Journal of Non-Crystalline Solids 481 (2018) 160–163
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Photoelastic and acousto-optic eﬀects in 65GeS2-25Ga2S3-10CsCl glass a
B. Mytsyk , O. Shpotyuk
, N. Demyanyshyn , Ya. Kost' , A. Andrushchak , L. Calvez
Karpenko Physico-Mechanical Institute, 5 Naukova Street, 79601 Lviv, Ukraine Vlokh Institute of Physical Optics, 23 Dragomanov Street, 79005 Lviv, Ukraine Institute of Materials of SRC “Carat”, 202 Stryjska str., 79031 Lviv, Ukraine d Jan Dlugosz University of Czestochowa, 13/15 al. Armii Krajowej, 42-200 Czestochowa, Poland e Lviv Polytechnic National University, 12 Bandery Street, 79013 Lviv, Ukraine f Equipe Verres et Céramiques, UMR-CNRS 6226 Institut des Sciences Chimiques de Rennes, Université de Rennes 1, 35042 Rennes CEDEX, France b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Chalcohalide glass Interferometry Piezo-optics Elasto-optics Photoelastic eﬀect Mechanical stress Acousto-optic ﬁgure of merit
The peculiarities of photoelastic and acousto-optic eﬀects are ﬁrst tested in chalcohalide 65GeS2-25Ga2S3-10CsCl glass exploring the interferometry method. The determined piezo-optic coeﬃcients occur to be (in Br) π11 = 2.8 ± 0.6, π12 = 6.0 ± 0.9 and π44 = −3.2 ± 1.1. In respect to maximal acousto-optic ﬁgure of merit М2 = 55.6 · 10− 15 s3/kg proper for longitudinal acoustic wave propagation and polarization along X2 (і = 2) direction, this glass seems more perspective for photoelastic and acousto-optic modulation in visible and near IR ranges, than many alternative candidates, such as crystalline quartz, LiNbO3, CaWO4, PbMoO4, β-BaB2O4, etc. For the ﬁrst time it has been shown that piezo-optic eﬀect of isotropic solids is anisotropic, and the degree of anisotropy is the diﬀerence of π11–π12 coeﬃcients.
1. Introduction Among a large group of functional media exploring IR spectral region, the special glasses based on chalcogenides, i.e. non-oxide compounds of chalcogens S, Se and/or Te prepared by quenching from a melt, which are often referred to as chalcogenide glasses, are in a sphere of tight interests for a great number of scientists in view of their promising implementation in functional optics (photonics, optoelectronics, telecommunication and information technologies, sensing electronics, etc.) [1–6]. Near two decades ago, it was shown that principal IR functionality of these glasses covering both telecommunication windows (3–5 and 8–12 μm) up to space telecommunication domain (20–25 μm) could be conveniently shared with high transmittance of halides in a visible range [7–9]. New class of disordered materials viz. mixed chalcohalide glasses (ChHGs) and glass-ceramics was emerged, thus comprising advantages of both chalcogenide and halide materials platforms [9,10]. This class of materials can be well exempliﬁed, in part, by glassy GeS2-Ga2S3-CsCl system with one of most typical representative of 65GeS2-25Ga2S3-10CsCl chemical composition [11–15]. Main optical properties of this ChHG (short-wave optical transmission edge, longwave optical transmittance cut-oﬀ, wavelength dispersion of refractive index, chromatic dispersion, etc.) were studied in details elsewhere [11–14]. Good transmittance in a visible spectral range in these ChHGs
is worth to be highlighted, along with their ability to be protected against atmospheric aggression by anti-reﬂecting ZnS coating, and excellent technological applicability in diﬀerent macrooptic performances due to highly reproducible molding route [13,14]. Such promising realization of chalcohalide platform serves as a basis for wider practical using of these glassy-like media, especially in controllable light-guiding acousto-optic systems [16–23]. In this respect, the changes in optical properties of the ChHGs (refractive index, birefringence) under mechanical strain (piezo- and elasto-optic eﬀects), allowing determination their acousto-optic eﬃciency, are of high importance. In this work, the magnitudes of piezo-optic coeﬃcients (POCs) were ﬁrst measured in 65GeS2-25GaS3-10CsCl ChHG by interferometry method. The elasto-optic coeﬃcients (EOCs) were calculated at the basis of POCs, the modulation parameter (which describes the change of optical path per sample's thickness and mechanical stress) was found, and thus the acousto-optic eﬃciency of this ChHG was estimated. The magnitudes of refractive indexes, elastic constants and acoustic velocities were also determined. 2. Experimental The ChHGs of 65GeS2-25Ga2S3-10CsCl composition (transparent in a range from ~ 0.5 μm to 11 μm [13,14]) were prepared from high-
Corresponding author. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.jnoncrysol.2017.10.036 Received 5 August 2017; Received in revised form 21 September 2017; Accepted 18 October 2017 Available online 07 November 2017 0022-3093/ © 2017 Published by Elsevier B.V.
Journal of Non-Crystalline Solids 481 (2018) 160–163
B. Mytsyk et al.
somewhat greater (near 5%) due to possible inhomogeneities in mechanical stress. Two independent control stresses σ11o and σ12o deﬁned experimentally with typical errors no more than 10% were + 12.2 and + 7.9 kG/cm, respectively. Using Eq. (2) with control stresses (σ11o and σ12o) and elastic coefﬁcient S12, the magnitudes of two independent POCs can be presented (in Br units, 1 Br = 1 Brewster = 10− 12 m2/N) as π11 = + 2.8 ± 0.6 (21%) and π12 = + 6.0 ± 0.9 (15%). The errors in POCs were found as mean square values from ﬁrst and second components in Eq. (2) by assuming that error in the ﬁrst component is formed by 10% error in the control stress σimo, and error in the second component is formed by 5% error in the elastic coeﬃcient S12. Noteworthy, the 65GeS2-25Ga2S3-10CsCl glass overcomes by POCs magnitudes many known acousto-optic media. Thus, the maximal magnitudes of principal POCs πim (i, m = 1, 2, 3) are known to be from 0.66 to 0.8 Br for lithium niobate LiNbO3 [32,33], 1.44 Br for gallium phosphide GaP , 1.86 Br for calcium wolframate CaWO4 [29,34], 3.11 Br for crystalline quartz , 3.34 Br for lead molybdate PbMoO4 , 3.7 Br for barium β-borate β-BaB2O4 [37,38]. The high magnitude was also obtained for rotation-shift coeﬃcient π44 = −(3.2 ± 1.1) Br deﬁned as π44 = π11 − π12 in respect to POCs matrix of isotropic solids [39,40]. Let's estimate the photoelastic eﬃciency of this glass due to δΔk/ (dkσm) parameter, which describes the change in the optical path per sample's thickness dk and mechanical stress unit σm. This parameter introduced in [30,32] can be presented at the basis of Eq. (1) as
purity raw materials (elemental Ge, Ga, S and CsCl of 5 N purity) using conventional melt-quenching route as was described elsewhere [12–14]. The puriﬁed ingredients weighed in stoichiometric proportions were inserted in a silica ampoule under 10− 4 Pa vacuum. The sealed ampoule was placed in a rocking furnace for several hours at 850 °C and quenched in room-temperature water. The polished (λ/4) cubic sample (7 × 7 × 7 mm) was cut from the resulting ingot, this sample being annealed 10 °C below the glass transition temperature (Tg = 405 °C) for 4 h to reduce residual mechanical stress induced during the quench. The optically isotropic materials like glasses are known to possess only two independent piezo-optic coeﬃcients πim (π11 and π12), which can be measured by interferometry method of the half-wave (control) stress with the Mach-Zehnder interferometer set-up . By using relation for diﬀerence in optical path lengths δΔk in the interferometer arm with studied sample under mechanical stress σm in the form of
1 δΔk = δ (ni dk ) = − πim σm dk ni3 + Skm σm dk (ni − 1), 2
the magnitudes of POCs πim can be calculated from experimental halfwave stresses σim under condition of δΔk = λ/2, σm = σim [24,25]:
πim = −
λ λ 2S 2S + km (ni − 1) = − o 3 + km (ni − 1); σim ni3 dk ni3 σim ni ni3
where ni = n is refractive index of isotropic sample, dk is sample's thickness in light propagation direction, Skm is elastic compliance coeﬃcient, σimo = σimdk is control stress; the k, i, m indexes denote light propagation, polarization and uniaxial pressure directions, respectively. The refractive index ni = n was determined by the interferometryturning method using set-up at the basis of Michelson interferometer . The longitudinal and transversal ultrasonic velocities V11 and V12 needed to obtain the coeﬃcients of elastic stiﬀness Сmn and elastic compliance Skm were determined by impulse Papadakis method .
δΔk 1 = − πim ni3 + Skm (ni − 1). dk σm 2
For real experimental conditions m = 1, k = 2, і = 1, and change in optical path is formed by πim = π11 and Skm = S12 coeﬃcients. Respectively, it is found that:
δΔ2 1 = − π11 n i3 + S12 (n1 − 1) = −12.6 (48%) − 13.7 (52%) = −26.3 Br. d2 σ1 2
3. Results and discussion
3.1. POCs π11 and π12 determination
The larger value of this parameter is character for m = 2, k = 3, і = 1 (corresponding to πim = π12, Skm = S32 = S12):
The value of refractive index in the studied 65GeS2-25Ga2S3-10CsCl glass at λ = 632.8 nm wavelength determined using the Michelson interferometer set-up occurred to be n = 2.08 ± 0.01. The elastic stiﬀness coeﬃcients С11 and С12 were deﬁned as  2 C11 = ρV11 ,
2 C11 − C12 = 2ρV12 .
δΔ3 1 = − π12 ni3 + S12 (n1 − 1) = −27.0 (66%) − 13.7 (34%) = −40.7 Br. d3 σ2 2 (9) In respect to calculated δΔk/(dkσm) parameters, the studied 65GeS225Ga2S3-10CsCl ChHG is better than such known crystalline photoelastic materials as GaP and PbMoO4, possessing maximal values of these parameters (+ 20.3 and − 24.9 Br, respectively [30,36]). So this glass belongs to better photoelastic materials in view of POCs magnitudes and high values of modulation parameter δΔk/(dkσm). Note that percentages in parenthesis in Eqs. (8) and (9) correspond to inputs into overall eﬀect from piezo-optic (ﬁrst component) and elastic (second component) contributions. The piezo-optic contribution in Eq. (9) is twice greater than the elastic one. The negative magnitudes in Eqs. (8) and (9) mean that optical path δΔk decreases under positive (expansion) mechanical stress.
The magnitudes of these coeﬃcients С11 = 24.4 GPa and С12 = 8.35 GPa were obtained using preliminary values of glass density ρ = 2.92 · 103 kg/m3 deﬁned by hydrostatic weighting in toluol and ultrasonic velocities V11 = 2890 m/s and V12 = 1658 m/s for longitudinal and transversal acoustic waves, respectively, determined by impulse Papadakis method . The magnitudes of elastic compliance S11 and S12 coeﬃcients were obtained as inverse components of elastic stiﬀness coeﬃcients matrix S = С − 1:
C11 + C12 , 2 2 + C11 C12 − 2C12 C11
S12 = −
C12 . 2 2 + C11 C12 − 2C12 C11
3.2. EOCs р11 and р12 determination
The р11 and р12 EOCs are calculated at the basis of experimental POCs (π11 and π12) and elastic stiﬀness coeﬃcients С11 and С12, using known tensor expression рin = πimCmn [39–41], which can be written for isotropic media as
With above С11 and С12 coeﬃcients, the S11 = 49.6 · 10− 12 m2/N and S12 = − 12.7 · 10− 12 m2/N values were obtained. The typically estimated errors do not exceed 0.3% in acoustic waves (V11 and V12) and 2% in elastic coeﬃcients (Сmn and Skm). Following to our previous works [29–32], we accept that realistically the latter could be 161
р11 = π11 C11 + π12 C21 + π13 C31 = π11 C11 + 2π12 C12,
р12 = π11 C12 + π12 C22 + π13 C32 = π11 C12 + π12 (C11 + C12).
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By inserting the above π11, π12, С11 and С12 magnitudes in Eqs. (10) and (11), it was found that р11 = 0.168 ± 0.022 and р12 = 0.220 ± 0.025. The mean square errors of these рin coeﬃcients were deﬁned from known expression δ(πimCmn) = [(δπim)2Cmn2 + πim2(δCmn)2]1/2, applied to each components in Eqs. (10) and (11). The δπim errors are given for πim coeﬃcients, while δCmn errors are taken as 5% from Cmn values (for more details in errors determination for рin coeﬃcients, the reader is addressed to ). Thus, the POCs errors are main contributions (up to ~ 95%) in δріn, while only 5% belongs to errors in elastic constants Cmn. The р44 coeﬃcient dependent on both р11 and р12 [39,40] was relatively small р44 = 1/2(р11 − р12) = −0.026 ± 0.017. 3.3. Piezo-optic and elasto-optic eﬀect anisotropy Fig. 1. The IS of piezo-optic eﬀect πim′ in ChHG and its cut-section by principal X1, X3 plane (all in Br units) under uniaxial pressure in m∥X1 (β = 90°, α = 0°) direction.
The piezo-optic eﬀect was commonly accepted to be isotropic in isotropic solids, i.e. the indicative surfaces (IS) πim′ of longitudinal (і ∥m, i.e. the vectors of light polarization і and uniaxial pressure m coincide) and transversal eﬀects (і⊥ m, i.e. the vectors of light polarization і and uniaxial pressure m are orthogonal) are spheres. Indeed, using known expressions for IS in cubic crystals in spherical coordinates 
serving as a measure of this anisotropy. The IS shown in Fig. 1 is transformed in a sphere, provided π11 = π12. So the general surfaces of piezo-optic eﬀect are more informative than IS of longitudinal and transversal eﬀects. It is quite understandable that general surface of elasto-optic eﬀect is also anisotropic with corresponding values ranging from р11 to р12.
πii′ = π11 + 2(π12 − π11 + π44 ) × (sin4 θ sin2 φ cos2 φ + sin2 θ cos2 θ), (12)
′ = π12 + 2(π11 − π12 − π44 )sin2 θ sin2 φ cos2 φ πim
3.4. Acousto-optic eﬃciency
Let's calculate the acousto-optic ﬁgure of merit M2 for 65GeS225GaS3-10CsCl ChHG in respect to the Gordon's formalism [44,45]:
for longitudinal and transversal eﬀects, respectively, and accepting that π44 = π11 − π12 for isotropic material, it is easily to prove that πii′ = π11, and πim′ = π12 for all θ and φ angles (where θ is angle between light polarization direction i and Х3 axis, φ is angle between projection of light polarization direction i upon Х1, Х2 plane and Х1 axis; Х1, Х2, Х3 are optical indicatrix axes). It means that IS of longitudinal and transversal piezo-optic eﬀects are spheres with characteristic π11 and π12 radii, respectively. The principal diﬀerent result will be, provided the general surfaces of piezo-optic eﬀect are reconstructed as proposed in [42,43]. Let's give the equation for general surface of piezo-optic eﬀect as for cubic crystals :
(14) where β and α are spherical coordinates of uniaxial pressure m direction (β is angle between m vector and Х3 axis, α is angle between vector m projection on Х1, Х2 plane and Х1 axis). If uniaxial pressure direction m is ﬁxed, e.g. along Х1 axis, then β = 90°, and α = 0°, thus resulting to plane equation:
′ (θ, φ) = πim
(sin2 θsin2 φ
For acoustic wave propagation and polarization along X1 axis (longitudinal acoustic wave) and light polarization along X1 (і = 1) direction, the values V = V11 = 2890 m/s, ni = n = 2.08 and ріn = р11 = 0.168 should be inserted in Eq. (16), resulting ﬁnally to М2 = 32.4 · 10− 15 s3/kg. If light is polarized along X2 (і = 2) direction, then М2 = 55.6 · 10− 15 s3/kg for the same acoustic wave (then ріn = р12 = 0.22). Let's ﬁnd М2 value for shear acoustic wave polarized along X2 axis, penetrating along X1 axis. This wave causes shear deformation ε4 within Х2, Х3 plane, and, correspondingly, the acousto-optic interaction is caused only by elasto-optic р44 coeﬃcient. So V = V12 = 1658 m/s and р44 = − 0.026 should be inserted in Eq. (16). The corresponding acousto-optic ﬁgure of merit is very small М2 = 4.1 · 10− 15 s3/kg in view of р44 coeﬃcient.
′ (θ, φ, β, α ) = [π11sin2 β cos2 α + π12 (sin2 β sin2 α + cos2 β )]sin2 θ cos2 φ+ πim + [π11sin2 β sin2 α + π12 (sin2 β cos2 α + cos2 β )]sin2 θsin2 φ + (π11cos2 β+ + π12sin2 β )cos2 θ + 0.5 π44 [sin2 θ sin 2φ sin2 β sin 2α + sin 2θ sin 2β × × (sin φ sin α + cos φ cos α )].
π11sin2 θ cos2 φ
4. Conclusions The chalcohalide (65GeS2-25GaS3-10CsCl) glass occurs to be an excellent elasto- and acousto-optic functional medium. Thus, in respect to maximal acousto-optic ﬁgures of merit М2, the POCs πim magnitudes and δΔk/(dkσm) parameter, this glass seems more perspective for elastoand acousto-optic modulation in visible and IR spectral regions, than many other alternative candidates. For example, М2 coeﬃcient of the investigated glass is much larger than in the known acousto-optic materials such as crystalline quartz, where M2 is equals 2.38  (in unit of 10− 15 s3/kg), LiNbO3 – 6.99 , CaWO4 – 13.8 , PbMoO4 – 39.0 , β-BaB2O4 – 30.0 .
which describes refractive index changes in whole space under uniaxial pressure along Х1 axis (Fig. 1). It is seen that in real the plane is anisotropic. The minimal and maximal values correspond to uniaxial pressure direction and orthogonal plane, respectively, these being equal to POCs magnitudes π11 and π31 = π12. In other arbitrary directions, these coeﬃcients are mediate between π11 and π12, which can be deﬁned from Eq. (15) for chosen θ and φ angles. It is noteworthy that at the basis of Eq. (14), the equation of plane describing changes in refractive index in a ﬁxed direction (e.g. along Х1 axis) under uniaxial pressure in arbitrary direction can be derived. This equation will be equivalent to Eq. (15), but in β and α variables. Therefore, the general piezo-optic IS show that piezo-optic eﬀect of isotropic solids is indeed anisotropic, the POCs diﬀerence (π11–π12)
Acknowledgements The authors acknowledge support from Science and Technology Center in Ukraine under target STCU-NASU project # 6174, as well as joint Ukraine-France R & D Project supported by CAMPUS FRANCE (project N° 37559QB) and Ministry of Education and Science of Ukraine 162
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