Linear and nonlinear refractive index of As–Se–Ge ...

JOURNAL OF APPLIED PHYSICS 107, 113527 共2010兲

doi:10.1063/1.3428441

Linear and nonlinear refractive index of As–Se–Ge and Bi doped As–Se–Ge thin films Pankaj Sharma1,a兲 and S. C. Katyal1 1

Department of Physics, Jaypee University of Information Technology, Waknaghat, Solan, Himachal Pradesh 173215, India

The present work reports the linear and nonlinear refractive index for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 thin films. The formulation proposed by Fournier and Snitzer has been used to predict the nonlinear behavior of refractive index. The linear refractive index and Wemple– DiDomenico parameters were used for the determination of nonlinear refractive index in the wavelength region 0.4 to 1.5 ␮m. Linear refractive index has been determined using the well known Swanepoel method. This is observed that nonlinear refractive index increases linearly with increasing linear refractive index. With Bi addition this has been found that nonlinear refractive index increases by 2.4 times, while on comparing with pure and doped silica glasses results are 2–3 orders higher. Density and molar volume has also been calculated. The obtained results may lead to yield more sensitive optical limiting devices and these glasses may be used as an optical material for high speed communication fibers. © 关 兴 I. INTRODUCTION

Chalcogenide glasses have emerged as important materials due to their applications in xerography, optoelectronics, optical switching, and nonlinear devices, etc.1–3 The properties of chalcogenide glasses can be tailored by varying their compositions. Optical properties of these glasses are mostly affected by the glass network formers4,5 though slight modifications are possible by selection of network modifying cations. Glasses with high atomic number anions and cations experience high optical polarizabilities resulting high linear and nonlinear refractive indices. All optical switching will play a crucial role in future high speed optical communication. All optical demultiplexing using third order optical nonlinearity is promising for future 1 Tbit/s networks. Silica glass fiber is one of the most promising nonlinear optical media.6,7 Chalcogenide glasses have also gained interest for their nonlinear effects. They have linear refractive index between 2 to greater than 3. It is apparent from Miller’s rule that nonlinear refractive index for chalcogenide glasses is two orders higher than for silica glass.8 Investigations on chalcogenide glasses have revealed large nonlinear refractive index values, fast response time, and promising properties as nonlinear optical media for all optical switches.9 Nonlinear optical media for all optical switches should provide a high degree of nonlinearity, a fast response time, a low rate of transmission loss, and a waveguide structure. Chalcogenide glasses posses this nonlinearity and can be used to form single mode fibers with low transmission loss. The experimental determination of the nonlinear optical properties of a material requires rather an elaborate technique, for example Z-scan method,10 four-wave mixing11 or optical third harmonic generation.12 These methods are not common in most of laboratories, and, hence, of interest are empirical or semia兲

Author to whom correspondence should be addressed. Electronic addresses: [email protected] and [email protected].

empirical relations to predict nonlinear refractive index 共n2兲 from some linear optical constants of a material. Since measurement of nonlinear refractive index is difficult and time consuming task, a predictive ability is useful in any program to develop low/high n2 materials depending upon the need. Various researchers13–17 have proposed different models to explain the nature of nonlinear phenomena in optics. Fournier and Snitzer18 have proposed a formulation for the determination of n2 on the basis of linear refractive index and Wemple–DiDomenico 共WDD兲 parameters. The main purpose of this paper is to study the effect of Bi on the linear and nonlinear refractive index for 共As2Se3兲90Ge10 system. Spectral dependence of linear refractive index has already been reported on 共As2Se3兲90Ge10 thin film.19 As2Se3 has been considered a proved material for nonlinear optics. The addition of Ge to As–Se system has also been studied for various compositions but not for the one investigated here. The results obtained are compared with pure silica,20,21 GeO2-doped fused silica,22 As2S3,9 and As–Se–Ge 共Ref. 23兲 compositions. II. EXPERIMENTAL DETAILS

Bulk glassy alloys of 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 systems were prepared by melt quench technique. The detail is given elsewhere.19 Thin films of these glassy alloys were deposited on cleaned glass substrate by thermal evaporation at ⬃10−4 Pa base pressure. The rate of evaporation 共r兲 共measured using DTM-101 fitted with HINDHIVAC model 12A4D, India兲 of deposited thin films under investigation is given in Table I. Thickness of the films 共Table I兲 deposited was measured by thickness monitor 共Model DTM-101兲 and found within ⫾35 nm as estimated later from the fitting of transmission spectra. The density of the samples has been measured 20 ° C using Archimedes Principle. The double distilled water is taken as reference liquid. The bulk glassy alloys were characterized by x-ray

TABLE I. Values of rate of evaporation 共r兲, density 共␳兲, molar volume 共Vm兲, density of polarizable constituents 共N兲, WDD parameters 共E0 and Ed兲, and linear refractive index 共n兲 at 800 nm for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 systems.

Composition

r 共Å/s兲

d2 共nm兲

␳ 共g/cc兲

Vm 共cc/mol兲

N ⫻1022

E0 共eV兲

Ed 共eV兲

n

共As2Se3兲90Ge10 关共As2Se3兲90Ge10兴95Bi5

13.1 13.6

910 948

5.178 5.412

14.846 15.425

4.0569 3.9048

3.24 3.21

13.63 27.61

2.62 3.48

diffraction technique and found to be amorphous in nature as no prominent peak was observed in the spectra. The compositions of evaporated samples have been measured by an electron microprobe analyzer 共JEOL 8600 MX兲 on different spots 共size ⬃2 ␮m兲. For the composition analysis, the constitutional elements 共As, Se, and Ge兲 and the bulk original alloys were taken as reference samples. The composition of 2 ⫻ 2 cm2 sample is uniform within the measurement accuracy of about ⫾1%–1.5%. The transmission spectra of the thin film in the spectral range 0.4– 1.5 ␮m were taken using a double beam ultraviolet-visible-near infrared spectrophotometer 共Perkin Elmer Lambda-760兲. Optical measurements were performed at room temperature 共303 K兲. III. RESULTS AND DISCUSSION

this method continuous envelops are generated through the tangents of maximum and minimum of fringes. A distinct advantage of using the envelopes of the transmission spectrum rather than only the transmission spectrum is that the envelopes are slow-changing functions of ␭, whereas the spectrum varies rapidly with ␭. The basic equation for interference fringes is 2nd = m␱␭.

The accuracy of refractive index can be improved after calculating thickness d. mo is an integer for maxima and a half integer for minima in transmission spectra. If na and nb are the refractive indices of two adjacent maxima and minima at wavelengths ␭1 and ␭2, then the thickness of the film is given by the expression

A. Density and molar volume

The density of the sample is calculated using the formula, ␳ = 关w1 / w1 − w2兴␳water, where w1 and w2 are the weight of the sample in air and the weight of the sample in the reference liquid, respectively, 共for detail see Ref. 24兲. The average recorded densities for different compositions are given in Table I. This is found that the density of the system increases monotonically with Bi addition. This may be due to the addition of denser Bi atoms. Another parameter related to the density, namely the molar volume 共Vm兲 was determined from the density data using relation, Vm = 1 / ␳兺ixiM i where M i is the molecular weight of the ith component and xi is the atomic percentage of the same element in the sample. The values of Vm for the prepared compositions are listed in Table I. The molar volume was found to increase with the addition of Bi, which may be due to the result addition of heavier and larger Bi atoms in the glass network. The atomic radius of As 共121 p.m.兲, Ge 共122 p.m.兲, and Se 共117 p.m.兲 in comparison to atomic radius of Bi atom 共152 p.m.兲 共Ref. 25兲 is smaller.

共1兲

d=

␭ 1␭ 2 . 2共␭,nb − ␭2na兲

共2兲

˜ 兲 of d can be used with n to deThe average value of 共d 1 1 a termine mo for the different maxima and minima using Eq. 共1兲. By taking the exact integer or half integer values of mo, accuracy of the film thickness can be increased significantly and d2, a new thickness, 共Table I兲 can be derived from Eq. 共1兲 by using the values of n. Further using the accurate values of mo and ˜d2, in Eq. 共1兲, the final values of the refractive index n2 are obtained. Now, nb can be fitted to Cauchy dispersion relationship,27,28 nb = 共a + b / ␭2兲, which can then be used for extrapolation the values of refractive index to shorter wavelength region. The accuracy of linear refractive index values of the films under investigation is ⫾1% over the whole transmission spectra. 1.0 0.8

The optical system under consideration corresponds to homogeneous and uniform thin films, deposited on thick transparent substrates. The thermally evaporated films have thickness d and complex refractive index nⴱ = n − ik, where n is the linear refractive index and k is the extinction coefficient. Figure 1 shows the transmission spectra of the thin films under investigation. From Fig. 1 it is found that transmission decreases to ⬃70% when Bi 共5 at. %兲 is added to the 共As2Se3兲90Ge10. This might be due to high reflectance in Bi containing films.26 Swanepoel’s envelope method27,28 has been applied for the calculation of linear refractive index. In

Transmittance

B. Linear refractive index 0.6 0.4

(As2Se3)90Ge10

0.2 0.0

[(As2Se3)90Ge10]95Bi5 600

800

1000

1200

1400

1600

Wavelength (nm) FIG. 1. Transmission spectra of 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 thin films.

0.24

4.4

0.20

(As2Se3)90Ge10

[(As2Se3)90Ge10]95Bi5

0.16 -1

3.6

2

(n n -1)

Linear Reffractive Index

4.0

3.2

0.12 0.08

2.8

(As2Se3)90Ge10

0.04

[(As2Se3)90Ge10]95Bi5

0.00 0.0

0.4

2.4 2.0 400

600

800

1000

1200

1400

Wavelength (nm) FIG. 2. Variation in linear refractive index with wavelength for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 thin films.

Spectral distribution of refractive index shown in Fig. 2 inferred that refractive index decreases with the increase in wavelength for the thin films under investigation. The decrease in refractive index with the increase in wavelength may be correlated with decrease in absorption coefficient. The decrease in the value of refractive index with wavelength shows the normal dispersion behavior of the material. On the part of 5 at. % Bi addition to 共As2Se3兲90Ge10 the refractive index has been found to have higher values. This increase in the refractive index may be ascribed to increase in disorder in the structure, change in stoichiometry, and internal strain caused with the addition of Bi. The increase in linear refractive index may also be explained on the basis of polarizability. Larger the atomic radius of the atom larger will be its polarizability and consequently according to Lorentz–Lorenz relation between refractive index and polarizability larger will be the refractive index. Lorentz–Lorenz relation is 2

1 n −1 = 兺 Ni␣pi , 2 n + 2 3␧0 i

共3兲

where ␧0 is the vacuum permittivity, Ni is the number of polarizable units of type i per unit volume with polarizability ␣ pi. The atomic radii25 of Ge 共1.22 Å兲, Se 共1.17 Å兲, As 共1.21 Å兲, and Bi 共1.52 Å兲 shows that Bi containing films may have higher refractive index. According to single oscillator model proposed by WDD model,29,30 the optical data could be described to an excellent approximation by the following expression: n2共h␯兲 = 1 +

E20

E 0E d , − 共h␯兲2

0.8

2

1.2

1.6

2

2.0

(hν) (eV)

1600

共4兲

where h␯ is photon energy, E0 is single oscillator energy, and Ed is dispersion energy which is a measure of the average strength of interband optical transitions. Plotting refractive index factor 共n2 − 1兲−1 against 共h␯兲2 allows us to determine the oscillator parameters by fitting a straight line to the points, as shown in Fig. 3. It is worth emphasizing the goodness of the fits to the large wavelength experimental data. The values of WDD dispersion parameters, E0 and Ed, for all thin films were directly determined from the slope 共E0Ed兲−1

FIG. 3. Plot of 共n2 − 1兲−1 关共As2Se3兲90Ge10兴95Bi5 thin films.

共h␯兲2

vs

共As2Se3兲90Ge10

for

and

and the intercept on the vertical axis 共E0 / Ed兲 of their corresponding least square straight lines. The values of these dispersion parameters are given in Table I for the thin films under investigation. Nevertheless, it must be noted that the WDD model is only valid in transparent region, where the absorption coefficient of chalcogenide thin films takes values ␣ ⬇ 0. The detailed analysis of the dispersion of refractive index, in terms of WDD model, throws very valuable light on the structure of material through the values of the dispersion energy parameter Ed. The calculated WDD parameters E0 and Ed are in good agreement with the earlier reported results.29,30 This has been observed that the single oscillator parameter, E0 is in concord to the relation, i.e., E0 ⬇ 2 obtained by Tanaka31 when studying vitreous films ⫻ Eopt g having a composition AsxS100−x, and which subsequently hold for other vitreous chalcogenide thin films.32,33 C. Nonlinear refractive index

When matter is exposed to intense electric fields, polarization is no longer proportional to electric field and the change in polarizability has to be extended by terms proportional to the square of electric field. For refractive index it follows as ⌬n = n2兩E兩2 where ⌬n is the intensity dependent change in refractive index, E is electric field, and n2 is nonlinear refractive index. Fournier and Snitzer18 had proposed a formulation to determine n2 on the basis of linear refractive index 共n兲 and WDD parameters 共E0 , Ed兲 in the following relation: n2 =

冋

册

共n2 + 2兲2共n2 − 1兲 Ed 共x32兲2 −1 , 共E0兲2 共x2g兲2 48␲nN

共5兲

where N is density of polarizable constituents 共calculated by making use of density/molar volume data兲, subscripts g, 2, and 3 to x denotes the ground state 兩g典, excited states 兩2典 and 兩3典. For a three level system the quantity 关共x32兲2 / 共x2g兲2 − 1兴 = 1, so Eq. 共1兲 reduces to n2 =

共n2 + 2兲2共n2 − 1兲 Ed . 共E0兲2 48␲nN

共6兲

Nonlinear refractive index is calculated in esu, for unit conversions see Refs. 9 and 34. The variation in n2 with photon energy and linear refractive index is given in Figs. 4 and 5.

Nonlinear Refractive Index (esu)

1.0x10

-10

9.0x10

-11

8.0x10

-11

7.0x10

-11

6.0x10

-11

5.0x10

-11

4.0x10

-11

3.0x10

-11

2.0x10

-11

1.0x10

-11

TABLE II. Comparison of nonlinear refractive index values with As2S3 共Ref. 9兲, pure silica 共Refs. 20 and 21兲, GeO2 doped silica 共Ref. 22兲, and Ge10As30Se60 共Ref. 23兲 at 1.55 eV.

(As2Se3)90Ge10

[(As2Se3)90Ge10]95Bi5

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Photon Energy (eV)

Nonlinear Refra active Index (esu)

This is clear from Fig. 4 that n2 increases linearly with n whereas n2 follows the same trend as n follows with photon energy 共wavelength兲. Glasses with Eopt g ⬇ 1.6 eV are promising for nonlinear applications, as demonstrated partially.35 Accordingly, the materials with or near to Eopt g ⬇ 1.6 eV are suitable for optical devices which are utilized at the communication wavelengths of ␭ = 1.3– 1.5 ␮m 共h␯ ⬇ 0.8 eV兲. This spectral insight can be applied as a rough approximation also to noncrystalline semiconductors having nondirect gaps.36 When considering optical nonlinearity in homogeneous media, we should take spectral dependence into account. Although here we have not considered directly the Eopt g values, but are compared with E0 values according to the relation 31 E0 ⬇ 2 ⫻ Eopt g proposed by Tanaka. The comparison of values of nonlinear refractive index with some other materials at 1.55 eV has been given in Table II. This is clear from the values given in table that with the addition of Bi the nonlinear refractive index increases by 2.4 times to that of 共As2Se3兲90Ge10. Our results are found to be in good agreement with As2S3 共Ref. 9兲 and Ge10As30Se60 共Ref. 22兲 at 1.55 eV. Nonlinear refractive index is higher by two orders in comparison to GeO2-doped fused silica22 and three orders in comparison to pure silica.20,21 Thus the systems under investigation may be used as an optical material for high speed communication fibers and also in optical limiting devices. -10

9.0x10

-11

8.0x10

-11

7.0x10

-11

6.0x10

-11

5.0x10

-11

4.0x10

-11

3.0x10

-11

2.0x10

-11

1.0x10

-11

(As2Se3)90Ge10

[(As2Se3)90Ge10]95Bi5

2.4

2.6

2.8

3.0

3.2

3.4

3.6

n2 共esu兲 at 1.55 eV

共As2Se3兲90Ge10 关共As2Se3兲90Ge10兴95Bi5 As2S3 a Pure silicab Pure silicac GeO2-doped fused silicad Ge10As30Se60 e

2.94⫻ 10−11 7.06⫻ 10−11 3.51⫻ 10−11 8.1⫾ 1.2⫻ 10−14 7.4⫻ 10−14 2.4⫻ 10−13 7.33⫻ 10−11

a

FIG. 4. Variation in nonlinear refractive index with photon energy for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 thin films.

1.0x10

Composition

3.8

4.0

4.2

Linear Refractive Index FIG. 5. Variation in nonlinear refractive index with linear refractive index for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 thin films.

Reference 9. Reference 20. c Reference 21. d Reference 22. e Reference 23. b

IV. CONCLUSION

Linear refractive index for 共As2Se3兲90Ge10 and 关共As2Se3兲90Ge10兴95Bi5 follows the normal dispersion behavior. Linear refractive index increases with the addition of 5 at. % Bi to 共As2Se3兲90Ge10. Nonlinear refractive index has been determined using Fournier and Snitzer formulation based on WDD single oscillator parameters. Nonlinear refractive index has been found to increase by 2.4 times with 5 at. % of Bi addition, while on comparing with doped and pure silica glasses results are 2–3 orders higher. The obtained results may lead to yield more sensitive optical limiting devices and these glasses may be used as an optical material for high speed communication fibers. 1

A. Zakary and S. R. Elliot, Optical Nonlinearities in Chalcogenide Glasses and Their Applications 共Springer, Berlin, Heidelberg, 2007兲. 2 A. M. Andriesh V. V. Ponomar’, V. L. Smirnov, and A. V. Mironos, Sov. J. Quantum Electron. 16, 721 共1986兲. 3 R. Fairman and B. Ushkov, Semiconducting Chalcogenide Glass III: Applications of Chalcogenide Glasses 共Elsevier, New York, 2004兲. 4 P. Sharma and S. C. Katyal, Thin Solid Films 517, 3813 共2009兲. 5 P. Sharma and S. C. Katyal, Appl. Phys. B: Lasers Opt. 95, 367 共2009兲. 6 T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, Electron. Lett. 32共9兲, 833 共1996兲. 7 K. Utchiyama, S. Kawanishi, H. Takara, T. Morioka, and M. Saruwatari, Electron. Lett. 30共11兲, 873 共1994兲. 8 V. G. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, Opt. Express 15, 9205 共2007兲. 9 M. Asobe, T. Kanamori, and K. Kubodera, IEEE J. Quantum Electron. 29, 2325 共1993兲. 10 M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14共17兲, 955 共1989兲. 11 D. W. Hall, N. F. Borelli, W. H. Dumbaugh, M. A. Newhouse, and D. L. Weldman, Proceedings of Symposium on Nonlinear Optics, Troy; 1988 共unpublished兲, p.293. 12 H. Nasu, Y. Ibara, and K. Kubodera, J. Non-Cryst. Solids 110, 229 共1989兲. 13 J. Phillips and J. van Vechten, Phys. Rev. 183, 709 共1969兲. 14 B. Levine, Phys. Rev. Lett. 22, 787 共1969兲. 15 C. Wang, Phys. Rev. B 2, 2045 共1970兲. 16 J. J. Wynne, Phys. Rev. 178, 1295 共1969兲. 17 W. Harrison, Phys. Rev. B 8, 4487 共1973兲. 18 J. Fournier and E. Snitzer, IEEE J. Quantum Electron. 10, 473 共1974兲. 19 P. Sharma and S. C. Katyal, J. Phys. D: Appl. Phys. 40, 2115 共2007兲. 20 S. Smolorz, F. Wise, and N. F. Borrelli, Opt. Lett. 24, 1103 共1999兲. 21 A. Boskovic, S. V. Chernikov, J. R. Taylor, K. L. Gruner-Nielsen, and O. A. Levring, Opt. Lett. 21, 1966 共1996兲. 22 T. Itoh, R. Morita, and M. Yamashita, Jpn. J. Appl. Phys., Part 2 35, L1107

共1996兲. H. Tichá and L. Tichý, J. Optoelectron. Adv. Mater. 4, 381 共2002兲. 24 P. Sharma and S. C. Katyal, Physica B 403, 3667 共2008兲. 25 C. N. R. Rao, M. V. George, J. Mahanty, and P. T. Narasimhan, A Handbook of Chemistry and Physics, 2nd ed. 共Affiliated East–West, New Delhi, 1970兲. 26 A. Sharma and P. B. Barman, Appl. Phys. B: Lasers Opt. 97, 835 共2009兲. 27 R. Swanepoel, Meas. Sci. Technol. 16, 1214 共1983兲. 28 R. Swanepoel, Meas. Sci. Technol. 17, 896 共1984兲. 29 S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 共1971兲. 30 S. H. Wemple, Phys. Rev. B 7, 3767 共1973兲. 23

K. Tanaka, Thin Solid Films 66, 271 共1980兲. J. M. González-Leal, A. Ledesma, A. M. Bernal-Oliva, R. Prieto-Alcón, E. Marquéz, J. A. Angel, and J. Carabe, Mater. Lett. 39, 232 共1999兲. 33 T. I. Kosa, T. Wagner, P. J. S. Ewen, and A. E. Owen, Philos. Mag. B 71, 311 共1995兲. 34 T. Topfer, J. Hein, J. Phillipps, D. Ehrt, and R. Sauerbrey, Appl. Phys. B: Lasers Opt. 71, 203 共2000兲. 35 K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, Opt. Lett. 29, 265 共2004兲. 36 N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials 共Clarendon, Oxford, 1979兲. 31 32