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Abstract
Stress-induced polarity inversion of crystal quartz using a quasi-phase matching (QPM) stamp is proposed for a QPM frequency conversion quartz device. Fabrication of QPM structure in x-cut quartz plate could be realized using the periodically patterned QPM stamp. Also, second-harmonic 532 nm generation with 16.8 kW peak intensity was demonstrated using a QPM quartz device with QPM period of 124 µm (3rd-order QPM) to confirm its polarity-inverted structure.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Crystal quartz (α-quartz) is one of major optical materials because of its excellent optical and mechanical properties. Also, quartz is well known as a nonlinear material used for the first demonstration of second-harmonic generation (SHG) by P. A. Franken et al. in 1961 [1]. Although its practical use by conventional birefringent phase matching (BPM) scheme has been prevented because of its small birefringence, an artificial control of nonlinear coefficient enables quartz both efficient and arbitrary wavelength conversions, which is called a quasi phase matching (QPM) scheme [2,3].
Compact-sized, high-intensity coherent light source as microchip laser (MCL) with sub-nanosecond (ns) pulse duration is becoming a practical tool for various applications, such as laser machining, laser-induced breakdown spectroscopy, and laser ignition [4]. Because of its superior laser characteristics as high-beam quality, high-peak intensity and narrow spectral bandwidth, the sub-ns MCL is also suitable for a pump source of an effective nonlinear wavelength conversion, compared to conventional ns lasers or ultrafast femtosecond lasers. On the other hand, these developments of laser systems as the MCL also changed requirements on nonlinear crystals for wavelength conversion, because crystal damage by laser irradiation easily and frequently occurs at the high-intensity wavelength conversion scheme [5]. Ferroelectric and semiconductor crystals with large nonlinear coefficient, such as LiNbO3, KTiOPO4, and GaAs [6–8], are major materials for current QPM scheme, though they show low durability against intense-laser irradiation. Although borate-type nonlinear crystals as LiB3O5 and CsLiB6O10 [9,10] are tough materials and applicable for ultraviolet generation, their wavelength conversion scheme is limited to conventional BPM and they have a drawback of hygroscopic susceptibility. Excellent characteristics of quartz compared to conventional nonlinear crystals as short absorption edge (∼150 nm), small absorption, and high durability against laser irradiation [11–13] are suitable for material of future high-intensity wavelength conversion, if we can construct an artificial QPM structure.
QPM quartz constructed by multi-plates stacking technique was previously reported [14], and we have also reported MCL-pumped 532 nm and 266 nm generation using the plate-stacked QPM quartz constructed by an optical contact method [12,13]. On the other hand, polarity inversion inside of quartz by a secondary twinning have been reported [15–17], which is similar technique to periodical poling of the ferroelectric crystals [6,7], and suitable for fabrication of precisely-patterned QPM quartz. In this paper, we present on a stress-induced polarity inversion of quartz using a QPM-patterned plate (QPM stamp). Periodic polarity inversion of quartz could be demonstrated using a QPM stamp. Also, QPM-SHG characteristics was evaluated by the sub-ns MCL-pumped experiments.
2. Nonlinear characteristics of quartz
Structure of quartz in normal pressure under 573°C (α-quartz) belongs to a trigonal structure of point group 32 (D3). According to Kleinman symmetry, nonzero nonlinear coefficients in quartz are limited to d11 = - d12 = - d26 and d14 = - d25. Therefore, nonlinear polarization P(2) = (Px(2), Py(2), Pz(2)) can be written as follows [1].
Because d14 (0.008 pm/V) is much small compared to d11 (0.3 pm/V) [18], we can ignore the d14-factor in Eq. (1) in most case of pump-wave propagations. Also, the d14-factor in Eq. (1) disappears in case of propagations along crystallographic x, y, z-axis as noted below.
In case of x-axis propagation scheme (Ex = 0) with linearly polarized light, both nonlinear polarization components Py(2) and Pz(2), perpendicular to the propagating x-axis, become zero.
In y-axis propagation (Ey = 0), nonlinear polarization components Px(2) and Pz(2), perpendicular to the propagating y-axis, become as
In z-axis propagation (Ez = 0), polarization components Px(2) and Py(2) can be presented as
Although nonlinear wavelength conversion using quartz can be expected in case of y- and z-axis (including directions close to y- and z-axis) propagation schemes, characteristics of resulting nonlinear polarization depends on both an axis of propagation and an angle of pump-wave polarization as in Eqs. (2) and (3), even if we can construct a QPM structure in quartz.
3. Optical rotation of quartz
Quartz shows an optical rotation (rotation of the plane of light polarization), when a light propagates along its optical axis, i.e., crystallographic z-axis. The optical rotatory power depends on the light wavelength, and rapidly increases with decreasing wavelength. For example, the optical rotatory power of quartz at the wavelength of 1064 nm, 532 nm, and 355 nm can be roughly estimated as 6.3 °/mm, 27 °/mm, and 66 °/mm, respectively, from previous report [19].
Therefore, in case of wavelength conversion by the z-axis propagation scheme, polarization angle of the pump wave rotates as it propagates, and polarization angle of the generated wave by wavelength conversion also rotates at a different rotation speed from that of the pump wave. Also, final angles of light polarization for both pump and generated waves differ each other, and depend on a propagation length in quartz, which indicates that there is some difficulty in the z-axis propagation scheme, compared to the y-axis propagation scheme.
4. Stress-induced polarity inversion using a QPM stamp
Quartz has various types of twinning structure. Among them, Dauphiné Law twin (also called an electrical twin) naturally has a polarity-inverted structure on its x-axis, and can be artificially fabricated in bulk quartz, which are suitable for realizing a QPM device using a quartz. Thermal and stress treatment by a lamp heating or a laser irradiation realized the x-axis inversion in a rotated y-cut (AT-cut) quartz plate by way of metal-film deposited on the plate surface as shown in Fig. 1(a) [15]. Twin-structured QPM quartz, realized by a stress application through a periodic metal film or a direct surface patterning on the plate surface under elevated temperature condition, was reported using a slightly-rotated y-cut plate, as Figs. 1(b) and 1(c) [16,17].
In conventional polarity inversion of quartz as Figs. 1(a)–1(c), a periodic pattern for stress application was directly fabricated on the quartz plate, which limits a repeatability and reproducibility of the QPM quartz. Also, because quartz is a hard material with an anisotropic etching property, direct fine patterning of its plate surface is not easy compared to other isotropic materials. On the other hand, QPM stamp method using a QPM-patterned plate shown in Fig. 1(d) can improve these problems in the polarity inversion process. The QPM stamp with the periodic pattern is kept on the quartz under elevated temperature condition, and high pressure for polarity inversion is applied to the quartz through the QPM stamp. Patterned QPM period Λ of the QPM stamp depends on refractive index of quartz, and Λ of SHG for 532 nm and 266 nm generation are 42 µm and 6 µm, respectively, at the 1st-order QPM structure.
Similar stamp method was previously proposed and have been used for high-voltage application to ferroelectric QPM materials [20,21]. We introduced the QPM stamp for thermal and stress application to quartz. Because the QPM stamp can be used repeatedly, this method is expected to be superior for reproducibility compared to the conventional method, which requires direct patterning of quartz plate.
5. Fabrication of polarity inversion structure
QPM stamp for the stamp method should be prepared by using a hard and stable material, such as stainless steel and borosilicate glass. Periodic pattern in these materials can be fabricated by mechanical dicing or chemical etching, which depends on material property of the stamp. For initial evaluation, a QPM stamp of Λ = 124 µm (3rd-order QPM for 532 nm generation) with duty ratio (pattern width / QPM period) = 0.17 was prepared using a stainless-steel plate (size of 30 mm x 20 mm) by mechanical dicing. Polarity inversion process using the QPM stamp were demonstrated at the elevated temperature environment as shown in Fig. 2(a). Surface photograph of the prepared QPM stamp is also shown in Fig. 2(a). Quartz plate (typical size from 15mm x 10 mm to 30 mm x 20 mm) was contacted with the QPM stamp, and pressed by temperature-controlled blocks at the temperature > 300°C with an estimated stress at the stamp surface > 100 MPa. After the stress application, the quartz plate was etched to reveal a result of polarity inversion process. Because of etching-rate difference between inverted and non-inverted surface of x-cut or x-related-cut face, we can check a result of polarity inversion, same as conventional LiNbO3 crystals.
Firstly, we evaluated possibility of polarity inversion using 1-mm-thick x- and y-cut quartz plate in several conditions. And QPM-stamp-related periodic patterns could be obtained after the etching in both-cut plates, which are proof of polarity inversion by the stamp method. Figure 2(b) shows a typical periodic pattern obtained at the stamp side of x-cut plate (size of 15 mm x 14 mm for y- and z-axis) obtained at the conditions of 310 °C and 800 MPa. Stress application using a QPM stamp well realized a polarity inversion to the quartz, although inverted patterns are not so fine and inhomogeneous region still exists. There are many possible reasons of the inhomogeneity as difference of flatness between quartz and stamp plate, stamp-shape accuracy, difference of thermal expansion between of quartz and stamp plate. All of these possibilities should be improved in next work to realize a fine-patterned QPM quartz.
6. SHG characteristics of QPM quartz device
Second-harmonic 532 nm generation characteristics of QPM quartz fabricated by the QPM stamp method was evaluated using a lab-made MCL (1064 nm wavelength, 0.7 ns pulse duration, 30Hz operation frequency, 3 mJ maximum energy) as a pumping source [4]. The QPM quartz device shown in Fig. 2(a) with Λ = 124 µm fabricated using a x-cut plate was put on a rotation stage in y-axis propagation scheme. Device length of the x-cut QPM quartz along y-axis is 15 mm. Precise tuning of phase matching condition was done by the device rotation at room temperature condition. Polarization angle θy of the pump wave against x-axis in x-z plane was tuned by a half-wave plate (HWP). Linearly-polarized pump beam was focused into the device at an estimated minimum beam 1/e2-diameter of 0.12 mm. Pumping energy EP was measured before the QPM device, and resulted SH energy ESH was measured after passing through both a dichroic mirror (MD) and a glass filter (GF) to cut the residual pump beam, as shown in Fig. 3(a).
Figure 3(b) presents ESH characteristics of fabricated QPM quartz, compared with a bulk (non inverted) quartz. The pump polarization θy was set parallel to x-axis of quartz (θy = 0), and maximum ESH recorded 9.07 µJ (corresponding peak power of 16.8 kW for 0.54 ns SH pulse) at EP = 1.82 mJ, which was >1000 times higher energy than that from a bulk quartz (ESH = 6.19 nJ at EP = 2.5 mJ). These results also proved successful polarity inversion by the QPM stamp method.
As presented in Eq. (2), nonlinear polarization P(2) from the QPM quartz in y-axis propagation scheme depends on the pump polarization angle θy, and has a limited polarization component Px(2) along x-axis of quartz. We evaluated both z- and x-polarized portion of the SH energy (ESHz, ESHx, respectively) after a polarization beam splitter (PBS) as in Fig. 4(a). From the measurements, we confirmed that ESHz keeps zero at any θy and that ESHx becomes maximized at θy = 0 and zero at θy = ± π/2, as Fig. 4(b), which well corresponded with Eq. (2).
Fig. 4. (a) Set up for pump polarization characterization, (b) SH characteristics on pump polarization.
Although current energy conversion efficiency of the fabricated QPM quartz device stays low as 0.5% because of high-order QPM structure, short-QPM length, and inhomogeneous inversion conditions, we can expect their improvements by using a low-order QPM structure, expansion of device length, and optimization of polarity-inversion condition.
7. Summary
We proposed a new technique on stress-induced polarity inversion of quartz by using a periodically patterned QPM stamp. Fabrication of polarity-inverted structure in quartz was realized, and SHG characteristics with peak intensity of 16.8 kW was evaluated using a sub-ns MCL pumping scheme. The QPM stamp method is expected to be superior in repeatability and reproducibility compared to the conventional method, which requires direct patterning of quartz plate. High intensity and high durability QPM device using quartz can be expected using this method.
Funding
Japan Society for the Promotion of Science (JP19142546); Japan Science and Technology Agency (Mirai Program, JPMJMI17A1).
Disclosures
The authors declare no conflicts of interest.
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