1. Introduction

Magneto-optical (MO) materials capable of influencing the light propagation under an applied magnetic field by use of the Faraday effect, magnetic Kerr effect, and magnetic circular dichroism have found a variety of applications ranging from optical switches, isolators, modulators to security encoding and sensing [1–3]. The Faraday effect, in which the polarization plane of a linearly polarized light beam is rotated by the interaction between the incident light and the MO material, has been extensively used for these applications. The Faraday effect of a MO material is usually quantified by the Verdet constant V, which is defined as the rotation of the polarization vector for a linearly polarized light beam under a certain longitudinal (along the light propagation direction) magnetic field (usually 1 Tesla) and 1-m optical path length in the MO material. MO materials with large V and low optical absorption are usually needed for the development of optical isolators and circulators [4,5], which have been extensively used in optical communication systems and laser systems in the near-infrared. In recent years, there is an increasing demand for MO devices operating at the 2 µm wavelength region, which is atmospheric transparent, eye-safe, and low-scattering and distortion for light propagation. Yttrium iron garnet (YIG) and bismuth-substituted yttrium iron garnet (Bi-YIG) crystals are currently the most prevalent MO materials for 2 µm applications. But their fabrication is time-consuming and cost-intensive. These crystalline materials are birefringent and cannot be used for applications where an isotropic material is required. Therefore, new isotropic MO materials with large V and low optical absorption at 2 µm are in great demand.

Glasses are amorphous, easy to fabricate, and cost-effective, and can be readily made into optical components with desired sizes and shapes and even drawn into optical fibers. Therefore, MO glasses have attracted significant interest and have been investigated for many years. Undoped oxide glasses usually have diamagnetic MO properties and their Verdet constants are relatively small. MO oxide glasses with large Verdet constants can be achieved by incorporating rare-earth dopants including Eu³⁺, Dy³⁺, Pr³⁺, Tb³⁺ and Ce³⁺ [6,7], which are paramagnetic and have large magnetic moments attributed to the electronic transition 4f ⁿ $\to $ 4f ^n-1 5d. The Verdet constant of a rare-earth doped glass can be described by Van Vleck-Hebb equation [8]:

However, most of these rare-earth ions have absorption peaks in the 2 µm wavelength region and thus cannot be used to make low-loss MO devices for 2 µm applications. Ce³⁺ and Dy³⁺ ions are candidates as dopants for MO glasses at 2 µm because they do not have absorption peaks in this wavelength region. However, it is still difficult to make highly Ce³⁺-doped glasses without producing any Ce⁴⁺, which is diamagnetic and reduces the Verdet constant of the glass accordingly [9]. Among the rare earth ions, Dy³⁺ (⁶H_15/2) has the largest effective magnetic moment (µ_eff= 10.6 µ_B) [10]. Large Verdet constants have already been measured with highly Dy³⁺-doped crystals and ceramics. A Verdet constant of 119 rad/T/m at 635 nm was obtained with a Dy³⁺-doped aluminum garnet [11]. Most recently, a Verdet constant as high as 297 rad/T/m at 633 nm was achieved with a (Dy_0.9Y_0.05La_0.05)₂O₃ ceramic with a Dy doping level of 90 mol.% [12]. Due to its half integer total moment J, the energy levels of Dy³⁺remain degenerate and thus a large magnetic moment can be obtained even for a low symmetry crystal field environment such as a glass [13]. Several studies have shown that Dy₂O₃ can be a modifier or turn into an exchange coupled Dy³⁺ ion in oxide glasses [13,14], resulting in large Verdet constants. It has been found that Dy³⁺-doped glass has the second largest V after Tb³⁺-doped counterpart glass in the visible range [15]. Therefore, Dy³⁺-doped glasses are quite promising MO materials for the 2 µm wavelength region.

In this work, highly Dy³⁺-doped multicomponent glasses were fabricated and their MO properties were measured from the visible to mid-infrared. A Verdet constant of −7.94 rad/T/m at 1950 nm was measured with a 75 wt.% Dy³⁺-doped glass. This is the highest reported Verdet constant around 2 µm for a paramagnetic glass to the best of our knowledge.

2. Glass fabrication and characterization

The highly Dy³⁺-doped multicomponent glasses were made by conventional glass fabrication methods. High purity chemical powders, SiO₂, P₂O₅, B₂O₃, Al₂O₃, AlF₃, Ga₂O₃, and Dy₂O₃, with specific weights according to the composition for making stable glasses, were prepared as the starting materials. The powders were mixed and loaded into a platinum crucible. The crucible was then put in a furnace at a temperature between 1450-1650 °C for a period of 15-48 hours depending on the quantity of the raw materials. During the process, chemical reactions occurred and a glass melt was formed. The crucible was then removed from the furnace and the glass melt was poured into a preheated metal mold and quenched to a glasssy solid. Finally, the glass was placed in an oven for annealing at its glass transition temperature for 2-10 hours depending on the volume of the glass and cooled down slowly to room temperature at a rate of 20 °C/hour.

In our experiment, five highly Dy³⁺-doped multicomponent glasses with Dy₂O₃ weight percentage of 40 wt.% (Dy40), 50 wt%. (Dy50), 60 wt.% (Dy60), 65 wt.% (Dy65), and 75 wt.% (Dy75) were successfully made. The other compositions of the five Dy³⁺-doped multicomponent glasses include Ga₂O3 (8-15.7 wt.%), P₂O₅ (3.2-7 wt.%), SiO₂ (3.24-7.6 wt.%), B₂O₃ (7.3-13.8 wt.%), Al₂O₃ (2-15.81 wt.%), and AlF₃ (1.14-1.22 wt.%), which are slightly different for making stable and quality glasses. The Dy³⁺ ion concentrations of the five Dy³⁺-doped multicomponent glasses are 5.5×10²⁷ m⁻³ (Dy40), 7.3×10²⁷ m⁻³ (Dy50), 9.4×10²⁷ m⁻³ (Dy60), 1.26×10²⁸ m⁻³ (Dy65), and 1.52×10²⁸ m⁻³ (Dy75), respectively.

The five Dy³⁺-doped glasses were cut into glass samples with cross-section of 10 mm × 10 mm and length of 15-35 mm for the measurement of their MO properties. Both front and back surfaces of each glass sample were polished. Their optical transmission spectra and refractive indices were measured with a Cary 5000 UV-Vis-NIR Spectrometer and a Metricon M2010 Prism coupling system, respectively. Their Verdet constants were measured with a setup as shown in Fig. 1. Diode lasers at 478 nm, 633 nm, 976 nm, 1480 nm, and 1950 nm were used as the light source. A Glan-Thompson polarizer with an extinction ratio of 1:500,000 was used to obtain linearly polarized light. Then an achromatic half-wave plate was used to rotate the plane of the linearly polarized light. A solenoid capable of producing a magnetic field as high as 100 mT was used as the magnet. The glass sample was placed inside the solenoid. A Wollaston polarizer with an extinction ratio of about 1:500,000 was used to separate the two polarization components of the polarized light coming from the glass sample and two photodetectors were used to measure their powers. The rotation angle of the linearly polarized light caused by the glass sample can be calculated from the power ratio of the two orthogonal polarization components.

 

Fig. 1. The schematic of the experimental setup for the Verdet constant measurement.

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The measurement resolution of this setup is higher than 0.01°. To verify the setup, the Verdet constant of BK7 glass was measured at 633 nm. The difference between the measured result and reported results was about 4%, which is excellent agreement for this type of measurement.

3. Results and discussion

All the five Dy³⁺ glasses were cut, polished and prepared for optical transmission measurements. The prepared samples were cut to the thicknesses of 3 to 5 mm with both sides polished. The optical transmission spectra of all five samples are shown in Fig. 2(a). Cleary, the Dy³⁺-doped glasses have high transmission around the 2 µm wavelength region. It should be noted that the Fresnel reflections of the glasses are included in the transmission spectra. The thermal expansion curves of the Dy³⁺-doped glasses were measured with dilatometry technique and used to obtain their glass transition temperature (T_g) and coefficient of thermal expansion (CTE). A typical thermal expansion curve of the Dy³⁺-doped glass is shown in Fig. 2(b). The T_g and CTE of the 5 samples are summarized in Table 1. Figure 2(c) shows the X-ray diffraction (XRD) measurement result of the Dy75 glass at room temperature. The broad diffraction with no peaks associated with any crystalline phase verifies the amorphous nature of Dy75.

 

Fig. 2. (a) Optical transmission spectra of Dy³⁺-doped glass samples with different concentrations; (b) A typical thermal expansion curve of a Dy³⁺-doped glass; (c) XRD measurement result for the Dy75 glass.

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Table 1. Glass transition temperature and thermal expansion coefficient of the five glass samples.

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A Metricon model 2010 prism coupler was used to measure the refractive indices of all 5 samples (Dy40, Dy50, Dy60, Dy65, Dy75) at 633, 816, 1305, 1555 nm. Figure 3 shows the refractive indices of Dy³⁺ glasses at different wavelengths. It is clear that the refractive index increases with the increased concentration of Dy³⁺. The refractive index dispersion of a glass can be described by Cauchy equation as following:

Table 2. Coefficients of the Cauchy equation for Dy³⁺-doped borate glasses.

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The refractive indices of the five samples as a function of Dy³⁺ concentration at 633, 816, 1305, 1555 nm are plotted in Fig. 4. The refractive indices increase linearly with the increased Dy³⁺ concentration for all the four wavelengths and their slopes were found to be close, ranging from 0.00190 to 0.00187, which were obtained by fitting the experimental data to line.

 

Fig. 3. The refractive indices of the five glasses measured at 633, 816, 1305, and 1555 nm and the fitting curves with Cauchy equation.

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Fig. 4. The refractive indices of the samples as a function of Dy³⁺ concentration at (a) 633 nm; (b) 816 nm; (c) 1305 nm; (d) 1555 nm.

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The Verdet constants of all five samples with different concentrations were measured at room temperature for five different wavelengths covering from visible to mid infrared (478, 633, 976, 1480, and 1950 nm) as shown in Fig. 5. It is clear that the Verdet constants increase with increased concentration of Dy³⁺, as shown in Eq. (1). In other words, V is proportional to paramagnetic susceptibility, which is linearly proportional to the ion concentration. The Verdet constants at all five wavelengths show a linear behavior as a function of Dy³⁺ concentration. The R² of linear fits were found to be between 0.99 to 0.98.

 

Fig. 5. Verdet constants of all five samples with different concentrations measured at 478, 633, 976, 1480, and 1950 nm. Inset shows the results at 1480 and 1950 nm in a small scale.

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For the paramagnetic rare earth ions, the Van Vleck-Hebb equation shown in Eq. (1) can be simplified to a single oscillator model as below:

 

Fig. 6. Inverse of the Verdet constant as a function of squared wavelength for Dy40, Dy50, Dy60, Dy65 and Dy75. Inset shows the experimental data and fitted lines at a squared wavelength range of 0-1 µm².

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The effective transition wavelength λ₀ and the constant a for the samples can be obtained by fitting the experimental results at the visible and short-wave near-IR with the Van Vleck-Hebb single oscillator model as shown in Fig. 6. The effective transition wavelength was found to be λ₀= 178 nm. The λ₀ of the single-oscillator model for the paramagnetic rare earth ions is related to 4f ⁿ $\to $ 4f ^n-1 5d and could marginally change in different host materials. The energy levels of the rare-earth ion in different host materials are slightly different depending on the interaction of the doped rare-earth ions with the host materials changes. For example, the transition wavelength of Dy³⁺ in CaF₂ crystal is 170 nm [18], those of Dy³⁺: LiYF₄, Dy³⁺: YF₃, and Dy³⁺: LaFS are 191 nm, 154 nm, and 154 nm, respectively [19]. The coefficients were found to be −0.06495, −0.04381, −0.03678, −0.02543, and −0.01963 (T·m)/(rad·µm²), for Dy40, Dy50, Dy60, Dy65, Dy75, respectively with the R² of 0.99 for all five samples, within the range of linear behavior. It is clear that the a coefficient decreases as the concentration increases.

4. Conclusion

In conclusion, highly Dy³⁺-doped multicomponent glasses were fabricated and their magneto-optical properties were studied. The refractive index measurement results indicate that the refractive index increases linearly with the increased Dy₂O₃ concentration. It was found that the measured Verdet constants of highly Dy³⁺-doped multicomponent glasses are in a good agreement with the Van Vleck-Hebb model in the visible and short-wave near IR region and are smaller than the modeling results at longer wavelengths. Nevertheless, a Verdet constant as high as −7.94 rad/T/m at 1950 nm was measured with a 75 wt.% Dy³⁺ glass which is the highest number reported for a paramagnetic glass at this wavelength. Our experimental results show that highly Dy³⁺- oxide glasses are promising amorphous MO materials in the 2 µm wavelength region.