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Abstract
The diamagnetic performance of GeS2-Ga2S3 and GeS2-Ga2S3-PbI2 chalcogenide glasses were investigated, and the composition, wavelength and temperature dependences of the Verdet constant were discussed in detail. It indicates that the contributions to the Verdet constant for each kind of ion are in the order of VPb>VGa>VGe in these chalcogenide glasses, and the Becquerel rule is proved to be an effective guidance for predicting the Verdet constant value. A large Verdet constant is obtained in 68GeS2·17Ga2S3·15PbI2 composition glass and the value is 0.230 min·G−1·cm−1 at 635nm, which is greatly larger than those of commercial diamagnetic glasses. Besides, the temperature coefficient of Verdet constant can be regarded as a constant between 278 and 368 K, indicating these chalcogenide glasses are good candidates for magneto-optical devices in temperature instability conditions.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Magneto-optical isolator, as an electromagnetic non-reciprocal device, is widely regarded as a promising component to meet requirements of high speed-optical signal processing and energy-efficient on-chip communication [1–6]. As a key element in fabricating non-reciprocal photonic devices, magneto-optical materials are commonly characterized by the parameter of Verdet constant and a large value is invariably needed in actual application thus sufficient rotation angle can be acquired in short operating distance and low magnetic field intensity. As of now terbium gallium garnet (TGG) [7,8] and terbium boroaluminosilicate glass (Kigre M-32) [9] have been widely used in telecommunication and high-power laser systems as Faraday rotators, in virtue of their large Verdet constant and low optical absorption. However, these materials generally show strong temperature dependence owing to their paramagnetic characteristics [10], which is harmful to the stability of optical systems operated at a varied temperature condition. Meanwhile, it is hard to integrate single crystal garnets on a semiconductor substrate due to the large lattice and thermal mismatch, which limits the feasibility of integrating of non-reciprocal photonic devices on a semiconductor platform [3].
Diamagnetic glass is one of the isotropic materials, and can be processed easily into waveguide form by using thermal evaporation, pulsed laser deposition, fibration technique, etc. Most importantly, considering the low dependence of Verdet constant to temperature [11,12], diamagnetic glass is expected to be used for optical isolator in rough occasions with large temperature variation. Up to now, several serial diamagnetic glass systems have been studied including of silicate, borate and tellurite ones [13,14]. The most practical shortcoming is their comparatively small Verdet constants compared to paramagnetic materials’.
Chalcogenide glasses, which are compounds primarily from chalcogen elements, possess a variety of unique advantages including of broad range of possible glass-forming systems [15], high refractive index dispersion [16] and good heavy-metal solubility [17,18]. These characteristics are beneficial for obtaining large Verdet constant through compositional optimization. Besides, they have a prominent wide transparent region from visible to infrared region [19,20], making them attractive as diamagnetic materials used in multi-spectral optical systems. So far the Faraday effects of several chalcogenide glasses such as As20S80, As40S60, Ge20As20S60 and Ge33As12Se55 compositions were measured [14,21], however, there is a lack of systematic research. In our previous works, the influence factors of some kinds of high polarizable ions on Faraday effect were studied in detail [5,22], but the relationship between the composition and the Verdet constant for basic chalcogenide glass system has not been cognized clearly, which makes a confusion in the design of novel diamagnetic glasses.
In this work, GeS2-Ga2S3 glass system was selected and prepared due to its excellent heavy-metal solubility which is beneficial for composition optimizing. GeS2-Ga2S3-PbI2 glass system was further prepared due to the high polarizability of Pb2+ ion, which is expected to get large Verdet constant based on the experience in oxide glasses. Some basic properties of these glasses have been studied in detail in [23,24]. This present work is helpful to clarify the influence factors following the glass composition’s variation on Faraday effect in chalcogenide glass, and affirm an effective theoretical guidance for estimating the Verdet constant and further optimizing the composition.
2. Experimental procedure
(100-x)GeS2·xGa2S3 and (100-x) (0.8GeS2·0.2Ga2S3)·xPbI2 bulk chalcogenide glasses were prepared by using the conventional melt quenching technique from the high purity Ge (grains, 6N, Nanjing Germanium Co., Ltd. R.R.C.), Ga (7N, grains, Aladdin Industrial Co. Ltd., R.R.C.), and In (grains, 5N, SCRC Co., Ltd. R.R.C.), S (5N, powers, Aladdin Industrial Co. Ltd., R.R.C.) and PbI2 (powers, 98%, SCRC Co., Ltd. R.R.C.). The raw materials were encapsulated in a silica ampoule with a 10−4 Pa vacuum and heated at 1240 K for 15 h. The melt was then quenched in cold water and annealed near the glass transition temperature for 2 h. Samples were finally obtained after the glass rods were cut and polished to mirror smoothness with a thickness of 3.0 mm. These samples have fine performances such as striae-free, the parallelism with 3 minutes of arc.
All measurements were carried out at room temperature. Refractive indices were conducted at 632.8, 934.7 and 1549.2nm using the Prism Coupler (Model 2010 M, Mctricon, USA) which can provide index accuracies of up to ± 0.0003. When the refractive indices of three wavelengths have been measured, the software of Prism Coupler will give the fitting curve automatically using Cauchy formula
where A, B and C are fitting constants associated with the glass component, and λ is the wavelength of the light.The Verdet constants were tested at 635, 808, 980 and 1340nm using a home-made optical bench (as seen in Fig. 1) consisting of a light source, two polarizers, a photo detector and a permanent magnet with hollow circular cylinder shape providing an axial magnetic field of 1 × 104 gauss at the center. One of polarizers was seated at a motorized high precision rotation mount (PRM1-Z7, THORLABS, USA) controlled by a computer. The light beam provided by semiconductor laser passed through a polarizer to produce a linear-input polarization state. After passing through the sample, the angle of the polarization rotation was detected by the polarimeter with an angular resolution of less than 0.1°, and the Verdet constant is determinedusing the following formula [11]
where V, B, L and θ are the Verdet constant, the magnetic-flux density, the thickness of the sample and the angle of the polarization rotation, respectively. The total estimated error is within ± 5%.3. Results and discussion
Figure 2(a) shows the refractive index dispersion of standard sample. The fitted curve agrees well with the true values, demonstrating that the measurement is working well. Figure 2(b) shows the wavelength dispersions of the refractive index for 90GeS2·10Ga2S3 and 76GeS2·19Ga2S3·5PbI2 glasses as examples. Other samples have the similar dispersion curves with them. The fitting constants of A, B and C for all examined glasses are listed in Table 1, which are used in the following theoretical calculation of the Verdet constant. The inset shows the relationship between the refractive index and the content of Ga2S3 at wavelength of 808nm. It can be seen that the refractive index of these glasses increases monotonously when Ge4+ ion is substituted by Ga3+ one. Actually, the refractive index of (100-x) (0.8GeS2·0.2Ga2S3)·xPbI2 serial glasses have the similar variation with (100-x)GeS2·xGa2S3 ones when PbI2 was added into the glasses. The refractive index is generally determined by the ionic polarization and the stacking density of structural units in network [23]. Larger ionic polarization and higher stacking density of structural units lead to larger refractive index. In this work, the polarizabilities of Ga3+ and Pb2+ ions are larger than that of Ge4+ ones. Thus the refractive index increases monotonously with the addition of Ga2S3 or PbI2.
Fig. 2 Refractive index dispersions for (a) standard sample; (b) 90GeS2·10Ga2S3 and 76GeS2·19Ga2S3·5PbI2 glasses. (The inset shows the relationship between the refractive index and the content of Ga2S3 for (100-x)GeS2·xGa2S3 glasses at wavelength of 808nm. The line is drawn as a guide for the eye.)
Table 1. Fitting constants of the refractive index for all investigated glasses in this work
Verdet constant of SiO2 glass was measured as a standard sample firstly, and the value is 0.013 min·G−1·cm−1 at the wavelength of 635nm, which agrees well with the reported value in previous work [21], demonstrating that the Verdet constant test bench is working well. The Verdet constants of (100-x)GeS2·xGa2S3 (x = 5, 10, 15, 20 and 25) serial glasses at 635, 808, 980 and 1340 nm are shown in Fig. 3. It can be seen that at each wavelength, the Verdet constant shows a nearly linear variation with the molar content of Ga2S3, and the largest value is as well as 0.138 min·G−1·cm−1 for 75GeS2·25Ga2S3 one at wavelength of 635nm, which is greatly larger than those of commercial diamagnetic glasses (Schott, SF 6, V = 0.069 min·G−1·cm−1@633nm for example) [25], and roughly 10 times larger than that of SiO2 at 635nm.
Fig. 3 Relationships between the Verdet constant and the molar content of Ga2S3 in (100-x)GeS2·xGa2S3 glasses at 635, 808, 980 and 1340 nm, respectively. Dashed lines are drawn as guides for the eye.
Faraday effect of the magneto-optical materials originates from the magnetic-field-induced Larmor precession of electron orbits [21]. Based on the classical electromagnetism theory, Becquerel deduced the relationship between the Verdet constant and the dispersion of the refractive index in diamagnetic materials [26]. The established equation is described as
where V, e, m and c are the Verdet constant, the charge of the electron, the mass of the electron and the light speed, respectively. dn/dλ is the wavelength dispersion, which can be obtained from Eqs. (1) and Table 1 for each glass. Figure 4 shows the theoretical and experimental values of the Verdet constant dispersions for 85GeS2·15Ga2S3 and 76GeS2·19Ga2S3·5PbI2 glasses as examples. It can be seen that the theoretical values are in good agreement with the experimental data in infrared wavelength range where away from the absorption edge and the errors are within 15%. The deviation is mortally large at 635nm. It is mainly caused by the error of the refraction index fitting formula which does not work well at the short wavelength near the absorption edge. The deviation may also become large when the wavelength beyond 3 μm because Cauchy formula used for refractive index fitting no longer applies at this wavelength region. The error can be cut down while a more precision formula is used for refractive index fitting.Fig. 4 Wavelength dependence of the Verdet constant for 85GeS2·15Ga2S3 and 76GeS2·19Ga2S3·5PbI2 glasses.
When a high polarizability cation such as Ga3+ ion doped into the glass, the refractive index and refractive index dispersion of the glass both increase, which leads to large Verdet constant according to Eqs. (3). For further optimizing the Verdet constant, Pb2+ ion, which has larger ionic polarization and been demonstrated to give rise to large refractive index and refractive index dispersion in oxide glass systems was added into the glass. The relationship between the Verdet constant and the molar content of PbI2 is shown in Fig. 5. It can be seen that the Verdet constant has a further increase and the largest Verdet constant is obtained when 15%mol content of PbI2 was added into 80GeS2·20Ga2S3 glass. The Verdet constant is 0.230 min·G−1·cm−1 @ 635nm, which is roughly twice as large as that of 80GeS2·20Ga2S3.
Fig. 5 The Verdet constants of (100-x)(80GeS2·20Ga2S3) ·xPbI2 glasses at 635, 808, 980 and 1340 nm, respectively. Dashed lines are drawn as guides for the eye.
Through the variations of Verdet constant values in these two serial glasses, it can be found that the contributions to Verdet constant for each kind of ion are in the order of VPb>VGa >VGe. It’s ascribed to the unique electronic structure of Pb2+ ion. The outer layer of Ga3+ and Ge4+ ions is 3d orbit and full of electrons. While Pb2+ ion has 2 electrons in its outer layer, viz. 6s6s electron configuration, thus there is a strong oscillator strength of s2-sp electron jumps involving 1S0→1P1, 3P0,1,2 transitions, which has been demonstrated to give rise to large Verdet constant in some kinds of oxide glass systems [14].
Figure 6 shows the relationship between the Verdet constant and the refractive index for all samples. The Verdet constant follows approximate linear dependence on refractive index, thus it can be estimated by the refractive index at corresponding wavelength using the following formula:
Fig. 6 Relationship between the Verdet constant and the refractive index for all samples. Dashed line is drawn as a guide for the eye.
According to previous works, ions with high polarizability can lead to higher Verdet constant, which means Verdet constant is related to the polarizability of materials. While refractive index is also associated with polarizability, thus there is a simple relationship between V and n. There is no denying the fact that three data have a large deviation marked with red circle in Fig. 6. It might be introduced by the measurement error because the rotation angle θ is too small to be measured exactly at 1340 nm wavelength.
In order to clarify the temperature dependence, the Verdet constant at 635 and 980 nm for 80GeS2·20Ga2S3, 72GeS2·18Ga2S3·10PbI2 and terbium aluminosilicate glass (Tb glass) are measured at different temperatures. The results are shown in Fig. 7. Tb glass as paramagnetic materials is used here as a reference sample and the absolute value of Verdet constant is used for contrast. It can be found that the Verdet constant of Tb glass decreases linearly when the temperature rises from 278 to 368 K, and the slope coefficients are about −8.9 × 10−4 and −2.6 × 10−4 K−1 at 635 nm and 980 nm, respectively. Whereas the Verdet constants of chalcogenide glasses have no obvious changes and can be regarded as constants. In particular, when the temperature exceeds 300 K, the Verdet constant of Tb glass will be smaller than that of 72GeS2·18Ga2S3·10PbI2 glass at 980 nm wavelength. The results show that chalcogenide glass is a promising candidate for the sensing element in high stability Faraday effect sensors.
Fig. 7 Temperature dependences of the Verdet constant at 635 and 980 nm, respectively. Dashed lines are drawn as guides for the eye.
4. Conclusions
The Verdet constants of GeS2-Ga2S3 and GeS2-Ga2S3-PbI2 chalcogenide glasses were measured at the wavelength of 635, 808, 980 and 1340 nm, respectively. High polarizability ions are responsible for large Verdet constant, especially the Pb2+ with s2-sp electron jumps involving 1S0→1P1, 3P0,1,2 transitions. The theoretical values obtained from Becquerel rule have relatively good coincidence with the experimental results in the infrared wavelength range, therefore the Verdet constant of chalcogenide glass can be estimated by the refractive index at corresponding wavelength. The temperature coefficient of the Verdet constant for these two serial glasses can be regarded as a constant between 278 and 368 K, which means chalcogenide glasses are good candidate for the Faraday sensing element in high stability occasion.
Funding
National Natural Science Foundation of China (61405241, 61475189); Project of Key Laboratory of Optoelectronic Detection Materials and Devices of Zhejiang Province (2017001).
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