1. Introduction

The continuous development of high-power laser-diodes and high-power fiber-lasers operating at shorter wavelengths is leading in short time to increased requirements for optical isolators (OIs). These devices are used for the unidirectional propagation of laser light, avoiding optical feedback. This factor is very important in order to avoid parasitic oscillations in amplifier systems and frequency instabilities that decrease the beam quality as well as the lifetime of laser sources. The central part of an OI is a Faraday rotator (FR), normally a single crystal, which rotates the polarization plane of the laser beam when a magnetic field B is applied parallel to its propagation path. The rotation angle β is proportional to both B and the crystal length L according to the well know equation β = VBL, where V is the proportionality factor known as Verdet constant (V).

The most common FRs are garnets single crystals. Yttrium-iron-garnet Y₃Fe₅O₁₂ (YIG) is used for long distance fiber communications in the near IR region, where it is transparent and exhibits an extremely high V value. Bellow 1100 nm terbium-gallium-garnet Tb₃Ga₅O₁₂ (TGG) is utilized, mainly for fiber-laser machinery applications. TGG is characterized by a high V in comparison with similar compounds [1], however, it presents two mayor disadvantages. Firstly, its transparency decreases continuously towards shorter wavelengths in the visible (VIS) wavelength region, leading to optical losses and other detrimental effects on the device performance. Secondly, although it melts congruently at 1825°C, its synthesis by the Czochralski (Cz) technique is not exempt of difficulties [2], as well as a high production cost [3]. Recently a new garnet crystal, [Tb₃][Sc_2-xLu_x](Al₃)O₁₂ (TSLAG), has been proposed as an alternative VIS-IR FR. It exhibits not only a higher VIS transparency and a higher V than TGG, but also favorable growth characteristics for its industrial implementation [4]. However, in spite of the superior properties respect to TGG, TSLAG presents the same limiting features, namely the strong absorption bands in the near UV and blue wavelength regions. These are originated in the partially spin-allowed 4f-4f transitions of the magneto-optical (MO) active ion Tb³⁺, and therefore these crystals cannot be used at wavelengths neither bellow 400 nm nor at around 490 nm. Consequently, there is a need to find FRs which can be used in non-covered UV and VIS wavelength regions.

In the search for new FR materials we have centered on the one hand on alternative MO active ions, and on the other hand on fluoride crystals, which in general exhibit a higher UV-VIS-IR transparency than oxide crystals. Among the rare earth (RE³⁺) ions Ce³⁺, Pr³⁺, Dy³⁺, and Tb³⁺ have been pointed to show the best MO properties [5,6], correlating inversely with the energy of the first electric-dipole allowed 4f-4f5d transitions [7,8]. There are only a few reports on MO single crystal RE³⁺-based fluorides (CeF₃, PrF₃ and NdF₃ [8,9], EuF₂ [10], KTb₃F₁₀, and LiTbF₄ [11]), and these are mainly devoted to only very specific wavelengths. In the present work we focus on the study of the FR properties of CeF₃ and PrF₃ single crystals, because these have the highest transparency among the considered RE³⁺, as well as the highest concentration among RE³⁺-fluorides. Ce³⁺ is characterized by a full transparency in the VIS region. Instead, Pr³⁺ is more transparent in the UV, but it presents two absorption bands in the VIS which induce a green crystal coloration. The MO characterization is carried out in the whole UV-VIS wavelength region, including the Verdet constant dispersion and the figure of merit. In order to compare these with the reference material TGG, the latter has been also measured under equivalent experimental conditions.

2. Experimental

CeF₃ and PrF₃ single crystals of high optical quality were grown by the Cz-technique with a 30 kW RF generator. High purity raw materials (>99,99%) of commercially available CeF₃ and PrF₃ were charged in a Pt-crucible. The growth was carried out under high purity CF₄ (>99,99%) atmosphere to effectively eliminate oxygen traces in the chamber and powder raw material. The rotation and pulling rates were fixed at 15 rpm and 2 mm/h, respectively. Further details about the crystal growth procedure are described in a previous report [12]. The TGG single crystal reference was purchased from Furuuchi Chemical Corporation.

Transmittance and reflectance spectra in the UV-VIS range were obtained with a Jasco V570 spectrophotometer. The dispersion of the absorption coefficient α was calculated for CeF₃, PrF₃ and TGG taking into account both spectra. The FR angles were measured in the same region using a Xe-lamp and a spectrometer. 10 mm long crystals were placed in a magnet located between two Calcite Glan-Taylor polarizers mounted on rotation holders. The transmitted signal was recorded by the aid of an optical fiber coupled multichannel analyzer. In the particular case of CeF₃ and PrF₃, the crystals were oriented with the optical c-axis parallel to the magnetic field. All measurements were performed at room temperature.

3. Results and discussion

The absorbance of the PrF₃ and CeF₃ single crystals in the UV-VIS wavelength region is shown in Fig. 1 . in comparison with the reference crystal TGG. PrF₃ presents the shortest cutoff among them at 210 nm, however, a narrow absorption band corresponding to the transition from the ground level ³H₄ to the excited state ¹S₀ reduces the transparency below 220 nm. The typical green color of PrF₃ is caused by two strong absorption bands in the blue (426-496 nm) and the red (564-618 nm) wavelength regions, attributed to the transitions ³H₄→³P_J and ³H₄→¹D₂, respectively. Instead, CeF₃ is completely transparent in the near UV-VIS region, with the cutoff at 306 nm. In their transparent ranges both compounds show a small dispersion, the absorption coefficient of CeF₃ being even lower than that of PrF₃. In contrast with them, TGG absorption continuously increases in the VIS till the beginning of the ⁷F₆→⁵D₃, ⁵D₂ Tb³⁺ absorption bands below 390 nm. This fact, together with the Tb³⁺ absorption peak at ~488 nm (⁷F₆→⁵D₄), are the reasons which critically limit the performance of TGG FRs in the VIS region, as mentioned in the introduction.

 

Fig. 1 Absorption coefficient dispersion of PrF₃, CeF₃ and TGG single crystals.

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The FR characteristics of PrF₃ and CeF₃ are displayed in Fig. 2 . together with the ones of TGG. In the VIS region both compounds show a similar Verdet constant dispersion to the one of TGG, the values of TGG just being slightly larger. The Verdet constant increment of CeF₃ and PrF₃ in the UV wavelength region is very remarkable: V _CeF3 varies from 414 to 1300 rad/Tm between 400 and 300 nm, while V _PrF3 reaches even larger values, increasing from 817 rad/Tm at 300 nm to 3143 rad/Tm at 220 nm.

 

Fig. 2 Verdet constant as a function of the wavelength for PrF₃ and CeF₃ in comparison with TGG.

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The standard theory of FR, considering a single transition frequency, predicts a linear dependence between the Verdet constant and the inverse of the wavelength square in the form [10]:

 

Fig. 3 Inverse of the ratio (V/N) as a function of the wavelength square for PrF₃ and CeF₃ in comparison with TGG. The experimental points are fitted by a linear regression.

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Table 1. Coefficients for the Verdet Constant Dispersion of PrF₃, CeF₃ and TGG According to the Eq. (1), and the Respective RE³⁺ ion Concentrations N_RE in the Crystals.

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The transition wavelengths of Tb³⁺ and Ce³⁺ in these compounds are close to each other at 239 and 258 nm, respectively, while the one of Pr³⁺ lies at a shorter wavelength, 184 nm. As the crystal field interaction with the RE³⁺ ions is smaller in ionic fluoride crystals, the transition wavelength is shorter than in the case of oxides. This relation found between the transition wavelengths, λ_ο−Tb>λ_ο−Ce>λ_ο-Pr, is the expected one for the case of fluorides since both compounds are very similar from the chemical point of view and the predicted 4f5d levels (E_g) of the free RE³⁺ ions present the same trend (i.e. E_g-Ce<E_g-Pr~E_g-Tb) [7]. Furthermore, in agreement with this relationship, it has been observed that the transition wavelength of Tb³⁺-based fluoride FRs lies at ~200 nm [13,14], also very close to the one of PrF₃ and clearly different from the one of CeF₃ and TGG.

In order to evaluate the rotation efficiency of the three RE³⁺ ions, it is necessary to consider their respective concentrations in the crystal (see Table 1). It is seen that although the concentration of both Pr³⁺ and Ce³⁺ is much higher than that of Tb³⁺, N _Tb<<N _Ce<N _Pr, from the slopes in Fig. 3 it can be deduced that the rotation efficiency of Tb³⁺ in TGG clearly overcomes that of Pr³⁺ and of Ce³⁺, i.e. (E/N)_TGG>>(E/N)_PrF3>(E/N)_CeF3 . It should be noticed that the rotation efficiency of Tb³⁺ in fluorides has been reported to be only slight larger than that of Pr³⁺ and Ce³⁺ in the presented trifluorides [14].

The two most relevant magnitudes to consider at the time to select a FR have been shown so far, namely the absorbance α and the Verdet constant. The figure of merit (FM) of a FR, defined as the ratio V/α, is helpful to compare different FRs performances because it aims at a compromise between both parameters. The FM dispersions of PrF₃, CeF₃ and TGG have been calculated using the experimental results of Figs. 1 and 2 and are depicted in Fig. 4 . In the VIS wavelength region CeF₃ presents a FM much higher than that of PrF₃ or TGG, mainly due to the higher transparency of this crystal. It should be mentioned, that this is the only compound which can be used in the 490 nm region, since the other compounds are opaque. In the near UV region, between 300 and 400 nm, due to the quadratic increase of V _Ce, the FM of CeF₃ rises rapidly, reaching a value as high as 10⁴ rad/Tm at about 300 nm. Below this wavelength, no FRs are available except PrF₃. In this particular UV region, V _Pr achieves exceptionally high values, which are comparable to those of YIG in the IR region. These values largely compensate for the absorption losses, yielding with it to an increase of the FM in the 224-300 nm range comparable to that of CeF₃ in the near UV.

 

Fig. 4 Figure of merit as a function of the wavelength for PrF₃ and CeF₃ in comparison with TGG.

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In addition to the superior properties found for the PrF₃ and CeF₃, it is noteworthy that these compounds present also very favorable growth characteristics in comparison with TGG. Contrary to TGG, CeF₃ and PrF₃ grow at a relatively low temperature with a moderate growth cost. In the particular case of CeF₃, large single crystals of very high optical quality are already commercially available, so that their implementation in OIs is feasible in the near future. In the case of PrF₃, due to its tendency to spiral growth during the pulling process, the Cz-technique is not industrially practicable, and instead, the use of the Bridgman-technique can be envisaged according to previous experiments.

4. Conclusions

Summarizing, the MO properties of CeF₃ and PrF₃ single crystals have been determined in the UV-VIS wavelength region from the point of view of Faraday rotators. The characteristic features of both crystals have been compared with those of the reference crystal TGG, which is the only FR available in the market in the considered wavelength region. The presented compounds show superior properties in the whole UV-VIS region. CeF₃ is noteworthy for its higher transparency and FM in the whole VIS, as well as a superior FM in the regions 300 to 400 nm and around 490 nm, where TGG is already opaque. Below the cutoff of CeF₃ only PrF₃ can be used. PrF₃ possesses a superior FM in the UV region from 220 to 300 nm. These results indicate that CeF₃ has a high potential to be implemented in OIs operating in the near UV-VIS wavelength region, while PrF₃ is the unique candidate for devices that should work in the UV, below 300 nm.