Open Access
Add to BibSonomyAbstract
As the first demonstration of Faraday effect in a TGG ceramics, its Verdet constant at 1053 nm is evaluated to be 36.4 rad/Tm at room temperature which is same as that of the single crystal. In addition, the temperature dependence of Verdet constant is obtained experimentally. At liquid helium temperature, it is 87 times greater than that at room temperature.
©2007 Optical Society of America
1. Introduction
Recently, pulse lasers with both of high pulse energy and high average power, are strongly desired for various industrial and scientific applications such as laser peening [1], laser processing [2,3], high-energy particle generation [4], hard x-ray generation [5], inertial fusion energy (IFE) [6–8] and so on. A Faraday element is one of the indispensable key optics for isolation of laser chains and birefringence compensation of laser materials in such high-power laser systems. There are three critical factors of high Verdet constant, high thermal strength and size scalability for the Faraday elements. Terbium-doped materials are the most popular due to a high Verdet constant. A terbium-doped glass has been often used for high pulse energy lasers due to its superior size scalability [6]. Its low thermal characteristics (thermal conductivity of Tb:doped glass FR-5 is 0.84 W/mK)[7], however, is not preferred for repeatable operation. On the other hand, a Faraday crystal shows excellent thermal conductivity to be suitable for high average power operation, but it is difficult to obtain a large aperture crystal. Many researches for development of Faraday medium are reported for the fiber laser [10, 11], optical wave guide [12] and solid-state laser system [13, 14], however those for high pulse energy and high average power operation has not been reported yet.
As one of solutions for the realization, a terbium gallium garnet (TGG) ceramics will be the promising Faraday element due to a high Verdet constant of 36–40 rad/Tm [15–17], high thermal conductivity of 4.5–7.4 W/mK [7,17–22], and excellent size scalability. The TGG ceramics have been reported in 2003 for the first time [23]. Then the theoretical analysis of thermal birefringence in TGG ceramics has been reported [24]. However, no Faraday effect measurement with TGG ceramics has been demonstrated because of its low optical quality. The recent ceramics technology [25–27] enables to produce laser-graded TGG ceramics. The size is still small now (Our sample size is 5.95 mm in length and 5 mm×1 mm cross section). The large aperture ceramics will be obtained by optimizing the process condition in future.
In an extremely high pulse energy laser system such as IFE lasers, there is another problem of a strong magnetic field, which is difficult to be isolated. The strong magnetic field often interferes with electronic control systems and diagnostic devices. Also, a huge magnet system is necessary. In fact, a huge superconductive solenoid has been used in fusion lasers [6]. Improving a Verdet constant, the required magnetic field strength will reduce and, the whole magnetic system size will become compact. Cryogenic cooling of materials often becomes an easy and effective method to control various material coefficients. Recently, cryogenic cooling of several active elements concerning to solid-state lasers has been demonstrated to improve thermal characteristics and to tune a stimulated emission cross section [28–32]. Using TGG crystal, some groups have been estimated the Verdet constant between 77K and 300K by measuring the rotation angle at a constant magnetic field [33–34]. At 77K, Faraday rotation angle was 3.5 times of that at 293K.
In this letter, we have measured the temperature dependence of Verdet constant of laser-graded TGG ceramics at 1053 nm wavelength. Also, a TGG single crystal was used for comparison. The Verdet constant difference between the ceramics and the crystal is only 0.8%. The Verdet constant of TGG ceramics increases at 1453 rad/Tm at 7.8K, which is over 40 times higher than that at 300K. This will be one of the promising Faraday materials for high-power lasers for inertial fusion energy.
2. Theoretical temperature dependence
The Faraday effect is caused by difference of the refractive indices between the right and the left circularly polarized light by applying the magnetic field to a Faraday material. The induced rotation angle of the linear polarization of the incident light can be written as
where V is Verdet constant, H is magnetic field and L is the pass length of the material. Verdet constant is proportional to magnet susceptibility χ, given by [35]
Here A and B is constant independent of temperature. For an atom with angular momentum of J, the magnetization M is given by [10,14]
Where B J(x) is the Brillouin function, N is the total number of atoms per unit volume, g is the Lande splitting factor, µ B is the Bohr magnetron and x is given by
If x≪1, χ is the expressed from (3) by [36],
When low temperature or high magnetic field, i. e., x →∞, the Brillouin function goes to 1 and χ is saturated. Taking into account (5) in (2), we can obtain the following relation between Verdet constant and absolute temperature:
To evaluate Faraday effect of a TGG ceramics, the filling ratio R is defined as
where D TGG is volume of TGG ceramics and D G is sum of single crystal grain volume in D TGG. Ion number of Tb3+ in TGG single crystal per unit volume is 1.29×1022 [17]. Therefore ion number of Tb3+ in TGG ceramics per unit volume is expressed as N ceramics=1.29×1022×R. From Eq. (6) and (7), we can deliver Verdet constant for TGG ceramics as
3. Experimental setup
A schematic diagram of the experimental set-up for the Verdet constant measurements of TGG ceramics is shown in Fig. 1. The laser light goes through a sample, which is between a pair of Glan laser prisms used for analyzer and polarizer respectively. The transmitted laser intensity is measured by a silicon photo diode. A polarization plane of laser light is rotated by Faraday effect owing to a magnetic field. The transmitted laser intensity I is expressed by Malus’s law with [37]
where I 0 is maximum light intensity, θ ′ is bias angle between the transmission axes of the two prisms, I min is minimum light intensity caused by extinction ratio of this experimental set-up. When the prisms are set at the cross nicols, θ ′ is π/2. θ is a rotation angle due to the Faraday effect. When θ=0 at no magnetic field, I is minimized. When a magnetic field is applied, the transmitted intensity is observed as a function of θ ′.
A diode-pumped Nd:YLF continuous wave laser (IRCL-100-1053, CrystaLaser) were used as optical sources. The wavelength and output power are 1053 nm and 500 mW at maximum respectively. The extinction ratio of the prism is 0.2×105. The analyzer prism is attached to a stepping motor driven rotation stage, which surface plane is perpendicular to the optical axis. A TGG ceramic (Konoshima Chemical Co., Ltd., 5.95 mm in length and 5 mm x 1 mm cross section) and a TGG single crystal (OFR, Inc) with <111> orientation (12.75 mm in length and 4.7 mm in diameter) are used as Faraday materials. Each of them is cramped by a copper holder. A thin indium hoil is used between the material and the holder to improve the thermal contact. The holder is attached to a temperature-controllable cryostat (Iwatani HE05) and set in the vacuum chamber, shown in Fig. 1. The temperature is measured by a calibrated Kp-Au thermo couple on the material surface. The controllable temperature range is between 7.8±2.1K and 300±0.1K. A spatially uniform magnetic field is applied to the material by using double Helmholtz coils. The applied magnetic field is temporally pulsed with duration of 100 ms because of suppression of the coil heating. The magnitude of the magnetic field is 253 G at maximum. The magnetic field strength, which is calibrated with a Gauss meter (MODEL5080, F.W. Bell), is controlled by an electric current of the Helmholtz coils. The laser intensity I is measured at uniform time-region of top-hat temporal magnetic field, then fluctuation of the detected intensity I was 0.8% RMS. The extinction ratio of the transmitted laser intensity is maintained better than 1:5000 during measurements. In consequence the accuracy of the rotation angle of this system was estimated to better than asin(1/5000)=0.2 mrad.
4. Result and discussion
Figure 2 shows the transmitted laser intensity as a function of θ ′. Solid line shows and a fitting curve with Eq. (9). Then we can determine Faraday rotation angle θ as a difference between π/2 and θ ′=θ min, where I is minimum. Using the estimated angle θ, the Verdet constant is delivered from Eq. (1) by the measured H and L. At room temperature of 300K±0.1K, the measured Verdet constant of TGG single crystal is 36.2 rad/Tm. That agreed with published values (35–40 rad/Tm) [14–16]. The Verdet constant of TGG ceramics is 36.4 rad/Tm at 300K±0.1K is almost same as that of single crystal, and the tiny difference is within the measurement error. The TGG ceramic is composed of TGG single crystal grains and boundary layers. When the boundary layer is very thin under assumption of no differences in quality between the ceramic grain and the single crystal, the filling factor R in Eq. (7) closes to 1. The obtained R of the ceramics is 0.997 or more, and the boundary layer occupation in volume is below 0.003. If the large-size ceramics are obtainable, a higher pulse energy operation will be realized.
The measured Verdet constants V of the TGG single crystal and TGG ceramic are plotted in Fig. 3 as a function of the absolute temperature. The Verdet constant of the ceramic at 7.8K is 1453 rad/Tm, which is 40 times larger than that at 300K, in addition, 1122 rad/Tm for the single crystal at 9.1K. Within this temperature range, the experimental data are inversely proportional to the absolute temperature, fitted well with the Eqs. (6) and (8). The slope of the straight line is
The magnitude of B in Eqs. (6) and (8) is less than 1% of Verdet constant under 30K. Therefore this value can neglect for estimation of Verdet constant at low temperature. In consequence, Verdet constant at 4.2K is extrapolated at 3164 rad/Tm from Eq. (10). The required magnetic field is, therefore, reduced to 1/87, resulting in the stable electric control of the laser system, the accurate diagnostics and the reduced magnetic system size. In addition, the length of the Faraday material can be shortened to 1/87 in the same magnetic field, which gives advantages for short pulse lasers in femto-seconds due to a lower spectral dispersion. Our measured thermal conductivity of the ceramics, which will be reported in another paper, is almost same as the published data for single crystal [22]. Compared with terbium-doped glass materials at room temperature, the magnitude is about one order higher between 100K and 300K, which is preferable for high average power operation.
Conclusion
The temperature dependence of Verdet constant of the paramagnetic TGG ceramics has been measured for the first time to our knowledge. The temperature dependence of its magnitude is almost same as that of a single crystal. If the large-size ceramics are obtainable, a higher pulse energy operation will realize. At low temperature, the Verdet constant increases, for example, to 87 times magnitude at liquid helium temperature compared with that at room temperature. The required magnetic field reduces, resulting in the stable electric control system without electromagnetic interference, the accurate diagnostics and the reduced magnetic system size. Also, the shortened Faraday material may be used in femto-second lasers due to lower spectral dispersion. In addition to these improvements, the observed thermal conductivity of ceramics is one order higher than glass materials. Using cryogenic cooled TGG ceramics, new laser systems with both of high pulse energy and high average power such like fusion reactor driver would be realized.
References and links
1. A. M. Korsunsky, J. Liu, D. Laundy, M. Golshan, and K. Kim, “Residual elastic strain due to laser shock peening,” J. Strain Analysis 41, 113–120 (2006). [CrossRef]
2. D. Ashkenasi, A. Rosenfeld, H. Varel, M. Wähmer, and E. E. B. Campbell, “Laser processing of sapphire with picosecond and sub-picosecond pulses,” Appl. Sur. Sci. 120, 65–80 (1997). [CrossRef]
3. K. Nawata, Y. Ojima, M. Okida, T. Ogawa, and T. Omatsu, “Power scaling of a pico-second Nd:YVO4 master-oscillator power amplifier with a phase-conjugate mirror,” Opt. Express 14, 10657–10662 (2006). [CrossRef] [PubMed]
4. M. I. K. Santala, M. Zepf, F. N. Beg, E. L. Clark, A. E. Dangor, K. Krushelnick, M. Tatarakis, I. Watts, K. W. D. Ledingham, T. McCanny, I. Spencer, A. C. Machacek, R. Allott, R. J. Clarke, and P. A. Norreys, “Production of radioactive nuclides by energetic protons generated from intense laser-plasma interactions,” Applied Phys. Lett. 78, 19–21 (2001). [CrossRef]
5. J. D. Kmetec, C. L. Gordon III, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527–1530 (1992). [CrossRef] [PubMed]
6. N. Miyanaga, H. Azechi, K.A. Tanaka, T. Kanabe, T. Jitsuno, J. Kawanaka, Y. Fujimoto, R. Kodama, H. Shiraga, K. Knodo, K. Tsubakimoto, H. Habara, J. Lu, G. Xu, N. Morio, S. Matsuo, E. Miyaji, Y. Kawakami, Y. Izawa, and K. MimaJ.-C. Gauthier, et al., ed., (EDP sciences, Les Ulis cedex A, France, 2006), pp. 81–87.
7. W. F. Krupke, “Solid State Laser Driver for an ICF Reactor,” Fusion Technol. 15, 377–382 (1989).
8. T. Kawashima, T. Kanabe, H. Matsui, E. Eguchi, M. Yamanaka, Y. Kato, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, and H. Kan, “Design and Performance of a Diode-Pumped Nd:Silica-Phosphate Glass Zig-Zag Slab Laser Amplifier for Inertial Fusion Energy,” Jpn. J. Appl. Phys. 40, 6415–6425 (2001). [CrossRef]
9. J. D. Mansell, J. Hennawi, E. K. Gustafson, M. M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40, 366–374 (2001). [CrossRef]
10. H. Seito, M. Kawase, and M. Saito, “Temperature dependence of the Faraday effect in As-S glass fiber,” Appl. Opt. 24, 2300–2302(1985). [CrossRef] [PubMed]
11. J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34, 6848–6854(1995). [CrossRef] [PubMed]
12. T. Shintaku and T. Uno, “Optical waveguide isolator based on nonreciprocal radiation,” J. Appl. Phys. 76, 8155–8159(1994). [CrossRef]
13. V. I. Chani, A. Yoshikawa, H. Machida, T. Satoh , and T. Fukuda, “Growth of Tb3 Ga5 O12 fiber and bulk crystals using micro-pulling-down apparatus,” J. Cryst. Growth 210, 663–669(2000). [CrossRef]
14. J. A. Davis and R. M. Bunch, “Temperature dependence of the Faraday rotation of Hoya FR-5 glass,” Appl. Opt. 23, 633–636(1984). [CrossRef] [PubMed]
15. M. Y. A. Raja, D. Allen, and W. Sisk, “Room-temperature inverse Faraday effect in terbium gallium garnet,” Appl. Phys. Lett. 67, 2123–2125(1995). [CrossRef]
16. Northrop Grumman, TGG data sheet. (2006). http://www.st.northropgrumman.com/synoptics/products/specialty/TGG.html
17. A. A. Kaminskii, H. J. Eichler, P. Reiche, and R. Uecker, “SRS risk potential in Faraday rotator Tb3Ga5O12 Crystals for high-peak power lasers,” Laser Phys. Lett. 2, 489–492 (2005). [CrossRef]
18. R. Wynands, F. Diedrich, D. Meschede, and H. R. Telle, “A compact tunable 60-dB Faraday optical isolator for the near infrared,” Review of Scientific Instruments 63, 5586–5590 (1992). [CrossRef]
19. E. A. Khazanov, N. F. Andreev, A. N. Mal’shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, “Compensation of thermally induced modal distortions in Faraday isolators,” IEEE J. Quantum Electron. 40, 1500–1510 (2004). [CrossRef]
20. G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, “Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers,” Class. Quantum Grav. 19, 1793–1801 (2002). [CrossRef]
21. X. Chen, R. Galemezuk, B. Salce, B. Lavorel, C. Akir, and L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999). [CrossRef]
22. G. A. Slack and D. W. Oliver, “Thermal conductivity of garnets and phonon scattering by rareearth ions,” Phys. Rev. B 4, 592–609(1971). [CrossRef]
23. E. A. Khazanov, “Investigation of Faraday isolator and Faraday mirror designs for multi-kilowatt power lasers,” Proc. SPIE 4968, 115–126, (2003). [CrossRef]
24. M. A. Kagan and E. A. Khazanov, “Thermally Induced Birefringence in Faraday Devices Made from Terbium Gallium Garnet-Polycrystalline Ceramics,” Appl. Opt. 43, 6030–6039(2004). [CrossRef] [PubMed]
25. T. Yanagitani, H. Yagi, and M. Ichikawa, Japanese Patent, 10-101333 (1998).
26. T. Yanagitani, H. Yagi, and M. Ichikawa, Japanese Patent, 10-101411 (1998).
27. J. Lu, H. Yagi, K. Takaichi, T. Uematsu, J.-F. Bisson, Y. Feng, A. Shirakawa, K.-I. Ueda, T. Yanagitani, and A. A. Kaminskii, “110 W ceramic Nd3+:Y3Al5O12 laser,” Appl. Phys. B 79, 25–28 (2004). [CrossRef]
28. J. Kawanaka, S. Tokita, H. Nishioka, M. Fujita, K. Yamakawa, K. Ueda, and Y. Izawa, “Dramatically improved laser characteristics of diode-pumped Yb-doped materials at low temperature,” Laser Phys. 15, 1306–1312 (2005).
29. S. Tokita, J. Kawanaka, Y. Izawa, M. Fujita, and T. Kawashima, “23.7-W picosecond cryogenic-Yb:YAG multipass amplifier,” Opt. Express 15, 3955–3961(2007). [CrossRef] [PubMed]
30. J. Kawanaka, H. Nishioka, N. Inoue, and K. Ueda, “Tunable continuous-wave Yb:YLF laser operation with a diode-pumped chirped-pulse amplification system,” Appl. Opt. 40, 3542–3546 (2001). [CrossRef]
31. J. Kawanaka, K. Yamakawa, H Nishioka, and K. Ueda, “30mJ, diode-pumped, chirped-pulse Yb:YLF regenerative amplifier,” Opt. Lett. 28, 2121–2123 (2003). [CrossRef] [PubMed]
32. D. J. Ripin, J. R. Ochoa, R. L. Aggarwal, and T. Y. Fan, “165-W cryogenically cooled Yb:YAG laser,” Opt. Lett. 29, 2154–2156 (2004). [CrossRef] [PubMed]
33. N. P. Barnes and L. B. Petway, “Variation of the Verdet constant with temperature of terbium gallium garnet,” J. Opt. Soc. Am. B 9, 1912–1915 (1992). [CrossRef]
34. D. S. Zheleznov, A. V. Voitovich, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Considerable reduction of thermooptical distortions in Faraday isolators cooled to 77 K,” Quantum Electron. 36, 383–388 (2006). [CrossRef]
35. J. H. Van Vleck and M. H. Hebb, “On the paramagnetic rotation of Tysonite,” Phys. Rev. 46, 17–32 (1934). [CrossRef]
36. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1971).
37. E. Hecht, Optics (Addison Wesley, San Francisco, 2002) 4th ed., Chap. 8, p. 333.
