Abstract

A Faraday isolator (FI) for high-power lasers with kilowatt-level average power and 1-µm wavelength was demonstrated using a terbium scandium aluminum garnet (TSAG) with its crystal axis aligned in the <001> direction. Furthermore, no compensation scheme for thermally induced depolarization in a magnetic field was used. An isolation ratio of 35.4 dB (depolarization ratio γ of 2.9 × 10−4) was experimentally observed at a maximum laser power of 1470 W. This result for room-temperature FIs is the best reported, and provides a simple, practical solution for achieving optical isolation in high-power laser systems.

© 2016 Optical Society of America

1. Introduction

A Faraday isolator (FI) is a key optical component of many laser systems as it is used to prevent backward reflection from the laser-irradiated materials or forward optics [1,2]. This device is important for laser-driven applications that utilize recently developed high-power lasers, such as high-energy and high-repetition lasers [3–5], ultra-high-power CW laser systems [6], and high-intensity laser systems [7,8]. However, it is difficult to use this device for high-average-power laser operation because of thermally induced effects, such as thermal birefringence effects that occur in the Faraday medium. More specifically, thermal birefringence degrades the extinction ratio of FIs, which is the most important parameter of such devices.

Many studies aimed at solving this problem have been performed in the past 15 years. These reports include compensation methods for FIs [9–11], material parameter control methods that use cryogenic temperatures [12,13], as well as the development of new Faraday materials, such as Tb3Ga5O12 (TGG) ceramics [14–18] and Tb3Al5O12 (TAG) ceramics [19,20]. Today, FIs for lasers with an average power of over 1 kW can be realized as the result of the studies mentioned above. The next point of interest in the development of high-average-power FIs concerns realizing FIs with ultra-high average powers (e.g., 100 kW lasers) [6]. In particular, material developments are important for increasing the operational average power of FIs. That is because high-average-power FIs require low absorption coefficients, good thermo-optic properties, and high Verdet constants.

A terbium scandium aluminum garnet (TSAG) crystal is the one of the best candidates for use in lasers with ultra-high average powers. This material has excellent characteristics for high-power laser operation [21,22]. TSAG has a high Verdet constant, which is 25% higher than that of the traditionally used TGG crystal, and exhibits good thermal properties (thermal conductivity, in particular) [23]. The characteristics of TSAG-based FIs show that they are suitable for high-average-power operation [24,25]. Furthermore, our recent study investigated the unique characteristics of TSAG [23]. In particular, this material has an extraordinary optical anisotropy parameter (ξ = − 101) and the highest magneto-optical figure of merit (μTSAG = 30∙μTGG) known for magneto-active materials at the moment [23]. This means that thermally induced depolarization can be reduced by using TSAG with <001> crystal orientation and with an optimum input polarization angle.

This manuscript reports on the first construction of an FI based on the TSAG crystal with <001> crystal orientation. Furthermore, our data evidence the efficient suppression of the thermally induced depolarization that results from using the TSAG crystal with <001> crystal orientation.

2. Experimental setup

Figure 1 shows the TSAG sample used in this experiment. The TSAG sample was polished to a rod shape with a length of 9 mm and diameter of 10 mm. Each edge surface was anti-reflection coated for mitigating reflections from the laser light. The <001> crystal axis was parallel to the axis of the rod.

 figure: Fig. 1

Fig. 1 Picture of the terbium scandium aluminum garnet (TSAG) crystal sample.

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Figure 2 shows a schematic of the TSAG-based FI. The TSAG rod was installed in the magnetic system using a copper holder. One end of the holder was water-cooled to maintain the temperature of the TSAG crystal. The Verdet constant of TSAG crystal is inversely proportional to temperature [26]; therefore, cooling is necessary to stabilize the rotation angle of the polarization for elements heated by laser radiation. The magnetic system, which has an aperture of 13 mm, provided a magnetic field strength as high as 2.5 T [27].

 figure: Fig. 2

Fig. 2 Schematic of the experimental setup used for thermally induced depolarization measurements.

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The assembled Faraday device was set between a calcite wedge and a Glan prism, as shown in Fig. 2. The TSAG crystal was irradiated by a fiber laser with a Gaussian laser beam profile within the measured laser power range. The Yb-fiber laser (IPG Photonics, YLS-1500) emitted radiation with a wavelength of 1.07 μm and an unpolarized maximum power of 1.5 kW. The radius (1/e) of the laser beam in the TSAG rod was 1.5 mm.

When measuring the intensity of the depolarized component (Id), the half-wave plate was removed, and the Glan prism was tuned to the maximum extinction ratio at each power point. The resulting distribution of the depolarized components was recorded using a CCD camera and then summed over the two-dimensional pattern. To measure the intensity of the polarized component (I0), a half-wave plate was installed in front of the Glan prism. The half-wave plate was tuned to the angle of rotation of the polarization plane of 90° relative to the unperturbed polarization plane rotation angle (45°). Heating slightly changed the rotation angle, and this deviation in the beam intensity was neglected. The resulting distribution of the polarized components was also recorded using a CCD camera and then summed over the area. The degree of depolarization was calculated by

γ=IdI0+Id

The calcite wedge and Glan prism produced a contrast ratio of 1 × 10−6.

3. Results and discussion

The laser power dependence of the depolarization ratio in the TSAG-crystal-based FI is shown in Fig. 3. In this experiment, a depolarization ratio γ of 2.9 × 10−4 was observed at a laser power of 1470 W using TSAG with its crystal axis in the <001> direction. From these results, the isolation ratio was calculated to be 35.4 dB. For the case of TSAG with its crystal axis in the <111> direction with a magnetic field, a γ value of 3.2 × 10−4 was observed for a laser power of 196 W. This isolation ratio was calculated to be 34.8 dB. TSAG with a <001> orientation can be used for laser powers that are 7.5 times higher than those associated with the <111> crystal. In addition, this performance of the TSAG-crystal based FI is superior to the best TGG-crystal-based FI with or without compensation [28]. In the case of the TGG crystal, the same isolation ratio of 35.4 dB in the FI scheme without compensation can be obtained only at a laser power of 300 W [27,28].

 figure: Fig. 3

Fig. 3 Experimental results of depolarization as a function of laser power. Open red circles show the results for terbium scandium aluminum garnet (TSAG) with <001> crystal orientation in the absence of a magnetic field. Closed blue circles show the results for TSAG with <001> crystal orientation in the presence of a magnetic field. Black triangles show the result for TSAG with <111> crystal orientation in the absence of a magnetic field. Green squares show the results for TSAG with <111> crystal orientation in the presence of a magnetic field. Solid lines show the theoretical curves. The dotted line shows the second term of (10) and the dash-dotted line shows the third term of (10).

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As can be seen from Fig. 3, thermally induced depolarization significantly increases upon placing a TSAG single crystal in a magnetic field. This behavior can be explained by the contribution to the thermally induced depolarization γVH from the temperature dependence of Verdet constant (1/V∙dV/dT) and inhomogeneity of magnetic field [29] and by the contribution of the thermally induced depolarization γT due to the large value of the optical anisotropy parameter of the TSAG crystal: ξ = −101 [23]. In general, the degree of thermally induced depolarization in the magneto-optical element is determined by the following equations [30]:

γ=1I002πdφ0R0sin2(δ2)sin2(2Ψδc2)δl2δ2I(r)rdr++1I002πdφ0R0(cos(δ2)sin(δc2)δcδcos(δc2)sin(δ2))2I(r)rdr,
I0=02πdφ0R0I(r)rdr,δ2=δl2+δc2,
where δl(r,φ) and Ψ(r,φ) are the linear phase difference and the direction of eigen axes of linear birefringence, respectively. Additionally, δc(r)=2V(r)0L(r)H(r,z)dz represents the phase difference of circular birefringence responsible for Faraday rotation. Here, V(r) = V0∙(1 + 1/V∙(dV/dT)[T(r)-T0]) is the Verdet constant; T(r) is the transverse temperature distribution; T0 is the average temperature of crystal; L(r) = L0∙(1 + αT[T(r)- T0])) is the thermally disturbed crystal length; αT is linear expansion coefficient; and H(r) = H0(1 + δHr2/R02) is the transverse distribution of the magnetic field [29]. For solid magneto-active materials, αT<<1/V∙(dV/dT) and can be neglected. For our magnet system dependence, H(r) is parabolic with a 2% difference between the center and r = 4 mm [27]. Here, I is the intensity distribution and F(r) = I(r)/I0 is the form of transverse distribution; R0 is the crystal radius; and r and φ indicate polar coordinates [30]. A Faraday rotation angle of 45° corresponds to the average value of the circular phase difference δc0 = 2V0H0L0 = π/2. The inhomogeneity of the magnetic field and the quality of the crystal determine depolarization at low laser power (cold depolarization), while the dependence of the Verdet constant on temperature and thermally induced birefringence determines depolarization at high laser power.

For a single crystal with <001> orientation, δl(r,φ) and Ψ(r,φ) can be expressed as follows [31]:

δl=ph1+ξ2tan2(2θ2φ)1+tan2(2θ2φ),tan(2Ψ2θ)=ξtan(2φ2θ),h(y=r2/rh2)=1y0ydz0zF(ζ)dζ,
where p = −α0L0QP0/(λκ) is the dimensionless normalized power; α0 is the linear absorption coefficient (for our sample α0 = 0.0025 1/cm according to information from the manufacturer); P0 is the laser power; Q is the thermo-optic coefficient; λ is the radiation wavelength; κ is the thermal conductivity; h is the dimensionless function of the transverse intensity distribution of laser radiation [32]; rh is the effective beam radius; and θ is the angle between the direction of polarization and one of the crystallographic axes.

In the case of weak linear birefringence δl<<1, Eq. (1) can be expanded in a Taylor series in powers of δl. Discarding terms above the sixth order and in the absence of circular birefringence (δc = 0), Eq. (2) can be rewritten as follows:

γ0=p2A18[1+(ξ21)cos2(2θ)]+p4A2384[3(ξ41)cos2(2θ)+ξ2+3]+O(p6),
where
A1=0h2(u)F(u)du,A2=0h4(u)F(u)du.
For a Gaussian beam, A1 = 0.137 and A2 = 0.042.

In the presence of circular birefringence and a Faraday rotational angle of 45° (δc = π/2), in the case of weak linear birefringence δl<<1 and (δc(r)-δc0)<<δc0, Eq. (2) can be rewritten as:

γ45=p2A1π2[1+(ξ21)cos2(2θπ4)]++p4A232π4[24(ξ41)(π4)cos2(2θπ4)+3(π2)2ξ4+2(π212)ξ2+3{(π+2)232}]++pV2A3+O(p6)
where [29,31]

pV=α016κ(P0+P0*)(1VdVdT+αT),P0*=δHT04πκα0rh2R02,A3=0f2(y)exp(y)dy[0f(y)exp(y)dy]2,f(y)=0ydzz0zF(ζ)dζ.

Equations (5) and (7) with | ξ | > 1 reach minima when θ0 = π/4 and θ45 = -π/8. When | ξ | >> 1 at an optimum θ value, Eqs. (5) and (7) can be written as:

γ0minA18p2+A2384p4ξ2,
γ45minA1π2p2+3(π2)2A232π4ξ4p4+pV2A3.
The first terms in these equations at the minimum do not depend on the optical anisotropy parameter ξ, and their ratio is γ45/γ0 = 8/π2 ≈0.81 [32]. However, the second terms in both equations depend on ξ. In the absence of a magnetic field, this term is proportional to p4ξ2; in the presence of a magnetic field, it is proportional to p4ξ4. The experimental FI theoretical curve (10) is plotted as a solid line; the second term of (10) is plotted on Fig. 3 as a dotted line, and the third term of (10) is plotted on Fig. 3 as a dash-dotted line.

From these equations, it is clear that the magnetic field can lead to an increase in the thermally induced depolarization due to the Verdet constant dependence on temperature and for crystals with | ξ | >> 1 and <001> orientation due to the second term in a Taylor series. In this case, the dependence of γ on the laser power for a crystal in a magnetic field at small laser power is proportional to ~p2 (Fig. 3 dash-dotted line), but at high laser power, it changes to ~p4(dotted line). This increasing of thermally induced depolarization after placing crystal into magnetic field was observed in the experiments using a TSAG single crystal with <001> orientation (ξ = −101 [23]) (see the circles in Fig. 3). For single crystals with <111> orientation, such behavior does not occur (see the squares and triangles in Fig. 3). That is because the first term for the degree of thermally induced depolarization dependence on laser power depends on ξ and is proportional to (p(1 + 2ξ))2; placing the TSAG crystal in a magnetic field leads to a decrease in the thermally induced depolarization by a factor of ~8/π2 for the case of <111> orientation [31]. It should be noted that the large optical anisotropy parameter in FIs leads to one negative effect. Power losses introduced by the FI at high average power are determined by the thermally induced depolarization in the direct passage γ = A1ξ2p22. Owing to the high value of ξ, losses are also high. This should be considered in FI design and the use of such materials.

4. Conclusion

We experimentally demonstrated the first construction of an FI based on the TSAG crystal with <001> crystal orientation. It was shown theoretically and experimentally that thermally induced depolarization significantly increases when the crystal, with a modulus of optical anisotropy parameter |ξ|>>1, is placed in <001> orientation in a magnetic field. Our data indicate the efficient suppression of the thermally induced depolarization over the 1 kW laser radiation. A γ value of 2.9 × 10−4 was observed at a laser power of 1470 W using TSAG with a <001> crystal axis orientation and with a 45° Faraday rotation angle. From these results, the isolation ratio was calculated to be 35.4 dB. This indicates that TSAG with <001> crystal orientation can yield an FI with a laser radiation that is 5 times higher than that of the TGG crystal. For these reasons, FIs that utilize TSAG with <001> crystal orientation are expected to accelerate the development of high-power laser-driven applications.

Acknowledgments

This work was partially supported by JSPS KAKENHI Grant No. 26709072, by the Matching Planner Program from Japan Science and Technology Agency, JST, and by the grant from AMADA foundation. Further, the experimental part of this work was supported by the mega-grant of the Government of the Russian Federation No. 14.B25.31.0024 and was performed in the Institute of Applied Physics, RAS.

References and links

1. D. J. Gauthier, P. Narum, and R. W. Boyd, “Simple, compact, high-performance permanent-magnet Faraday isolator,” Opt. Lett. 11(10), 623–625 (1986). [CrossRef]   [PubMed]  

2. R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992). [CrossRef]  

3. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012). [CrossRef]   [PubMed]  

4. R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett. 33(15), 1711–1713 (2008). [CrossRef]   [PubMed]  

5. T. Sekine, S. Matsuoka, R. Yasuhara, T. Kurita, R. Katai, T. Kawashima, H. Kan, J. Kawanaka, K. Tsubakimoto, T. Norimatsu, N. Miyanaga, Y. Izawa, M. Nakatsuka, and T. Kanabe, “84 dB amplification, 0.46 J in a 10 Hz output diode-pumped Nd:YLF ring amplifier with phase-conjugated wavefront corrector,” Opt. Express 18(13), 13927–13934 (2010). [CrossRef]   [PubMed]  

6. E. Shcherbakov, V. Fomin, A. Abramov, A. Ferin, D. Mochalov, and V. P. Gapontsev, “Industrial Grade 100 kW Power CW Fiber Laser,” in Advanced Solid-State Lasers Congress, G. Huber and P. Moulton, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ATh4A.2. [CrossRef]  

7. T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20(10), 10807–10815 (2012). [CrossRef]   [PubMed]  

8. M. Aoyama, K. Yamakawa, Y. Akahane, J. Ma, N. Inoue, H. Ueda, and H. Kiriyama, “0.85-PW, 33-fs Ti:sapphire laser,” Opt. Lett. 28(17), 1594–1596 (2003). [CrossRef]   [PubMed]  

9. E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, and D. H. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17(1), 99–102 (2000). [CrossRef]  

10. I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011). [CrossRef]   [PubMed]  

11. I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012). [CrossRef]  

12. D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010). [CrossRef]  

13. R. Yasuhara, S. Tokita, J. Kawanaka, T. Kawashima, H. Kan, H. Yagi, H. Nozawa, T. Yanagitani, Y. Fujimoto, H. Yoshida, and M. Nakatsuka, “Cryogenic temperature characteristics of Verdet constant on terbium gallium garnet ceramics,” Opt. Express 15(18), 11255–11261 (2007). [CrossRef]   [PubMed]  

14. R. Yasuhara and H. Furuse, “Thermally induced depolarization in TGG ceramics,” Opt. Lett. 38(10), 1751–1753 (2013). [CrossRef]   [PubMed]  

15. R. Yasuhara, H. Nozawa, T. Yanagitani, S. Motokoshi, and J. Kawanaka, “Temperature dependence of thermo-optic effects of single-crystal and ceramic TGG,” Opt. Express 21(25), 31443–31452 (2013). [CrossRef]   [PubMed]  

16. I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014). [CrossRef]   [PubMed]  

17. R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014). [CrossRef]   [PubMed]  

18. R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014). [CrossRef]  

19. H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011). [CrossRef]  

20. C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012). [CrossRef]  

21. Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004). [CrossRef]  

22. A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002). [CrossRef]  

23. I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015). [CrossRef]  

24. E. A. Mironov and O. V. Palashov, “Faraday isolator based on TSAG crystal for high power lasers,” Opt. Express 22(19), 23226–23230 (2014). [CrossRef]   [PubMed]  

25. I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015). [CrossRef]  

26. A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015). [CrossRef]  

27. E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013). [CrossRef]  

28. I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014). [CrossRef]  

29. E. A. Mironov, A. V. Voitovich, A. V. Starobor, and O. V. Palashov, “Compensation of polarization distortions in Faraday isolators by means of magnetic field inhomogeneity,” Appl. Opt. 53(16), 3486–3491 (2014). [CrossRef]   [PubMed]  

30. E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29(1), 59–64 (1999). [CrossRef]  

31. E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999). [CrossRef]  

32. E. Khazanov, N. Andreev, O. Palashov, A. Poteomkin, A. Sergeev, O. Mehl, and D. H. Reitze, “Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power,” Appl. Opt. 41(3), 483–492 (2002). [CrossRef]   [PubMed]  

References

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  1. D. J. Gauthier, P. Narum, and R. W. Boyd, “Simple, compact, high-performance permanent-magnet Faraday isolator,” Opt. Lett. 11(10), 623–625 (1986).
    [Crossref] [PubMed]
  2. R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
    [Crossref]
  3. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012).
    [Crossref] [PubMed]
  4. R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett. 33(15), 1711–1713 (2008).
    [Crossref] [PubMed]
  5. T. Sekine, S. Matsuoka, R. Yasuhara, T. Kurita, R. Katai, T. Kawashima, H. Kan, J. Kawanaka, K. Tsubakimoto, T. Norimatsu, N. Miyanaga, Y. Izawa, M. Nakatsuka, and T. Kanabe, “84 dB amplification, 0.46 J in a 10 Hz output diode-pumped Nd:YLF ring amplifier with phase-conjugated wavefront corrector,” Opt. Express 18(13), 13927–13934 (2010).
    [Crossref] [PubMed]
  6. E. Shcherbakov, V. Fomin, A. Abramov, A. Ferin, D. Mochalov, and V. P. Gapontsev, “Industrial Grade 100 kW Power CW Fiber Laser,” in Advanced Solid-State Lasers Congress, G. Huber and P. Moulton, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ATh4A.2.
    [Crossref]
  7. T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20(10), 10807–10815 (2012).
    [Crossref] [PubMed]
  8. M. Aoyama, K. Yamakawa, Y. Akahane, J. Ma, N. Inoue, H. Ueda, and H. Kiriyama, “0.85-PW, 33-fs Ti:sapphire laser,” Opt. Lett. 28(17), 1594–1596 (2003).
    [Crossref] [PubMed]
  9. E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, and D. H. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17(1), 99–102 (2000).
    [Crossref]
  10. I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011).
    [Crossref] [PubMed]
  11. I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012).
    [Crossref]
  12. D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
    [Crossref]
  13. R. Yasuhara, S. Tokita, J. Kawanaka, T. Kawashima, H. Kan, H. Yagi, H. Nozawa, T. Yanagitani, Y. Fujimoto, H. Yoshida, and M. Nakatsuka, “Cryogenic temperature characteristics of Verdet constant on terbium gallium garnet ceramics,” Opt. Express 15(18), 11255–11261 (2007).
    [Crossref] [PubMed]
  14. R. Yasuhara and H. Furuse, “Thermally induced depolarization in TGG ceramics,” Opt. Lett. 38(10), 1751–1753 (2013).
    [Crossref] [PubMed]
  15. R. Yasuhara, H. Nozawa, T. Yanagitani, S. Motokoshi, and J. Kawanaka, “Temperature dependence of thermo-optic effects of single-crystal and ceramic TGG,” Opt. Express 21(25), 31443–31452 (2013).
    [Crossref] [PubMed]
  16. I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014).
    [Crossref] [PubMed]
  17. R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014).
    [Crossref] [PubMed]
  18. R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
    [Crossref]
  19. H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
    [Crossref]
  20. C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
    [Crossref]
  21. Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
    [Crossref]
  22. A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
    [Crossref]
  23. I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
    [Crossref]
  24. E. A. Mironov and O. V. Palashov, “Faraday isolator based on TSAG crystal for high power lasers,” Opt. Express 22(19), 23226–23230 (2014).
    [Crossref] [PubMed]
  25. I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015).
    [Crossref]
  26. A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
    [Crossref]
  27. E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013).
    [Crossref]
  28. I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
    [Crossref]
  29. E. A. Mironov, A. V. Voitovich, A. V. Starobor, and O. V. Palashov, “Compensation of polarization distortions in Faraday isolators by means of magnetic field inhomogeneity,” Appl. Opt. 53(16), 3486–3491 (2014).
    [Crossref] [PubMed]
  30. E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29(1), 59–64 (1999).
    [Crossref]
  31. E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
    [Crossref]
  32. E. Khazanov, N. Andreev, O. Palashov, A. Poteomkin, A. Sergeev, O. Mehl, and D. H. Reitze, “Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power,” Appl. Opt. 41(3), 483–492 (2002).
    [Crossref] [PubMed]

2015 (3)

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015).
[Crossref]

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

2014 (6)

2013 (3)

2012 (4)

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012).
[Crossref]

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012).
[Crossref] [PubMed]

T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20(10), 10807–10815 (2012).
[Crossref] [PubMed]

2011 (2)

I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011).
[Crossref] [PubMed]

H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
[Crossref]

2010 (2)

2008 (1)

2007 (1)

2004 (1)

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

2003 (1)

2002 (2)

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

E. Khazanov, N. Andreev, O. Palashov, A. Poteomkin, A. Sergeev, O. Mehl, and D. H. Reitze, “Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power,” Appl. Opt. 41(3), 483–492 (2002).
[Crossref] [PubMed]

2000 (1)

1999 (2)

E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29(1), 59–64 (1999).
[Crossref]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

1992 (1)

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

1986 (1)

Akahane, Y.

Andreev, N.

Aoyama, M.

Babin, A.

Banerjee, S.

Boyd, R. W.

Chen, C.

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

Collier, J. L.

Diedrich, F.

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

Ertel, K.

Fujimoto, Y.

Fukuda, T.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Furuse, H.

Gauthier, D. J.

Hernandez-Gomez, C.

Ikegawa, T.

Inoue, N.

Izawa, Y.

Jeong, T. M.

Kagamitani, Y.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Kan, H.

Kanabe, T.

Katai, R.

Katin, E. V.

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Kawanaka, J.

Kawashima, T.

Khazanov, E.

Khazanov, E. A.

I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
[Crossref]

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29(1), 59–64 (1999).
[Crossref]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

Kiriyama, H.

Kiselev, A.

Kulagin, O. V.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

Kurita, T.

Lee, J.

Lee, S. K.

Lin, H.

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
[Crossref]

Loeser, M.

Ma, J.

Machida, H.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Martinek, J.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

Mason, P. D.

Matsumoto, O.

Matsuoka, S.

Mehl, O.

Meschede, D.

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

Mironov, E.

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

Mironov, E. A.

Miyamoto, M.

Miyanaga, N.

Motokoshi, S.

Mukhin, I.

Mukhin, I. B.

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Nakatsuka, M.

Narum, P.

Norimatsu, T.

Nozawa, H.

Palashov, O.

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015).
[Crossref]

R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
[Crossref]

R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014).
[Crossref] [PubMed]

I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011).
[Crossref] [PubMed]

E. Khazanov, N. Andreev, O. Palashov, A. Poteomkin, A. Sergeev, O. Mehl, and D. H. Reitze, “Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power,” Appl. Opt. 41(3), 483–492 (2002).
[Crossref] [PubMed]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, and D. H. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17(1), 99–102 (2000).
[Crossref]

Palashov, O. V.

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

E. A. Mironov and O. V. Palashov, “Faraday isolator based on TSAG crystal for high power lasers,” Opt. Express 22(19), 23226–23230 (2014).
[Crossref] [PubMed]

I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014).
[Crossref] [PubMed]

E. A. Mironov, A. V. Voitovich, A. V. Starobor, and O. V. Palashov, “Compensation of polarization distortions in Faraday isolators by means of magnetic field inhomogeneity,” Appl. Opt. 53(16), 3486–3491 (2014).
[Crossref] [PubMed]

I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
[Crossref]

E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013).
[Crossref]

I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012).
[Crossref]

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Pawlak, D. A.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Phillips, P. J.

Poteomkin, A.

Reitze, D. H.

Sato, H.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Sekine, T.

Sergeev, A.

Siebold, M.

Snetkov, I.

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015).
[Crossref]

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014).
[Crossref] [PubMed]

R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
[Crossref]

I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011).
[Crossref] [PubMed]

Snetkov, I. L.

I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014).
[Crossref] [PubMed]

I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
[Crossref]

E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013).
[Crossref]

I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012).
[Crossref]

Starobor, A.

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014).
[Crossref] [PubMed]

R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
[Crossref]

Starobor, A. V.

Sung, J. H.

Tanner, D. B.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

Telle, H. R.

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

Teng, H.

H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
[Crossref]

Tokita, S.

Tsubakimoto, K.

Ueda, H.

Voitovich, A. V.

E. A. Mironov, A. V. Voitovich, A. V. Starobor, and O. V. Palashov, “Compensation of polarization distortions in Faraday isolators by means of magnetic field inhomogeneity,” Appl. Opt. 53(16), 3486–3491 (2014).
[Crossref] [PubMed]

I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
[Crossref]

E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013).
[Crossref]

Wynands, R.

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

Yagi, H.

Yamakawa, K.

Yanagitani, T.

Yasuhara, R.

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
[Crossref]

I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014).
[Crossref] [PubMed]

R. Yasuhara, I. Snetkov, A. Starobor, D. Zheleznov, O. Palashov, E. Khazanov, H. Nozawa, and T. Yanagitani, “Terbium gallium garnet ceramic Faraday rotator for high-power laser application,” Opt. Lett. 39(5), 1145–1148 (2014).
[Crossref] [PubMed]

R. Yasuhara, H. Nozawa, T. Yanagitani, S. Motokoshi, and J. Kawanaka, “Temperature dependence of thermo-optic effects of single-crystal and ceramic TGG,” Opt. Express 21(25), 31443–31452 (2013).
[Crossref] [PubMed]

R. Yasuhara and H. Furuse, “Thermally induced depolarization in TGG ceramics,” Opt. Lett. 38(10), 1751–1753 (2013).
[Crossref] [PubMed]

T. Sekine, S. Matsuoka, R. Yasuhara, T. Kurita, R. Katai, T. Kawashima, H. Kan, J. Kawanaka, K. Tsubakimoto, T. Norimatsu, N. Miyanaga, Y. Izawa, M. Nakatsuka, and T. Kanabe, “84 dB amplification, 0.46 J in a 10 Hz output diode-pumped Nd:YLF ring amplifier with phase-conjugated wavefront corrector,” Opt. Express 18(13), 13927–13934 (2010).
[Crossref] [PubMed]

R. Yasuhara, T. Kawashima, T. Sekine, T. Kurita, T. Ikegawa, O. Matsumoto, M. Miyamoto, H. Kan, H. Yoshida, J. Kawanaka, M. Nakatsuka, N. Miyanaga, Y. Izawa, and T. Kanabe, “213 W average power of 2.4 GW pulsed thermally controlled Nd:glass zigzag slab laser with a stimulated Brillouin scattering mirror,” Opt. Lett. 33(15), 1711–1713 (2008).
[Crossref] [PubMed]

R. Yasuhara, S. Tokita, J. Kawanaka, T. Kawashima, H. Kan, H. Yagi, H. Nozawa, T. Yanagitani, Y. Fujimoto, H. Yoshida, and M. Nakatsuka, “Cryogenic temperature characteristics of Verdet constant on terbium gallium garnet ceramics,” Opt. Express 15(18), 11255–11261 (2007).
[Crossref] [PubMed]

Yasyhara, R.

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

Yi, Q.

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

Yoon, J. W.

Yoshida, H.

Yoshida, S.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

Yoshikawa, A.

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Yu, T. J.

Zelenogorskii, V. V.

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Zheleznov, D.

Zheleznov, D. S.

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Zhou, S.

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

Zhou, S. M.

H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

I. L. Snetkov and O. V. Palashov, “Compensation of thermal effects in Faraday isolator for high average power lasers,” Appl. Phys. B 109(2), 239–247 (2012).
[Crossref]

Appl. Phys. Lett. (2)

R. Yasuhara, I. Snetkov, A. Starobor, and O. Palashov, “Terbium gallium garnet ceramic-based Faraday isolator with compensation of thermally induced depolarization for high-energy pulsed lasers with kilowatt average power,” Appl. Phys. Lett. 105(24), 241104 (2014).
[Crossref]

C. Chen, S. Zhou, H. Lin, and Q. Yi, “Fabrication and performance optimization of the magneto-optical (Tb1−xRx)3Al5O12 (R = Y, Ce) transparent ceramics,” Appl. Phys. Lett. 101(13), 131908 (2012).
[Crossref]

IEEE J. Quantum Electron. (3)

I. Snetkov, R. Yasuhara, A. Starobor, E. Mironov, and O. V. Palashov, “Thermo-Optical and Magneto-Optical Characteristics of Terbium Scandium Aluminum Garnet Crystals,” IEEE J. Quantum Electron. 51(7), 1–7 (2015).
[Crossref]

I. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50(6), 434–443 (2014).
[Crossref]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. B. Tanner, and D. H. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35(8), 1116–1122 (1999).
[Crossref]

J. Mater. Res. (1)

Y. Kagamitani, D. A. Pawlak, H. Sato, A. Yoshikawa, J. Martinek, H. Machida, and T. Fukuda, “Dependence of Faraday effect on the orientation of terbium-scandium-aluminum garnet single crystal,” J. Mater. Res. 19(2), 579–583 (2004).
[Crossref]

J. Opt. Soc. Am. B (1)

Mater. Res. Bull. (1)

A. Yoshikawa, Y. Kagamitani, D. A. Pawlak, H. Sato, H. Machida, and T. Fukuda, “Czochralski growth of Tb3Sc2Al3O12 single crystal for Faraday rotator,” Mater. Res. Bull. 37(1), 1–10 (2002).
[Crossref]

Opt. Express (7)

E. A. Mironov and O. V. Palashov, “Faraday isolator based on TSAG crystal for high power lasers,” Opt. Express 22(19), 23226–23230 (2014).
[Crossref] [PubMed]

I. Snetkov, I. Mukhin, O. Palashov, and E. Khazanov, “Compensation of thermally induced depolarization in Faraday isolators for high average power lasers,” Opt. Express 19(7), 6366–6376 (2011).
[Crossref] [PubMed]

R. Yasuhara, S. Tokita, J. Kawanaka, T. Kawashima, H. Kan, H. Yagi, H. Nozawa, T. Yanagitani, Y. Fujimoto, H. Yoshida, and M. Nakatsuka, “Cryogenic temperature characteristics of Verdet constant on terbium gallium garnet ceramics,” Opt. Express 15(18), 11255–11261 (2007).
[Crossref] [PubMed]

R. Yasuhara, H. Nozawa, T. Yanagitani, S. Motokoshi, and J. Kawanaka, “Temperature dependence of thermo-optic effects of single-crystal and ceramic TGG,” Opt. Express 21(25), 31443–31452 (2013).
[Crossref] [PubMed]

I. L. Snetkov, R. Yasuhara, A. V. Starobor, and O. V. Palashov, “TGG ceramics based Faraday isolator with external compensation of thermally induced depolarization,” Opt. Express 22(4), 4144–4151 (2014).
[Crossref] [PubMed]

T. Sekine, S. Matsuoka, R. Yasuhara, T. Kurita, R. Katai, T. Kawashima, H. Kan, J. Kawanaka, K. Tsubakimoto, T. Norimatsu, N. Miyanaga, Y. Izawa, M. Nakatsuka, and T. Kanabe, “84 dB amplification, 0.46 J in a 10 Hz output diode-pumped Nd:YLF ring amplifier with phase-conjugated wavefront corrector,” Opt. Express 18(13), 13927–13934 (2010).
[Crossref] [PubMed]

T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20(10), 10807–10815 (2012).
[Crossref] [PubMed]

Opt. Lett. (6)

Opt. Mater. (3)

I. Snetkov and O. Palashov, “Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field,” Opt. Mater. 42, 293–297 (2015).
[Crossref]

A. Starobor, R. Yasyhara, I. Snetkov, E. Mironov, and O. Palashov, “TSAG-based cryogenic Faraday isolator,” Opt. Mater. 47, 112–117 (2015).
[Crossref]

H. Lin, S. M. Zhou, and H. Teng, “Synthesis of Tb3Al5O12 (TAG) transparent ceramics for potential magneto-optical applications,” Opt. Mater. 33(11), 1833–1836 (2011).
[Crossref]

Quantum Electron. (3)

E. A. Mironov, I. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe,” Quantum Electron. 43(8), 740–743 (2013).
[Crossref]

E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29(1), 59–64 (1999).
[Crossref]

D. S. Zheleznov, V. V. Zelenogorskii, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Cryogenic Faraday isolator,” Quantum Electron. 40(3), 276–281 (2010).
[Crossref]

Rev. Sci. Instrum. (1)

R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60dB Faraday optical isolator for the near infrared,” Rev. Sci. Instrum. 63(12), 5586–5590 (1992).
[Crossref]

Other (1)

E. Shcherbakov, V. Fomin, A. Abramov, A. Ferin, D. Mochalov, and V. P. Gapontsev, “Industrial Grade 100 kW Power CW Fiber Laser,” in Advanced Solid-State Lasers Congress, G. Huber and P. Moulton, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ATh4A.2.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Picture of the terbium scandium aluminum garnet (TSAG) crystal sample.
Fig. 2
Fig. 2 Schematic of the experimental setup used for thermally induced depolarization measurements.
Fig. 3
Fig. 3 Experimental results of depolarization as a function of laser power. Open red circles show the results for terbium scandium aluminum garnet (TSAG) with <001> crystal orientation in the absence of a magnetic field. Closed blue circles show the results for TSAG with <001> crystal orientation in the presence of a magnetic field. Black triangles show the result for TSAG with <111> crystal orientation in the absence of a magnetic field. Green squares show the results for TSAG with <111> crystal orientation in the presence of a magnetic field. Solid lines show the theoretical curves. The dotted line shows the second term of (10) and the dash-dotted line shows the third term of (10).

Equations (10)

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γ= I d I 0 + I d
γ= 1 I 0 0 2π dφ 0 R 0 sin 2 ( δ 2 ) sin 2 ( 2Ψ δ c 2 ) δ l 2 δ 2 I( r )rdr+ + 1 I 0 0 2π dφ 0 R 0 ( cos( δ 2 )sin( δ c 2 ) δ c δ cos( δ c 2 )sin( δ 2 ) ) 2 I( r ) rdr,
I 0 = 0 2π dφ 0 R 0 I( r )rdr , δ 2 = δ l 2 + δ c 2 ,
δ l =ph 1+ ξ 2 tan 2 ( 2θ2φ ) 1+ tan 2 ( 2θ2φ ) , tan( 2Ψ2θ )=ξtan( 2φ2θ ), h( y= r 2 / r h 2 )= 1 y 0 y dz 0 z F( ζ )dζ ,
γ 0 = p 2 A 1 8 [ 1+( ξ 2 1 ) cos 2 ( 2θ ) ]+ p 4 A 2 384 [ 3( ξ 4 1 ) cos 2 ( 2θ )+ ξ 2 +3 ]+O( p 6 ),
A 1 = 0 h 2 ( u )F( u )du, A 2 = 0 h 4 ( u )F( u )du.
γ 45 = p 2 A 1 π 2 [ 1+( ξ 2 1 ) cos 2 ( 2θ π 4 ) ]+ + p 4 A 2 32 π 4 [ 24( ξ 4 1 )( π4 ) cos 2 ( 2θ π 4 )+3 ( π2 ) 2 ξ 4 +2( π 2 12 ) ξ 2 +3{ ( π+2 ) 2 32 } ]+ + p V 2 A 3 +O( p 6 )
p V = α 0 16κ ( P 0 + P 0 * )( 1 V dV dT + α T ), P 0 * =δH T 0 4πκ α 0 r h 2 R 0 2 , A 3 = 0 f 2 ( y ) exp( y ) dy [ 0 f( y ) exp( y ) dy ] 2 ,f( y )= 0 y dz z 0 z F( ζ )dζ .
γ 0 min A 1 8 p 2 + A 2 384 p 4 ξ 2 ,
γ 45 min A 1 π 2 p 2 + 3 ( π2 ) 2 A 2 32 π 4 ξ 4 p 4 + p V 2 A 3 .

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