Nonlinear characterization of GeS2–Sb2S3–CsI glass system

Nonlinear characterization of GeS 2 – Sb 2 S 3 – CsI glass system

K. Fedus, G. Boudebs, Q. Coulombier, J. Troles, and X. H. Zhang

Citation: Journal of Applied Physics 107, 023108 (2010); doi: 10.1063/1.3289607 View online: http://dx.doi.org/10.1063/1.3289607

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Nonlinear characterization of GeS

₂

– Sb

₂

S

₃

– CsI glass system

K. Fedus,^1,a兲 G. Boudebs,¹Q. Coulombier,²J. Troles,²and X. H. Zhang²

1POMA, FRE CNRS 2988, Université d’Angers, 2 Bd Lavoisier, 49045 Angers Cedex 01, France

2UMR CNRS 6226, “Sciences Chimiques de Rennes,” Université de Rennes I, 35042 Rennes Cedex, France

共

Received 24 October 2009; accepted 10 December 2009; published online 28 January 2010

兲

We present the results of Z-scan measurements

共

1064 nm, 17 ps

兲

of nonlinear refractive indices and nonlinear absorption coefficients for different compositions of chalcogenide glasses in GeS₂– Sb₂S₃– CsI system. We show that the simple well known Boling, Glass, and Owyoung model based on the theory of the semiclassical harmonic oscillator can be a useful tool for theoretical predictions of the nonlinear refractive index in these infrared glasses. A quasi-linear behavior is observed relating the nonlinear index and the linear one. Some of the compositions reveal properties potentially useful for all optical switching applications. © 2010 American Institute of Physics.

关doi:10.1063/1.3289607兴

I. INTRODUCTION

The amorphous glasses based on the chalcogen elements

共

S, Se, and Te

兲

are well known for possessing a large optical nonlinear refraction combined with an infrared transparency^1,2and, hence these materials are promising can- didates for linear and nonlinear optical elements. Therefore, many different compositions, binary as well as ternary, have been fabricated and studied in order to optimize optical prop- erties for a wide range of possible applications. For example, the optical switching applications require high nonlinear re- fractive index

共n

2

兲

and low nonlinear absorption coefficient

共

␤

兲

while the optical limiting proprieties need both high n₂ and␤ coefficients. It is also important to have simple theo- retical expressions allowing to predict the magnitude of non- linearities and hence facilitating the choice of glass compo- sitions with the desired optical properties. It was found experimentally

共chapter 4 in Ref.

1 and references inside兲, that n₂ and␤ increase with the linear refractive index

共n

0

兲

and the normalized photon energy

共h

␯/E_g, where h is the Planck’s constant,␯is the incident photon frequency, and E_g the energy band gap of the material兲. Results of Z-scan³mea- surements published in our previous works dealing with tellurium⁴ and germanium⁵ based chalcogenide glasses are consistent with this tendency. Therefore, the general trend in the nonlinearity is accounted for by the linear refractive in- dex and the normalized photon energy, hence both n₀ and h␯/E_g should be decisive parameters in the theoretical esti- mation of nonlinearities. However, the theory of nonlinear optical absorption

共

␤

兲

in amorphous materials and insulators is still a field of investigation⁶ on the contrary of that in crystals which has been better understood based on the band theory.⁷ One of the problems in the case of amorphous ma- terials is the definition of E_gsince the absorption edge is not sharp as in crystals and the interpretation of the band gap is ambiguous.^8,9The estimation of n₂on the basis of the linear optical index would be preferable because no ambiguity in the measurements of n₀ can appear especially in the trans- parency region. One of the n₂ predictive capabilities is pro-

vided by Boling, Glass, and Owyoung

共BGO兲.

¹⁰On the basis of a semiclassical model of the simple harmonic oscillator and the dispersion of linear refractive index, they derived the so-called BGO model giving an expression relating n₂ with n₀. Despite its simplicity, the BGO formula stays in suffi- ciently good accuracy with experimental results for different oxide and tungstate fluorophosphates glasses.^11,12

The aim of this paper is to present the results of nonlin- ear characterization for a family of chalcogenide glasses, namely the bulk GeS₂– Sb₂S₃ glass forming system doped with halide, CsI. The latter component has been chosen in order to enlarge the band gap and consequently to decrease the linear and nonlinear absorption at the infrared region. We will show that the BGO model can be a useful tool for quick and accurate theoretical prediction of the nonlinear refractive index for this investigated family of chalcogenides.

II. EXPERIMENTS

The different compositions were prepared according to the method described in.¹³ High purity materials

共99.999%

for Ge, Sb, S and 99.99% for CsI

兲

are used for the glass preparation in silica tube under vacuum

共

10⁻⁵ mbar

兲

. The sealed silica tube is heated to 850 ° C in a rocking furnace and maintained 10 h at this temperature to ensure a good reaction between the starting materials and a good homog- enization of the melt. The glass is obtained by quenching the tube in water and by annealing the sample near its glass temperature, before cooling down to room temperature in order to release stresses induced by quenching. The glass is then cut into disks of about 1mm thick, which are then pol- ished to obtain two parallel faces.

The measurements of n₂ and ␤ have been done using modified Z-scan method inside a 4f imaging system

共Fig.

1兲.

Excitation is provided by a neodymium doped yttrium alu- minum garnet

共Nd:YAG兲

laser delivering linearly polarized 17 ps single pulses at 1064 nm. The focal length of the two lenses composing the 4f system is f₁= f₂= 20 cm. The beam waist at the focal plane is ␻0= 35 ␮m giving a Rayleigh range z₀= 3.5 mm. The latter value is larger than 1 mm, the typical thickness of the samples. The photoreceptor is a

a兲Electronic mail: kamil.fedus@univ-angers.fr.

共 兲

0021-8979/2010/107共2兲/023108/5/$30.00 107, 023108-1 © 2010 American Institute of Physics

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1000⫻1018 pixels cooled

共

−30 ° C

兲

charge-coupled device

共

CCD

兲

camera with fixed linear gain. The camera pixels have 4095 gray levels and each pixel is 12⫻12 ␮^{m2. Open and} closed aperture Z-scan normalized transmittance can be nu- merically processed from the acquired images, by integrating over all the pixels of the CCD camera in the first case and over a circular numerical filter in the second one. To avoid the contribution of any permanent linear change of the re- fractive index attributed to photo-induced effects

共PIE兲, a

shutter is mounted at the input of the setup letting only one laser-shot-interaction with the material for each step of the Z-scan motor. The overall repetition rate is about 0.1 to 0.2 Hz depending on the size of the acquired images

共to be

stored to the hard disk兲. To check the absence of the perma- nent PIE, three sequential Z-scan acquisitions, in the linear, the nonlinear, and again in the linear regime were carried out illuminating the sample on the same impact region. No photo-induced modifications were observed as in¹⁴ for the considered bulk material in this paper. Moreover, recently we showed that it is possible to characterize the permanent lin- ear modification inside the sample after relatively long illu- mination in the focal region.¹⁵ In the Z-scan analysis, here the number of impacts is reduced to approximately five laser shots along the Rayleigh range and the intensity was chosen carefully in order to obtain a sufficient signal in the Z-scan traces without photo-inducing other permanent measurable linear modifications inside the glasses.

Moreover, we have reported on Z-scan absolute measurements¹⁶ of nonlinear refractive index in CS₂ and fused silica

共SiO

2

兲, two references materials generally used

in nonlinear experiments to calibrate the incident intensity in the focal plane. We obtained absolute values 7.5 times less than those usually given in the literature at 1064 nm in the picosecond regime. Here the calibration of the intensity in the focal plane of our Z-scan setup was done using fused silica and considering n₂= 4⫻10⁻²¹ m²/W as obtained in our absolute measurements in reference.¹⁶It should be added that for comparison purpose n₂and␤ given here have to be multiplied by a factor 7.5 in order to obtain the equivalent of the nonlinear coefficients when the calibration is done taking into account the n₂= 3⫻10⁻¹⁸ m²/W of CS₂ found in.³

The optical absorption measurements performed with a UV-visible-near IR spectrometer

共CARY500兲

show negli- gible linear absorption in the infrared region for all the com- positions and particularly at 1064 nm. The energy band gap

共E

g

兲

was determined from absorption spectra as the wave- length for which the linear absorption coefficient is equal to 10 cm⁻¹. The linear refractive indices were measured at two wavelengths, 1331 and 1551 nm, using a polarized laser with TE incidence in a Metricon prism coupler system.

III. RESULTS AND DISCUSSION

The results of the Z-scan measurements of the investi- gated glasses and the measured linear optical coefficients are summarized in TableI. The n₂values are given in column 5

共within the parenthesis the ratio of n

2 to that of the fused silica兲. The nonlinearity of the investigated glasses is at least 50 times higher than that of the fused silica. Sample J exhib- its the highest nonlinear refraction index. A careful revision of the experimental data shown in TableIcould suggest that the optical properties of the investigated glasses depend strongly on the antimony

共Sb兲

content. One can notice an improvement of n₂, with a redshift of the optical gap

共col-

umn 8兲 and an increase in the linear refractive index

共col-

umns 9 and 10

兲

with the amount of Sb₂S₃

共

column 3

兲

. A similar behavior has been already observed in Refs.17 and 18dealing with linear and nonlinear optical properties of the glass-host system xGeS₂−

共

1 − x

兲

Sb₂S₃, respectively.

CCD

f1 f1 f2

L1 L2

L3

M1

Sample BS1

BS2

f2

z' y x

M2

0 +z -z

FIG. 1. Schematic of the 4f imaging system. The sample is moved around the focal region. The labels refer to lenses共L₁-L₃兲, mirrors共M₁, M₂兲, and beam splitters共BS₁, BS₂兲.

TABLE I. Compositions of the investigated glasses共GeS₂+ Sb₂S₃+ CsI兲and their optical coefficients: column 5, n₂共within the parenthesis the ratio of n₂to that of the fused silica兲; column 6,␤, and column 7 the figure of merit 2␤␭/n₂at␭= 1064 nm共h␯= 1.17 eV兲. The normalized photon energies共h␯/E_g兲 together with the linear refractive indices measured at 1331 nm and 1551 nm are shown in the last three columns.

No

Percentage composition Optical coefficients

GeS₂ Sb₂S₃ CsI n₂共10⁻¹⁹ m²/W兲 ␤共10⁻² cm/GW兲 2␤␭/n₂ h␯/E_g^a n₀共1331 nm兲 n₀共1551 nm兲

A 90% 10% 0 2.0⫾0.4共50兲 ⬍0.2 ⬍0.22 0.470 2.146 2.140

B 75% 10% 15% 3.6⫾0.9共90兲 1.0⫾0.4 0.6 0.560 2.154 2.146

C 51.25% 26.25% 22.5% 3.9⫾0.6共97.5兲 2.0⫾0.4 1.08 0.571 2.274 2.265

D 66.25% 26.25% 7.5% 3.9⫾0.6共97.5兲 1.0⫾0.3 0.54 0.556 2.303 2.293

E 35% 35% 30% 4.7⫾0.7共117.5兲 3.0⫾0.7 1.36 0.584 2.309 2.299

F 42.5% 42.5% 15% 5.6⫾1.8共140兲 3.0⫾1.0 1.14 0.590 2.420 2.408

G 26.25% 51.25% 22.5% 7.5⫾2.2共187.5兲 10⫾1 2.84 0.622 2.457 2.444

H 10% 60% 30% 9.0⫾2.0共225兲 19⫾2 4.50 0.629 2.484 2.469

I 26.25% 66.25% 7.5% 9.7⫾1.9共242.5兲 20⫾2 4.38 0.660 2.619 2.602

J 10% 75% 15% 10.8⫾3.0共270兲 16⫾5 3.16 0.652 2.646 2.629

aE_gis defined as the energy for which the linear absorption coefficient is 10 cm⁻¹

023108-2 Feduset al. J. Appl. Phys.107, 023108共2010兲

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Changes in n₂ by ⬇400% were observed when varying x from 10% to 40%. Recently,⁵it was shown that in Ge–Sb–S systems, the nonlinear refractive index is correlated with a number of heteropolar Sb–S and Ge–S bonds and n₂ is en- hanced with decreasing Ge/Sb ratio. A careful analysis show that n₂ decreases with increasing Ge/Sb ratio for the glasses investigated here. The deviation from this tendency can be attributed to CsI component. Generally, the introduction of halide component reduces the linear refraction and moves the energy gap toward the blue region of the visible spectrum.¹⁹ Therefore, higher amounts of CsI elements should decrease the nonlinear refractive index.

In the column 7 of TableI, we give the figure of merit

共

FOM

兲

defined as 2␤␭/n₂.²⁰ It is a geometry-independent factor widely adopted in the literature to classify different nonlinear materials for optical switching or optical limiting applications. According to reference,²⁰ all optical switching capabilities require a FOM⬍1 in order to avoid large losses induced by nonlinear absorption. It can be seen that samples A, B, and D fulfill this criterion. The other samples seem to be more appropriate for optical limiting applications. How- ever, the expected diminution of␤at the telecommunication wavelength

共1550 nm兲, where most of the optoelectronic de-

vices operate, could give lower values of FOM.²¹ In Fig.2, we show the FOM versus the normalized photon energy. As it is pointed out in Refs. 22 and 23, the FOM in chalco- genides depends on the proximity of the light frequency to

two-photon absorption edge and it reaches a minimum for h␯/E_g just below 0.5. Our experimental results agree with this observation.

From the optical point of view the nonlinearities in chal- cogenides are correlated with the optical gap and the linear refraction. On the one hand, high third order susceptibility in chalcogenide glasses is attributed to their high n₀accordingly to the Miller’s generalized rule.²On the other hand there are many experimental results revealing an increase in nonlin- earities with h␯/E_g for different families of chalcogenide glasses

共see, for example, Refs.

22–24兲. Figures 3共a兲 and 3共b兲show n₂ and␤ as a function of the normalized photon energy for our specimens. The observed variations confirm the strong dependence on absorption gap for a fixed excita- tion wavelength. The interdependence of nonlinearities on n₀ and E_g comes from the fact that the linear refractive index and energy gap are generally related. In crystals the correla- tion between n₀ and E_g is usually expressed by the Moss rule²⁵ stating that n₀=␥/E_g^x, wherex= 0.25 and␥ ^{is a mate-} rial dependent constant. In amorphous materials as chalco- genide glasses a similar behavior between n₀ and E_g also seems to be valid. In Fig.4, we can see the refractive index at 1064 nm versus the energy gap for our specimens

共filled

circle兲as well as for another two families of chalcogenides, namely tellurium

共empty circles兲 关4兴

and germanium

共stars兲 关5兴

based glasses. In all cases, the energy band gap is defined

0.450 0.5 0.55 0.6 0.65 0.7

1 2 3 4 5

h/Eg

2/n2

FIG. 2. Figure of merit defined as␤␭/n₂versus normalized photon energy 共h␯/E_g兲.

0.450 0.5 0.55 0.6 0.65 0.7

0.2 0.4 0.6 0.8 1 1.2 1.4x 10^-18

n2(m2 /W) a)

h/E_g

b)

h/E_g (10-2 cm/GW)

0.450 0.5 0.55 0.6 0.65 0.7

5 10 15 20 25

FIG. 3. Variations of共a兲n₂and共b兲␤as a function of the normalized photon energy共h␯/E_g兲.

1.2 1.4 1.6 1.8 2 2.2 2.4

2 2.2 2.4 2.6 2.8 3

Eg

n0

FIG. 4. Linear refractive index共n₀兲at 1064 nm vs the energy gap共E_g兲for GeS₂+ Sb₂S₃+ CsI glass system共filled circle兲as well as for tellurium共empty circles兲 共Ref.4兲and germanium共Ref.5兲 共stars兲based chalcogenide glasses.

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as the wavelength for which the linear absorption coefficient is 10 cm⁻¹. The values of n₀ at 1064 nm in the glasses in- vestigated here were obtained from the experimental data at 1331 and 1551 nm using the dispersion model described in Eq.

共2兲 共given below兲. The dashed line in Fig.

4is the best fit to the experimental data of n₀=␥/E_g^x

共obtaining

x= 0.37 and

␥= 3.1 when E_gis expressed in eV兲. The absolute values ofx and␥are not important because these coefficients are depen- dent on the energy gap definition, which is ambiguous in amorphous materials. However, this modified Moss relation is to be considered as a rough approximation in order to show a general tendency in the relationship between E_g and n₀. This dependency permit us

共

i

兲

to use indifferently one these parameters to predict the nonlinearities and

共ii兲

to ex- plain qualitatively why a model

共as the one to come hereaf-

ter兲using only one of these parameters can be considered as valid from the physical point of view.

We have chosen the linear refraction data as the basic input to estimate the nonlinear refraction indices because the measurement of n₀ is not ambiguous in the transparency re- gion. The BGO model¹⁰ offers such an advantage. This model assumes that the third order hyperpolarizability is pro- portional to the square of the linear polarizability. It supposes also that the linear optical dispersion of the medium is deter- mined by only one resonance frequency ␻0 and the fre- quency of the light is far away from the resonance

共

␻ Ⰶ␻0

兲. Moreover the dielectric response should have a pure

electronic nature. The nonlinear refractive index expressed in SI units is given by

n₂

共m

²/W兲=

共gS兲共n

₀²+ 2兲²

共n

₀²− 1兲²

12n₀²cប␻0

共NS兲

,

共1兲

whereg is a dimensionless anharmonity parameter, S is the effective oscillator strength, N is the ion density depending on the composition, and cis the speed of light. The linear refractive index for a wavelength␭ fulfils the following ex- pression:

1 3

共n

₀²+ 2兲

共n

₀²− 1兲= ␻02−␻²

共

e²/m_e␧0

兲共

NS

兲

,

共

2

兲

where␧0is the vacuum permittivity,eandmeare the charge and the mass of the electron, respectively. The parameters NS and ␻0 are obtained from the values of n₀

共␭

= 1331 nm兲and n₀

共␭

= 1551 nm兲measured for each sample.

Then, the values ofNSand␻0are introduced into Eq.

共1兲

to determine n₂. The best agreement with experimental data was obtained for a scaling factorgS= 0.59. The comparisons of the experimental and the theoretical values are shown in Fig.5as a function of the linear refractive index at 1064 nm.

The values of n₀

共␭

= 1064 nm兲 were determined using Eq.

共2兲

with the values ofNSand␻0obtained for each sample. A very good agreement is found between the experimental and theoretical values. Note that due to the new calibration the obtained value ofgSis approximately 7.5 less than the ones adopted upto now. The latter values

共between 3 and 4.5兲

have been always chosen empirically in order to fit the experimen- tal results. Anyway the effect of the calibration produces only a vertical shift into the predicted n₂values but does not change the variation inside Fig. 5. Moreover note that the presence of the nonlinear absorption does not affect the pre- dictions of the BGO model.

IV. CONCLUSION

We have measured the nonlinear refractive indices

共

n₂

兲

and the nonlinear absorption coefficients

共

␤

兲

for GeS₂– Sb₂S₃– CsI chalcogenide glasses. We have confirmed that the nonlinear refractive index behavior is closely related to the linear one. Following this property, we have shown that the BGO model could be a useful tool to estimate n₂ values. A very good agreement with the experimental data is obtained. Three compositions among ten inside investigated glass family have a figure of merit 2␤␭/n₂⬍1, thus they can be suitable candidates for optical switching applications.

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n0

n2(m2 /W)

2.1 2.2 2.3 2.4 2.5 2.6 2.7

0 0.2 0.4 0.6 0.8 1 1.2 1.4x 10^-18

FIG. 5. Comparison between experimental n₂data共filled dots兲and values calculated from the BGO formula Eq.共1兲共stars兲.

023108-4 Feduset al. J. Appl. Phys.107, 023108共2010兲

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