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Abstract
In this work, we investigated the mid-infrared (MIR) optical properties of selenide (Se-based) chalcogenide glasses (ChGs) within an As- and Ge-free system, namely the environment-friendly and low-cost tin–antimony–selenium (Sn-Sb-Se, SSS) ternary system, which has not been systematically studied to the best of our knowledge. As compared to ChGs within those conventional Se-based systems, SSS ChGs were found to exhibit extended infrared transmittance range as well as larger linear refractive index (n0). Femtosecond Z-scan measurements show the presence of evident three-photon absorption from Urbach absorption of the SSS ChGs at MIR wavelength, which resonantly enhanced the nonlinear refractive behavior and resulted in large nonlinear refractive index (n2).
© 2017 Optical Society of America
1. Introduction
Chalcogenide glasses (ChGs) known as a category of amorphous infrared material have been regarded as a promising candidate for nonlinear optical devices due to their infrared transparency, low phonon energy, high linear refractive index and large third-order optical nonlinearities (TONL, χ(3)) with ultrafast response time (<200 fs). These advantages in combination with the flexibility in size and alterable chemical compositions make ChGs suitable for fabrication of infrared photonic devices [1], especially for super-continuum generation [2], Raman laser [3], micro [4] and integrated photonic devices [5].
In the three groups (sulfide, selenide and telluride) of ChGs, selenide (Se-based) ChGs have received frequent usage since the commercial compositions of ChGs are mainly based on As-S-Se, As-Ge-Se and Ge-Sb-Se systems due to their high glass forming ability and thermal stability. Therefore, previous studies [6–9] with respect to optical properties of Se-based ChGs were focused on the As- and Ge-contained binary and ternary systems, while continuous attentions [10–15] have also been paid to the development of new Se-ChGs in As- and Ge-free systems in consideration of the toxicity of As and the high melting point and price of Ge. In particular, the environment-friendly and low-cost ChGs within tin–antimony–selenium (Sn–Sb–Se, SSS) ternary system has drawn attentions. Adam et al [12,13] reported large glass forming region of the SSS ternary system, and gave a brief introduction about the structural property of SSS ChGs. Imran and Lafi [14,15] reported the thermal properties of SSS ChGs, and found that the thermal stability was enhanced after incorporation of Sn to the Se-Sb ChGs. However, a survey of literature indicated that study with respect to optical properties of SSS ChGs, especially in mid-infrared (MIR) wavelength region remains limited.
More importantly, according to Miller’s rule [16] expressed as follows,
It is deduced that the third-order nonlinear susceptibility (χ(3)) of optical materials increases with increase of the linear component (χ(1)), i.e. high TONL property is expected for ChGs with high linear refractive index (n0). Therefore, incorporation of heavy-metal elements to ChGs which increase n0 could be considered as an effective approach to promote TONL performance of ChGs [17,18]. For SSS ChGs containing heavy metal of both Sn and Sb, high TONL performance are expected, but there was no or rare published report that specified TONL properties of SSS ChGs.The aim of this work is to present the MIR optical properties (including infrared transmittance spectra, linear refractive index and dispersion) and TONL property (including nonlinear refraction and nonlinear absorption) of the SSS ChGs at infrared wavelength region. To achieve this, eleven SSS ChGs were selected and prepared (the detailed chemical compositions of the glasses are given in Table 1). The infrared spectral property of the SSS ChGs were obtained by using Fourier transform infrared spectrometer, linear refractive index (n0) were measured by infrared ellipsometer, and the TONL property of SSS ChGs at the MIR wavelength of 4 µm was investigated by Z-scan technique. The variation of the infrared optical parameters with chemical composition of the SSS ChGs was interpreted in term of structural changing by employing Raman spectra.
Table 1. Chemical composition, linear and and nonlinear infrared optical parameters of the SSS ChGs as well as the ChGs for reference.
2. Experimental
The eleven SSS ChG samples were prepared from high purity polycrystalline of tin (Sn, 5N), antimony (Sb, 5N) and selenium (Se, 5N), which were carefully weighted (in accuracy of ± 0.001g) and loaded in a pre-cleaned silica tube. The tube filled with chemical mixtures was evacuated to vacuum (<10−4 Pa) and sealed by acetylene flame, and then melted in a rocking furnace for 12 hours. It should be noted that the melting temperature was selected at 700 °C to guarantee minimum evaporation of Se as well as the complete melting of Sb. After this, the melt was quenched in water and annealed for another 12 hours to room temperature. The sample plates were cut and polished to1 mm for the subsequent optical measurements.
Fourier transform infrared (FTIR) transmission spectra for the SSS ChGs at the range from 2.5 μm to 25 μm were recorded by FTIR spectrometer (Nicolet 380, Thermo Scientific, USA). Linear refractive index (n0) of the SSS ChGs was measured by an infrared-variable angle spectroscopic ellipsometer (IR-VASE Mark II, J.A. Woollam, USA). The angle of incidence was set at 75°, and the experimental error of measured n0 value was estimated to be ± 0.02. Raman spectra of the SSS ChGs were obtained using back (180°) scattering configuration from the confocal micro Raman spectrometer (InVia, Renishaw, UK) with excitation wavelength of 488 nm, and the resolution in frequency is 0.15 cm−1. The laser intensity was set between 0.1 to 0.5 mW, and the exposure time was 10 s for each scan. Analysis of the Raman spectra (including decomposition and integration) was presented by the application software (Wire 3.2) in the Raman spectral system.
MIR third-order optical nonlinearities of the SSS ChGs and a reference glass (As40Se60) were investigated by Z-scan technique at the wavelength of 4μm. An optical parametric amplifier (OPA, Coherent, USA) with the pulse width of 150 fs and repetition frequency of 1 KHz was adopted as laser source. The incident laser power detected by highly sensitive power probe (Laser Probe, Rkp-575, USA) was set at 50 ± 5 µW and focused on the samples utilizing a CaF2 lens. The waist of laser beam (ω0) at focus is estimated to be 27 ± 5 µm, corresponding to laser intensity (I0) of 85.7 ± 16 GW/cm2. Therefore, the main error in Z-scan measurements that originated from calculation of I0 is estimated to be ± 18%. Each Z-scan measurement was conducted three times on different spots on the glass sample, and repeated twice on the same spot. In the closed aperture Z-scan measurements, a diameter-variable aperture was used to keep the linear transmittance (S) at 0.1. Besides, no optical damage to the glass samples was observed during the Z-scan measurements, and all the Z-scans in this work are original ones without any numerical processing.
All above optical testing were conducted at room temperature.
3. Results
3.1 Fourier transform infrared (FTIR) spectra
Figure 1 shows the FTIR transmittance spectra of the SSS ChGs as well as two other Se-based glasses (As40Se60 and Ge20Sb15Se65) for reference. Firstly, as FTIR spectra of the SSS ChGs grouped by Sn content given in Figs. 1(a)-1(c), infrared transmittance region of the SSS ChGs cuts off at ~24 µm, and the cut-off wavelength shows no significant variation with composition modification. Besides, infrared transmittance of the ChGs in each figure decreases slightly (as noted by the arrow) with increase of Sb content, as a result of the enhanced reflection due to increase of refractive index which will be demonstrated in the following section.
Fig. 1 FTIR spectra of SSS ChGs (a) the series with constant Sn content of 8 mol% ; (b) Sn content of 10 mol%; (c) Sn content of 12 mol%; (d) As40Se60, Ge20Sb15Se65 and a SSS glass sample (Sn12Sb10).
Figure 1(d) compares the infrared transmittance range between a representative SSS glass sample (Sn12Sb10) and the reference Se-based ChGs (As40Se60 and Ge20Sb15Se65) which were used as commercial ChG compositions. It is clear that the infrared transmittance region of the SSS ChG is apparently extended as compared to those of the other two glasses. The long wavelength cut-off for the SSS ChG sample red-shifted ~1.5 and ~3.6 µm as compared to those of the As40Se60 and Ge20Sb15Se65 ChGs, respectively. In general, long wavelength cut-off of optical materials is usually determined by multi-phonon lattice band, which can be qualitatively expressed by the fundamental frequency (v) of a simple free diatomic vibration:
where f is force constant related to energy of chemical bonds and M is atom mass of the constituent elements. Adam’s study [13] had shown that glass network of SSS ChGs is mainly constructed by Sn-Se, Sb-Se heteropolar bonds and Se-Se homopolar bonds, and the corresponding bond energy had been calculated to be 196.9 (Sn-Se bonds), 187.6 (Sb-Se bonds) and 183.9 (Se-Se) kJ/mol respectively. Besides, the bond energy of Ge-Se and As-Se bonds [19] are 205.3 and 214 kJ/mol respectively. It should be noted that all the ChGs in this study are in Se-rich state or chemical stoichiometry, indicating that the network structure can be considered as the combination of the corresponding heteropolar bonds and Se-Se homopolar bonds, without the presence of other metallic homopolar bonds (i.e. Sn-Sn and Sb-Sb bonds). Therefore, overall mean bond energy (E) of the SSS ChGs in Se-rich state can be calculated as follows [14]: where Ecl is the mean bond energy of the average crosslinking per atom, Erm is the average energy of the remaining matrix, Dcl is the crosslinking parameter, x, y, and c are the atomic percentages of the constructing elements, namely Sn, Sb and Se, Ehp is the average heteropolar bond energy, D(Se-Sn) and D(Se-Sb) are the heteropolar bond energies, and D(Se-Se) is the homopolar bond energy, Z is the average coordination number. The calculated mean bond energy (E) for the SSS sample (Sn12Sb10) is 211.3kJ/mol, and the E value for As40Se60 and Ge20Sb15Se65 calculated by using the same procedure is 256.8 and 252.2 kJ/mol respectively. The lowest E value manifests the smaller force constant (f) of SSS ChGs as compared to those of the other two glasses, which resulted in smaller v value for the SSS ChGs. In addition, the relatively larger molar mass (M = xMA + yMB + cMC, MA, MB and MC is the molar mass of the constructing elements) of the SSS ChG (MSn12Sb10 = 88 g/mol, MAs40Se60 = 77.3 g/mol, MGe20Sb15Se65 = 84.1 g/mol) reduced the overall v value as well, which extended the infrared transmittance region of the SSS ChGs.On the other hand, no significant absorption owing to extrinsic impurity (except the Se-H absorption at 4.53 µm) can be observed in infrared transmittance region of the SSS ChGs. In contract, evident impurity absorption due to stretching vibration of Ge-O bonds (at ~12.7 µm) can be seen in the FTIR spectrum of the Ge20Sb15Se65 glass. According to the stability of the oxides, Sn-O impurity can be formed more easily as compared to that of Ge-O impurity, but the former have absorption bands between 20 and 30 μm, thus no impact of Sn-O impurity to infrared transmittance of the present SSS ChGs was observed.
3.2 Linear refractive index
Table 1 gives the linear refractive index (n0) of the SSS ChGs at the MIR wavelength of 4 µm. An evident linear dependence of n0 on the Sb/Se ratio can be observed (as shown in Fig. 2), while it varies randomly with the Sn/Se ratio. Therefore, the Sb content can be considered as the main factor in determination of the linear refractive behavior of ChGs within the ternary system.
Fig. 2 Plot of linear refractive index (n0 at 4 μm) as a function of molar content ratio between Sb and Se, the solid line is linear fitting. Inset shows the n0 as a function of the Sn/Se ratio, the solid lines are guide for eyes.
The compositional dependence of n0 can be correlated to bandgap energy (Eg) which manifests the overall polarizability and network connectivity of optical materials [20]. Eg value for the SSS ChGs (given in Table 1) was calculated from the fundamental absorption edge at short wavelength region where the absorption coefficient α = 100 cm–1. It should be noted that the calculated Eg for bulk SSS ChGs (Eg = ~1.1 eV) is remarkably smaller than those of SSS thin-films (Eg = ~2.3 eV) reported by Imran et al [14], because ChGs thin-film contain more defect units as compared to ChGs bulks which made phonon-involved indirect transition [20] dominant in former and consequently resulted in larger value of bandgap energy (Eg) [21]. By plotting n0 values against Eg as shown in Fig. 3, an inverse relationship between n0 and Eg can be observed, which is in consistent with the literature date from oxides [22], Ga-La-S [23] and Ge-Sb-Se [24] ChGs. For SSS glass series with constant Sn content, the increase of n0 and decrease of Eg can be attributed to the enhancement of total polarizability due to the increasing number of iono-covalent bonds (namely the Sb-Se bonds) [25] with addition of Sb content. Furthermore, n0 value of the SSS ChGs is larger than those of the Ge-Se based ChGs (n0 = 2.42~2.75) found in literature [26]. According to the semi-empirical theory (i.e. Miller’ rule present in the Introduction part), higher TONL performance is expected for the SSS ChGs, which will be proved in the following section.
Fig. 3 Plot of linear refractive index (n0 at 4 μm) as a function of bandgap energy (Eg) for the all SSS ChGs.
On the other hand, n0 value of optical materials and its wavelength dependence (namely dispersion) are essential for the design of infrared photonic devices. As compared to other glass materials, ChGs usually have large dispersion due to their relatively high n0 value. For the present SSS ChGs, the dispersion curves are plotted in Fig. 4, and the dispersion exhibit smooth wavelength dependence throughout the infrared transmission window, with increased dispersion at the fundamental absorption in near infrared region. Accordingly, partial dispersion v3-5 and v8-12 that are commonly used to define dispersion at the two MIR atmosphere windows (3-5 µm and 8-12 µm) for infrared materials can be used to characterize infrared dispersion of the SSS ChGs:
where S and L are the short and long wavelengths of interest and M is the wavelength halfway between them. As the calculated data present in Table 1, it can be seen that SSS ChGs with large dispersion (small v3-5 and v8-12 values) are obtained from samples with high Sb content (Sn8Sb20 and Sn10Sb20), while the relatively small dispersion is obtained in sample Sn8Sb10 with low Sb content. For the v3-5 value of the SSS ChGs in each series (grouped by Sn content), its dependence on Sb content is not evident because the measurement of n0 for the SSS ChGs at 3 and 5 µm is influenced by impurity absorption of -OH (~3 µm) and Se-H (~4.53 µm). For the dispersion from 8 to 12 µm (v8-12), no impurity absorption is present in this wavelength region, thus the n0 value of the SSS ChGs had not been influenced by the impurity and the dispersion parameter (v8-12) shows more regular variation with increase of Sb content in each series as compared to the v3-5 value, which indicates that the infrared dispersion of the SSS ChGs also depends on the Sb content which has been considered as a dominant factor to the linear refractive index.Fig. 4 Dispersion curves of the five SSS glass samples (Sn6Sb20, Sn8Sb15, Sn8Sb20, Sn10Sb20 and Sn10Sb10).
3.3 Third-order optical nonlinearity
As mentioned above, the SSS ChGs are expected to exhibit high TONL properties for their large n0 values, which had been proved previously from chalcogenide glasses within other glass systems [6,8]. In this study, mid-infrared TONL properties including nonlinear refractive (n2) and nonlinear absorption (β) behavior of the SSS ChGs and a reference glass (As40Se60) were investigated by femtosecond Z-scan technique at the wavelength of 4 μm. Firstly, it should be noted that free-carrier nonlinearity known as a fifth-order process is believed to be negligibly due to the use of femtosecond laser [27,28]. Figure 5 presents the close-aperture (CA) Z-scans of three representative SSS glass samples, which illustrates the typical nonlinear refractive behavior of all the SSS ChGs at the MIR wavelength of 4 μm. The configuration (peak following valley) manifested the presence of defocusing behavior as the ChGs were irradiated by femtosecond laser at 4 μm, which indicated that the sign of the n2 value for the SSS ChGs is positive [29]. Further, the CA Z-scans in Figs. 5(a)-5(c) showed that the Z-scan signal (distance between valley and peak, ΔTv-p) had been promoted by increase of Sb content, namely the increase of the n2 value which behaved similarly to that of the linear refractive index (n0) as discussed in section 3.2. By fitting the normalized transmittance in CA Z-scans (TCA) using the well-established Gaussian decomposition method [30,31] as given in Eq. (10), n2 value of the SSS ChGs and As2Se3 glass can be calculated:
where nonlinear phase change Δϕ0 = (n2λ)/(2πI0Leff), λ is laser wavelength (4 μm), z is sample position and z0 = πω02/λ is Rayleigh length, ω0 is waist of laser beam at focus, I0 is laser intensity at focus, effective path length Leff = [1-exp(−2α0L)]/2α0, α0 is linear coefficient of the SSS samples at 4 μm and L is sample thickness. As the data shown in Table 1, maximum n2 for the SSS ChGs reaches ~1.0 × 10−17 m2/W, nearly one order higher than that of the As40Se60 glass. However, for majority of the SSS ChGs as well as the reference glass (As40Se60 glass), magnitude of the n2 at 4 μm are in order of 10−18 m2/W, one order lower as compared to the literature date of As40Se60 glass measured at near-infrared (n2 = ~1.0 × 10−17 m2/W at 1.55 μm) [32], as a result of the presence of TONL dispersion. It should be noted that n2 value of the SSS ChGs at the MIR wavelength of 4 μm is significantly larger than that of the As40Se60 glass, indicating that heavy metals (namely Sb and Sn) could enhance the MIR TONL property of the SSS ChGs.Fig. 5 Closed-aperture (CA) Z-scans of three SSS glass samples (Sn10Sb20, Sn10Sb15 and Sn10Sb10) as well as the As40Se60 glass. The solid lines are theoretical fitting.
Figure 6(a) shows the open-aperture (OA) Z-scans of three SSS ChGs and the As40Se60 glass, which qualitatively represents typical behavior in the OA Z-scan measurements on all the glasses prepared in this study. The presence of a valley in central of the OA Z-scans for the SSS ChGs indicated the presence of nonlinear absorption at the MIR wavelength of 4 µm, while no such signal can be observed in OA Z-scan of the As40Se60 glass manifesting the absence of nonlinear absorption.
Fig. 6 (a) Open-aperture (OA) Z-scans of three SSS glass samples (Sn10Sb10, Sn10Sb15 and Sn10Sb20) as well as the As40Se60 glass, the solid lines are theoretical fitting; (b) Plotting of ln(1-TOA) versus lnI0 for the a representative SSS glass samples (Sn10Sb20), slope of ~2 confirms three-photon absorption, inset is OA Z-scans of the sample tested at laser power of 40, 45 and 50 μW respectively.
Since femtosecond (150 fs) laser pluses with low repetition frequency (1 KHz) was utilized as the excitation source for Z-scan measurements, the main contribution of nonlinear absorption of SSS ChGs can be attributed to electronic effect originated from multiple-photon absorption (MPA) [33]. By repeating the OA Z-scan measurement at various laser irradiance, type of the MPA behavior can be identified according to the relationship between ln(1-Tv) and ln(I0) (Tv is normalized transmittance of OA Z-scans at valley and I0 is laser intensity at focus). Figure 6(b) gives the linear fitting of ln(1-Tv) at three different I0 obtained from sample Sn10Sb20, and the slope of ~2 illustrated the presence of three-photon absorption (3PA) [34] which is also observed in other SSS ChGs. At the MIR wavelength of 4 μm (photon energy hv = 0.31 eV), the normalized photon energy (hv/Eg) for the SSS ChGs ranges from 0.26 to 0.3, between a quarter and a third of the Eg (1.0~1.2 eV) indicating that the 3PA occurred below one-third of the bandgap which can be attributed to electronic transitions in Urbach absorption band [35]. Our previous study [9] had also observed the Urbach absorption induced 3PA behavior below the 1/3Eg of ChGs in Ge-Sb-Se system. By fitting the normalized transmittance in OA Z-scans (TOA) using a 3PA model [33] as Eq. (11) shown below, 3PA coefficient (a3) of the SSS ChGs can be calculated.
As the calculation results listed in Table 1, the values of a3 for the SSS ChGs are in order of 10−26 m3/W2, nearly one order higher than those obtained from Ge-Sb-Se ChGs [9] measured at 2 μm, owing to the smaller value of Eg for the SSS ChGs. By plotting the relationship between n2 and a3 (as shown in Fig. 7), it can be seen that the n2 value generally exhibit positive dependence on the 3PA coefficient, which is in good agreement with Kramers-Kronig relation indicated that nonlinear refractive behavior could be resonantly enhanced by nonlinear absorption, namely the 3PA resonance for SSS ChGs in this study.Fig. 7 Plot of nonlinear refractive index (n2 at 4 μm) with three-photon absorption coefficient (a3 at 4 μm) for the all SSS ChGs as well as the As40Se60 glass.
4. Discussion
It is believed that the modification of optical properties of glass materials by means of composition changing or post-treatment can be interpreted in term of structural variation of the glass network. For the SSS ChGs in this work, Raman spectra were employed to correlate the infrared refractive behavior (in both linear and nonlinear properties) with the structural property. Figure 8 shows the Raman spectra of the SSS ChGs that grouped by Sn content, it can be seen that the main Raman band of all the SSS ChGs in three groups located at ~175 cm−1 that belongs to vibration mode of Sn-Se heteropolar bonds in SnSe4 tetrahedral units. The second strongest band located at 259 cm−1 can be assigned to vibration mode of Se-Se homopolar bonds in Se8 rings. The double-peak configuration of the Raman spectra indicated that the main structural frame of the SSS ChGs is constructed by SnSe4 tetrahedron and Se8 rings.
By decomposing each Raman spectrum into a series of Gaussian peaks, more details about the variation of structural property with respect to composition of the SSS ChGs can be obtained. As referred from the experimental results in Adam’s previous work [13], each Raman spectrum can be perfectly decomposed into four Gaussian peaks (present in Fig. 9) located at ~180, ~190, ~220 and ~252 cm−1 belonging to vibration modes of tetrahedral SnSe4, pyramidal SbSe3, Se8-rings bending and Se8-rings stretching, respectively. Grouping the decomposed spectra of the SSS ChGs with respect to Sn content as shown in Figs. 9(a)-9(c), it is clear to observed that the intensity of Raman peak belonging to symmetric stretching of SnSe4 tetrahedral mode (at ~180 cm−1) in each group kept unchanged due to the constant Sn content, but the peak location (as noted in Fig. 9) slightly shifted to lower frequency with increase of Sb content, indicating that the SnSe4 tetrahedrons have connected to more SbSe3 pyramidal units which would slow down the vibration frequency of the neighboring structural units due to the highest atomic weight of Sb within the ternary system. Consequently, the Gaussian peak at ~190 cm−1 belonging to SbSe3 pyramidal vibration symmetrical stretching mode became stronger and shifted towards high frequency region, which manifested as the increase of linear refractive index (n0). On the other hand, the Gaussian peaks at ~220 and ~250 cm−1 belonging to bending and stretching modes of Se8-rings attenuated evidently as Se was replaced by Sb, and the vibration of Se8 bending almost disappeared in sample Sn12Sb20 with highest Sn and Sb content, indicating that SbSe3 pyramidal and SnSe4 tetrahedral units had completely dissolved in the SSS glass network, resulted in the maximum n0 value of this glass sample. Figure 10 summaries the size variation of the Gaussian peaks in each group, which illustrated the structural changing of the SSS glass network with respect to substitution of Se by Sb.
Fig. 10 Variation of integral area for each Gaussian peak in Raman spectrum as a function of Sb content; The data points was obtained from SSS ChGs with Sn content of 8 mol% (black square), 10 mol% (red circle) and 12 mol% (green triangle).
As compared to the linear optical properties, nonlinear optical property of ChGs is more sensitive to type of chemical bonds formed in glass network [18,24,32]. From the above Raman analysis, glass network of the SSS ChGs can be regarded as the combination of iono-covalent (Sb-Se) bonds and covalent (Sn-Se, Se-Se) bonds. Nasu’s study [36] on TONL property of oxide glasses had demonstrated that ionic bonds in glass network are more easy to be distorted with laser irradiation (namely polarized) and gave rise to higher TONL as compared to the presence of covalent bonds, which can be referred to explain the larger value of n2 in SSS ChGs with more Sb-Se bonds that are iono-covalent in nature. On the other hand, both 4-fold coordinated Sn and 3-hold coordinated Sb could cause cross-linking of the SSS glass network, while the degree of cross-linking that related to connectivity of glass network is higher in glass with more Sn atoms for its larger coordinated number, and consequently the structure of SSS ChGs tends to be more compact as Sb was replaced by Sn. The increased network connectivity resulted in reduction of the overall polarization of the SSS ChGs, thus the minimum and maximum values of n2 in this work were obtained respectively from SSS samples with lowest (Sn12Sb10) and highest (Sn6Sn20) Sb/Sn ratio.
On the other hand, average coordination number (Z) that presents the topological characteristics of materials is also a key factor that determines the physical properties, especially for ChGs consisting of a network of covalent bonds. As Fig. 11(a) shown below, the overall variation tendency of n0 against Z is increasing while it is decreasing for Eg, which is in good consistent with the relationship between n0 and Eg as illustrated in Fig. 3. It is easy to understand the increase of n0 with Z since replacement of Se (2-fold coordinated) with Sn (4-fold coordinated) or Sb (3-fold coordinated) with higher polarizability could promote the linear susceptibility (χ(1)) of the SSS ChGs, leading to enhancement of the linear refractive behavior.
Fig. 11 (a) Variation of optical band gap (Eg) and linear refractive index (n0 at 4 μm) as a function of average coordination number (Z); (b) Variation of nonlinear refractive index (n2 at 4 μm) as a function of Z.
For the nonlinear refractive index (n2), it also exhibits an overall increasing tendency with increase of the Z value as illustrated in Fig. 11(b). More importantly, evident transition of n2 value as the Z approaching 2.33 can be observed, as a result of the rigidity percolation transition of the glass network from a underconstrained “floppy” network to an overconstrained “rigid” phase [37]. It should be noted that the transition threshold (Z = 2.33) is slightly smaller as compared to that obtained from Ge-Se ChGs (Z = 2.4) [37] that were constructed by pure covalent Ge-Se bonds. For the present SSS ChGs, parts of the Se-linked (with heavy metals Sn or Sb) bonds are iono-covalent in nature, which broke the covalent glass network and caused the shifting of the rigidity percolation transition threshold, and the similar observation had been reported in Ge-Sb-Se ChGs [38].
5. Conclusions
In summary, infrared optical properties including transmittance spectra, linear refractive index and third-order optical nonlinearity (TONL) of chalcogenide glasses within Sn-Sb-Se (SSS) ternary system were investigated. As compared to As40Se60 and Ge-Sb-Se ChGs, the SSS ChGs exhibited extended infrared transmittance region which has cut-off wavelength at ~24 µm. Raman spectra indicated that the dissolution of Sb atoms in the Se chains which formed SbSe3 pyramidal units caused the remarkable increase of infrared refractive index and dispersion of the SSS ChGs. Mid-infrared TONL property of the SSS ChGs were measured utilizing femtosecond Z-scan technique at the wavelength of 4 µm. The results show that nonlinear refractive index (n2) can also promoted by addition of Sb, and the maximum n2 reaches 1.02 × 10−17 m2/W which is nearly one order higher than that of the As40Se60 glass at 4 µm. Three-photon absorption (3PA coefficient a3) of the SSS ChGs was observed at 4 µm, and the a3 value shows a positive dependence on the n2 value. Thus, the 3PA-resonant effect can be considered as the main factor that caused the large TONL of the SSS ChGs.
Funding
National Key R&D Program of China (2016YFB0303803), National Natural Science Foundation of China (61435009, 61675106), Natural Science Foundation of Zhejiang Province (LY14F050001) and K.C. Wong Magna Fund in Ningbo University.
Acknowledgments
We acknowledge Prof. Peiqing Zhang for operation of the OPA laser, Prof. Changgui Lin for Raman spectral measurements, and Doc. Yongxin Liu for operation of the ellipsometer.
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