Deep-ultraviolet (DUV) light sources are critical owing to their high photon energies and small diffraction limits, and synthetic quartz glass (SQ) is suitable for the Faraday rotators of DUV light. The Verdet constant in SQ was evaluated within the wavelength range of 190–300 nm. In addition to a high Verdet constant over the DUV region, this material exhibits a high transmittance without transitional absorption bands. The Verdet constants were found to be 70.1 rad/(T·m) at 193 nm, which is the shortest observed wavelength for silica glass. SQ glass has excellent structural properties; thus, it is suitable as a DUV Faraday rotator for high-average-power optical isolators.
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Deep-ultraviolet (DUV: λ=190–300 nm) light sources, which have small diffraction limits owing to their shorter wavelengths, play important roles in various applications such as photolithography. Excimer lasers are widely used industrially because they provide the highest pulse energy in this wavelength region, and solid-state lasers are being developed worldwide as well because of various advantages such as high repetition rate and high beam quality. In addition, owing to their high photon energies, both types of lasers can be employed for the direct cutting of atomic or molecular bonds, thus inducing energy transitions with higher energy gaps. Hence, these light sources are widely employed in semiconductor lithography processes using excimer lasers  and laser micromachines , in addition to the determination of neutral particle density by laser-induced fluorescence measurements . In such applications, a high output power is required to obtain a high throughput in the manufacturing process or precise measurement resolution. Under the high-power operation of a laser system, the damage of the optic or laser sources by the returning light is severe. This problem can be solved using an optical isolator that allows for the transmission of light in only one direction. A typical optical isolator consists of two polarizers and a Faraday rotator (FR). The FR rotates the angle of polarization based on the Faraday effect, which is a magneto-optical effect. The rotation angle θF of the polarization can be expressed as follows:4–6]. However, these materials cannot be employed for wavelengths shorter than 390 nm owing to their large absorption by interband transitions.
The Verdet constants of synthetic quartz glass (SQ) [7–9], rare-earth fluoride single crystals [10,11], and KDP-type crystals  have been reported as FR media in DUV. In particular, the properties of SQ are suitable for DUV-FR. It exhibits high transparency over a wide wavelength range without transitional absorption lines. Moreover, it is an extensively studied material that is commonly used as an optical element, with the capacity for large-size fabrication with high uniformity; which is important for high-power lasers, given that the expansion of the beam diameter prevents the thermal lens effect . In addition, it can suppress nonlinear effects which are a critical problem in ultrashort pulse operations. The Verdet constant was reported as 33.5 rad/(T·m) (λ = 248 nm)  and 29.8 rad/(T·m) (λ = 253.7 nm) . These Verdet constant values were reported at several wavelengths in the visible region as well [14,15]. Therefore, SQ was selected as a target medium. To design the FR for many types of DUV light sources, the wavelength dependence of V is required to be derived, particularly at wavelengths shorter than the reported values. The absorption edge is close, and the change in V is large. Therefore, it is necessary to obtain detailed data. In this study, the Verdet constant was experimentally evaluated using an optical-discharge plasma light source and a solid-state laser with a wavelength range from 190–300 nm. In addition, its suitability as a DUV-FR was confirmed.
2. Materials and methods
The Verdet constant was measured using a polarization-stepping measurement method , which is a simple and robust technique. The experimental setup is shown in Fig. 1. An optical-discharge plasma light source (ODPLS, Energetiq Technology, Inc. EQ-99X LDLS) was used as the seed light for the Verdet constant measurement within the wavelength range of 190–300 nm. The input light propagated the first Wollaston and GlanTaylor (WoG) polarizer (Pol. 1, Kogakugiken Corp. WoG-193-E), which induced the linear polarization, and then passed through the medium in an external magnet (B = 1.06 T). The SQ, which represents the DUV optics (excimer laser grade), was purchased from Shin-etsu Quartz (SUPRASIL-P700), with a length of L = 20 mm and a width/height of 5 mm. This sample exhibited a high transmittance, with a wavelength longer than approximately 155 nm. The absorption coefficient (λ = 200 nm) and the thermal conductivity of SQ were reported as k < 0.006 cm-1 and κ = 1.38 W/(m·K) at room temperature, respectively . The magnet and the material are fixed on separate mounts. It is possible to apply the same magnetic field strength on the material with precise position repeatability of less than ± 1 mm. The error from the magnetic field is expected to be about ∼0.004 T, calculated from the magnetic field strength distribution. The second WoG polarizer (Pol. 2) was mounted on a motor rotator with a sampling pitch of 1°. For each angle, the spectrum was captured using a spectrometer (Ocean Insight Maya 2000 Pro). The Verdet constants were evaluated continuously within the wavelength range of 190–300 nm. To confirm the reliability of the evaluation system, the Verdet constant was measured at a single wavelength using a solid-state laser (SSL) and power meter (Thorlabs, S120VC) in the DUV region. This light source was of the same configuration as that in . The laser consisted of Yb-fiber (λ = 1030 nm) and Er-fiber (λ = 1553 nm) lasers, in addition to frequency conversion chains; with multiband emissions at wavelengths of 258 nm, 221 nm, and 193 nm, respectively. By combining the results of the two optical systems, the wavelength dependence of the Verdet constant in the DUV region can be extensively evaluated.
3. Results and discussion
Figure 2 presents the typical results of the polarization-stepping method using light with a wavelength of 221 nm from the SSL. The intensity after transmission through the second polarizer was fitted using the following formula:1)].
Figure 3 presents the wavelength dependence of the evaluated Verdet constant in SQ. For example, the following results were obtained for the measurements using the ODPLS: V = 70.1 rad/(T·m) and λ = 193 nm, V = 43.6 rad/(T·m) and λ = 221 nm, and V = 27.3 rad/(T·m) and λ = 258 nm. The obtained Verdet constants were in good agreement with the previously reported values [7,8,14] in both DUV and visible regions, and the results obtained by the SSL (red-colored points) were within approximately 10%. The Verdet constant increased significantly with a decrease in the wavelength. It should be noted that the SQ is a diamagnetic material, and the Verdet constant formula is provided in .
The optimum medium length for the FR can be calculated using the fitting function. In the simplest optical isolator, the rotation angle by the FR should be 45°. Table 2 presents the optimum thicknesses of SQ for the FR in a typical UV-DUV laser. The strength of the magnetic field was assumed to be 1 T for this calculation. Evidently, those thicknesses are in the range of 10-45 mm, and they are acceptable for assembling a compact optical isolator at the DUV wavelength range. The critical characteristic is that the Verdet constant of diamagnetic materials is not dependent on temperature . Therefore, it can be concluded that the term of thermal depolarization caused by the temperature dependent Verdet constant can be ignored . The thermal depolarization by the change of eigenpolarizations caused by the photoelastic effect can be estimated by following equation .
ν is the Poisson coefficient, n0 is the refractive index, pi,j are photo elastic coefficients, and
By using λ = 200 nm, L = 20 mm, Q ≈ 10−7 K-1(calculated from Ref. [8,21]). Assuming P0 = 100- W, the thermal depolarization γP can be estimated to be ∼0.001 (30 dB). Also, the thermal lens effect can be estimated by following equation .
Where A is the rod cross-sectional area, Pa is the absorption power, α is the thermal coefficient of linear expansion and Cr,Φ is the photo elastic coefficient, r0 is the radius of the rod. From the Eq. (7), the thermal lens can be estimated to f > 100 m assuming the following condition. A = 1.26×10−3 m2, Pa = 1.3 W (100 W input power), dn/dT = 1.49×10−5 K-1, α = 5.10×10−7 K-1, Cr,Φ = 3.47 (nm/cm)/(kg/cm2), n0 = 1.51 , r0 = 20 mm. This suggests that it can be used for high-average-power laser applications. The data indicate the suitability of UV-DUV FRs as optical isolators for various light sources.
The wavelength dependence of the Verdet constants in SQ was measured within the DUV region. By combining two optical systems, detailed and precise measurements within the wavelength range of 190–300 nm were realized. This combined system enables a detailed determination of the values for various materials. In addition, it can be measured from 170 nm in the Nitrogen purge. In particular, this paper presents the first measurement of the Verdet constant of SQ for wavelengths shorter than 248 nm, with reference to the literature, which was found to increase rapidly toward the absorption edge. Based on the results, the Verdet constants of SQ were found to be V = 70.1 rad/(T·m) at λ = 193 nm, V = 43.6 rad/(T·m) at λ = 221 nm, and V = 27.3 rad/(T·m) at λ = 258 nm. These values allow for the development of an FR with an appropriate thickness of 10–50 mm within the abovementioned wavelength region. By deriving a detailed wavelength dependence curve from the measured data, the medium length required for the FR for each wavelength laser can be determined. The results reveal that the SQ is highly suitable for the wavelength range of 193–300 nm, and it is not dependent on temperature; thus, it can be used as an optical isolator for high-average-power lasers. Moreover, given that an optical isolator with a large diameter can be realized, it can be used in the fabrication of various DUV light sources such as excimer lasers with high pulse energies (on the order of a few Joules) and solid-state lasers with short pulse durations (on the order of a few picoseconds) and high peak powers.
Japan Society for the Promotion of Science (18H01204); National Institute for Fusion Science (ULHH040); Amada Foundation (AF-2019221-B3).
The authors declare no conflicts of interest.
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