Thermo-optic effects of ceramic TGG in the 300–500 K temperature range

Hiroaki Furuse; Ryo Yasuhara; Keijiro Hiraga

doi:10.1364/OME.5.001266

1. Introduction

In recent years, high-quality transparent ceramics technology has been widely used for developing both joule-class ns-pulse lasers and kilowatt-class continuous wave (CW) lasers [1–4]. In the future, ultra-short-pulse lasers with high energy and high repetition rates (e.g., > 10 mJ pulse energy, > 100 kHz repetition rate, and < 1 ps pulse width) will be in high demand in industrial fields for next-generation laser processing. Accordingly, the damage and the thermal problems caused by the laser that are associated with the optical elements should be addressed.

A Faraday rotator is one of the most important optical elements in laser systems and applications for polarization control, optical isolation, and birefringent compensation. The terbium gallium garnet (TGG) single crystal is the most widely used material in Faraday rotators for high average power lasers because it has a high Verdet constant of 35–40 rad/Tm for a 1 μm wavelength [5,6] and a high thermal conductivity of 4.9 W/mK [7]. However, a large optical aperture, which prevents laser damage due to high-intensity laser fields, is limited for single-crystal TGG. In addition, a radical temperature gradient occurs when a laser with high average power is introduced to the TGG rod because slight laser energy absorption of about 0.5% exists in the TGG crystal [8]. For this reason, commercially obtainable Faraday rotators are not appropriate for lasers with over 100 W of average power.

Khazanov et al. proposed a transparent polycrystalline ceramic TGG with a large aperture as a new Faraday material [9]. In 2007, Yasuhara et al. measured the temperature dependence of the Verdet constant for ceramic TGG and demonstrated that it is equal to that of single-crystal TGG [6]. In 2010, Yoshida et al. were the first to demonstrate the Faraday effect using ceramic TGG, and they obtained 35 dB of optical isolation at a laser power of 200 mW [10]. After that, thermal effects in ceramic TGG, including thermal lensing and depolarization, have been actively studied beyond the range of 100 W [11–14]. Most recently, 35 dB of optical isolation has been demonstrated with a laser output power of 1 kW [15]. Moreover, 10 cm² ceramic TGG has been manufactured by Konoshima Chemical Co. Ltd.

In the near future, the ceramic TGG Faraday rotator will be replaced by current materials in not only joule-class high-energy pulse lasers, but also in kilowatt-class, high-average-power, ultra-short-pulse lasers for industrial applications. For some applications – such as laser ignition [16] – the Faraday rotator may be used in a hot or vacuum environment. To achieve this, a new Faraday rotator design with an active cooling system (along with a complete thermal analysis) would be necessary. For detailed analyses, we believe that the temperature dependence of thermal properties above room temperature requires investigation.

Accordingly, in this work we measure the thermal expansion coefficient α and the thermo-optic coefficient dn/dT of ceramic TGG in the 300–500 K temperature range. For comparison, we also measure the characteristics of single-crystal TGG with <111> orientation. In addition, we propose fitting curves for α and dn/dT that can be applied to a temperature range of 64–500 K using previously reported experimental results. From the results, we evaluate thermally induced depolarization and the thermal lens focal length for an average laser power of 1 kW.

2. Experimental method

We used a Fizeau interferometer to measure the temperature dependence of α and dn/dT [17] in TGG specimens. The details of the specimens of ceramic and single-crystal TGG, along with the experimental setup, can be found in [18] and [19], respectively. In this paper, we briefly explain it for the sake of completeness.

Figure 1 shows the experimental setup of α and dn/dT measurement including photos of the ceramic and single-crystal TGG. We used H-character ceramic TGG (Konoshima Chemical Co., Ltd.) and single-crystal TGG (CASTECH Inc.) specimens for the measurements. The ceramic TGG was diffusion bonded to the ends of the piece of ceramic TGG. By using the H-character specimen, we were able to form two interferometers: one with a vacuum path, and one with a TGG medium path. The lengths of the round trip interferometer paths for the vacuum and TGG medium are 29.8 mm and 41.5 mm, respectively, for ceramic TGG; they are 40.2 mm and 53.2 mm, respectively, for single-crystal TGG. The TGG specimen was attached to a copper holder with thermally conductive Ag paste to improve the thermal contact, and was set in a vacuum chamber. The specimen was heated, and the temperature of the specimen was measured by a thermo-couple. A He-Ne laser (λ = 632.8 nm) was used as a probe beam. The reflected signals formed two interference fringes, along with the fringe shift due to temperature variation; these were separated by a half mirror and recorded with photodiodes. The amount of phase shift for each signal within a 5 K temperature range was used for evaluating α and dn/dT. We performed the experiments between 300 K and 500 K using a 5 K interval.

Fig. 1 Experimental setup of the α and dn/dT measurement.

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3. Experimental results

Figures 2(a) and 2(b) show the experimental results of measuring α and dn/dT, respectively. The open circles and triangles over the 300 K temperature range represent the results of this work for ceramic and single-crystal TGG, respectively. The closed marks represent the experimental results below room temperature, as reported in [18]. The measured values of α and dn/dT for both ceramic and single-crystal TGG are listed in Table 1. For ceramic TGG, the experimental values of α and dn/dT at 300 K were 7.0 $\times$ 10⁻⁶ K⁻¹ and 17.5 $\times$ 10⁻⁶ K⁻¹, respectively. These results were in good agreement with the results of the previous work on ceramic TGG at room temperature: 7.1 $\times$ 10⁻⁶ K⁻¹ for α and 17.0 $\times$ 10⁻⁶ K⁻¹ for dn/dT [18].

Fig. 2 Temperature dependence of (a) the thermal expansion coefficient α and (b) the thermo-optic coefficient dn/dT of ceramic and single-crystal terbium gallium garnet (TGG). The dotted lines represent the fit proposed in this work.

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Table 1. Experimental results of α and dn/dT for ceramic and single-crystal TGG.

View Table

As can be seen in Fig. 2, α and dn/dT increase with increasing temperature. The temperature dependencies of α and dn/dT for ceramic TGG are equal to those of single-crystal TGG throughout the 300–500 K temperature range. The black dotted lines trace out the fitting curves of ceramic TGG obtained from the experimental results in the 64–500 K temperature range. For the fitting curve, we used the following function for α and dn/dT, along with [19]: $α (T) = A \exp (- B / T)$ and $d n (T) / d T = M_{0} + M_{1} T + M_{2} T^{2} + M_{3} T^{3}$ . For the results, we obtained A = 1.23 $\times$ 10⁻⁵ K⁻¹, B = 166.7 K, M₀ = −4.0002 $\times$ 10⁻⁶ K⁻¹, M₁ = 1.4612 $\times$ 10⁻⁷ K⁻², M₂ = −3.3083 $\times$ 10⁻¹⁰ K⁻³, and M₃ = 2.9108 $\times$ 10⁻¹³ K⁻⁴.

4. Discussion

In the present experimental results, the temperature dependencies of α and dn/dT for ceramic TGG are equal to those of single-crystal TGG with <111> orientation. Sato et al. reported recently that, for isometric crystals such as TGG and YAG, α and dn/dT are independent of the crystal orientation because these coefficients are second-order tensors [20]. To this report, our experimental data are consistent. There is thus a possibility that our experimental results regarding α and dn/dT for ceramic TGG with <111> orientation will be the same for other orientations. In order to discuss this possibility in more detail, α and dn/dT for single-crystal TGG with other orientations will be measured in the future.

By contrast, the effects of crystal orientation on thermally induced depolarization have been studied in ceramic and single-crystal YAG [21,22] and TGG [8,23], and they have been shown to depend on crystal orientation. The amount of depolarization in ceramics is nearly the same as that in <111>-oriented crystals because ceramic materials consist of many crystal grains with various orientations. Furthermore, the birefringence effect in ceramic can be considered an average of the effects in those grains.

For analyzing depolarization and the thermal lens effect in Faraday materials based on ceramic TGG, the thermo-optic parameters Q and P can be defined as follows [11,24]:

Q = α \frac{n_{0}^{3}}{4} \frac{1 + ν}{1 - ν} \cdot (p_{11} - p_{12}),

and

P = \frac{d n}{d T} - α \frac{n_{0}^{3}}{4} \frac{1 + ν}{1 - ν} \cdot (p_{11} + p_{12}),

where n₀ is the refractive index, ν is Poisson’s ratio, and p₁₁ and p₁₂ are the photo-elastic constants. By using our experimental data for α and dn/dT at room temperature, we obtained |Q| = 12.4

\times

10⁻⁷ K⁻¹ and P = 15.4

\times

10⁻⁶ K⁻¹. In the evaluation, we used the following values: n₀ = 1.966, ν = 0.22, p₁₁ = 0.02, and p₁₂ = 0.08 [25]. Figure 3 shows the temperature dependencies of |Q| and P between 100 K and 500 K. In the calculation, we assumed that Poisson’s ratio and the photo-elastic constants did not vary with temperature. As shown in Fig. 3, |Q| and P tend to increase with increasing temperature. This means that cryogenic cooling is one of the methods for reducing thermal problems in TGG for lasers with high average power [26]. However, we think that this system is not appropriate for industrial applications owing to its associated costs and difficulties. Thus, we will discuss thermo-optic effects in ceramic TGG over the range of 300–500 K.

Fig. 3 The temperature dependencies of thermo-optic parameters P and |Q|.

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We now examine the temperature dependence of the depolarization ratio when a 1 kW laser is passed through a 20-mm-long ceramic TGG rod (the typical length of a Faraday rotator). The thermally induced depolarization ratio γ can be expressed as the sum of two main components: $γ = γ_{p} + γ_{V}$ [24,26]. The first term, $γ_{p}$ , results from the photo-elastic effect, and can be expressed as:

γ_{p} = \frac{C}{8} \frac{\sin^{2} (φ)}{φ^{2}} {(\frac{L a_{0} P_{in} Q}{λ K})}^{2} X^{2},

where C is the beam profile parameter (for a Gaussian beam, C = 0.137 [8]),

φ

is the polarization rotation angle (we assume that

φ = π / 4

at room temperature), L is the length of the TGG rod,

a_{0} = 2.0 \times 10^{- 3}

cm⁻¹ is the typical absorption coefficient of ceramic TGG [14], P_in = 1 kW is the input laser power, λ = 1064 nm is the wavelength of the laser, Κ is the thermal conductivity, and X is a function of crystal orientation (for ceramic TGG, X_TGG = 1.74 [26]). The second term,

γ_{ν}

, results from the temperature dependence of the Verdet constant, and is defined as:

γ_{ν} = D {(\frac{φ}{\frac{π}{4}} \frac{a_{0} P_{in}}{K} \frac{1}{V} \frac{d V}{d T})}^{2},

where D is a constant (for a Gaussian beam, D = 0.00104 [26]) and V is the Verdet constant. Using Eqs. (3) and (4), we calculated the depolarization ratio.

Figure 4(a) shows the temperature dependence of both $γ_{p}$ and $γ_{ν}$ . In the calculation, we used the temperature dependence of the thermal conductivity of ceramic TGG [7]. As a reference, we also show the experimental results of K(T) in Fig. 4(b). We fitted the experimental results between 100 K and 300 K according to:

K (T) = C_{0} + \frac{C_{1}}{T} + \frac{C_{2}}{T^{2}} + \frac{C_{3}}{T^{3}} .

We obtained C₀ = 3.05 W/mK, C₁ = 8.45

\times

10² W/m, C₂ = −9.95

\times

10⁴ WK/m, and C₃ = 4.50

\times

10⁶ WK²/m. In Fig. 4(a), we also used the temperature dependence of the Verdet constant,

V (T) = 13290 / T

rad/Tm [6].

Fig. 4 (a) Depolarization as a function of temperature, assuming an input laser power of 1 kW. (b) Temperature dependence of the thermal conductivity of ceramic terbium gallium garnet (TGG) reported in [7]. Dotted line represents the fitting curve used for the calculations.

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From Fig. 4(a), we can see that $γ_{p}$ significantly increases with temperature, whereas $γ_{ν}$ decreases because the temperature dependence of the Verdet constant decreases over the range of 300–500 K. However, $γ_{ν}$ is 3 orders of magnitude lower than $γ_{p}$ . Therefore, $γ_{ν}$ can be ignored over the range of 300–500 K. To reduce the main depolarization $γ_{p}$ at high-power operation, we think that a split-disk configuration would be more effective than the rod configuration.

We also examine the thermal lens focal length in a ceramic TGG rod with a laser power of 1 kW. The thermal lens focal length f can be evaluated using thermo-optic parameters P and Q as follows [27]:

\frac{1}{f} = \frac{L a_{0} P_{L a s e r}}{2 π r_{h}^{2} K} (P - S (1 - ξ) Q),

where r_h is the laser beam radius, S is the orientation-dependent constant (for ceramics, S = 1/5), and ξ is the optical anisotropy parameter (ξ = 2.25 for TGG). Figure 5 shows the thermal lens focal length as a function of beam radius for 300, 400, and 500 K. As seen in Fig. 5, the temperature dependence of f is very slight compared to its dependence on the beam radius. The size limit of a typical aperture for single-crystal TGG is about 10 mm, whereas an aperture of 50 mm is possible for ceramic TGG. This larger aperture represents a distinct advantage in achieving a large thermal lens focal length.

Fig. 5 Thermal lens focal length at 1 kW of input power as a function of laser beam radius.

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5. Conclusions

We measured the values of α and dn/dT for ceramic TGG over a temperature range of 300–500 K. For comparison, we also measured the parameters for single-crystal TGG with <111> orientation. The values of ceramic TGG correspond to those of single-crystal TGG. Both α and dn/dT values increased with temperature. The depolarization ratio and thermal lens effect were also analyzed for 1 kW of input power for the ceramic TGG Faraday rotator over the range of 300–500 K. We found that thermally induced depolarization was over 0.01. To decrease this, a compensation technique using additional optical elements would be effective [15,28]. In addition, we believe that a split-disk configuration and an active cooling system should be introduced. On the other hand, the temperature dependence of the Verdet constant may be ignored at room temperature. The thermal lens effect strongly depends on beam radius rather than temperature. Therefore, the thermal lens effect can be resolved by using a large-aperture ceramic TGG. We believe that this study will be useful for developing and designing a new Faraday rotator that can be used for laser systems with over 1 kW of average power, ultra-short pulses, and high pulse energy.

Acknowledgments

This work was performed with the support and under the auspices of the NIFS Collaboration Research program (NIFS13KBAH006). This work was also supported in part by the CASIO Science Promotion Foundation.

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Temperature (K)	α ( $\times$ 10⁻⁶ K⁻¹)		dn/dT ( $\times$ 10⁻⁶ K⁻¹)
Temperature (K)	Ceramic	Single-crystal	Ceramic	Single-crystal
300	7.0	7.1	17.5	17.5
350	7.6	7.6	19.2	19.5
400	8.0	8.2	20.5	20.4
450	8.4	8.5	21.5	22.1
500	8.6	8.8	22.5	23.0

Thermo-optic effects of ceramic TGG in the 300–500 K temperature range

Abstract

1. Introduction

2. Experimental method

3. Experimental results

4. Discussion

5. Conclusions

Acknowledgments

References

Cited By

Figures (5)

Tables (1)

Equations (6)

Optical Materials Express