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
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 , 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) . 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) . 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 . 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 . 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 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 ; 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 .
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
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 . 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].
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  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 . In general, the degree of thermally induced depolarization in the magneto-optical element is determined by the following equations :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 . 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 . 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 :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:
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:29,31]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 ) (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 . 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 = A1ξ2p2/π2. Owing to the high value of ξ, losses are also high. This should be considered in FI design and the use of such materials.
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.
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.
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