 1 .

p = X(I)'£+X(2):EE+X(3): EEE+ .... 1 .

The ratio of successive terms in the polarization P can be described approximately by Equation 2.

2.

Here E is the applied electric field, and Eat the atomic field strength; the absolute value IEatl � 3 x 1 08 Vjcm in general. It is well known that two facts are implied in Equation 2. (a) NLO effects in matter can be observed only with a sufficiently powerful optical source. For example, despite a laser source with power density 109 Wjcm2, the electric field strength is about 106 Vjcm, which is quite small in comparison with Eat. (b) The generation of new frequencies that are not available with existing laser sources is easiest via the lowest order nonlinear response, i.e. the second term in Equation 1 , which obviously cannot be generated if the crystal structure is centric. It was this important conclusion that enabled scientists to successfully search for NLO materials among the numerous known piezoelectric, ferroelectric, and electro-optical crystals. During this period, Miller (3) proposed that the X(2) coefficient in Equation 1 can be expressed as X(2) � (X(l))3. (i(2w). Here X(I) is the linear susceptibility, and (i(2w) is remarkably constant for nonlinear materials, despite the fact that X(2) varies over four orders of magnitude, as Miller noted in 'his paper. This was an important step towards the quantitative estimation of second harmonic generation (SHG) coefficients for crystals with acentric space structures; it led to a search for NLO materials in crystals with large birefractive index, and it accelerated progress in understanding the physical origin of the NLO effect.

The second stage in the development of NLO began in the mid 1960s. This was an important period in the development of a theoretical understanding of NLO materials and devices. Research during this stage progressed in two directions.

1 . After a large number of NLO crystals were studied during the previous stage and experimental data was accumulated, scientists began to study the relationship between macroscopic properties of NLO crystals and their microscopic structures in order to better understand the structure-properties relationship. Representative of that period are the work of Bloembergen (4), the anharmonic oscillator model of Kurtz & Robinson (5) and Garrett & Robinson (6), the bond parameter model of Jeggo & Boyd (7) and Bergman & Crane (8, 9), the bond charge model of Phillips & van Vechten ( 10) and Levine (1 1 , 12), the two harmonic oscillator models of DiDomenico et al ( 13, 14), the charge transfer theory

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 205

(for organic NLO crystals) of Chemla and co-workers ( 1 5-17), and C. T. Chen's (Academia Sinica) anionic group theory ( 18-21 ) for the NLO effect in crystals. These theoretical studies revealed the origin of NLO effects at a microscopic level and, furthermore, enabled scientists to construct certain structural criteria for determining whether or not compounds possess large SHG effects.

2. In light of the theoretical studies and experimental measurements of various NLO devices, some requirements that must be met by materials designed for practical use as NLO devices have been suggested. They include proper birefringence that is phase-matchable in SHG, three­frequency processes and optical parametric oscillator (OPO) devices, high optical damage threshold and high optical homogeneity, and larger, second-order susceptibility. These requirements make it clear that a single factor, such as larger X(2) coefficients, is not sufficient for NLO crystals to be useful in NLO or EO applications, and that comprehensive criteria are necessary in evaluation. Another major advance during this period was the work by Kurtz & Perry (22) at Bell Laboratories in 1968. They developed a powder SHG test technique that permits rapid evaluation of NLO properties of materials in powder samples without the growth of single crystals. In 1 978 Tang and co-workers (23) improved this technique using a dye laser source to determine not only the effective SHG coefficient but also the phase-matchable region of materials in powder.

The third stage of NLO development has been from the mid 1970s to the present. Owing to previous theoretical studies, which contributed towards an understanding of the relationship between NLO effects and microstructures in NLO crystals, it seemed feasible for the search for new NLO and EO materials to proceed under the guidelines of structural criteria. Subsequently, in 1 976 an entirely new concept of "molecular engineering" (24) of NLO crystals was developed.,Chemla, Ouder, Zyss (private communication), and Chen and his co-workers (26) independently designed a complete set of experimental procedures for searching for new types of NLO crystals. They achieved some important results in organic NLO crystals and ultraviolet NLO crystals of boron-oxygen compounds, respectively. It is noteworthy that progress in theoretical studies during this period was to a great extent related to the adoption of quantum chemistry approximation methods: for example, the CNDO (completely neglected differential overlap) approximation was used to calculate localized molecular orbitals and microscopic second-order susceptibilities of anionic groups of inorganic compounds (27) and of molecules (28-30). Moreover, with the help of the combined use of the irreducible tensor theory with the anionic group theory (20) and organic NLO theory (3 1), even the macroscopic SHG coefficients of crystals have been estimated.

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206 CHEN & LID

These theoretical successes promoted the development of the so-called molecular engineering approach to NLO crystals.

Since the mid 1 970s there have been numerous review articles in this field; they include the work of Byer (32), l'llikogosyon (33), Hulme (34), Kurtz (35), Gunter (36), and Badan et al (37), who recently published a monograph on organic NLO materials. All these reviews, except that of Badan et aI, emphasize the properties of NLO materials and the requirements of NLO devices. In this review we emphasize advances in research on the structure-property relation in NLO and EO materials, particularly those that have occurred since the mid 1970s. In the next section we briefly discuss the various requirements for NLO and EO devices and applications ; then in the following section we discuss in detail the structure-property relation of NLO materials. In the section on molecular engineering we summarize developments in that approach to NLO (EO) crystals, with emphasis on applications of the concept of molecular engineering to the search for new types of organic NLO crystals and ultraviolet NLO crystals of boron-oxygen compounds. In the section on recent advances some important NLO materials results reported since the mid 1970s are summarized, and in thc last section we discuss new techniques for growth of NLO and EO crystals that probably represent the future direction of technical progress in the field.

NLO AND EO MATERIALS: APPLICATIONS AND REQUIREMENTS

In the early stage of NLO development, NLO (or EO) devices were limited to harmonic generation, parametric amplification and oscillation in the visible and near infrared regions, and to EO amplitude modulation in the visible region. But since the mid 1 970s, as new NLO phenomena such as the photorefractive effect and phase conjugation have been discovered, new materials and devices are continuously found, and the quality of crystals has steadily improved, the applications of NLO (or EO) materials have been greatly broadened. Henceforth for convenience of description we will use four classifications with emphasis on the requirements for practical applications.

Tunable Coherent Light Sources for Spectroscopy and Related Applications Thanks to the combination of tunable dye lasers, tunable color-center solid state lasers, and tunable semiconductor injection lasers with nonlinear processes in crystals (such as harmonic generation, parametric up- and down-conversion), the spectral regions used today can cover, almost con­tinuously, the range from 170 nm (38) to 1 8 /lm (39). Furthermore, be-

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 207

cause the transparency region of NLO crystals was extended from 165 nm (38) to 25 flm (40, 41), there could doubtless be a further extension of applications to the vacuum ultraviolet and far-infrared regions. This broad gain in the coherent radiation output wavelength band makes laser spectroscopy an ideal optical technique. Moreover, ultrashort-pulsed, tunable, coherent light sources, used jointly with NLO crystals, have made picosecond time-resolved spectroscopy realizable, an important advance in studies of transient phenomena and in the measurement of short relaxation times.

High-Power, Pulsed Coherent Optical Sources for Laser Fusion

Theoretical studies of laser fusion have demonstrated (42) that if the wavelength of the laser source is converted from the 1 .06-flm range to the blue and ultraviolet by NLO devices, the efficiency of absorption Of the in­cident light energy by the target pellet can be raised as much as 3-5 times. Hence, development of short-wavelength, high-power coherent optical sources is an important task in laser technology. But until now, research has largely been restricted to the application of larger size KDP (or KD*P) crystals (200 x 200 mm2 cross-section) to second (SHG) or third harmonic generation (THG) devices with incident light from high peak, power pulsed Nd lasers. However, certain disadvantages of KDP (or KD*P), including deliquescence, weak mechanical properties, and a low damage threshold under high power pulsed Nd laser light, have made it necessary to develop improved NLO crystals.

Holography and Optical Phase Conjugation

In 1 966, researchers (43) from Bell Laboratories discovered that the refractive index of LiNb03 crystals was changed on exposure to intense blue or green laser light. About a year later, Chen et al (44) reported that crystals showing this photo refractive effect could be used as storage media in holographic memory systems. Since then, many research workers in this field, including Kogelnik (45), Amodei et al (46), Kukhtarev et al (47), Yariv (48, 49), Gunter (50), and Feinberg et al (5 1 ), have made important advances. The development of holography and the related phase-conjugation technique will result in a completely new area of research. But, of course, further success is also dependent upon finding new photo refractive materials and growing crystals of high optical quality (50).

Integrated Optics and Optical Communication Systems

In the last few years optical signal processing has been strongly influenced by integrated optics. The combination of integrated optics and optical

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208 CHEN & LIU

fiber technique has had a major eifect on the development of commercial optic fiber communication. It is important to note that the basic waveguide elements applied in integrated optics, for example, optical waveguide switches, intensity and phase modulators, wavelength filters, and polar­ization controllers, all rely upon EO materials, particularly crystals like LiNb03, LiTa03, and GaAs (52). Moreover, it seems likely that in the future it will be possible not only to fabricate various film waveguide elements from the EO cr:ystal but also to fabricate fibers (53) directly from NLO crystals in order to realize all optical processing functions, including laser output, harmonic generation, switching modulation, etc, in an integrated optical system.

Novel applications, whether for frequency conversion by NLO crystals, light amplitude and phase modulation by EO crystals, or holography and phase conjugation by photorefractive crystals, await further advances in materials, particularly crystals. Hence we think it useful to outline in some detail the main requirements for such applications.

Materials Requirements for NLO Devices

Since 1 96 1 , several hundred NLO crystals have been found ; some of them, such as KDP, KD*P, LiNb03, BNN, KTP, and the newly discovered p-BaB204 (54), are very useful. From the standpoint of NLO materials, one can say that the laser frequency conversion problem in the visible region has been essentially solved. The main task scientists now face is the search for new NLO crystals for the ultraviolet (even vacuum ultraviolet) and far-infrared regions (�5-30 j.lm). For example, a crystal for harmonic generation and parametric oscillation that is suitable for use in infrared regions is not yet available. In addition, there is a need for organic crystals, e.g. benzene derivatives providing a huge microscopic second-order susceptibility, that are suitable as film materials in integrated optic devices, and ones that can sustain the high intensity of � 109-1010 W /cm2 generated by today's pulsed laser sources. Since the requirements are increasingly rigorous, an excellent NLO crystal must satisfy the following five basic conditions: (a) a large NLO effect, for which d2/n3 values are a figure of merit ; (b) a high optical damage threshold; (c) phase-matchable and high optical homogeneity ; (d) appropriate transparent wavelength range; (e) and good chemical-physical properties, e.g. nondeliquescent and good mechanical properties.

Materials Requirements for EO Devices

To date several hundred EO crystals have been found. Although some of them possess a large n3• r value (55), a figure of merit for modulator crystals, no currently known crystals possess both a large EO effect and

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 209

a high damage threshold (or small optical-induced refractive index change). Oxygen-octahedra ferroelectric crystals, for example, LiNb03, KNb03, are generally characterized by a value of n3 • r (36, 56) that is an order of magnitude larger than that of KDP-type crystals. However, they are very susceptible to induced refractive index change, so that most high pulse power Q-switch devices today still use KDP or KD*P as EO modulation crystals. Likewise, in the far-infrared region there is still no EO crystal that works well.

In the search for new EO materials, the main task is to find crystals that are characterized by a large figure of merit, a high damage threshold (or small optical-induced refractive index change), and appropriate far infrared transmission. For an excellent EO crystal, the following six requirements must be satisfied: (a) a large EO effect or large n3• r value; (b) a small optical-induced refractive index change and a high optical damage threshold; (c) high optical homogeneity and temperature stability of birefringence; (d) a small dielectric loss factor; (e) appropriate transparent wavelength ranges, and (f) good surface workability.

Materials Requirements for Holography and Phase Conjugation The application of EO crystals to holography and phase conjugation relies largely upon light-induced refractive index changes, i .e. the so-called photo refractive effect. The physical origin of this effect may be the space charge field between ionized donor centers and displaced charges trapped after electronic migration induced by non-uniform illumination. The space charge field modulates the refractive index of photorefractive crystals via the EO effect. Hence, many EO crystals may potentially give rise to light­induced changes of refractive index, but their photorefractive sensitivity is often very small. For EO crystals to exhibit a high photorefractive sensitivity, some transition metal ions, particularly iron ions, are added as dopants to produce donors and traps. Therefore, in principle, any EO crystal with a large EO coefficient may be converted to a useful photorefractive material through suitable doping and impurity control. For more details, readers can refer to the latest review article by Gunter (50).

STRUCTURE-PROPERTY RELATIONSHIP IN NLO AND EO CRYSTALS

In the previous section the basic materials requirements for NLO and EO devices are briefly discussed. In order to expedite the search for new materials by using the "molecular engineering" approach, as suggested

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210 CHEN & LIU

by Chemla et al (24), we must first try to clarify the relationship between the properties of materials and their microscopic structures, i .e. the arrangement of atoms or ions in lattice space, and the electronic structure. Although much effort has been expended to achieve this goal, unfortunately, only the relationship of the NLO and EO effects to microscopic structure has been explored in depth. Other properties are still not understood at the microscopic level, and one must rely on empirical data.

Strictly speaking, the physical origin of NLO or EO effects was first discussed by Miller in 1 964 (3). On the basis of the thermodynamic principle of free energy, he proposed that the SHG and EO coefficients in crystals are related to the linear susceptibilities by

dijk = Xii(W)' Xjiw)' Xkk(W)' A�kw),

X�"k) = Xii(W)' Xjj(w)' Xkk(O)' A�"kl, 3.

where dijk is the SHG coefficient of the crystal ; xW is the EO coefficient; Xjj = (nl- 1 )/4n, linking the linear susceptibility with the index of refrac­tion; and l1ijk is Miller's coefficient.

As observed by Miller, despite the fact that dijk and x�'f) may vary by about 2-3 orders of magnitude from one material to another, 11��w) and I1W are surprisingly constant and vary by no more than a factor of four over the entire range of the materials that were investigated. For example, X�');) coefficients of KDP isomorphs can change by factors of about 3-4, whereas the difference between A&"kJ values is only 12%. This illustrates that Miller's coefficient can be considered a constant for the same structural type of NLO or EO materials ..

Because Miller's coefficient I1jjk was thought to be very important in elucidating the structure-property relation for NLO and EO effects, many efforts were made to explore the physical origin of the Aijk coefficient with theoretical methods during the period 1965-1975. Using a one­dimensional anharmonic vibronic oscillator model, Bloembergen (4) and Kurtz & Robinson (5) pointed out that Miller's constant 11(2w) (or A(w») is directly proportional to the anharmonic potential in accordance with the formula

A(w) = . -- . V 4n (K+2) 3Nee'w5 K-l '

4.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 211

where me is the electronic mass; Ne the number of electrons per unit volume; Wo the resonance frequency of the harmonic oscillator ; K the dc electric constant; and V the anharmonic force constant.

For ferroelectric materials, Kurtz & Robinson (5) further indicated that V � (4n' e' N;/3)jme' Ps; here Ps is the spontaneous polarization of the ferroelectric phase.

In 1968, using the anharmonic vibronic oscillator model for both electronic and ionic motion, Garrett & Robinson (6) demonstrated that when the applied optical frequency w is larger than the lattice vibration frequency Wo> the contribution of ionic anharmonic vibration to the SHG coefficient can be ignored completely, and the A(2w) expression of Equation 4 is quite accurate.· However, for the A(w) coefficient the situation is completely different and the contribution of ionic anharmonic vibration is comparable with that of electronic anharmonic vibration, so A(w) ought to obey the following formula:

2'S2 1 [(3D) (C) ] A(w) = - __ 0 '- ' - 'Xe(O)+ - 'X;(O) , e2, N5 x(O) ec ej

5.

where e o is the dielectric constant of free space; Xe(O) and X;(O) are the linear susceptibilities of electrons and ions respectively with W = 0; ee, e; are the charges of electrons and ions ; D is the anharmonic force acting upon the electrons; and C is the anharmonic force produced by ionic polarization against the electrons and represents the effect of the photo­phonon deformation potential on the electronic anharmonic motion. Since it is known that CjD:::::: -6.83, as obtained by Garrett from GaP Raman scattering spectroscopy, and ee :::: ei, Xe(O) ;2; Xi(O), it follows that the second term in Equation 5 apparently cannot be omitted. This demonstrates why the EO effect ought to include the contributions of both electrons and electron-ion interactions. But it is well known that the classical anharmonic oscillator model cannot help us further understand the physical origin of anharmonic potential in NLO or EO crystals from microscopic structure. Therefore, subsequent theoretical work that placed special emphasis upon exploring the origin of the anharmonic potential in microscopic structure was undertaken using the following methods.

1 . The bond parameter method. In 1967 on the basis of the anharmonic oscillator model for NLO (or EO) effects in crystals, Robinson (57) suggested that the macroscopic NLO susceptibility (i.e. SHG coefficient dijk) in crystals is the geometric superposition of the microscopic second­order susceptibility, /3, of each bond, which he considered the basic structural unit of the crystal. Therefore, the macroscopic second-order

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2 12 CHEN & LID

susceptibility dijk of the crystal can be obtained by using the relevant space structural and P parameters. This is called the bond parameter method (34). Jeggo & Boyd (7) used this empirical approach to successfully calculate the SHG coefficients dijk of B06 octahedra crystals and EO coefficients rij of KDP-isomorphs. This approach was also used by Bergman and his co-workers (8, 9) to calculate dijk of iodate crystals, with results in agreement with experimental findings. These successes clearly showed the bond parameter method to be an improvement over the classical anharmonic oscillator model and supported the view of chemical bonds as the basic structural units that produce NLO and EO effects. Obviously, according to this model, there are at least two requirements that must be met for a crystal to exhibit a large NLO effect : (a) The microscopic NLO susceptibility P of each bond must be as large as possible; (b) each bond must be spatially located and oriented in such a manner that it favors the superposition of microscopic susceptibilities.

2. The bond-charge model of the NLO effect. The bond parameter model and the one-dimensional anharmonic oscillator model, supported by numerous experimental findings, have provided reasonable evidence that the NLO susceptibility f3 for each bond comes from the nonsymmetric response of bond charge under applied optical electric field. Many theoretical models have arisen, such as the two-band model of Phillips & van Vechten (10); the charge-transfer model (58�59), and the bond-charge model ( 1 1 , 1 2, 60, 61) . These models have been used to search for the physical origin of bond NLO susceptibility fJ and to calculate its value. Of these, the most successful and representative is the bond-charge model suggested by Levine ( 1 1 , 1 2, 60, 61) . Because it agrees well with experimental findings and can accommodate complex crystal structures, it is discussed in detail. The disadvantages and limitations of the model are also presented.

According to the harmonic oscillator model, the low-frequency linear susceptibility in crystals can be expressed as

_ �o {hQp)2 of Xw - 4n Eg , 6.

where Qp is the plasma frequency, Eg is the average energy gap, and f the local-field factor.

For semiconductors, including zinc blende and wurtzite type structures, Phillips & van Vechten (62�65) indicated that the average energy gap Eg consists of homopolar Eh and heteropolar C parts :

Ei = m+CZ, 7.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 2 1 3

which are given in Equation 8, respectively.

E� [(r A -rO)2s + (rB -rO)2.]

2a'

8.

where b and a' are constants ; ZA and ZB are the valences of atoms A and B that form the bond; ks is the Thomas-Fermi screening constant; and ro = l/2(rA +rB) is the average atomic radius.

In 1 969-1973, Levine ( 1 1 , 1 2) pointed out that the bond NLO susceptibility /3 could be attributed to the displacement l1r of bond charge 9 under applied optical electric field and that this displacement causes a change of Eb and C in Equation 8. A change of energy Eg then takes place, which in turn gives rise to a dependence of the susceptibility XW on the applied field. The final result is the microscopic second-order optical susceptibility /3 of each bond.

Levine (12) further indicated that when the crystal structure contains more than one type of bond, macroscopic nonlinear susceptibility dijk of the crystal can be expressed as

d - " Gil ·NIl-/31l ijk - L.. ijk b , Il

9.

where Jl represents the type of bond ; /31l is the longitudinal nonlinear susceptibility of the fl-type bond (the transverse nonlinear susceptibility is assumed to be zero, i.e. /31- = 0 in Levine's bond-charge model) ; Nb is the number of Jl-type bonds per cm 3; and Gijk is the geometrical factor of the Jl-type bond, i.e. the sum over all Jl-type bonds.

/31l is composed of two parts:

10.

where CIl and Eh represent the heteropolar and homopolar susceptibilities C and Eh of fl-type bonds, respectively.

In the same way, Miller's � also consists of two parts :

11.

For complete expressions for f3!1 and �Il, refer to formulas 50-59 given by Levine in Reference 1 2.

Levine further proved that Miller's coefficient � is in agreement with

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2 14 CHEN & LIU

the following formula :

..1. � 3.7 X 10 -6 x U;-4p) esu, 12 .

where J. = 0/E� is the bond ionicity, and p = (rA-rB)/(rA+rB) is the normalized displacement of 9 from the exact center of the bond. It is worth noting that all calculations of the bulk NLO susceptibility dijk of the tetrahedrally coordinated zinc-blende, wurtzite, and chalcopyrite-type crystals, made by Levine using the known linear properties .of these crystals together with his formula of PI' ( 1 2) and Equation 9, were in excellent agreement with experimental data both in magnitude and sign without introducing any adjustable parameters. It should be emphasized that Levine's bond-charge modei gives a quite good explanation of why d333 and d311 of BeO are anomalously small and show the same sign. This problem had not been elucidated by other models. Levine's bond-charge model is considered more successful than other methods not only because it can be applied to a wider range of complex crystal structures but also because of its profound theoretical contribution, i.e. its explanation of the relationship between the nonlinear susceptibility dijk of crystals with tetrahedral coordination of covalent bonds and their microscopic structure. In particular, the physical origin of the bond nonlinear polarizability P was accounted for by the nonsymmetric displacement ..1.r of 9 under applied electric field, and Miller's ..1. in Equation 1 2 was found to be directly related to the deviation of bond charge 9 from the bond center.

Tang et al (58, 59), Flytzanis & Ducuing (66), Phillips ( 10), and Kleinman (67) have also contributed towards understanding the physical origin of bond NLO susceptibility.

When application of the bond-charge model was extended to NLO crystals beyond the Sp3 hybrid type, particularly to oxygen-octahedra ferroelectric crystals with d electrons, some serious defects were gradually exposed. For example, in the case of B06 oxygen-octahedra ferroelectric crystals in the ferroelectric phase the two bond lengths, d(B - 03) and d(B-06) (shown in Figure 1), along the Ps direction differ both in magnitude and sign. As a result, if the bond-charge model is used to calculate their dijk coefficients, it is necessary to derive the dependence of the average values of nonlinearity P on the bond length, which was found by Levine (61 ) to be P = Po(d/do)"NL. Here Po is the average value of bond nonlinearity, do is the average bond length (for example, do = 2.00 A in LiNb03), and d the actual bond length. When the deviation of actual bond length d from average value do in the ferroelectric phase is defined as ..1.Z, according to the bond-charge model (68), the dependence of nonlinear susceptibility dijk on ..1.Z and bond length d must be expressed

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS ' 215

as

13.

where we can obtain the relation (TNL = d333/d311 and, by using experimental values of dijk' the (J NL values can be easily calculated. But, in fact, the results of calculated (JNL for various (B06) oxygen-octahedral ferroelectric crystals obtained in this way show a difference that is too great. For example, the (JNL values of KTa03, SrTi03, and BaTi03 are 2.86, 0.74, and 0.37, respectively (68, 69), which is quite suspect for oxygen-octahedra crystals of the same type.

Anionic Group Theory for NLO Susceptibility in Crystals

The theoretical models in which chemical bond is considered the basic structural unit for the production of nonlinear susceptibility in crystals have achieved considerable success in dealing with crystals of Sp3 hybrid tetrahedrally coordinated structures. But they have not proved equally successful for other types of crystals in which the energy band structure cannot be simply expressed as Phillips' average energy gap Eg (62-65), as in the case of perovskite and tungsten-bronze type materials. This greatly limits their usefulness. In 1968-1970, two research groups in the United States and China independently discovered that the basic structural unit for the production of nonlinear susceptibility in most acentric crystals must be a much more delocalized region of the valence electron orbitals that belong to more than two atoms, rather than the region localized around two atoms of a bond. In 1968-1969, DiDomenico & Wemple (13-14) found that the nonlinear susceptibilities (including the EO effect) of perovskite and tungsten-bronze type materials are largely the result of distortion in B06 oxygen-octahedra. Thus the latter is the basic structural unit for the production of nonlinear susceptibility in these crystals. In accordance with energy band theory, they also introduced a parameter called the polarization potential tensor, /3ij' to describe the energy band perturbations (or shifts) induced by the applied optical electric field. Using a two-harmonic oscillator model, /3 is related to the quadratic electro­optical coefficient 9 as

14.

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216 CHEN & LIU

where K is a constant determined by the two-harmonic oscillator model, and p3 is the stacking density of B06 oxygen-octahedra.

On the basis of Equation 14, both the NLO susceptibility dijk and the linear EO coefficient rij under applied optical or static electric field can be derived through their dependence on the quadratic electro-optical coefficient g. These successful calculations enable us to ascertain three important facts : (a) For perovskite and tungsten-bronze type materials, the basic structural unit producing nonlinear susceptibility (including EO effect) is not the B-O bond but the B06 oxygen-octahedra. (b) The physical origin of nonlinear susceptibility in the crystal is intimately related to the energy-band shifts (particularly the d conduction band shift) that are derived from induced polarization Pi in the crystal under applied optical electric field. Therefore, it is rational to introduce the polarization potential tensor {3ij as a characteristic constant for nonlinear susceptibility in the crystal. (c) The fact that the optical and static electric polarization potential tensors {3ij are nearly the same, and that both of them are related physically to the same polarization-induced modulation of the (pdn) energy-overlap integral, means that the physical origin of SHG and EO effects is fundamentally the same in all the oxygen-octahedra ferroelectrics.

At approximately the same time, a new theoretical model called anionic group theory (18-21) for NLO susceptibility in crystals was put forward by Chen. The basic premises of this model are outlined below.

The NLO susceptibility in crystals is a localized effect of the incident light on the electrons in certain clusters of orbitals. The appropriate grouping of orbitals may be an anionic group in inorganic crystals (or a molecule in the molecular crystals, see the next paragraph) which is thought of as the basic structural unit and primary source of the NLO susceptibilities. For example, the anionic group in the perovskite and tungsten-bronze materials is the B06 oxygen-octahedra, in iodate it is the r03 group, in phosphate it is the P04 group, and it is acentric benzene derivatives in organic crystals. There are a few exceptions ; in zinc-blende crystals the region of the localized orbitals should be chosen as that assigned to form an A-B bond between two atoms (70). To calculate the bulk SHG coefficient of the crystal, we make two basic assumptions in our model. First, the overall SHG coefficient of the crystal is the geometric superposition of all the microscopic SHG coefficients of the relevant groups and has little to do with the cation. The former can be expressed as

X(2W)-N' P ."NI"{3JJ'yJJ 'XI' Uk - J1 L. IJ..ji' jj' kk' fj'k" JJ

1 5.

where N is the number of cells per unit volume; PI' is the number of

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 217

equivalent groups per unit cell; (x/", /31', yJ', are the directional cosines between the macroscopic coordinates of the crystal and the microscopic coordinates of the J,L-type group ; and 'Y}j'k' is the microscopic SHG coefficient of the ,u-th group. Secondly, the microscopic SHG coefficients of the anionic groups can be calculated by using the localized molecular orbital wave functions of the groups with the formula for calculation of SHG coefficient given by ABDP theory (7 1 ) and Reference 27. A complete computer program made up of three subroutines has been devised to perform such calculations. The subroutines are (a) the CNDO subroutine, which calculates the localized electron orbitals in the anionic group or molecule using a CNDO-type approximation method; (b) the single- or two-center dipole transition matrix calculation subroutine ; and (c) the SHG subroutine, which calculates the microscopic SHG coefficients of the groups and the macroscopic SHG coefficients of the crystal.

With this computer program, we have calculated the SHG coefficients of almost all the known principal types of NLO crystals, including new types of NLO crystals, such as boron-oxygen compounds, that have recently been found by our laboratory, but not including AB-type semiconductor materials, in which the chemical bond is the basic structural unit and therefore the bond-charge model is suitable. Numerous cal­culations and experimental facts accumulated over the years have verified the results of our computer program. A few typical examples are given below.

I . Of the perovskite and tungsten-bronze type crystals, the three NLO crystals LiNb03, KNb03, and BNN are well known. Their basic structural units are (Nb06) oxygen octahedra that are distorted in different ways: i.e. a threefold axis distortion along the body diagonal direction of the unit cell in LiNb03, a twofold axis distortion in KNb03, and a mainly fourfold axis distortion in BNN, respectively, as shown in Figure 1. According to the basic principles of our anionic group theory, the magnitudes of the SHG coefficients of these three crystals depend entirely on the localized molecular orbitals of the oxygen-octahedra and on their manner of distortion, and the contribution from the A-site cation is negligible. On this basis, we have calculated the SHG coefficients of these three crystals (72) with the help of the Wigner-Eckart theorem of group representation. The results are listed in Table 1 . We have concluded that of the three types of B06 oxygen-octahedra distortion, the one along a fourfold axis in B06 oxygen octahedra is most likely to produce a large SHG coefficient, whereas the one along a threefold axis is ineffective, which coincides with the conclusions reached by DiDomenico in Reference 14. In 1978, Chen & Chen (73) also calculated the SHG coefficients of KTiOP04 (KTP) by using the anionic group theory and found that the

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2 1 8 CHEN & LIU

large SHG coefficient of KTP is produced by a large distortion of Ti06 oxygen octahedra.

2. There are four iodate crystals, a-LiI03, a-HI03, K2H(l03)2CI, and Ca(I03)2' 6H20, that are well-known NLO materials whose SHG coefficients have been determined. X-ray studies show that their basic structural units are stacks of (I03)�1 oriented in different manners in the four crystals. Again, according to our theory, their apparent overall SHG coefficients obviously are the geometrical superposition of the microscopic SHG coefficients that are assigned to the relevant (l03)�1 groups. The contribution from the A-site cations is negligible; that is to say, the former can be easily calculated so long as the microscopic SHG coefficient of (103) � I is known. In Reference 20, we made detailed calculations, listed in Table 2, which show much higher precision than results calculated by the bond parameter method (8). For example, in the K2H(I03)2CI crystal, the calculated value of xW!i by the bond parameter method is eight times larger than the experimental value, and the value of x(lt? is three times smaller. By the anionic group theory, the average difference between experimental and theoretical values is nearly equal to the average error of experimental values, which implies that the (I03)� I group, rather than the (1-0) bond, should be used as the basic structural unit in calculation of the microscopic SHG coefficients.

3. In recent years new NLO crystals of boron-oxygen compounds have been found by Chen and co-workers and by other groups. These include f3-BaB204 (54), KBsOs' 4H20 (KB5) (74, 75), CdLiB03 (76), LiB30s (78),

4-fold axis

2

�Metal ion o Oxygen Figure 1 (Bo.)-n oxygen octahedron and its three different distortion patterns.

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Table 1 The SHG coefficients of LiNbOJ, KNbO" and BNN crystals (units: 10-9 esu, A. = 1.064 .urn)

xWi xSf'? xYrd x.W"i x�',wi x.\',w?

LiNb03 Experimental -(72.0 ± 18.0) -(12±1) 5.74±2.25

Calculate<! -77.5 -15.26 7.09

KNb03 Experimental -(53.0 ± 2.8) 30.68±2.8 -(34.87± 2.8) 32.09±5.6 -(33.47 ± 5.6) Calculated -57.85 28.15 -35.9 33.2 -28.0

BNN Experimental -(47.6±3.47) -(34.65± 1.74) -(34.65 ± 3.47) -(34.65±3.47) -(32.95 ± 1.74) Calculated -46.98 -47.24 -47.24 -35.85 -35.85

Table 2 The SHG coefficients of iodate crystals (J. = 1.06 JIm, unit: 10-9 esu)

Crystals (ijk) (333)

Experimental -(12.4±2.5)

a-LiI03 -(14.01 ± 3.34) Calculated -12.4

a-HIOJ Experimental

Calculated

K,H(IOJ),CI Experimental ± (12.43 ± 0.565) Calculated -10.497

Ca(I03)2 - 6HP Experimental ±(5.65± 1.47) Calculated -6.3097

(311)

-(11.9±2.38) -(13.37±0.7)

-11.9

± (2.49 ± 0.542) -3.5944

+(1.75±0.44) 1.243

(322)

-(11.9 ± 2.38) (13.37 ±0.7) -11.9

± (O.l36± 0.113) -0.105

± (0.226 ± 0.057)

-0.120

(123)

± (1 L53± 2.94) 9.987

�

� �

i � � t""

�

� N ,.....

\0

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220 CHEN & LID

and Y AI3(B03)4 (77). X-ray studies revealed that, except for LiB305, the basic structural units of these crystals are their anionic groups, such as the B306 group in p-BaB204 (79), the B50lO group in KB5 (80), and the B03 group in CdLiB03 (76) and Y AI3(B03)4 (77). The SHG coefficients are expected to be the geometric superposition of the microscopic anionic group SHG coefficients, with the contribution from the A-site cations being negligible. By using the complete computer program mentioned above and in Reference 27, we have made detailcd calculations for the SHG coefficients of p-BaB204, KB5, CdLiB03, and YAI3(B03)4 crystals! (see 8 1 , 82). Again, the agreement between the calculated and experimental values is quite satisfactory, although the SHG measurement accuracy was limited in the case of powder samples of Y AI3(B03)4 and LiCd(B03) compounds.

Charge-Transfer Theory for Organic NLO Crystals

In 1 970, Soviet scientists Davydov and co-workers (83) recognized that the second-order susceptibilities of organic crystals originated in the molecules that constitute the basic structural unit of the crystal. They began to study the relationship between second-order susceptibility of molecules and structure. After analyzing the general quantum mechanical formula of NLO susceptibility given by ABDP theory (7 1 ), they pointed out the two basic conditions that must be met when organic molecules exhibit a large second-order susceptibility. (a) The oscillator strength of electric dipole transition of the molecules must be quite large. (b) When electrons transfer from the ground state to an excited state, the dipole moment of the molecules changes.

Based on the above analysis, they suggested that conjugated organic molecules with donor-acceptor radicals would be the most likely to exhibit a larger second-order susceptibility. This idea was further developed by Chemla et al (15-17), who analyzed in detail the overall second-order susceptibilities of organic crystals (for which the SHG coefficients had been determined) and the microscopic second-order susceptibilities of the constituent molecules. They reached the following conclusions about the nonlinear response in organic crystals.

1 . Because most organic crystals are molecular crystals in which the interaction between molecules is as weak as if they were independent of each other, the bulk second-order susceptibilities of the crystals can be seen as the geometric superposition of the microscopic second-order susceptibility of each molecule. This bulk-to-microscopic relationship of second-order

I The overall SHG coefficients of the LiB30, crystals have not been calculated with our computer program owing to the basic structural unit of (B307)n�oo chains.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 221

susceptibility can be expressed with the irreducible tensor form of SHG coefficients given by Jerphagnon (84).

2. For organic molecules with acentric planar structure and donor­acceptor radicals, the second-order susceptibilities arise almost entirely from the distortion of the delocalized n electrons and are directly proportional to the mesomeric moment of conjugated molecules as expressed in Equation 16 .

p = 3(�}AJi' 16 .

where ex i s the linear susceptibility, ')I is the third-order susceptibility of the molecule, and AJi is the mesomeric moment.

3. For molecules with high distortion of delocalized electrons, like benzene derivatives, the second-order susceptibilities associated with donor-acceptor radical contributions cannot combine additively.

All these theoretical advances enabled us to develop a greater under­standing of the physical origin of NLO susceptibility in organic crystals and they aided in the search for new organic molecules with large second­order susceptibilities.

In 1 978-1979 at least three research groups (28-30) adopted the semiempirical CNDO-type all-valence electrons approach in order to study the second-order susceptibility f3 of benzene derivatives with electron donor-acceptor substituents. In References 28 and 29 the semiempirical CNDOjS (spectroscopic data) approximation was first used to calculate the molecular orbital (MO) energy levels of p-nitroaniline and their MO wave functions and then was used to calculate second-order suscepti­bilities f3 via the expression for microscopic NLO susceptibility given by Armstrong et al (71) . Another semiempirical treatment of molecular second-order susceptibility is the perturbated INDO (intermediate neglected differential overlap) approach, a modified INDO method suggested by Zyss in Reference 30. Zyss systematically calculated the second-order susceptibilities of monosubstituted and disubstituted benzene derivatives. Because of these experimental and theoretical studies, we now understand the second-order susceptibilities of molecular crystals in terms of molecular structure. Some important conclusions are as follows.

1 . The second-order susceptibilities f3 of.conjugated molecules consist of two parts : P = P" + pn. Here p" represents a (J bond contribution that is additive; pn is the conjugated n bond contribution, which is nonadditive and whose contribution is much larger than that of the (J bond.

2. The conjugated n bond contributes to the molecular second-order

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222 CHEN & LIU

susceptibility P largely as a result of the charge transfer between donors and acceptors. Therefore, the larger their difference in electronegativity and the more extensive the charge transfer from donor to acceptor in conjugated molecules, the larger the second-order susceptibility p that will be obtained.

3. Increasing the number of conjugated n bonds greatly enhances the molecular second-order susceptibility p.

4. For conjugated molecules, the {3 value is related to the dipole moment not only of ground states but also of excited states, viz. it is directly proportional to AJl (the difference in dipole moment between excited states and ground states) as expressed in Equation 17.2

p oc L «nlrln) - <glrlg»). 1 7. n

From the statements above, it would seem that to enhance molecular second-order susceptibilities the organic conjugated molecules should be selected to contain as many conjugated n bonds as possible and be substituted by radicals with a large difference between the electronegativity of the donors and the acceptors. But, as shown by recent experiments, particularly in the case of organic noncentrosymmetric crystal growth, the arrangement of such molecules in space often appears to be cen­trosymmetric, in unfavorable alignment for NLO susceptibility (3 1) . This is due to the increase of electrostatic dipole-dipole interaction when the ground state dipole moment increases, and leads to a null or much weaker NLO geometrical factor.

To avoid this disadvantageous effect, Zyss et al suggested (85) that the organic conjugated molecule have both a high value for the excited state dipole moment (that means an important charge transfer) and a small value for the ground state to produce a large dipole moment difference between the two states and favor a noncentrosymmetrical crystalline structure. It is interesting to note that by using this approach the new organic NLO crystal 3-methyl-4-nitropyridine-l -oxide (POM) was found (85) and successfully grown; it possesses a small ground state moment, a high excited state moment, and a large bulk dijk value. Notwithstanding, it is still hard to prove that the noncentrosymmetric structure of POM is really connected with its nearly vanishing permanent dipole, as suggested by Zyss.

The above principles seem to be applicable not only for organic molecules but also for inorganic ionic groups, as Chen's research group

2 Equation 17 is only derived from the simple two-energy-level model for NLO sus­ceptibility.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 223

demonstrated (27, 86). They calculated the second-order susceptibilities of the inorganic conjugated N02 group and showed that an inorganic ionic group containing conjugated n-orbitals and characterized by a charge-transfer process in the excited and ground states will also possess a large second-order susceptibility. Using this assumption, Chen's research group has found and grown an excellent new NLO crystal-fJ-BaB204 (54).

ADVANCES IN MOLECULAR ENGINEERING OF NLO (EO) CRYSTALS

In 1976, Chemla et al made a novel suggestion (24) : the use of a "molecular engineering" approach to search for organic NLO crystals, based on current understanding of the structure-properties relationship in these crystals. Since then, considerable progress has been made with this approach, so that one can now not only predict properties (24, 25) but also the possibility of successful crystal growth (25, 85). In 1979, based on the anionic group theory and relevant experimental advances in the search for inorganic NLO crystals, Chen's research group in China also suggested the possibility of using a molecular engineering approach to search for inorganic NLO materials. Because of the importance of this concept, we shall briefly summarize the present state of development of the molecular engineering approach.

From a theoretical aspect, we now can prove that the bulk second­order susceptibility of a noncentrosymmetric crystal is additive, i.e. the former is simply the geometric addition of the microscopic second-order susceptibilities of the relevant basic structural units that constitute the crystal. Examples are the anionic groups in inorganic compounds, the molecules in organic molecular crystals, and even the clusters in atomic cluster complexes. Therefore, if NLO crystals are to exhibit large optical nonlinearities their structural unit, whether anionic group, molecule, or cluster, must be of a type that produces large microscopic second-order susceptibilities. One of the fundamental subjects in molecular engineering, this is called the molecular optimization process. At present, we have accumulated enough theoretical and experimental knowledge to judge which structural types are favorable and which are not. Chen's research group and Chemla and co-workers have shown that any of the following three structural features are advantageous in the anionic groups (or molecules).

1. Large distortion of the B06 oxygen octahedra or other similar anionic groups. For the kinds of groups shown in Figure 1 , the greater the distortion, the larger the microscopic second-order susceptibility will

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224 CHEN & LIU

be. Chen has shown (72) that, of the three distortion directions, C4v distortion is the most advantageous while C3v is unfavorable.

2. The existence of a lone electron pair. As shown by Chen's calculation in Reference 87, groups containing a lone electron pair, like (103) - 1 or (SbFs) -2, have larger p values by one order of magnitude than groups missing the lone electron pair, like (P04)

3- . In the latter, the increase of

bond number in the center atom accompanies formation of a tetrahedral radical. Figure 2 shows the structural types of the (103) 1 - , (P04)3 - , and (SbFs)2- groups.

3. The existence of planar structure and asymmetric, conjugated TC

orbitals. As pointed out by Chemla's research group ( 1 5-17, 30) and other scientists (28, 29), molecules with large delocalized and large asymmetric TC electron systems, accompanied by an important charge

. transfer process, may be two or three orders of magnitude larger in p value than aliphatic molecules of the same size. This conclusion is also valid for inorganic groups, as Chen and co-workers described in References 27, 86.

Another basic structural requirement for NLO crystals, as stated above, is that groups, molecules, and even clusters must be spatially aligned in a manner favoring the addition of the relevant microscopic second-order susceptibilities p instead of favoring their cancellation. They also must possess an optical birefringence that is larger than the index dispersion. This aspect of crystal structural engineering or the crystal optimization process has been discussed in detail by Chen & Chen (20) and Zyss & Oudar (3 1) . It is unfortunate that at present there are no structural criteria that one can use to foresee when optimization of the crystallographic process will occur. Nevertheless, the following useful guidelines based on experimental findings can be offered to help predict and control molecular ( or group) orientation.

(a)

1 . According to Zyss et al (25, 85) and as discussed above, in order to

Lone-electron

pair

(b) (c) Lone-electron

pair

Figure 2 The geometric configurations of (a) (10,)- 1, (b) (P04) -" and (c) (SbF,)-2 groups.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 225

suppress the electrostatic dipole-dipole interaction, which is unfavorable to the formation of noncentrosymmetric structure, while at the same time maintaining a large molecular fJ value, the molecules should have both a small ground state dipole moment and a high excited state dipole moment, and therefore a large charge transfer effect.

The new NLO organic crystal, 3-methyl-4-nitropyridine- I -oxide (POM), is a probable example (85).

2. As several research groups (25, 88, 89) have demonstrated, the chiral molecule is much more likely to ensure the formation of a noncentrosymmetric point group. For example, p-nitroaniline without chirality possesses a large ground state dipole moment that results in a centro symmetric point group. Its derivative, methylnitroaniline (MNA), with a methyl group substituted at position 3,

CH3

NH�NO',

possesses chirality that results in an acentrosymmetric point group. This has been proved by a SHG test of MNA crystalline samples (89). In this case, the single methyl group may be decisive in forming a non­centro symmetric crystalline structure. The situation is similar for 4-nitropyridine- I-oxide(l) (85) and methyl-(2,4-dinitrophenyl)-amino­propanoate (MAP) molecules (88).

3. As early as 1 969, Bergman et al (90) had indicated that inorganic materials generally have only a ",20% probability of acentricity, but those composed of anionic groups with a lone electron pair may have a very high tendency to form a noncentrosymmetric point group. For instance, according to Bergman's SHG powder and piezoelectric tests, the incidence of acentricity for (103)- 1 group materials (90) (see Figure 2) is close to 100%. This shows that the principle of a greater probability of acentricity with a lone electron pair seems to be an important structural criterion in searching for NLO crystals.

4. Recently, Wang & Eaton (109) reported a new method for controlling organic molecular orientation in lattices using host-guest inclusion com­plexation. They used fJ-cyclodextrin ({J-CD) as the host and p-nitroaniline (P-NA) as the guest molecule. P-NA has a very large second-order susceptibility but never produces macroscopic second-order susceptibility in its centrosymmetric crystal habit. The powder tests of {J-CD/P-NA inclusion complexation demonstrate that specific molecular alignment of P-NA is achieved through {J-cyclodextrin inclusion complexation because the relative SHG powder efficiency of {J-CD/P-NA complexation with

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226 CHEN & LIU

Nd : Y AG laser is two to four times larger than that for urea powder samples, while the powder samples of either P-NA or fJ-cyc1odextrin do not give any detectable second-harmonic signal. Since a wide variety of host molecules are generally available, this new method of aligning molecules through guest-host complexation should be of great importance in developing "molecular engineering" of NLO crystals.

There is another important microscopic factor that contributes to macroscopic NLO susceptibility. The crystal should have as many contributing structural units as possible in a unit volume of the crystal. This means that space has to be used as effectively as possible. In fact, this is the very reason why AB semiconductor type crystals can exhibit a large second-order susceptibility dijk.

Regarding practical devices and their applications, while it is essential that a crystal possess a large NLO effect, this condition alone is not sufficient for the crystal to be usable. A good crystal for practical purposes should also possess other qualities such as phase matchability, excellent optical homogeneity, a high damage threshold, and a proper transparent region, which in combination are very difficult to predict theoretically. Experience from past searches for NLO crystals has shown us that in order for this search to be more directed, more effective, and more convenient it is necessary to design a complete set of experimental procedures to test and correct the above theoretical rules and hypotheses, as well as to determine those properties of NLO materials that we cannot evaluate from theory. Both Chemla's and Chen's research groups have independently designed such a complete set of experimental procedures, which may also be considered as a first attempt to explore experimentally the possibilities of molecular engineering (or even crystal engineering). The flow diagram of this procedure is shown in Figure 3. Chen and Chemla have shown that these procedures not only organically combine the theoretical working model with the experimental work, but that they also effectively promote the search for new NLO materials. Many organic NLO (EO) crystals (25, 85) and the new ultraviolet NLO crystal, fJ­BaB204 (54), have been discovered using these experimental procedures.

RECENT ADVANCES IN NLO (EO) MATERIALS

During the earlier period of the search for NLO materials, from 1 96 1 to 1 975, several hundred crystals that showed potential as NLO materials were discovered. Further study soon confirmed, however, that only a very small minority were of practical value. Those crystals include : (a) those with high optical quality grown by the aqueous solution method, like

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 227

New ideas

Powder test

Crystal growth

centric----<&> acentric -'------:-7"-1 phase matchable ,r---,.----I

Defect analysis Identification o f

J-o------i crystal quality

(3 )

Computation

Structural

analysis on

single crystals

Test 0 f crystal

properties

Applications

Figure 3 Flow diagram of the sequence of procedures in the search for new types of nonlinear optical crystals.

ADP, KD*P, CD*A, and (b) those grown by the Czochralski method, like LiNb03 and LiTa03' The others, which includes BNN, KNb03, have been gradually eliminated from practical use because of intrinsic defects. Since the mid 1970s, and especially since the successful adoption of the molecular engineering approach, many new NLO crystals have been found that are useful and valuable and have broad applications.

KTiOP04 (KTP) Crystal

Since the 1 960s, many NLO (EO) crystals of the perovskite and tungsten­bronze type have been examined. But experimental data show that these materials have two serious, inherent defects : They are easily damaged, even at a moderate level of laser power ( < 100 MWjcm2), and their optical homogeneity is not good owing to their nonstoichiometric composition. Therefore, their practical applications [although some of them, like LiNb03, BNN, and KNb03, have a high NLO (EO) effect] are greatly limited. Studies by Nassau & Lines (91 ) and van Vitert et al (92, 93) indicated that these two defects are mainly related to the manner in which the B06 oxygen-octahedra are stacked in space. The X-ray diffraction determination of this crystal structure (94) showed that the tungsten­bronze type structure consists of a framework of B06 octahedra (B is

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228 CHEN & LIU

commonly Ti, Nb, Ta, or W) that share their corners in such a way that three types of interstitial sites, called A, B, and C sites, are formed. These sites in turn form three types of tunnels in the lattice that may be partly occupied by different metal atoms. These interstitial sites easily introduce changes in the stoichiometric composition of crystals and stacking-fault defects, which in turn result in optical inhomogeneity and light-induced changes of refractive index. A similar situation exists for perovskite and quasi-perovskite type structures like LiNb03• One way to eliminate these defects is to fill all the interstitial sites with different metal atoms, as in the case of K6LiNbIO03o (95). But for most perovskite and tungsten­bronze type crystals, many of their interstitial sites tend to remain unoccupied. A basic way of overcoming the above limitations is to change the structure while keeping B06 octahedra as building blocks. As indicated by Chen's group ( 19, 72), these basic structural units produce a large second-order susceptibility in perovskite and tungsten-bronze type crystals. This idea was implemented in 1 976 by Zumsteg and co-workers (96), who reported a new series of NLO materials, KxRb1 _x TiOP04 (0.0 � X � 1 .0), with the most favorable stoichiometric ratio at x = I . KTiOP04 (RTP) represents a great improvement over the shortcomings of

existing oxygen-octahedron materials. The structural characterization of this new crystal (97) shows that it consists of two types of building blocks, P04 tetrahedra and Ti06 octahedra. These are linked with each other via four shared corners and appear to have two important features : a large distortion of the Ti06 octahedra that enhances the second-order susceptibility of the crystal, and only one type of interstitial site which is completely occupied by K atoms. As a result, the KTP crystal possesses a large NLO coefficient comparable with that of BNN, while the inherent disadvantages commonly found in the perovskite and tungsten-bronze type crystals disappear. In addition, the crystal is also phase-matchable by rotation at 1 .06 ]lm either in a type I or type II configuration at room

temperature. The latter configuration, which shows a larger angular phase-matching aperture and wider thermal phase-matching range, offers better tolerance to beam divergence and temperature variation (98). Recently, Fahlen & Perkins (99) reported an intracavity Q-switched Nd : Y AG oscillator using the NLO crystal KTP with an average power over 20 W at 0.53 pm. Y. S. Liu et al (98) have constructed similar devices, with an average power, which is only limited by the current and is not saturated, of up to 5.6 W. K. C. Liu et al ( 100) reported a THG device of KTP at 355 nm with high peak, power pulsed Nd laser source at 1 064 nm and a KD*P crystal used as a frequency tripleT. An average UV output of 1 20 MW with 100-psec pulses has been obtained. Hence KTP is proving to be an excellent NLO crystal in the visible region.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 229

fJ-BaB204 Ultraviolet NLO Crystal

As pointed out earlier, an important aspect of the application of NLO crystals is that they extend the coherent light region to include 100 nm to 20 /lm ; at present, the most interesting regions are the ultraviolet and far infrared. However, only a few crystals are suitable for the far infrared and ultraviolet regions ; and strictly speaking, there is no NLO crystal that functions well in these important spectral regions. In 1979, Chen's research group indicated (54, 86) that planar conjugated n-electron systems in some inorganic groups contribute a larger NLO effect than nonplanar structural groups, just as in the case of benzene derivative systems. They found that the (B306)3 - ionic group in boron-oxygen compounds may be an ideal planar structural unit for inorganic NLO crystals. In particular they also noticed that the B-O bond can transmit ultraviolet light because of the large electronegativity difference between boron and oxygen. Through the experimental procedure of Figure 3, including powder SHG tests, phase diagram investigation of BaB204-Na20 and BaB204-Na2B204 ( 10 1 ), determination of physical properties and structural characterization (79), Chen et al finally arrived at the crystal BaB204 (/3-BaB204) with a low temperature phase. It has been identified as an excellent ultraviolet NLO crystal that is suitable for a wide variety of practical applications and has the following major advantages : (a) a wide transparent region ( 190 nm-3.5 /lm) ; (b) a wide phase-matchable region (200 nm-1 .5 /lm SHG output) ; (c) a large SHG coefficient [deff = 6.20 (KDP), at 1 .06 /lm] ; (d) a high damage threshold (4.6 GWjcm2, at 1 .06 /lm ; 6--7 GWjcm2, at 0.53 /lm) ; (e) good optical quality (An � 1 O-6jcm) ; and (f) nondeliquescence and good mechanical properties, e.g. easy to cut and polish. A SHG conversion efficiency of -70% has been obtained with Q-switched Nd : YAG pulsed laser (500 mJ, 10 ns, 0.6 lillad; ¢ 8 rrnn) at 1 .06 /lm.

In this period, Tang's research group ( 102-104) also made important advances : They grew a large transparent urea crystal with good optical quality by using the aqueous solution growth method. The urea molecule also possesses a planar structure with a conjugated n-electron system. Thus, in spite of an absorption edge that extends out to 210 nm in the ultraviolet region, the crystal still exhibits a larger SHG coefficient than d36 of KDP crystal (see Table 3) and has proven to be an excellent ultraviolet NLO crystal.

New Organic NLO Crystals

As mentioned earlier, Davydov (83), Chemla, Oudar, Zyss, and other research groups developed theoretical models of the NLO effect in organic

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Table 3 Some parameters for basic properties among various ultraviolet SHG crystals

Transmission SHG coefficient Phase matchable Damage threshold Crystals (nm) d36(KDP) (SHG, nm) (GW/cm2)

4.6 (1064 nrn) f:I-BaB204 190-3000 dll = 4.10 200-1500 10 (694.3 nrn)

(single pulse) ADP 1 50-1400 1 .2 260-700 0.4 (530 nm) KBsOs ' 4H2O 1 65-1200 0. 1 1 190-590 1 .0 (450 nm) Li(CH02)H2O 220-1 200 2.5 295-590 Urea 2 1 0-1400 2.8 240-700 5 (1064 nrn)

3 (532 nm)

Physical and chemical properties

nondeliquescent good mechanical properties

deliquescent deliquescent deliquescent deliquescent

Ref.

54

74, 75 100a

103, 104

tv W o

� Ro

§

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 23 1

crystals and accumulated experimental data on the synthesis of organic n-conjugated molecules. The search for new types ofNLO organic crystals relies increasingly on molecular engineering. Today's focus is on crys­tals possessing extremely large dZjn3 values. Several interesting NLO crystals, for which the figure of merit dZjn3 is '" 1-3 orders of magnitude larger than that of LiNb03, have been found by Oudar & Hierle (88), Zyss et al (85), and Levine et al (89). Table 4 lists the relative values of NLO and linear optical parameters. The striking advantage of these organic crystals is that their huge d2jn3 values lead to a high SHG conversion efficiency, even in very thin ('" I mm) crystals and thin-film devices. On the other hand, it is very difficult to grow these organic crystals to a large size with good optical homogeneity. Likewise, their mechanical and physicochemical properties are not very good. Therefore, whether or not the practical applications of these crystals can be realized depends to a great extent on the progress of integrated optics. For example, NPP (l05) and MNA (89) crystals possess values that are '" 2-4 orders of magnitude larger (d2jn 3) than LiNb03. Hence the two crystals obtained by various film growth methods can potentially have a high SHG conversion efficiency in a distance as short as the coherence length. These organic crystals appear to have a great potential for practical use, for example, as waveguide elements.

Infrared NLO Crystals

Until recently, there were no important advances in the search for new NLO crystals for the far infrared region. Research focused on how to improve optical quality ( 106, 1 07) and how to raise the damage threshold ( l08) of several chalcopyrite-type crystals like AgGaS2' AgGaSe2' and CdGeAs. Despite large NLO coefficients and a wide phase-matchable range, the optical quality of these crystals is usually not good enough, their damage threshold is low (only about l O MWjcm2), and their use as NLO materials is greatly restricted. In the near future, research efforts may proceed along the following two directions. First, the growth of chalcopyrite-type crystals has to be improved further so as to enhance their optical quality, particularly their optical homogeneity. The scattering centers observed during the growth process must be eliminated. Con­siderable work is required to identify the physical origin of the surface optical damage that is always observed in chalcopyrite-type crystals ( l08). It will then be possible to overcome the low damage threshold of these infrared NLO crystals. Second, the low intensity threshold for damage of chalcopyrite-type crystals seems to be an inherent defect that is very difficult to overcome via improvement of the growth method, alone. Our goal, therefore, should not be limited to materials of Sp3 hybrid type but

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Table 4

Crystal

MAP

POM

MNA

NPP

Some parameters of basic properties of organic crystals

Molecular

formula

N02

N02 --Q- N H - R

H R : -{- CCOCH3

CH3

CH3

N02--O N - O

CH3

NH2-b-- N02

CH20H

No2-Q-b

Trans-mission

(}.tm)

0.5 -+ 2.5

0.5 -+ 1 . 7

0.48 -+ 2.0

0.48 -+ ?

Refractive index

(1 .06 Jim)

nx = 1 .5078 ny = 1 . 5991 n, = 1 . 8439

nx = 1 .663 ny = 1 .829 n, = 1 .625

nx = 2.0 ± 0. 1 ny = 1 .6 ± 0. 1 n = ? , . (,\ = 0.6328 Jim)

?

N (jJ N

SHG d2/n3 Damage coefficient [ x d� dn3 threshold (")

( x 10-9 esu) (LiNb03)] (GW/cm2) Ref. � Z Ro I:"" a

d21 = 40 ± 5 1 5 (Type I) 3 GW/cm2 d22 = 44 ± 5 6 (Type II) at 1 .06 pm

d23 = 8.8 ± 2 1 50 MW/cm2 88 d2S = - 1 .3 ± 1 at 0.53 pm

d = d14 = d2S = 3.3 (Type I) 2 GW/cm2

d36 = 22 ± 3 0.82 (Type II) at 1 .06 pm 85 1 50 MW/cm2

at 0.53 pm dll = 394.0 ± 20% d12 = 59 ± 25% �2000 89 d33, dl 3, d31 �

10- 3 dl l

? � 1000 50 MW/cm2

at 0.53 pm l OS Ann

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 233 should also include other materials, with the help of theoretical models, that can produce a larger SHG effect and sustain a higher laser intensity in the far infrared region.

PROGRESS IN CRYSTAL GROWTH

Crystal growth of nonlinear optical and electro-optical materials provides samples for characterization of properties and determines the feasibility of device applications. In this section we outline the progress that has been made in techniques of crystal growth for these materials. Because of the emphasis on miniaturization and integration of electronic and optical devices, we shall focus on the growth of film and fiber crystals. Numerous guided-wave devices have been fabricated from electro-optical crystals, and single crystal fibers of nonlinear and laser host materials have been grown. Hence it is possible that in laser output, harmonic conversion, switching, and modulation could be performed consecutively in an integrated optic device. This trend represents the future development of laser techniques.

Growth of Single Crystal Fibers

The growth of single crystal fibers is desirable because of their application to linear and nonlinear optic devices. In addition, the rapid growth rate of the fibers makes them useful for material surveys. Their applications are shown in Table 5. The content of this subsection owes much to the work of Fejer et al ( l 08a).

At Stanford University fibers of more than thirty materials have been grown ; a few of them are shown in Table 6.

The single crystal fiber growth apparatus uses a laser-heated miniature pedestal growth technique. A focused waveguide CO2 laser provides a controlled heat source to melt the source rod. A specially designed optical system focuses the laser beam on to the source rod in a 3600 axially symmetric distribution, which results in the formation of a molten zone ( lO9). The source rod is translated into the laser beam by a belt drive translation system, and the rod may be fabricated from either polycrystalline or hot pressed powder materials. To initiate growth, an oriented seed rod is dipped into the molten zone. The seed rod defines the crystallographic orientation of the fiber. Growth proceeds by simul­taneously translating the source and seed rods. During growth the molten zone remains fixed. Conservation of mass determines the fiber diameter reduction. Diameter reductions of 3 : 1 are typical. Figure 4 shows schematically the growth of a single crystal fiber using this technique.

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Table 5 Some applications of single crystal fibers of NLO materials'

Passive devices Light guide Thermometer Polarizer

Active devices Laser amplifier Laser oscillator

Nonlinear devices Modulator Mixer Harmonic generator Parametric oscillator

Material surveys Laser host-ion combinations

• Mter Reference J08a.

Growth of Single Crystal Film

Al20,

Nd) + : YAG Cr'+ : AI20, Tj3+ : Al20,

LiNbO,

Ti : Al20,

A variety of techniques are used to grow film crystals. Here we mention epitaxial growth from the vapor phase, epitaxial growth from the liquid phase, molecular beam epitaxy, and metallorganic vapor phase epitaxy.

VAPOR PHASE EPITAXY (VPE) In semiconductor and integrated optical devices, a wide variety of heterostructures are used. VPE is the most widely used growth technique. Thin films with good quality of Si, III-V, and II-VI compounds have been grown using this method. VPE includes

Table 6 Representative single crystal fibers'

Length Diameter Material Orientation (cm) (pm)

Alp) (001) 20.0 170 3.5 50

Alp)+0.05 wt.% Cr (001) 10.0 170 3.0 95

YAG+ 0.9 wt.% Nd ( 1 1 1 ) 3.5 1 10

LiNbO, (00 1 ) 3 .5 50 ( 1 00) 3.0 1 70

• Mter Reference lO8a.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 235

two classes of main growth systems : an open-tube irreversible reaction system and a closed-tube reversible reaction system.

Thin films of Si can be grown by the following reaction in the open­tube system ( 1 1 0) :

SiH4_xYx(g) + (x- 2)H2(g) -t Si(s) +xHY(g),

where Y is a halogen and x has values from 1 to 4. Compounds ofIII-V materials are often grown by closed-tube reversible

reaction using halogens as the transport reagent. A typical reaction is ( 1 1 1 )

TJ 3 InCI(g) + 2 AS(g) ¢ InC13(g) + 2 [nAs(s)' T,

LIQUID PHASE EPITAXIAL GROWTH (LPE) LPE can be described as a solution growth from a molten metal solvent. On the basis of the geometric arrangements of the epitaxial apparatus in which the contact between the substrate and the liquid phase can be realized, three versions of LPE are generally used. They are the tipping method, horizontal furnace sliding, and vertical furnace techniques. Their schematic representations are shown in Figures 5, 6, and 7.

The tipping method was first used by Nelson to grow GaAs and Ge

CO2 laser

b eam

- seedt 1 crys a

- fre e z ing int erfa c e

molt en zone

f------. - melt ing int erfa c e

- sourc e rod

1 feed

Figure 4 Schematic of miniature pedestal growth for fiber crystals (after Reference 108a).

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236 CHEN & LIU

react ion chamb er

metal solut ion

Figure 5 A tipping method for LPE.

( 1 1 2) . The GaAs substrate was placed at the higher end of the boat-like crucible while flux and the solute were at the lower end, to form a high temperature solution. The flux was heated initially to a higher temperature and then was cooled to the saturation point. The substrate was brought in contact with the supersaturated solution by "tipping" ; epitaxy took place as the temperature was lowered.

To produce the sequences of controlled compositions and doping that are needed for lasers and light-emitting diodes, the horizontal furnace "slider" apparatus is generally employed (1 1 3, 1 14).

Garnet films can be produced by temperature gradient transport in a vertical furnace apparatus ( 1 1 5).

Wave-guiding LiNb03 films of optical quality have been produced on LiTa03 substrates by LPE. This method is superior to VPE, RF sputter, interdiffusion, and the melt method ( 1 1 6) .

react ion chamber

, slider

met al so lut ion

boat Figure 6 Horizontal furnace LPE method (after Reference 1 14).

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 237

� substrat e holder

crucible : metal solut ion

Figure 7 Vertical furnace LPE method.

MOLECULAR BEAM EPITAXY (MBE) The technique of MBE can be defined as the growth of epitaxial films of compounds or alloys from thermal energy molecular beams that impinge on a crystalline surface under ultrahigh vacuum conditions, as shown in Figure 8.

The basic components of an MBE system are an ultrahigh vacuum (UHV) chamber, a specimen heater block, and molecular beam effusion sources. In addition, facilities for in situ monitoring of the substrate surface and the epitaxial film are often included (1 1 7).

Os. -I(. As*

substrat e heat er

substrat e

shut ter furnace effus ion cell sources

Figure 8 Schematic of MBE apparatus (after Reference 1 14).

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238 CHEN & LID

Ovens of the Knudsen effusion type are the molecular beam sources and are contained within the UHV chamber. The molecular beams are individually controlled by shutters. In MBE of AlxGa l _xAs, the ovens in Figure 8 might contain Ga, AI, As, and a dopant element, respectively. A change from AlxGa l -xAs to GaAs epitaxial growth can be made by simply shutting off the Al oven.

The important advantages of MBE include a controlled growth rate ( 1-35 A/s), a low substrate temperature (300-750°C), and the capability to abruptly stop and start growth with atomic layer precision and to grade with any predetermined composition or by doping profile. Numerous in situ diagnostic techniques are possible during growth. MBE also allows simultaneous ion-implantation and other processing in situ. Selective area growth of different materials is possible by shadow masking (1 14).

METALLORGANIC CHEMICAL VAPOR DEPOSITION (MOCVD) Recently, MOCVD has been increasingly used by a number of laboratories to fabricate sophisticated multilayer devices with very thin layers and abrupt inter­faces. For example, the semiconductor injection laser and the III-V field effect transistor can be fabricated by MOCVD. Both kinds of devices need ultra-thin layers and abrupt interfaces, especially in laser structures based on quantum well concepts. In this kind of structure the widths of layers in the active region have dimensions less than an electron de Broglie wavelength, i.e. less than 1 0-20 nm. To achieve layers of this dimension one must be able not only to control the growth rate but also to achieve essentially monolayer abruptness in the transition between layers. In addition, the graded regions may require the growth of 20-50 layers of different composition in sequence. MOCVD can meet these requirements.

MOCVD was pioneered in 1 968 by Manasevit ( 1 1 8), who first produced GaAs by the following reaction :

H , (CH3)3Ga(g) + AsH3(g) � 3CH4(g) + GaAs(s)·

The most likely path of the reaction involves thermal and/or surface catalyzed decomposition of the initial reactants, followed by recom­bination of the Ga and As at the substrate surface. Doping is accomplished by introducing an appropriate reactant into the gas flow ( 1 1 9) .

Growth of Large Potassium Dihydrogen Phosphate (KDP) Crystals

The KDP crystal is one of the most widely used nonlinear materials. Recently, because of the need for a pulsed laser of high power as a heating source in laser fusion, interest in growing large KDP crystals has increased. At present, attempts are being made to grow KDP crystals with a cross section of 20-40 em, or even larger.

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NONLINEAR AND ELECTRO-OPTICAL MATERIALS 239

The three-zone crystallizer system, which was improved by Loiacono et al ( 120), has become a promising design for the production of such large crystals from aqueous solution. This system, with a total internal volume of 144 liters, consists of three chambers, the crystallizer, the superheater and the saturator, all of which are interconnected via heated tubes and form a closed-loop system. The optical quality of the crystals grown in this system is good. Crystal growth rates exceeding 5 mm day- l for large KDP seed crystals have been demonstrated. The maximum rate of growth lies somewhere above this value and could be 10 to 1 5 mm day- I .

In order to control supersaturation in the growth of KDP from aqueous solution, scientists in the same group ( 1 21) have developed a method for in-line bulk supersaturation measurement that could be practically and economically applied to production-scale single crystal growth.

Another method for obtaining fast growth of large KDP crystals is electrodialysis (122).

Crystal Growth of Certain New Nonlinear Materials

Recently, many new nonlinear materials have been discovered. The growth methods for some of these are summarized in Table 7.

Table 7 Growth methods of some NLO materials

Material (formula) Growth method Reference

Urea (H2NCONH2) Solution growth Slow cooling 123 Solvent : methanol or

methanol + glycerine

MAP Solution growth Slow cooling Solvent : a mixture of 88

34% ethyl acetate in n-hexane

POM Solution growth Evaporation Solvent : methylene chloride 124

MNA Solution growth Evaporation 89

Solvent : methyl alcohol

KTP(KTiOP04) Hydrothermal growth 96

p-BaB204 High-temperature solution top-seeding method 54

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240 CHEN & LIU

CONCLUSION

We wrote this review for two reasons. First, we believe that the NLO crystal (including EO and photorefractive crystals) will play an increasing role in the future development of optical processing techniques. Some scientists even regard the NLO crystal as the optic-semiconductor of the next century. Secondly, the theoretical work of the mid 1970s on the structure-property relation of NLO crystals laid the ground work for the implementation of "molecular engineering" and "crystal engineering" in the laboratory. It is obvious that "molecular engineering" will be very important not only in the search for new NLO crystals but also for the material sciences in general. Therefore, in this review we have focused on advances in understanding the physical origin of NLO phenomena and properties at the molecular level, including the relationship between macroscopic NLO effects and their microscopic structure. Then we discussed how to use these theoretical results and some advances in experimental measurement techniques to establish a primarily "molecular engineering" or "crystal engineering" approach to the search for NLO crystals. We summarized the main achievements in the search for NLO crystals since the mid 1970s, with emphasis on the organic and ultraviolet NLO crystals. In the last section we briefly introduced recent developments in growth techniques, particularly the fiber and film crystal growth techniques, because these two crystal growth techniques may represent the future direction of technical progress in the field.

Finally, we would like to point out that in 1 974 Byer wrote a review (32) entitled "Nonlinear Optical Phenomena and Materials" for the Annual Review of Materials Science. We have tried in this review to provide coverage of the major developments that have take place since that article was published.

ACKNOWLEDGMENTS

The authors are very grateful to Mr. Chen Qi-xian of the Fujian Institute of Research on the Structure of Matter for his assistance in the preparation of this manuscript.

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Annual Review of Materials Science Volume 16, 1986

CONTENTS

PREFATORY CHAPTER

On Material Structure and Human History, Cyril Stanley

Smith

EXPERIMENTAL AND THEORETICAL METHODS

Ion-Selective Electrodes, J. Koryta 13 Surface Second Harmonic Generation: A New Technique for

Surface Studies, Y. R. Shen 69 Studies of the Dynamic Properties of Materials Using

Neutron Scattering, Stephen W. Lovesey and Colin G. Windsor 87

Application of Impedance Spectroscopy to Materials Science, Ian D. Raistrick 343

Computer Modeling of Mass Transport Along Surfaces, George H. Gilmer and Jeremy Q. Broughton 487

Computer Simulation Studies of Transport in Solids, C. R. A. Catlow 517

PREPARATION, PROCESSING, AND STRUCTURAL CHANGES

Plasma-Surface Interactions in Plasma-Enhanced Chemical Vapor Deposition, Dennis W. Hess 163

Materials Modification and Synthesis Under High-Pressure Shock Compression, R. A. Graham, B. Morosin, E. L. Venturini, and M. J. Carr 315

Preparation of Ultrasmooth Surfaces, Norman J. Brown 371 Nanostructures, R. E. Howard, W. J. Skocpol, and L. D. Jackel 441

PROPERTIES AND PHENOMENA

Compositionally Graded Semiconductors and Their Device Applications, Federico Capasso 263

Mechanical Properties of Composition-Modulated Metallic Foils, T. Tsakalakos and A. F. Jankowski 293

Crack Stability and Toughness Characteristics in Brittle Materials, Yiu-Wing Mai and Brian R. Lawn 415

SPECIAL MATERIALS

Oxynitride Glasses, Sumio Sakka 29 Composite Electroceramics, R. E. Newnham 47

vii

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viii CONTENTS (continued)

Ultralow-Loss Glasses, M. E. Lines 113 Low-Dimensional Chalcogenides as Secondary Cathodic

Materials: Some Geometric and Electronic Aspects, J. Rouxel and R. Brec 137

Electrochromic Materials, Tetsu Oi 185 Recent Advances in Nonlinear Optical and Electro-optical

Materials, Chuang-tian Chen and Guang-zhao Liu 203 Polymer Electrolytes, Michel B. Armand 245 Physical and Chemical Behavior of Welding Fluxes,

Charles A. Natalie, David L. Olson, and Milton Blander 389 Rare Earth-Iron-Boron Materials: A New Era in Permanent

Magnets, J. F. Herbst, R. W. Lee, and F. E. Pinkerton 467

INDEXES Subject Index 549 Cumulative Index of Contributing Authors, Volumes 12-16 569 Cumulative Index of Chapter Titles, Volumes 12-16 571

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