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The prospective magnetooptical TGG, TAG and Ce:TAG ceramics for large-aperture Faraday isolators for lasers with average power more than 100W are compared. TGG ceramics is 1.5 times inferior to TGG crystals, whereas TAG ceramics is comparable with TGG crystals in maximum radiation power at the same isolation ratio. Optical power of their thermal lenses is also identical. Improvement of ceramics growth technologies and using doping for increasing Verdet constant is expected to additionally reduce thermal distortions in ceramics.
© 2014 Optical Society of America
1. Introduction
Laser power enhancement imposes increased requirements to characteristics of the optical elements. In particular, it is demanded to increase diameters of the elements and reduce the negative effects caused by thermal self-action of laser radiation.
Optical devices based on the effect of nonreciprocal rotation of polarization plane, such as Faraday rotators and isolators are widely employed in laser engineering for isolation of optical radiation, organization of multipass schemes of laser amplifiers, compensation of thermally induced birefringence in active lasers elements, and so on. The key component of such devices is a magneto-optical element placed in a constant magnetic field.
The Faraday isolator (FI) is a device strongly subject to the influence of thermal self-action due to relatively high absorption in its magnetooptical element (MOE) [1–3]. Heat absorption in MOE gives rise to birefringence caused by the photoelastic effect which leads to distortions of the wave front of the optical radiation passing through the FI (thermal lens) and to appearance of depolarized component of radiation. Depolarized component of radiation passed through the polarizer, which in turn reduces the isolation ratio of the device. The aberrations induced by the thermal lens do not lead to polarization distortions but affect the divergence and mode composition of the optical radiation passing through the FI.
Currently, terbium gallium garnet (TGG) crystals are almost the only material for FI for lasers with high average power. However, the aperture of the grown TGG crystals is restricted to the 30-40 mm [4], so they cannot be used for large-aperture FIs.
The present day MOEs for large-aperture FIs are made of magnetooptical glasses whose heat conductivity, Verdet constant and other characteristics are inferior to those of crystals [1]. A possibility of using gadolinium gallium garnet crystals (GGG) for MOE was considered by Starobor [5]. The diameter of GGG crystals may amount to 12 cm, but because of its relatively low Verdet constant cryogenic cooling is demanded. Optical ceramics is a medium that combines the advantages of crystals and glasses. Its thermooptical and magnetooptical parameters are the same as in monocrystals and size is like in glass. Significant progress has been made in creating high quality optical ceramics. Magnetooptical ceramics based on traditional (TGG) media as well as on media that cannot be grown as crystals (terbium aluminum garnet, TAG) are available today.
In this work we compare the TGG ceramics produced by the Konoshima Chemical Co. and the TAG and cerium-doped TAG (Ce:TAG) ceramics produced in SIOM in terms of their application in large-aperture FIs for high-power lasers. Thermooptical characteristics of the materials: thermal lens and thermally induced depolarization as a function of laser radiation power are compared.
2. Depolarization in ceramics
The characteristic grain size of the ceramics under study is comparable with the radiation wavelength (~1 µm). Therefore, the laser beam passes through a many grains (~103). Samples of high optical quality are fully transparent, have no inclusions and visible defects in the bulk of the element. The photographs of the elements are shown in Fig. 1.
These ceramic samples were studied in several recent works: TGG [6–9], TAG [10–12]. The techniques for measuring thermally induced depolarization and thermal lens were the same in all the studies. Comparative analysis of the ceramics was not performed earlier but the identical measurement techniques allow direct comparison of characteristics of the media.
Thermally induced depolarization γp in a cubic crystal in a magnetic field with the angle of rotation of polarization plane, φ, may be calculated by the following formula [13]:
where А is the coefficient depending on the laser beam profile (А = 0.137 for a Gaussian beam), α is the absorption coefficient, Q is the thermooptical constant responsible for depolarization, L is the MOE length, Plas is the laser radiation power, κ is the thermal conductivity (κ = 4.9 W/m/K for TGG ceramics [6] and κ = 4.5 W/m/K for TAG [11] at room temperature), λ is the laser radiation wavelength, and X is the function of the crystal orientation and optical anisotropy parameter ξ (ξ = 1 for amorphous media and ξ = 2.25 for TGG [3]). For ceramics of a cubic crystal X = (2 + 3ξ)/5 [14] or X = (53 + 75ξ)/128 [13], depending on the grain statistics; for TGG, X calculated by both formulas at room temperature is XTGG = 1.74. For ceramics this formula works in the approximation of a large number of grains in the beam path, as the characteristic size of the grains in our study was ~1 µm and the sample length was not less than 6 mm, this approximation fits well [13,15].When comparing media it should be taken into consideration that the angle of rotation of the radiation polarization plane in MOE must be 45 degrees and is determined from the formula (Faraday effect):
where Н is the intensity of the magnetic field in which MOE is placed, V is the Verdet constant of MOE. Therefore, the depolarization must be normalized to the length L45 at which a required angle of rotation φ = 45° is obtained in the given magnetic system.The Verdet constant of TAG at the wavelength of 1.07 µm is 21% higher than the Verdet constant of TGG [10], and for the best Ce:TAG (with 0.05 at. % content of cerium) sample it is 37% higher [12]. As a result, the MOE length needed for creation of a FI reduces from 9 mm for TGG to 7.5 mm for TAG and to ~7 mm for Ce:TAG. On cooling to 77К the difference increased to 36% and to 66%, correspondingly. The temperature dependence of the Verdet constants of the media is plotted in Fig. 2[16,17].The depolarization measurements from [6,10,12] were normalized to these length and zero magnetic field according to Eq. (1); the depolarization as a function of radiation power for L = L45 is plotted in Fig. 3.
Fig. 2 Temperature dependence of the Verdet constant of different ceramics: TGG – solid curve, TAG – rhombs, Ce:TAG –triangles).
Fig. 3 Power dependence of depolarization at L = L45: TGG – crosses, TAG – rhombs, Ce:TAG – triangles.
According [17], depolarization in Ce:TAG depends on the content of cerium. We chose for comparison a sample with weakest depolarization and cerium content of 0.05 at. %. Depolarization in a pure TAG is less that in TGG by a factor of 3.5 and about twice less than in Ce:TAG, which permits increasing the radiation power for the same depolarization degree by a factor of 1.9 and 1.5, respectively. Note samples of Ce:TAG and TAG were additionally annealed in the atmosphere at a temperature of 1200°С, as a result Ce:TAG did not change its properties, but depolarization in TAG was reduced the by about 5 times compared with the data obtained in [17]. TGG samples were already annealed by manufacturer. Annealing in some cases can decrease absorption arising from the presence of color centers.
3. Thermal lens in ceramics
Another important characteristic of FI is the optical power D of the arising thermal lens that may be calculated by the formula [18]:
where P is the thermooptical constant responsible for thermal lens [19], rh is the laser beam radius, and S is the orientation-dependent constant: for ceramics S = 1/5. The contribution of the thermally induced surface curvature of the sample is not taken into account in Eq. (3). Three-dimensional numerical simulation of thermal conductivity and elasticity equations showed that the values for the measured samples of TAG ceramics and for the samples with L = L45 differ by 10%, which was taken into consideration when constructing the plots in Fig. 3. For TGG, the length coincided with the required one.The plots for the optical power of thermal lens as a function of the laser power obtained in [7,10,12] and recalculated for the length L = L45 and the beam with a diameter of 2.4 mm are presented in Fig. 4.The arising thermal lenses are approximately the same for TAG and TGG, and about two times stronger for Се:TAG.
Fig. 4 Optical power of thermal lens versus radiation power for L = L45: TGG – crosses, TAG – rhombs, Ce:TAG – triangles.
4. Ceramics-based Faraday isolators
These media were used to produce water cooled FIs with a classical scheme [7,10] and a scheme with depolarization compensation [8,12]. The FIs based on TGG ceramics had the isolation ratio of 30 dB at the power up to 340 W and the focal distance of the thermal lens was estimated to be up to 6.5 m at the same power. According to the estimates made in [7] the absorption coefficient of this ceramics is 1.4∙10−3cm−1, which is comparable with the absorption of present day samples of TGG crystals. Depolarization in ceramics is times stronger than in a crystal with the [001] orientation (for TGG it is three times stronger), because of different orientation of crystallographic axes in grains. The Faraday isolator on the TGG crystal in the same magnetic system [20] provided the isolation ratio of 30 dB at the laser power of 650 W, with the focal distance of the thermal lens (recalculated for a beam diameter of 2.4 mm) being 6.5 m.
In magnetooptical TAG ceramics, the isolation ratio of 38 dB was obtained at the radiation power of 300 W with the focal distance of the thermal lens of about 8 m. Our earlier estimates show that the isolation ratio of 30 dB will be attained at a kilowatt power level [10]. For an FI based on Ce:TAG we used a sample with 0.1% cerium content which gave the isolation ratio of 31 dB at the power of 300 W, sample has a higher absorption than in the case of the optimal 0.05% content of cerium. Note that for TAG and Се:TAG ceramics water cooling is necessary because of strong scattering and heating of the FI parts by the scattered radiation. At the laser radiation power of 300 W, the time during which a steady-state regime sets in is about 4 min. Data on Faraday isolators are shown in Table 1.The angle of rotation of the plane of polarization in this time interval reduces by 3-10° due to the temperature dependence of the Verdet constant. Thus, the currently available FIs based on TAG ceramics have the isolation rate the same as the FIs on TGG crystals, and are only slightly inferior to them in the optical power of thermal lens. However, optimal alloying by cerium or some other dopants and annealing are expected to provide a several-fold increase of the isolation ratio and will enable creating FIs on TAG ceramics for a kilowatt power level.
Table 1. Ceramic-based FI characteristics.
5. Conclusion
In this work we have compared magnetooptical ceramics that are potential candidates for large-aperture Faraday isolators. TGG ceramics has absorption like in monocrystals, hence it is only 1.8 times inferior to them in maximum radiation power at the same isolation ratio. Also, they have the same optical power of thermal lens. It is worth noting that TGG ceramics with apertures up to 10∙10 cm2 is commercially available [21].
TAG ceramics is comparable with TGG crystals in depolarization and thermal lens. However, the currently available samples have relatively poor quality; their strong radiation scattering impedes their practical application in FIs. Further improvement of growth technology of such ceramics and use of doping for increasing Verdet constant will allow additional reduction of thermally induced distortions.
Acknowledgment
This work was supported by the mega-grant of the Government of the Russian Federation No. 14.B25.31.0024 executed at the Institute of Applied Physics RAS and by a grant of the President of the Russian Federation NºМК-2934.2014.2 also executed in the Institute of Applied Physics RAS.
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