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Optik 124 (2013) 686– 688

Contents lists available at SciVerse ScienceDirect

Optik

j o ur nal homepage: www.elsev ier .de / i j leo

ptical properties of Sr3NbGa3Si2O14 crystal

hiliang Wua,∗, Jie Liana, Ping Songa, Shang Gaoa, Xiao Wanga, Zheng Maa, Yingshun Wanga,enli Guanb

School of Information Science and Engineering, Shandong University, Jinan, Shandong 250100, ChinaDepartment of Physics, Qilu Normal University, Jinan, Shandong 250013, China

r t i c l e i n f o

rticle history:eceived 7 September 2011

a b s t r a c t

Single crystal of Sr3NbGa3Si2O14 was successfully grown using the conventional Czochralski technique.UV–VIS–NIR spectrometry and spectroscopic ellipsometry have been used to study the optical properties

ccepted 9 January 2012

eywords:rystal growthptical materials and properties

of SNGS crystal. From the transmission spectrum, the cut-off wavelength is determined to be 284 nm.Refractive indices of SNGS crystal were accurately determined in the wavelength region between 350 nmand 800 nm, based on the analysis of the transmission spectrum and SE measurements at multiple anglesof incidence. The effects of varied values of k on no and ne were also discussed. Furthermore, the phasematching angle of SNGS crystal is 39.00◦.

pectroscopic ellipsometry

. Introduction

Sr3NbGa3Si2O14(SNGS) is a new kind piezoelectric single crystalnd has the advantages of low Ga2O3 content and good proper-ies, such as temperature compensation, high acoustic velocity andow acoustic loss [1,2], that allows SNGS to have enormous poten-ial in bulk acoustic wave (BAW) and surface acoustic wave (SAW)pplications. While there are some previous reports concerning therowth of SNGS crystals and optical activities [2–5] to our knowl-dge, only Ref. [2] has referred to the refractive indices of SNGSrystal. However, the result seems unacceptable compared withhe refractive indices of as-grown crystals (CNGS and CTGS) [6].

Spectroscopic ellipsometry (SE) is a versatile, powerful andigh-precision optical technique for the investigation of the opti-al properties of a wide variety of materials, especially in thereas of thin films and multilayer structures. Recently, SE has beenpplied extensively for the study of optically anisotropic mate-ials [7–9]. However, only the optical constant spectra of someell-known materials were updated or extended into unknown

pectral regions revising existent n and k spectra for crystals. Thetudies of anisotropy situations are by far not complete, and theeld of generalized ellipsometry applications continues to grow10]. In the present paper, a method, based on SE and transmis-ion spectrum, was used to study the refractive indices of SNGS

rystal. Compared with other optical techniques [11,12], such ashe prism refractometry method which is the most accurate tool of

∗ Corresponding author. Tel.: +86 15066650650; fax: +86 531 88364613.E-mail address: wushiliang@yeah.net (S. Wu).

030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2012.01.047

© 2012 Elsevier GmbH. All rights reserved.

measuring the refractive indices, the method based on SE and trans-mission spectrum is non-destructive and contactless.

2. Experimental

2.1. Single crystal growth

The SNGS crystal [5] with ordered langasite structure was grownin the State Key Laboratory of Crystal Materials of Shandong Univer-sity, using the Czochralski (CZ) method. X-ray powder diffraction(XRPD) experiments showed that the SNGS crystals were singlephase and had the same structure as the La3Ga5SiO14 (LGS) crystal.Finally, a 14 mm × 8 mm × 0.7 mm (X × Y × Z) crystal plate of SNGSwas cut and polished.

2.2. Measurement of transmission spectrum

The transmission spectrum along c(Z)-axis (optical axis) of SNGScrystal wafer was measured as a function of wavelength at roomtemperature in the range 190–3000 nm, using Hitachi UV–VIS–NIRU-4100 Spectrophotometer.Measurement of SE

In the experiment, optical axis lies perpendicular to the sam-ple surface (and therefore parallel to the plane of incidence). Theellipsometric dates were measured as a function of wavelength atroom temperature in the range 300–800 nm, using SOPRA GES5 SEinstrument.Results and discussions

3.1. Transmission spectrum

The transmission spectrum is shown in Fig. 1(a). It shows thatthe crystal has good optical quality and the highest transmittance

S. Wu et al. / Optik 124 (2013) 686– 688 687

30002700240021001800150012009006003000

102030405060708090

100110 a

Tran

smis

sion

[%]

SNGS crystal,Z-cut

8007006005004003005.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

2.5x10-6

3.0x10-6 bSNGS crystal,Z-cut

Ext

inct

ion

coef

ficie

nt (k

)

ng c(Z

ew2

tT

I

wmi

ta

˛

(erotl

R

I

wdtt

aSe

c

�

wron

r

r

Wavelenth[nm]

Fig. 1. (a) Transmission spectrum of SNGS crystal alo

xceeds 90%. The cut-off wavelength of SNGS is about 284 nm,hich is smaller than 294 nm measured in Ref. [4], bigger than

68 nm measured in Ref. [13].In optics, the Beer–Lambert law relates the absorption of light to

he properties of the material through which the light is traveling.he Beer–Lambert law can be shown by the following formula [14]:

= I0e−˛l (1)

here I0 and I are the intensity of the incident light and the trans-itted light. ̨ is the absorption coefficient of the substance and l

s the distance the light travels through the material.In physics, the extinction coefficient (k) is the imaginary part of

he complex index of refraction (N = n + ik), which also relates to thebsorption coefficient, as follows [14]:

= 4�k�

(2)

In this experiment, two suppositions should be made firstly:1) suppose ko = ke = k, considering the dispersions of ordinary andxtraordinary lights are very weak; (2) suppose there are onlyeflection at the front surface and absorption existed when a beamf light lies perpendicularly to the surface of the sample. In this case,he reflection of normal incidence and the intensity of transmissionight can be written as [14]:

= (n − 1)2

(n + 1)2(3)

= I0(1 − R)e−˛l (4)

here n is the refractive index of the sample and the originalates of refraction indices can be approximatively obtained withhe model of bulk calculate of GES5. I/I0 can be obtained from theransmission spectrum.

Inserting Eqs. (2) and (3) into Eq. (4), the values of k can bepproximatively worked out from the transmission spectrum ofNGS crystal in the order of magnitude of 10−6. The fitting result ofxtinction coefficient (k) is shown in Fig. 1(b).Refractive indices

The experimentally measured functions are tan (�) andos �(�), defined from the complex ellipsometric ratio �(�) [10]:

(�) = rsrp

= tan (�)ei�(�) (5)

here � is the wavelength of incidence and rp(rs) is the Fresnel’seflection coefficient of the sample for p(s)-polarized light. Whenptical axis lies perpendicular to the surface of single crystal, Fres-el’s reflection coefficient can be simply written as [15]:

s = rss = cos � − (N2o − sin2 �)

1/2

2 2 1/2(6)

cos � + (No − sin �)

p = rpp = NoNe cos � − (N2e − sin2 �)

1/2

NoNe cos � + (N2e − sin2 �)

1/2(7)

Wavelenth(nm)

)-axis; (b) extinction coefficient (k) of SNGS crystal.

where � is the angle of incidence, No = no + iko (Ne = ne + ike) is thecomplex refractive index of the ordinary light (extraordinary light).

In Eq. (5), there are four parameters unknown, namely the realand imaginary parts of the complex ordinary and extraordinaryrefractive indices. The four parameters can be inverted numericallyfrom at least two sets of SE dates by minimizing the error functiong:

g =m∑i=1

[(�i − �c)2 + ( i − c)

2] (8)

where �i and i is the values of measurements, �c and c is thecalculated values. m means different angles of incidence.

Firstly, considering the values of no and ne are closely interre-lated to ko and ke, the effects of different values of k on no and ne

will be discussed. The precision of the extracted index data dependson the accuracy of the ellipsometer components. For the sampleswhose extinction coefficients are lower than 10−4, due to the accu-racy of the ellipsometer components, it is difficult to obtain accuratek(�) because cos �(�) in the results is nearly 1.000000 and theextinction coefficients calculated is 0. In the former programmingcalculations, the values of k usually take 0, and it will be provedinfeasible by the following discussion. The SNGS crystal is a goodexample that the sample has good optical quality and there wereno dispersion observed in the measured cos �(�). However, it doesnot mean that there is no dispersion (ko = ke = 0). Suppose k equalto some tiny values (k = 0, k = 1 × 10−6, k = 2 × 10−6). We will findthat tiny dispersion really play a big role on the values of no andne and the method of supposing k equal to some special values isunbelievable, as shown in Fig. 2. It also shows that when k takesdifferent values, the values of ne change more obvious than no atthe same wavelength, and the curves of no are more smooth thanne.

Secondly, from the front discussion, we can know that suppos-ing extinction coefficient to some fixed values is infeasible, and itis difficult to get reasonable results just from the analysis of SEdates. So it is necessary to calculate the values of extinction coef-ficient at each wavelength by other means, just as we have doneabove in Fig. 1. Inserting the extinction coefficient obtained fromthe transmission spectrum into Eq. (5), the refractive indices canbe obtained, using the method of numerical inversion with MAT-LAB. Fig. 3 shows the no and ne fitted by a three parametric Cauchyequation of the form

n(�) = A + B

�2+ C

�4(9)

where n(�) is the real part of the complex refractive index at thewavelength �, A–C are the Cauchy coefficients and � is the wave-length (�m). In Fig. 3, several dates have tiny deviation from the

fitting line, it may be due to the instrument-made error of the mea-surement, such as the tiny oscillating of cos �(�) around 1.000000or the tiny deviation of tan (�). �n of the crystal declines from0.11 to 0.083 along with the wavelength changing from 350 nm

688 S. Wu et al. / Optik 124

0.80.70.60.50.41.74

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1.94

1.96 no(k=0) ne(k=0) no(k=1E-6) ne(k=1E-6) no(k=2E-6) ne(k=2E-6)

no/n

e

Wavelenth(um)

Fig. 2. The values of no and ne of SNGS crystal with k = 0, k = 10−6, k = 2 × 10−6. Theopen icons show the results of numerical inversion. The solid lines represent thefitting result using Cauchy equation.

0.80.70.60.50.41.75

1.80

1.85

1.90

1.95

2.00 no ne

no/n

e

Wavelenth(um)

Fig. 3. The values of no and ne of SNGS crystal vary with wavelength. The open iconsshow the results of numerical inversion. The solid lines represent the fitting resultusing Cauchy equation.

Table 1Cauchy equation coefficients of SNGS crystal and two as-grown crystals.

Sample Coefficients no ne

SNGS A 1.76351 1.83761B 0.00956 0.01542C 4.08651E−4 2.31342E−4

CNGS A 1.77062 1.84461B 0.00451 0.01098C 8.66509E−4 7.38243E−4

ttip

3

o

[

[

[

[

CTGS A 1.74826 1.81017B 0.00831 0.01162C 1.25284E−4 1.12963E−4

o 800 nm. The corresponding Cauchy coefficients of SNGS crys-al and two as-grown crystals are shown in Table 1. The refractivendices of CNGS and CTGS [6] crystals were measured using therism refractometry method.

.3. Phase matching angle

SNGS is a kind of positive uniaxial crystals, and a phase-matchedptical second harmonic generation (SHG) is possible. One can find

[[

[

(2013) 686– 688

a direction for n2ωo = nωe , referring to the phase-matching type I:

e + e → o [16]. The phase matching angle can be calculated by thefollowing formula:

�m = sin−1

{n2

e(ω)[n2o(ω) − n2

o(2ω)]

n2o(2ω)[n2

o(ω) − n2e(ω)]

}1/2

(10)

In the experiment, take � = 1064 nm into account, the wave-length of SHG is 532 nm. The phase matching angle of SNGS crystalis 39.00◦. In Ref. [6], the phase matching angle of CNGS (CTGS) is40.38◦ (36.8◦).

4. Conclusions

In this paper, we report the optical properties of SNGS crys-tal and use a date analysis method based on SE and transmissionspectrum. The refractive indices of an uniaxial anisotropic crys-tal of SNGS were determined from the analysis of SE dates andtransmission spectrum. Furthermore, the cut-off wavelength isdetermined to be 284 nm and the phase matching angle of SNGScrystal is 39.00◦. At last, the crystal possibly has some potentialapplications in the area of nonlinear optics, which require furtherstudies.

Acknowledgements

This work was supported by grants from the National Programon Key Basic Research Project of China (Grant No. 2009CB929400),the Natural Science Foundation of Shandong Province of China(Grant No. ZR2009GM023) and the Scientific Research Foundationfor Returned Scholars, Ministry of Education of China.

References

[1] A. Wu, J. Xu, et al., Bridgman growth of Sr3NbGa3Si2O14 single crystal, Mater.Res. Bull. 41 (2006) 861–866.

[2] Z.M. Wang, D.R. Yuan, et al., Optical and dielectric properties of Sr3NbGa3Si2O14

crystals, J. Alloys Compd. 425 (2006) 264–267.[3] I.H. Junga, A. Yoshikawa, Growth and structure of A3NbGa3Si2O14 (A = Sr, Ca)

compounds, J. Alloys Compd. 339 (2002) 149–155.[4] Z. Wang, D. Yuan, et al., Growth, thermal and optical properties of

Sr3NbGa3Si2O14 single crystals, J. Cryst. Growth 258 (2003) 349–352.[5] Z. Wang, D. Yuan, et al., Study on the growth and optical activity of

Sr3NbGa3Si2O14 single crystals, Mater. Sci. Eng. B107 (2004) 255–258.[6] X. Shi, Study on the growth and properties of CNGS and CTGS crystals, Degree

Thesis, Shandong University, China, 2007.[7] H. Touir, M. Stchakovsky, R. Ossikovski, M. Warenghem, Coherent and inco-

herent interference modeling and measurement of anisotropic multilayerstacks using conventional ellipsometry, Thin Solid Films 455–456 (2004)628–631.

[8] P. Boher, J.P. Piel, B. Sacépé, Generalized ellipsometry for the charac-terization of anisotropic materials: influence of the sample adjustmenton the extracted optical indices, Thin Solid Films 455–456 (2004)581–585.

[9] A. Sassella, R. Tubino, A. Borghesi, M.E. Giardini, L. Quadrelli, Spectroscopicellipsometry measurements on an anisotropic organic crystal: potassium acidphthalate, Thin Solid Films 313–314 (1998) 347–350.

10] H.G. Tompkins, E.A. Irene (Eds.), Handbook of Ellipsometry, William Andrew,Springer, 2005.

11] T. Zhou, D. Zhang, H. Yang, et al., Measurement of refractive index of the crystalwith angle of minimum deviation method, J. Synth. Cryst. 26 (3–4) (2000) 377.

12] C. Zhang, J. Wang, C. Chen, et al., Growth and properties of a noval NLO crystalK2Al2B2O7, Chinese J. Mater. Res. 16 (6) (2002) 595–599.

13] J. Chen, E. Shi, et al., Growth habits and characterization of Sr3NbGa3Si2O14

crystal, J. Cryst. Growth 292 (2006) 404–407.

14] X. Shen, Optical Properties of Semiconductor, Science Press, Beijing, 1992.15] F. Meyer, E.E. de Kluizenaar, D. den Engelsen, Ellipsometric determina-

tion of the optical anisotropy of gallium selenide, J. Opt. Soc. Am. 63(1973) 529.

16] G. Jin, J. Li, Laser Metrology [M], Science Press, Beijing, 1998.