Characteristics and Recent Development of Fluoride Magneto-Optical Crystals

Abstract

Magneto-optical materials are the fundamental component of Faraday isolators; therefore, they are significantly important for solid-state laser systems. Fluoride magneto-optical crystals such as CeF₃, KTb₃F₁₀ and LiTbF₄ exhibit advantages of wide transmittance range, high optical homogeneity, smaller thermal lensing and weaker thermal induced depolarization effect, and thus are promising candidates for Faraday isolators in high-power solid-state lasers. Recent progress in crystal growth and characterizations of these fluoride magneto-optical crystals are introduced. Possible applications of Faraday isolators based on various fluoride crystals are discussed, especially for solid-state lasers in the ultraviolet (UV) or infrared (IR) spectral region.

1. Introduction

Magneto-optical materials are the key component of Faraday isolators (FIs), which is of great importance in high-power solid-state laser systems and optical communication techniques [1]. The magneto-optical materials used in the FI devices are often called Faraday rotators. A brief structure of the Faraday isolator is shown in Figure 1. Taking advantage of the Faraday effect of magneto-optical materials, the polarization of the induced polarized light beam will be rotated by the angle

$$\theta =V·B·L$$

(1)

where $V$ is the Verdet constant of the magneto-optical material, $B$ is the magnetic flux density along the propagating direction and $L$ is the length of the beam path inside the magneto-optical materials. If the length of magneto-optical materials and the magnetic flux density are designed to produce a rotation angle of $\theta =\pi /4$ (or 45°), the reflected light will be perpendicular to the input polarizer because the polarization of the reflected light beam will be rotated twice when propagating backwards along the magneto-optical materials; thus, the reflect light beam will be completely prevented.

As the light beams can only be propagated along one direction, the FI devices are also known as optical diodes for an optical system. In optical communication techniques, IF devices can prevent backwards-propagated light beams and improve the noise-to-signal ratios [1,2]. Meanwhile, for high-power laser systems, FIs are crucially important for protecting pumping LD sources from being damaged by the scattering laser beams. Furthermore, the beam propagation between adjacent amplifier stages in high-power systems will be completely irreversible when separated by FI devices; therefore, the laser operation within each stage can be more stable by eliminating amplified spontaneous emission (ASE), reducing parasitic oscillations, etc. [3,4,5].

The main challenge for the power scaling of FI devices in high-power laser systems is thermal effect, e.g., thermal-induced depolarization [6] and the thermal lensing effect [7]. Thus, high thermal conductivity is often considered one of the basic requirements for magneto-optical materials, which is necessary to improve heat dissipation efficiency. Another important requirement of magneto-optical materials is lower propagation losses in order to reduce the distortion of propagated light beams due to local optical absorption. Simultaneously, as the magnitude of thermal effect is proportional to the length of sample, a larger Verdet constant of magneto-optical materials is thus favorable as a smaller $L$ is allowed according to Formula (1).

Considering both the requirements for intrinsic properties and the difficulty of manufacturing high-quality crystals, magneto-optical materials such as terbium gallium garnet (Tb₃Ga₅O₁₂, GGG) and yttrium iron garnet (Y₃Fe₅O₁₂, YIG) crystals were widely used for FI devices within the visible-to-near-infrared (NIR) spectral range and mid-infrared (mid-IR) spectral range, respectively [8,9]. Faraday rotators using TGG crystals have been widely used in high-power laser systems based on Nd³⁺/Yb³⁺-doped laser materials or Ti:sapphire crystals. High-quality TGG crystal samples of apertures as large as Φ40 mm have been reported [10]. However, the development of TGG-based FI devices of a larger aperture is often limited by the dimension of available TGG crystals as well as the thermal effect of larger Faraday rotators, which is considered a potential bottleneck of high-power laser techniques. In addition, the absorption bands of Tb³⁺ within the UV range below 390 nm, in the visible range around 488 nm (⁷F₆→⁵D₄), as well as in the IR range over 2.1 μm also limit its applicant spectral range [11].

YIG-based FI devices, on the other hand, exhibit excellent compactness, taking advantage of its high Verdet constant, therefore are often used to fabricate compact and integrated isolators for optical fibers [12]. The excellent transmittance of YIG crystals within the IR spectral range from 1.1 μm until 5 μm also allows its application in the mid-IR spectral range [13]. The main obstacle to producing large-aperture YIG FI devices is the difficulty of growing large-scale YIG crystals due to its incongruent melting characteristics. Although various crystal growth techniques, including the flux method [14], float-zone method [15] as well as the liquid phase epitaxial method [16], have been developed to fabricate YIG crystals or films, the growth of large-volume YIG crystals is still a bottleneck for the development of high-power systems, especially for application in a high-power mid-IR laser facility.

Under this circumstance, efforts to develop novel magneto-optical materials are frequently proposed, which can be divided into two categories. One is mainly aimed for the application of laser systems of higher average or peak power within the visible to NIR range by solving the limitation of FI device aperture or reducing the thermal effect [17]. Several fluoride crystals, such as KTb₃F₁₀ [18], TbF₃ [19] and LiTbF₄ [20], exhibit high Verdet constants and low propagation losses, thus are frequently investigated recently. It is worth noticing that these fluoride crystals have small/negative thermo-optic coefficients, which are favorable to inhibit thermal effects by reducing the inhomogeneity of thermal dissipation and compensate for thermal-induced distortion [21]. The other category is to develop novel magneto-optical crystals for potential applications in UV or mid-IR laser systems. Indeed, several fluoride crystals, such as PrF₃ [11] and EuF₂ [22] have wide transmittance ranges and high Verdet constants [6,7,23,24] and therefore constitute an important category of magneto-optical materials for high-power laser systems. In the following paragraphs, the development and state of the art of these fluoride magneto-optical crystals will be introduced. The applications and prospects of several fluoride magneto-optical crystals will be introduced briefly.

2. Terbium (Tb³⁺)-Containing Fluoride Magneto-Optical Crystals for High-Power Laser Applications

2.1. KTb₃F₁₀ (KTF) and LiTbF₄ (TLF) Crystal

Many magneto-optical materials are paramagnetic compounds containing rare earth (RE) ions, and the magnetic susceptibility of the RE nucleus in the materials is strongly related to its Verdet constant. Terbium-containing fluoride crystals have thus been frequently investigated recently as Tb³⁺ often shows higher susceptibility over other trivalent RE ions [25]. Among the terbium containing fluorides, ternary compounds KTb₃F₁₀ (KTF) and LiTbF₄ (TLF) are most attractive [26]. Although the potential of KTF and TLF crystals for Faraday rotators had already been reported in the 1970s, e.g., Griffin et al. [27] and Weber et al. [28] reported the magneto-optical properties of both crystals in 1978, substantial development of these crystals for large-aperture FI devices has occurred after the first decades of this century. In 2012, Vasyliev et al. [20] reported a series of fluoride magneto-optical crystals, LiREF₄ (RE = Tb, Dy, Ho, Er and Yb). In 2016, Stevens et al. [26] from Northrop Grumman SYNOPTICS reported the optical and magneto-optical properties of both KTF and TLF crystals, pointing out that “KTF has reduced depolarization for higher laser powers and a smaller focal shift than TGG” [26] under similar experimental conditions, indicating it is a promising candidate for high-power laser applications.

LTF belongs to the tetragonal scheelite structure of space group $I{4}_1/a$, consistent with the widely used laser host lattice LiYF₄ (YLF). The crystal growth behavior of TLF is also similar to that of YLF due to its similar incongruent melting characteristics [29]. The Czocharalski method is the most widely used crystal growth technique for TLF; meanwhile, the excess of LiF in the starting materials could be as high as 63% [30], much higher than the typical growth condition of YLF [31], mainly due to larger deviation of TLF composition away from the eutectic point of the LiF-TbF₃ system. Nevertheless, a large-aperture TLF crystal boule of Φ 40 mm with a length of 70 mm can be fabricated using the conventional crystal growth technique.

KTF belongs to the cubic structure of space group $Fm\overline{3}m$, the same as the laser host KY₃F₁₀ (KYF). However, the melting characteristic of KTF is incongruent, differing from KYF [32,33]. The original attempts at KTF crystal growth mainly employed the Czochralski method using a mixture of 30 mol% KF and 70 mol% TbF₃ as starting materials [28]. Top-seeded solution growth (TSSG) [26] and vertical Bridgman (VB) techniques [33] have been used recently to grow KTF crystals. A large-aperture TLF crystal boule of Φ 30 mm with a length of 40 mm was reported by Northrop Grumman SYNOPTICS in 2016 [26].

As the applications of TLF and KTF crystals, i.e., large-aperture FI devices for high-power lasers in the NIR region, are quite similar to those of TGG crystals, the Verdet constants of those crystals are compared with those of TGG in Figure 2. The Verdet constants and optical and thermal properties of these crystals are listed in Table 1. The Verdet constants of these Tb³⁺-containing ternary compounds at 1.06 μm are TLF > TGG > KTF; however, the differences are rather small, indicating the design and geometry of FI devices based on these crystals can be very similar. Recent investigations indicated the extinction value of KTF-based FI devices can reach 30~40 dB at low input power and remains above 20 dB when propagated by a laser beam of power over 370 W [18,26], better than TGG-based devices under the same experimental condition. Despite the fact that the thermal conductivities of these fluoride crystals are obviously lower than those of TGG, as shown in Table 1, the excellent performances of KTF-based FI devices mainly benefit from the small and negative thermo-optical coefficient (dn/dT in Table 1), reducing the thermal effects by compensating for thermal lensing.

Table 1. Verdet constant and optical and mechanic properties of fluoride magneto-optical crystals.

	Lattice Type	Thermal Conductivity (W·m−1·K−1)	Refractive Index (@ 1.06 μm)	dn/dT (×10−6 K−1 @ 300 K)	Verdet Constant (Rad·m−1·T−1)	Transmittance Range
TGG	cubic	4.94 [34,35]	1.94 [18]	17.5 [34]	41.7 @ 1.06μm 133.2 @ 633 nm 20.39 @ 1.5 μm [11]	400 nm~1.5 μm (480~500 nm excepted)
LiTbF4	tetragonal	-	no = 1.468 ne = 1.497 [20]	−5.67 [30]	42.7 @ 1.06 μm [20]
KTb3 F10	cubic	1.67 [30]	1.50 [18]	~1 [26]	34 @ 1.06 μm [18]
TbF3	tetragonal	-	nx = 1.602 ny = 1.588 nz = 1.569 (@ 589 nm [36])	-	48 @ 1.06 μm [19]
CeF3	trigonal	2.51//−c [37] 1.92⊥c [37]	no = 1.6217 ne = 1.6147 (@ 531 nm [38])	-	39.5 @ 1.06 μm [11]	300 nm~2.1 μm
PrF3	trigonal	-	no = 1.6240 ne = 1.6179 (@ 531 nm [38])	-	125.3 @ 633 nm [11]	220~420 nm 500~560 nm 620~950 nm
EuF2	cubic	2.13 [39]	1.555 [40]	-	21.36 @ 1.5 μm [22]	1~7 μm (Eu3+ absorption excepted) [22]

Table 1. Verdet constant and optical and mechanic properties of fluoride magneto-optical crystals.

	Lattice Type	Thermal Conductivity (W·m−1·K−1)	Refractive Index (@ 1.06 μm)	dn/dT (×10−6 K−1 @ 300 K)	Verdet Constant (Rad·m−1·T−1)	Transmittance Range
TGG	cubic	4.94 [34,35]	1.94 [18]	17.5 [34]	41.7 @ 1.06μm 133.2 @ 633 nm 20.39 @ 1.5 μm [11]	400 nm~1.5 μm (480~500 nm excepted)
LiTbF4	tetragonal	-	no = 1.468 ne = 1.497 [20]	−5.67 [30]	42.7 @ 1.06 μm [20]
KTb3 F10	cubic	1.67 [30]	1.50 [18]	~1 [26]	34 @ 1.06 μm [18]
TbF3	tetragonal	-	nx = 1.602 ny = 1.588 nz = 1.569 (@ 589 nm [36])	-	48 @ 1.06 μm [19]
CeF3	trigonal	2.51//−c [37] 1.92⊥c [37]	no = 1.6217 ne = 1.6147 (@ 531 nm [38])	-	39.5 @ 1.06 μm [11]	300 nm~2.1 μm
PrF3	trigonal	-	no = 1.6240 ne = 1.6179 (@ 531 nm [38])	-	125.3 @ 633 nm [11]	220~420 nm 500~560 nm 620~950 nm
EuF2	cubic	2.13 [39]	1.555 [40]	-	21.36 @ 1.5 μm [22]	1~7 μm (Eu3+ absorption excepted) [22]

2.2. Other Tb³⁺-Containing Fluoride Magneto-Optical Crystals

As the Faraday effect of paramagnetic Tb³⁺-containing crystals is mainly contributed by Tb³⁺, increasing the density of rare earth sites is a reasonable strategy for improving the Verdet constant. TbF₃ crystals, whose Tb³⁺ densities (N_Tb = 2 × 10²² cm⁻³) are obviously higher than TGG (N_Tb = 1.275 × 10²² cm⁻³), TYF (N_Tb = 1.365 × 10²² cm⁻³) and KYF (N_Tb = 1.487 × 10²² cm⁻³) crystals, are expected to have higher Verdet constants. In 2017, Valiev et al. reported the synthesis of TbF₃ crystals by vertical Bridgman method [36]. As indicated in Figure 2 and Table 1, the Verdet constant of TbF₃ is higher than that of TGG [19]. However, the attempts of using TbF₃ crystals for FI devices are dramatically limited by its low symmetry. Indeed, TbF₃ is a biaxial crystal with a monoclinic space group $Pnma$. As the propagation direction of Faraday rotators should be parallel with the optical axes for non-cubic materials in order to avoid the influence of birefringence, fabricating a TbF₃ crystal for FI devices is quite difficult because its optical axes differ from all the crystallographic axes.

Na_0.37Tb_0.63F_2.26 (NTF) is another novel Tb³⁺-containing fluoride magneto-optical crystal of high Tb³⁺ density (N_Tb = 1.456 × 10²² cm⁻³) and belongs to a cubic $Fm\overline{3}m$ space group. Karimov et al. reported the crystal growth of NTF by the Bridgman method in 2014 [41] and afterwards investigated its thermo-optical characteristics in 2015 [42]. The thermo-optical constant dn/dT was found to be very small (3.44 × 10⁻⁶ K⁻¹). After analyzing the performance of IF devices based on NTF crystals of various orientations, it is indicated that NIF basedFI devices with isolation ratios larger than 30 dB for propagation power kilowatts level were possible to be obtained [43].

3. Novel Fluoride Magneto-Optical Crystals for UV or MIR Laser Applications

3.1. CeF₃—Faraday Rotators for High-Power System from UV to MIR Spectral Range

CeF₃ is a uniaxial crystal of a trigonal space group of $P\overline{3}c1$. CeF₃ had exhibited excellent radiation hardness and thus is considered as a potential scintillator for calorimeters [44,45]. Scintillation cylinders which are 30 cm long have been synthesized for potential application in high-energy physics facilities [46], indicating, on the other hand, that it is technically feasible to grow large-size CeF₃ by conventional crystal growth techniques such as the Czochralski process and the vertical Bridgman method.

As shown in Figure 2 and Table 1, the Verdet constant of CeF₃ is slightly lower but very close to that of TGG at 1.06 μm [11,47]. In the ~1 μm spectral region, the CeF₃-based FI devices exhibit excellent performances, benefiting from its thermo-optical characteristics even though the thermal conduction of CeF₃ is obviously lower than TGG [6,7]. In 2019, Starobor et al. reported a CeF₃-based FI device of over 30 dB isolation degree at an average laser power of 700 W, indicating CeF₃ is also a promising Faraday rotator for high-power laser systems even in the NIR region [24].

Additionally, as shown in Figure 3a, CeF₃ exhibits high transmittance continuously from 300 nm to over 2.5 μm, thus is a promising Faraday rotator material in both the UV region [20] and mid-IR range [48,49]. Indeed, considering the fast development of a 355 nm solid-state UV laser [50,51] and the urgent demand for high-power MIR laser sources in the near future [52], large-aperture FI devices based on CeF₃ crystals could be of crucial importance in both the UV and mid-IR spectral regions.

3.2. Absorption-Related Defects in CeF₃

The absorption caused by localized defects will lead to the inhomogeneity of temperature distribution, and therefore is an important origin of thermal effects for magneto-optical crystals. Thus, it is important to reduce these absorption-related defects in magneto-optical crystals. Similar to other fluoride crystals, the contamination of oxygen impurity during the crystal growth of CeF₃ will have an obvious influence on its transmittance [49]. The strict control of oxygen contamination during crystal growth at a high-temperature stage is necessary to obtain CeF₃ crystals with high transmittance.

Scattering centers are another category of defects that will cause local absorption. The influence of these defects can be observed macroscopically by the scattering of laser beams propagated through the CeF₃ crystals, as shown in Figure 3b. Meanwhile, hexagonal hallow structures of milimeter size can be observed inside the crystal by an optical microscope. The shape and symmetry of these defects are consistent with the crystal structure of CeF₃. The scattering due to these hallow structure defects will give rise to serious local attenuation; thus, it is very important to improve the purity of crystal growth atmosphere and decrease the pulling rate of the crucible in the vertical Bridgman crystal growth process in order to inhibit the formation of these defects.

Using optimized crystal growth parameters, large-size CeF₃ crystals of high quality were grown by Shanghai Institute of Ceramics, Chinese Academy of Sciences. As shown in the inset of Figure 4, crystallographic -c axis cut CeF₃ crystals with apertures larger than 20 mm have been obtained. The performance of the FI device using the Φ15 mm CeF₃ sample was investigated, as shown in Figure 4. The Faraday rotation angle increases linearly with magnetic field strength.

3.3. PrF₃—Potential Faraday Rotators for UV Applications

Similar to CeF₃, PrF₃ is a uniaxial crystal of a LaF₃-type trigonal space group of $P\overline{3}c1$ [53]. Molina et al. reported the crystal growth and magneto-optical properties of PrF₃ in 2011 [11]. Although magneto-optical crystals such as LiYbF₄ exhibit UV cut-off even at shorter wavelengths, the PrF₃ crystal is still considered as the best candidate for Faraday rotators from 220 nm to over 300 nm, combining both high transmittance and large Verdet constants, as shown in Figure 2 and Table 1. The appearance of a PrF₃ crystal is green-colored due to the absorption bands from the ground state to the ³P_0,1,2/¹I₆ states (420 nm~500 nm) and the ¹D₂ state (560 nm~620 nm) in the visible region [54]. Under this circumstance, the applicable spectral range of PrF₃-based Faraday rotators is strictly limited to avoid those absorption peaks. Nevertheless, as reported in Reference [11], PrF₃ is the only candidate for FI devices in the UV region below 300 nm.

3.4. EuF₂-based Magneto-Optical Materials for MIR Lasers

The magneto-optical properties of EuF_2.11, one typical composition of an EuF₂-based compound, were reported firstly in 2019 by Mironov et al. [22]. The Verdet constant of EuF_2.11 crystal is 12.3 rad·m⁻¹·T⁻¹ at 2 μm, which is sufficient for the fabrication of FI devices. Moreover, the wide transmittance of 1~7 μm indicates the potential application of EuF₂ in the mid-IR or even long-wave IR range. The most crucial obstacle to be solved associated with this material is the synthesis of a high-purity EuF₂ compound. Indeed, Eu³⁺ is the most stable valence state for europium in fluoride compuonds and can be hardly removed completely in the reduction chemical reaction process. The residual Eu³⁺ will generate a series of absorption bands within the 2~4 μm range and significantly influence the application of EuF₂-based magneto-optical materials in this region.

4. Discussion

4.1. The Analysis of Thermal Effect in Fluoride Magneto-Optical Crystals

The interactions between laser beams and magneto-optical crystals of FI devices are transient phenomena rather than absorption/emission processes in the laser gain materials; thus, the most influential thermal effect is thermal lensing and thermally induced depolarization. As these thermal effects are mainly due to the inhomogeneity of temperature distribution that is caused by the local absorption of the propagated laser beam, it is possible to inhibit them by employing magneto-optical crystals of higher thermal conductivity, as was by decreasing those defects that introduce local absorption, as discussed for CeF₃ crystals in Section 3.2. Nevertheless, some other characteristics, such as optical anisotropy and the thermo-optical coefficient, also have crucial influence on the performances of FI devices.

For the thermal lensing effect, the focal length of the thermal lens $F$ can be defined as [6]:

$$\frac{1}{F}=\frac{1}{4\pi a^2}\frac{\alpha L}{\kappa }P·P_0$$

(2)

where $a$ is the beam radius, $\alpha$ is the absorption coefficient, $\kappa$ is the thermal conductivity and $P_0$ is the induced laser power. In Formula (2), $P$ is a thermo-optical-related constant, which can be defined for the isotropic materials as [7]:

$$P=\frac{dn}{dT}-{\alpha }_T\frac{n^3}{4}\frac{1+\upsilon }{1-\upsilon }\left(p_{11}+p_{12}\right)$$

(3)

where ${\alpha }_T$ is the thermal expansion, $\upsilon$ is Poisson’s ratio and $p_{ii}$ is the element of the photoelastic tensor.

As described by Formulas (2) and (3), the optical and thermo-optical characteristics of several fluoride crystals, including a lower thermo-optical coefficient $dn/dT$, a smaller refractive index $n$ and lower absorption loss, are favorable for reducing the thermal lensing effect. Starobor et al. reported a comparison of the thermal lensing effect of CeF₃, KTF and NTF crystals with that of a TGG crystal at the ~1 μm spectral region [7]. As shown in

Table 2. The comparison of thermal lensing effect between TGG and fluoride magneto-optical crystals [7].

	TGG	CeF3	KTF	NTF
Length of sample when $\theta =45, B=2T$ (mm)	10.6	10.8	11.2	12.9
$\frac{\alpha }{\kappa }P$ (10−8 W−1)	57	−8.9 ± 1.1	−2.5 ± 0.3	−14 ± 1.7
$\frac{\alpha L}{\kappa }P$ (10−8 W−1·m)	6.04	−0.96 ± 0.12	−0.28 ± 0.02	−1.81 ± 0.22

, the required length of Faraday rotators of these crystals only slightly varies from 10.6 mm to 12.9 mm. The factor $\mathsf{\alpha }\mathrm{P}/\mathsf{\kappa }$ of CeF₃, KTF and NTF crystals are negative due to the negative thermo-optical coefficients $dn/dT$ of fluoride crystals. Considering the influence of the sample length, the magnitude of the factor $\mathsf{\alpha }\mathrm{LP}/\mathsf{\kappa }$ of TGG is about 6.04 × 10⁻⁸ W⁻¹·m, about 6, 21 and 3 times larger than CeF₃, KTF and NTF, respectively. Thus, the thermal lensing effect of these fluoride magneto-optical crystals is much weaker than TGG, indicating they are promising Faraday rotators for high-power laser systems over kilowatt level.

Thermally induced depolarization is another kind of common thermal effect for magneto-optical crystals. The definition of depolarization $\gamma$ can be expressed as [6]:

$$\gamma =\frac{P_d}{P_0}$$

(4)

where $P_d$ is the depolarized light component after propagating the magneto-optical crystal. As the polarization of the reflected light beam is not completed perpendicular to the input polarizer of FI devices, the overall extinction value of IF devices will be decreased due to thermally induced depolarization.

The origin of thermally induced depolarization is the thermally induced birefringence due to inhomogeneous absorption or anisotropic thermal expansion, both increasing with the intensity of the propagated light beam. Therefore, the extinction value of IF devices will decrease when a more powerful light beam propagates. As reported in Reference [24], the CeF₃-based FI devices could still remain an isolation degree over 30 dB when the propagated laser power increases above 800 W, obviously higher than that of TGG-based devices (600 W).

4.2. The Performances of FI Devices based on Uniaxial Crystals

Traditional FI devices usually employ cubic crystals as Faraday isolators in order to avoid the effect of natural birefringence. The rotation angle of the major axis of the polarization ellipse has an oscillatory character that depends on the wavelength [55]. This characteristic, though often used to measure the Faraday rotation of a uniaxial or biaxial crystal, is of course unfavorable to achieving a high isolation degree in FI devices. Thus, the Faraday rotators of optical anisotropic magneto-optical materials must be fabricated along the optical axis.

Nevertheless, orientation deviations of uniaxial magneto-optical crystals are still common due to machining tolerance or crystals’ inhomogeneity, which could result in a reduction in the isolation degree. The dependence of depolarization due to optical anisotropy is estimated in Ref. [24]. When the deviation between the laser propagation direction and the optical axis is small, the depolarization $\gamma$ of a uniaxial crystal can be calculated by formula [24]:

$$\gamma =si{n}^{2}2\mathsf{\Psi }si{n}^2\left(\frac{\pi L}{\lambda }\mathsf{\Delta }n{\rho }^2\right)$$

(5)

where Ψ is the polar angle counted from the direction of polarization, L is the length of the crystal and $\rho$ is the deviation of laser propagation off the optical axis. For the uniaxial crystal CeF₃, it is claimed that an isolation degree of over 30 dB can still be maintained in CeF₃ FI devices if the interval of the deviation of propagation orientaion from the optical axis is smaller than 22 mrad or 1.26°, which is easy to achieve in practical usage [24]. As the crystallographic -c axis cut samples are generally easy to fabricate, the applications of uniaxial magneto-optical crystals such as CeF₃, PrF₃ and TLF for high-power IF devices are feasible.

5. Conclusions

The characteristics and developments of several fluoride magneto-optical crystals, including optically isotropic KTF and EuF₃, uniaxial CeF₃, PrF₃ and TLF, as well as biaxial TbF₃, are introduced. The terbium-containing magneto-optical crystals, including KTF, TLF and TbF₃, show comparable Verdet constants with TGG and similar transmittance spectral ranges. When propagated by a laser of 400 W, the thermal lensing effect and thermally induced depolarization effect of KTF-based FI device are obviously weaker than that of TGG-based one, indicating its advantages for application in high-power systems in the visible-to-NIR spectral region. CeF₃ crystals exhibit high transmittance continuously from 300 nm to 2.1 μm, thus could be used for FI devices from UV to mid-IR spectral range. Moreover, CeF₃-based FI devices maintain high isolation degrees over 30 dB with a propagated laser power up to 800 W. On the other hand, PrF₃ and EuF₂ crystals are favorable for IF devices in the UV and mid-IR range, respectively, taking advantage of their high transmittances and large Verdet constants in these spectral regions. As the laser peak power and average power of high-power laser systems keep reaching higher levels and the wavelengths of solid-state lasers continue expanding to the UV and mid-IR spectral range, these fluoride magneto-optical crystals could find important applications in solid-state techniques.