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Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field
Optical Materials 42 (2015) 293–297
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field Ilya Snetkov ⇑, Oleg Palashov Institute of Applied Physics of the Russian Academy of Science, Nizhny Novgorod 603950, Russia
a r t i c l e
i n f o
Article history: Received 14 November 2014 Received in revised form 17 December 2014 Accepted 19 January 2015 Available online 11 February 2015 Keywords: Magneto-optical materials Thermal effects Isolators Faraday effect
a b s t r a c t A Faraday isolator based on a terbium scandium aluminum garnet (TSAG) single crystal with compensation of thermally induced depolarization inside magnetic field was demonstrated. An isolation ratio of 32 dB at 350 W cw laser radiation power was achieved. Thermally induced depolarization and thermal lens were studied and compared with similar thermal effects arising in the widely used terbium gallium garnet crystal (TGG) for the first time. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Steady growth of the average power of both continuous and pulsed-periodic lasers necessitates creating optical components that would meet the increasing requirements. Solution of the problem of thermal effects and heat sink associated with laser radiation absorption at high average output power demands materials for optical elements with good thermo-optical and mechanical properties. At the same time, lasers with high peak power require materials that have weak nonlinearity, high laser damage threshold and allow fabricating large-aperture (tens of centimeters) optical samples to reduce the influence of nonlinear processes. The Faraday isolator (FI) is one of the important optical devices that is most affected by thermal self-action due to relatively high absorption (103 cm1) in magneto-optical elements (MOE) and their relatively large length (10 mm). As was shown earlier in [1], the arising thermally induced birefringence fully determines the FI basic characteristic – the isolation ratio. A number of problems are currently being solved aimed at creating FIs for high peak and, at the same time, high average output power. First, a better magneto-optical material with a higher Verdet constant and better thermo-optical properties is sought for [2,3]. For this, the magnetooptical figure-of-merit l = Vj/aQ (where V is the Verdet constant, j is thermal conductivity, a is absorption coefficient, and Q is thermo-optical constant [4]) was introduced in [1]. This parameter ⇑ Corresponding author. Tel.: +7 9159592343. E-mail address: [email protected] (I. Snetkov). http://dx.doi.org/10.1016/j.optmat.2015.01.015 0925-3467/Ó 2015 Elsevier B.V. All rights reserved.
characterizes a material in terms of thermal depolarization introduced by it and, consequently, in terms of the maximum achievable isolation ratio at high average power of laser radiation. Simultaneously, there is a search for magneto-optical materials with a low nonlinearity coefficient [5]. Second, technologies for growing large-aperture crystals and fabricating optical-quality ceramics are being optimized. To date, FIs for high-power laser radiation based on a large-aperture terbium gallium garnet (TGG) single crystal 30 mm in diameter [6], TGG ceramics [7–9] and terbium aluminum garnet (TAG) ceramics [10,11] have been fabricated, and high optical quality TGG ceramics 100 mm 100 mm 10 mm in size produced by Konoshima Chemical Co., Ltd. [12] have been demonstrated. Third, various methods of compensating thermally induced depolarization in MOEs and FI optical schemes which would increase its isolation ratio and advance further to higher power levels are being developed. Such optical scheme was first proposed in [13] and was later called the FI scheme with compensation inside magnetic field. The scheme was further improved in [14]. In this scheme, two 22.5° MOEs with a quartz rotator placed between them are used instead of a single 45° MOE. Another FI scheme is the scheme with compensation outside magnetic field. Its idea consists in adding a compensator comprised of a quartz rotator and an additional optical element which can be made of the same material as the MOE [14] or of a different material [15]. To the best of our knowledge, the record isolation ratio of 33 dB was obtained in the FI with thermal depolarization compensation inside magnetic field at 1.5 kW power of cw radiation [6]. Fourth, magnetic systems ensuring record-breaking values
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of magnetic fields in the region of MOE location [6,16,17] are being developed. They enable reducing the thermally induced depolarization by shortening the MOE length. The most widely used and commercially available magnetooptical material today is the TGG crystal due to its relatively high magneto-optical figure-of-merit and the possibility to be grown by the Czochralski method. Meanwhile, a material with better magneto-optical properties has been long known (since the mid1960s). It is terbium aluminum garnet (TAG) [18], which surpasses TGG in the Verdet value. Based on this material, a compact FI was fabricated [19]. However, TAG has not found widespread use and was quickly replaced by TGG because of the difficulties in growing a TAG single crystal of acceptable aperture due to its incongruent melting nature and unstable TAG phase in the Tb2O3–Al2O3 system [20]. To obtain a congruent melting composition or a stable TAG phase and for subsequent growth of a single crystal from the melts, part of Tb3+ or Al3+ ions were substituted by different ions: Lu3+ [21], Yb3+ [22], Tm3+ [23], Ga3+ [24], Lu3+ + Sc3+ [25,26], and Sc3+ [27–31]. A material of promise is TAG in which part of Tb3+ or Al3+ ions are substituted by Sc3+ ions (TSAG), which permits obtaining stable phase and growing single crystals by the Czochralski method. Synthesis of a stable TSAG phase by the Czochralski method was first reported in [27]. Further, the composition and growth technique of TSAG for FI were patented [28], the material was rediscovered [29], other growth methods were proposed [31], and magneto-optical properties of the new material [30] which demonstrated the Verdet constant as high as in the TAG crystal were studied. The first FI with a traditional scheme based on a TSAG crystal with [1 1 1] orientation for high-power laser radiation was recently reported in the work [32], where the isolation ratio of 30 db at the power of 500 W was achieved. However, no thermal lens measurements were done and no studies or estimations of the thermo-optical characteristics of the TSAG crystal were performed. In this paper, we report results of fabrication and experimental study of the first FI with thermal depolarization compensation inside magnetic field at high average laser power based on a TSAG crystal with composition Tb2.78Y0.02Sc1.76Al3.37O12 grown at the General Physics Institute RAS [33]. Thermal lens measurements and some estimates of thermo-optical characteristics of TSAG material are presented. Prospects of using this crystal in FIs at the kilowatt laser power level are discussed.
2. Measurement of thermally induced depolarization We used two samples of an optical-quality TSAG single crystal, each having a diameter of 6.3 mm and length of 5.2 mm, with the orientation of crystallographic axes differing from the [1 1 1] orientation by 6°. Both the samples were fabricated from one optical element 6.3 mm in diameter and 20 mm long with linear absorption coefficient a = 2.5 103 1/cm (measured by the manufacturer). Samples which were used differed from that was used in [32]. For each TSAG sample, the dependence of the thermally induced depolarization on the power of the transmitted light was measured. The layout of the experiment is shown in Fig. 1.
Fig. 2. Thermally induced depolarization versus power of laser radiation in TSAG samples.
A 350 W cw Yb fiber laser operating at 1070 nm and producing Gaussian beams with a beam diameter of 1.2 mm was used as a laser source. Linearly polarized light after calcite wedge 1 passed through sample 3, then was attenuated by fused silica wedges 4 and eventually came to Glan prism 5. Depending on the orientation of the Glan prism, the distribution of either main or depolarized component of the field was measured by CCD camera 6. By the ratio of the integrals of these distributions, the value of the thermally induced depolarization c in the sample was determined. The experimental results are shown in Fig. 2, illustrating the difference in the absorption of the studied optical elements. It is noteworthy that the cold depolarization in each sample was less than 4 104, thus proving the good optical quality of the single crystals used in our study. The ratio of the normalized powers of heat release for the two samples was D = p2/p1 = 0.90. Since both the elements are of the same length and made of the same material, D = a2/a1 = 0.9 [15], where ai is the coefficient of linear absorption of each element. The integral depolarization in a crystal with [1 1 1] orientation is described by the following expression [34]:
c¼
2 A1 aQ ð1 þ 2nÞ LP laser ; 8 j k 3
ð1Þ
where A1 is the constant dependent on the laser beam profiles and equal to 0.137 for the Gaussian intensity distribution; n is the optical anisotropy parameter [4,35,36]; a is the absorption coefficient; Q is the thermooptical constant; j is the thermal conductivity; L denotes the length of the optical element; k is the radiation wavelength; and Plaser is the power of laser radiation. So, by using the expression (1) and the results of measurements we can estimate the coefficient aQ(1 + 2n)/3j to be 1.96 107 1/W for the first sample and 1.76 107 1/W for the second one. The green1 dotted line given for comparison in Fig. 2 is the calculated thermally induced depolarization in a TGG single crystal with [1 1 1] orientation, linear absorption coefficient a = 2.5 103 1/cm, and length L = 5.2 mm. For a TGG material we have n = 2.2 [34], Q = 17 107 K1 [37], j = 5 W/K m and calculate aQ(1 + 2n)/3j = 1.53 107 K1. The authors of the work [3] proposed a magneto-optical figureof-merit for crystals with [1 1 1] orientation for comparison of magneto active materials with such orientation:
l½1 1 1 ¼
Vj 3 ; aQ ð1 þ 2nÞ
ð2Þ
where n is optical anisotropy parameter [4,35,36]. We measured the Verdet constant at the wavelength of 1070 nm. For our samples, the Verdet constant was found to be 46 ± 3 rad/T m, which is 24% higher than in the TGG crystal (37 rad/T m), the magneto-optical Fig. 1. Schematic of thermally induced depolarization measurements. 1 – calcite wedge polarizer; 2 – absorber; 3 – sample; 4 – fused silica wedges; 5 – Glan prism and 6 – CCD camera.
1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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figure-of-merit of TSAG for the [1 1 1] orientation was close to that of TGG with the same absorption and orientation. A scheme with compensation of thermal depolarization inside magnetic field was chosen for fabricating FI. The source of magnetic field was a permanent magnet system producing a maximum magnetic field of 2.5 T along the axis, which was described in [6,17]. Optical elements made of a TSAG single crystal were glued into copper tubes for heat sink. A quartz rotator was placed between the elements. The angle of rotation of the polarization plane in the quartz rotator was chosen to be 67.5°, as the orientation of the elements was close to [1 1 1]. The magneto-optical elements were placed in the magnetic field, where their total nonreciprocal Faraday rotation was 45°. Then, the power dependences of the thermally induced depolarization were measured for two cases: with quartz rotator (blue circles in Fig. 3) and without it (red squares in Fig. 3), which allowed us to estimate the compensation efficiency. In the absence of quartz rotator, the thermally induced depolarization demonstrated the well-known quadratic dependence on the power of the transmitted radiation. When the quartz rotator was added between the magneto-optical elements, the thermally induced depolarization reduced considerably and its power dependence was no longer quadratic, instead it was proportional to the fourth order of the transmitted laser radiation power, which is well illustrated by the obtained experimental data (blue circles in Fig. 3). The red and blue solid lines are the approximations proportional to the second and fourth order of laser power, respectively. The isolation ratio of FI we calculated as I = 10 log(c). At a maximum laser power of 350 W, the thermally induced depolarization reduced by a factor of 5.4, and the FI with compensation of the thermally induced depolarization provided an isolation ratio of 32 dB. Let us estimate the possibility of further increasing the isolation ratio in the high average power FI based on TSAG with the compensation scheme. Using our crystals with the orientation close to [1 1 1] we were able to increase the power of laser radiation Pmax at which the isolation ratio of 30 dB is achieved by a factor of 2.7, namely, from 150 to 400 W. Theoretical estimates in the FI scheme with compensation inside magnetic field show that at equal absorption coefficients of the magneto-optical elements with [1 1 1] orientation of the crystallographic axes a 12-fold increase in Pmax can be obtained [14], which for our crystals would lead to an increase of Pmax up to 1800 W. Another possibility to increase the Pmax value is to use a crystal with [0 0 1] orientation. In this orientation, thermally induced depolarization depends on crystal rotation [38] and compared with the [1 1 1] orientation can be reduced at least by a factor of (1 + 2n)2/9 for |n| > 1 and by a factor of (1 + 2n)2/9n2 for |n| < 1 [34]. For TGG crystals, n = 2.2 and the thermally induced depolarization may be reduced by a factor of
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3.2. For TSAG crystals, the value of parameter n is still unknown. We want to dedicate to this issue one of our future works. Still another important parameter is the linear absorption coefficient a, which is rather high for the sample under study, probably due to the relatively high level of impurities in the TSAG crystal. If, by improving the crystal growth process, the linear absorption coefficient is decreased to the level of TGG absorption a = (1.3 1.5) 103 1/cm, it will be possible to expect creation of an FI with an isolation ratio better than 30 dB up to powers of a few kW of cw radiation.
3. Thermal lens measurements The thermal lens occurring in the FI was measured using the phase-shifting interferometry scheme [39,41]. The experiment is outlined in Fig. 4. A 350 W cw Yb-fiber laser was used as a source of heating radiation. The laser radiation was directed to the sample by means of dielectric 45° mirrors at a wavelength of 1070 nm. The heated sample was placed in one of the Michelson interferometer arms formed by beam-splitting cube 4 and metallic mirror 6 attached to piezo elements. Images of the element of interest were transferred by telescope 7 to CCD camera 8 which was synchronized with mirror 6 and took a sequence of 4 interferometry images differing from each other by k/8 change of the arm length. The phase front distribution was restored by processing the captured video sequence [42]. Measurements were made both with no heating radiation and at certain values of heating radiation. The obtained distributions of the phase front, as in [43], were processed and the thermal lens strength was found. The results are illustrated in Fig. 3b (red squares). For comparison, the blue circles in Fig. 3b show the power dependence of the thermal lens strength in the FI with compensation of thermal depolarization based on TGG ceramics with linear absorption coef-
Fig. 4. Schematic diagram of thermal lens measurement. 1 – 45° dielectric mirror; 2 – absorber; 3 – sample; 4 – beam splitter; 5 – metallic mirror; 6 – metallic mirror attached to piezo elements; 7 – telescope and 8 – CCD camera.
Fig. 3. (a) Thermally induced depolarization versus laser power with compensation (blue circles) and without compensation (red triangles) and (b) thermal lens strength versus laser power for FI based on TSAG crystal (red squares), and for FI based on TGG ceramics with the same magnetic system (blue circles). Green dotted line is the theoretical calculation of the thermal lens strength for TGG crystal with absorption equal to that of TSAG crystal. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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ficient a = 1.46 103 1/cm. This FI was made using the same magnetic system with the same quartz rotator, the only difference was the material of the magneto-optical elements and their length needed for 45° Faraday rotation of the polarization plane. The green line shows the recalculated power dependence of the thermal lens in the FI on a TGG single crystal with a = 2.5 103 1/cm. Comparison of the plots shows that the TSAG crystal with [1 1 1] orientation has a 1.5 times stronger thermal lens, all other conditions being equal. Theoretically, the thermal lens power in crystals with [1 1 1] orientation is described by the expression [41]
1 aLPlaser 1 ¼ P ð1 nÞQ ; 2 F 3 2p r h j
ð3Þ
where F is the focal length, rh is the beam radius (1/e intensity level), and P is the thermooptical constant [4]. By using the expression (3) and the experimental data on the thermal lens strength it is possible to estimate the value of a/j(P–(1–n)Q/3) to be 1.91 106 1/W. In garnets, the thermooptic constant P is much larger than Q (for example, P/Q = 10 for TGG [44] and P/Q = 13 for YAG (calculated from [45]), and the parameter n is of the order of several units (nTGG = 2.2, nYAG = 3.2), so the second term in the expression (3) can be neglected. We used the value of absorption coefficient measured by the manufacturer for TSAG and estimated P/j to be 7.65 106 m/W for our crystals. For comparison, for TGG, P/j = 3.8 106 m/W. 4. Conclusion In conclusion, the thermally induced depolarization and thermal lens in a TSAG crystal with [1 1 1] orientation have been measured. Some thermo-optical properties of TSAG material were estimated by the obtained data for the first time and compared with those in the widely used TGG crystal. It was found that a TSAG crystal with [1 1 1] orientation has a magneto-optical figure-ofmerit same as the [1 1 1] oriented TGG crystal and a 22% larger Verdet constant. This suggests that the use of TSAG instead of TGG as a magneto-optical material for FI seems to be very promising. However, TSAG demonstrates a stronger (1.5 times) thermal lens, necessitating its additional correction or use of compensation techniques. An FI with compensation inside magnetic field based on a new magneto-active material – a TSAG single crystal with [1 1 1] orientation – has been reported for the first time. This FI demonstrates a stable isolation ratio better than 32 dB at up to 350 W cw power of transmitted laser radiation. It is shown that the use of crystals with similar absorption will enable creating an FI with an isolation ratio better than 30 dB at up to 1 kW power, while improving the growth technology of single crystals and decreasing the linear absorption coefficient to the level of absorption in TGG crystals will additionally increase power by more than 2 times with the isolation ratio being unchanged. Acknowledgement 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. References [1] E.A. Khazanov, O.V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, Investigation of self-induced depolarization of laser radiation in terbium gallium garnet, IEEE J. Quantum Electr. 35 (1999) 1116–1122. [2] M.J. Weber, Faraday rotator materials for laser systems, in: Proc SPIE, 1987, 75–90.
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
Faraday isolator based on a TSAG single crystal with compensation of thermally induced depolarization inside magnetic field Ilya Snetkov ⇑, Oleg Palashov Institute of Applied Physics of the Russian Academy of Science, Nizhny Novgorod 603950, Russia
a r t i c l e
i n f o
Article history: Received 14 November 2014 Received in revised form 17 December 2014 Accepted 19 January 2015 Available online 11 February 2015 Keywords: Magneto-optical materials Thermal effects Isolators Faraday effect
a b s t r a c t A Faraday isolator based on a terbium scandium aluminum garnet (TSAG) single crystal with compensation of thermally induced depolarization inside magnetic field was demonstrated. An isolation ratio of 32 dB at 350 W cw laser radiation power was achieved. Thermally induced depolarization and thermal lens were studied and compared with similar thermal effects arising in the widely used terbium gallium garnet crystal (TGG) for the first time. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Steady growth of the average power of both continuous and pulsed-periodic lasers necessitates creating optical components that would meet the increasing requirements. Solution of the problem of thermal effects and heat sink associated with laser radiation absorption at high average output power demands materials for optical elements with good thermo-optical and mechanical properties. At the same time, lasers with high peak power require materials that have weak nonlinearity, high laser damage threshold and allow fabricating large-aperture (tens of centimeters) optical samples to reduce the influence of nonlinear processes. The Faraday isolator (FI) is one of the important optical devices that is most affected by thermal self-action due to relatively high absorption (103 cm1) in magneto-optical elements (MOE) and their relatively large length (10 mm). As was shown earlier in [1], the arising thermally induced birefringence fully determines the FI basic characteristic – the isolation ratio. A number of problems are currently being solved aimed at creating FIs for high peak and, at the same time, high average output power. First, a better magneto-optical material with a higher Verdet constant and better thermo-optical properties is sought for [2,3]. For this, the magnetooptical figure-of-merit l = Vj/aQ (where V is the Verdet constant, j is thermal conductivity, a is absorption coefficient, and Q is thermo-optical constant [4]) was introduced in [1]. This parameter ⇑ Corresponding author. Tel.: +7 9159592343. E-mail address: [email protected] (I. Snetkov). http://dx.doi.org/10.1016/j.optmat.2015.01.015 0925-3467/Ó 2015 Elsevier B.V. All rights reserved.
characterizes a material in terms of thermal depolarization introduced by it and, consequently, in terms of the maximum achievable isolation ratio at high average power of laser radiation. Simultaneously, there is a search for magneto-optical materials with a low nonlinearity coefficient [5]. Second, technologies for growing large-aperture crystals and fabricating optical-quality ceramics are being optimized. To date, FIs for high-power laser radiation based on a large-aperture terbium gallium garnet (TGG) single crystal 30 mm in diameter [6], TGG ceramics [7–9] and terbium aluminum garnet (TAG) ceramics [10,11] have been fabricated, and high optical quality TGG ceramics 100 mm 100 mm 10 mm in size produced by Konoshima Chemical Co., Ltd. [12] have been demonstrated. Third, various methods of compensating thermally induced depolarization in MOEs and FI optical schemes which would increase its isolation ratio and advance further to higher power levels are being developed. Such optical scheme was first proposed in [13] and was later called the FI scheme with compensation inside magnetic field. The scheme was further improved in [14]. In this scheme, two 22.5° MOEs with a quartz rotator placed between them are used instead of a single 45° MOE. Another FI scheme is the scheme with compensation outside magnetic field. Its idea consists in adding a compensator comprised of a quartz rotator and an additional optical element which can be made of the same material as the MOE [14] or of a different material [15]. To the best of our knowledge, the record isolation ratio of 33 dB was obtained in the FI with thermal depolarization compensation inside magnetic field at 1.5 kW power of cw radiation [6]. Fourth, magnetic systems ensuring record-breaking values
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of magnetic fields in the region of MOE location [6,16,17] are being developed. They enable reducing the thermally induced depolarization by shortening the MOE length. The most widely used and commercially available magnetooptical material today is the TGG crystal due to its relatively high magneto-optical figure-of-merit and the possibility to be grown by the Czochralski method. Meanwhile, a material with better magneto-optical properties has been long known (since the mid1960s). It is terbium aluminum garnet (TAG) [18], which surpasses TGG in the Verdet value. Based on this material, a compact FI was fabricated [19]. However, TAG has not found widespread use and was quickly replaced by TGG because of the difficulties in growing a TAG single crystal of acceptable aperture due to its incongruent melting nature and unstable TAG phase in the Tb2O3–Al2O3 system [20]. To obtain a congruent melting composition or a stable TAG phase and for subsequent growth of a single crystal from the melts, part of Tb3+ or Al3+ ions were substituted by different ions: Lu3+ [21], Yb3+ [22], Tm3+ [23], Ga3+ [24], Lu3+ + Sc3+ [25,26], and Sc3+ [27–31]. A material of promise is TAG in which part of Tb3+ or Al3+ ions are substituted by Sc3+ ions (TSAG), which permits obtaining stable phase and growing single crystals by the Czochralski method. Synthesis of a stable TSAG phase by the Czochralski method was first reported in [27]. Further, the composition and growth technique of TSAG for FI were patented [28], the material was rediscovered [29], other growth methods were proposed [31], and magneto-optical properties of the new material [30] which demonstrated the Verdet constant as high as in the TAG crystal were studied. The first FI with a traditional scheme based on a TSAG crystal with [1 1 1] orientation for high-power laser radiation was recently reported in the work [32], where the isolation ratio of 30 db at the power of 500 W was achieved. However, no thermal lens measurements were done and no studies or estimations of the thermo-optical characteristics of the TSAG crystal were performed. In this paper, we report results of fabrication and experimental study of the first FI with thermal depolarization compensation inside magnetic field at high average laser power based on a TSAG crystal with composition Tb2.78Y0.02Sc1.76Al3.37O12 grown at the General Physics Institute RAS [33]. Thermal lens measurements and some estimates of thermo-optical characteristics of TSAG material are presented. Prospects of using this crystal in FIs at the kilowatt laser power level are discussed.
2. Measurement of thermally induced depolarization We used two samples of an optical-quality TSAG single crystal, each having a diameter of 6.3 mm and length of 5.2 mm, with the orientation of crystallographic axes differing from the [1 1 1] orientation by 6°. Both the samples were fabricated from one optical element 6.3 mm in diameter and 20 mm long with linear absorption coefficient a = 2.5 103 1/cm (measured by the manufacturer). Samples which were used differed from that was used in [32]. For each TSAG sample, the dependence of the thermally induced depolarization on the power of the transmitted light was measured. The layout of the experiment is shown in Fig. 1.
Fig. 2. Thermally induced depolarization versus power of laser radiation in TSAG samples.
A 350 W cw Yb fiber laser operating at 1070 nm and producing Gaussian beams with a beam diameter of 1.2 mm was used as a laser source. Linearly polarized light after calcite wedge 1 passed through sample 3, then was attenuated by fused silica wedges 4 and eventually came to Glan prism 5. Depending on the orientation of the Glan prism, the distribution of either main or depolarized component of the field was measured by CCD camera 6. By the ratio of the integrals of these distributions, the value of the thermally induced depolarization c in the sample was determined. The experimental results are shown in Fig. 2, illustrating the difference in the absorption of the studied optical elements. It is noteworthy that the cold depolarization in each sample was less than 4 104, thus proving the good optical quality of the single crystals used in our study. The ratio of the normalized powers of heat release for the two samples was D = p2/p1 = 0.90. Since both the elements are of the same length and made of the same material, D = a2/a1 = 0.9 [15], where ai is the coefficient of linear absorption of each element. The integral depolarization in a crystal with [1 1 1] orientation is described by the following expression [34]:
c¼
2 A1 aQ ð1 þ 2nÞ LP laser ; 8 j k 3
ð1Þ
where A1 is the constant dependent on the laser beam profiles and equal to 0.137 for the Gaussian intensity distribution; n is the optical anisotropy parameter [4,35,36]; a is the absorption coefficient; Q is the thermooptical constant; j is the thermal conductivity; L denotes the length of the optical element; k is the radiation wavelength; and Plaser is the power of laser radiation. So, by using the expression (1) and the results of measurements we can estimate the coefficient aQ(1 + 2n)/3j to be 1.96 107 1/W for the first sample and 1.76 107 1/W for the second one. The green1 dotted line given for comparison in Fig. 2 is the calculated thermally induced depolarization in a TGG single crystal with [1 1 1] orientation, linear absorption coefficient a = 2.5 103 1/cm, and length L = 5.2 mm. For a TGG material we have n = 2.2 [34], Q = 17 107 K1 [37], j = 5 W/K m and calculate aQ(1 + 2n)/3j = 1.53 107 K1. The authors of the work [3] proposed a magneto-optical figureof-merit for crystals with [1 1 1] orientation for comparison of magneto active materials with such orientation:
l½1 1 1 ¼
Vj 3 ; aQ ð1 þ 2nÞ
ð2Þ
where n is optical anisotropy parameter [4,35,36]. We measured the Verdet constant at the wavelength of 1070 nm. For our samples, the Verdet constant was found to be 46 ± 3 rad/T m, which is 24% higher than in the TGG crystal (37 rad/T m), the magneto-optical Fig. 1. Schematic of thermally induced depolarization measurements. 1 – calcite wedge polarizer; 2 – absorber; 3 – sample; 4 – fused silica wedges; 5 – Glan prism and 6 – CCD camera.
1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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figure-of-merit of TSAG for the [1 1 1] orientation was close to that of TGG with the same absorption and orientation. A scheme with compensation of thermal depolarization inside magnetic field was chosen for fabricating FI. The source of magnetic field was a permanent magnet system producing a maximum magnetic field of 2.5 T along the axis, which was described in [6,17]. Optical elements made of a TSAG single crystal were glued into copper tubes for heat sink. A quartz rotator was placed between the elements. The angle of rotation of the polarization plane in the quartz rotator was chosen to be 67.5°, as the orientation of the elements was close to [1 1 1]. The magneto-optical elements were placed in the magnetic field, where their total nonreciprocal Faraday rotation was 45°. Then, the power dependences of the thermally induced depolarization were measured for two cases: with quartz rotator (blue circles in Fig. 3) and without it (red squares in Fig. 3), which allowed us to estimate the compensation efficiency. In the absence of quartz rotator, the thermally induced depolarization demonstrated the well-known quadratic dependence on the power of the transmitted radiation. When the quartz rotator was added between the magneto-optical elements, the thermally induced depolarization reduced considerably and its power dependence was no longer quadratic, instead it was proportional to the fourth order of the transmitted laser radiation power, which is well illustrated by the obtained experimental data (blue circles in Fig. 3). The red and blue solid lines are the approximations proportional to the second and fourth order of laser power, respectively. The isolation ratio of FI we calculated as I = 10 log(c). At a maximum laser power of 350 W, the thermally induced depolarization reduced by a factor of 5.4, and the FI with compensation of the thermally induced depolarization provided an isolation ratio of 32 dB. Let us estimate the possibility of further increasing the isolation ratio in the high average power FI based on TSAG with the compensation scheme. Using our crystals with the orientation close to [1 1 1] we were able to increase the power of laser radiation Pmax at which the isolation ratio of 30 dB is achieved by a factor of 2.7, namely, from 150 to 400 W. Theoretical estimates in the FI scheme with compensation inside magnetic field show that at equal absorption coefficients of the magneto-optical elements with [1 1 1] orientation of the crystallographic axes a 12-fold increase in Pmax can be obtained [14], which for our crystals would lead to an increase of Pmax up to 1800 W. Another possibility to increase the Pmax value is to use a crystal with [0 0 1] orientation. In this orientation, thermally induced depolarization depends on crystal rotation [38] and compared with the [1 1 1] orientation can be reduced at least by a factor of (1 + 2n)2/9 for |n| > 1 and by a factor of (1 + 2n)2/9n2 for |n| < 1 [34]. For TGG crystals, n = 2.2 and the thermally induced depolarization may be reduced by a factor of
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3.2. For TSAG crystals, the value of parameter n is still unknown. We want to dedicate to this issue one of our future works. Still another important parameter is the linear absorption coefficient a, which is rather high for the sample under study, probably due to the relatively high level of impurities in the TSAG crystal. If, by improving the crystal growth process, the linear absorption coefficient is decreased to the level of TGG absorption a = (1.3 1.5) 103 1/cm, it will be possible to expect creation of an FI with an isolation ratio better than 30 dB up to powers of a few kW of cw radiation.
3. Thermal lens measurements The thermal lens occurring in the FI was measured using the phase-shifting interferometry scheme [39,41]. The experiment is outlined in Fig. 4. A 350 W cw Yb-fiber laser was used as a source of heating radiation. The laser radiation was directed to the sample by means of dielectric 45° mirrors at a wavelength of 1070 nm. The heated sample was placed in one of the Michelson interferometer arms formed by beam-splitting cube 4 and metallic mirror 6 attached to piezo elements. Images of the element of interest were transferred by telescope 7 to CCD camera 8 which was synchronized with mirror 6 and took a sequence of 4 interferometry images differing from each other by k/8 change of the arm length. The phase front distribution was restored by processing the captured video sequence [42]. Measurements were made both with no heating radiation and at certain values of heating radiation. The obtained distributions of the phase front, as in [43], were processed and the thermal lens strength was found. The results are illustrated in Fig. 3b (red squares). For comparison, the blue circles in Fig. 3b show the power dependence of the thermal lens strength in the FI with compensation of thermal depolarization based on TGG ceramics with linear absorption coef-
Fig. 4. Schematic diagram of thermal lens measurement. 1 – 45° dielectric mirror; 2 – absorber; 3 – sample; 4 – beam splitter; 5 – metallic mirror; 6 – metallic mirror attached to piezo elements; 7 – telescope and 8 – CCD camera.
Fig. 3. (a) Thermally induced depolarization versus laser power with compensation (blue circles) and without compensation (red triangles) and (b) thermal lens strength versus laser power for FI based on TSAG crystal (red squares), and for FI based on TGG ceramics with the same magnetic system (blue circles). Green dotted line is the theoretical calculation of the thermal lens strength for TGG crystal with absorption equal to that of TSAG crystal. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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ficient a = 1.46 103 1/cm. This FI was made using the same magnetic system with the same quartz rotator, the only difference was the material of the magneto-optical elements and their length needed for 45° Faraday rotation of the polarization plane. The green line shows the recalculated power dependence of the thermal lens in the FI on a TGG single crystal with a = 2.5 103 1/cm. Comparison of the plots shows that the TSAG crystal with [1 1 1] orientation has a 1.5 times stronger thermal lens, all other conditions being equal. Theoretically, the thermal lens power in crystals with [1 1 1] orientation is described by the expression [41]
1 aLPlaser 1 ¼ P ð1 nÞQ ; 2 F 3 2p r h j
ð3Þ
where F is the focal length, rh is the beam radius (1/e intensity level), and P is the thermooptical constant [4]. By using the expression (3) and the experimental data on the thermal lens strength it is possible to estimate the value of a/j(P–(1–n)Q/3) to be 1.91 106 1/W. In garnets, the thermooptic constant P is much larger than Q (for example, P/Q = 10 for TGG [44] and P/Q = 13 for YAG (calculated from [45]), and the parameter n is of the order of several units (nTGG = 2.2, nYAG = 3.2), so the second term in the expression (3) can be neglected. We used the value of absorption coefficient measured by the manufacturer for TSAG and estimated P/j to be 7.65 106 m/W for our crystals. For comparison, for TGG, P/j = 3.8 106 m/W. 4. Conclusion In conclusion, the thermally induced depolarization and thermal lens in a TSAG crystal with [1 1 1] orientation have been measured. Some thermo-optical properties of TSAG material were estimated by the obtained data for the first time and compared with those in the widely used TGG crystal. It was found that a TSAG crystal with [1 1 1] orientation has a magneto-optical figure-ofmerit same as the [1 1 1] oriented TGG crystal and a 22% larger Verdet constant. This suggests that the use of TSAG instead of TGG as a magneto-optical material for FI seems to be very promising. However, TSAG demonstrates a stronger (1.5 times) thermal lens, necessitating its additional correction or use of compensation techniques. An FI with compensation inside magnetic field based on a new magneto-active material – a TSAG single crystal with [1 1 1] orientation – has been reported for the first time. This FI demonstrates a stable isolation ratio better than 32 dB at up to 350 W cw power of transmitted laser radiation. It is shown that the use of crystals with similar absorption will enable creating an FI with an isolation ratio better than 30 dB at up to 1 kW power, while improving the growth technology of single crystals and decreasing the linear absorption coefficient to the level of absorption in TGG crystals will additionally increase power by more than 2 times with the isolation ratio being unchanged. Acknowledgement 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. References [1] E.A. Khazanov, O.V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, Investigation of self-induced depolarization of laser radiation in terbium gallium garnet, IEEE J. Quantum Electr. 35 (1999) 1116–1122. [2] M.J. Weber, Faraday rotator materials for laser systems, in: Proc SPIE, 1987, 75–90.
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