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The pioneering material utilized in first optical mixing revisits nonlinear optics with the cutting-edge polarity-control technology stress-induced twinning. Periodically twinned quartz with modulated polarity demonstrates quasi-phase-matched SHG emitting vacuum UV light at 193 nm.
©2011 Optical Society of America
1. Introduction
Crystal quartz has a mature growth technology and an annual production weight of over 3000 tons [1]. Major applications of the crystal are radio-frequency filters, timing and frequency control, and recently, optical low-pass filters for video and digital cameras. The crystal has high thermal and chemical stability, and fascinating features for optics including high laser-damage threshold (400 GW/cm2) [2], and short ultraviolet (UV) band edge (~150 nm). The high damage resistance and thermal stability are particularly important for handling high-power laser beams. Especially to handle a high power laser beam, an optical device should be damage-resistant and thermally stable.
The first nonlinear-optical (NLO) wave mixing of laser light utilizing second-harmonic generation (SHG), was demonstrated in 1961 by Franken et al. with crystalline quartz [3]. Although the superior optical characteristics of quartz are well known, there has been no way to realize efficient NLO interaction under phase matching. Conventional phase matching, i.e. birefringent phase matching (BPM), requires moderate birefringence to compensate for the phase mismatch between the input and the converted optical signals due to refractive index dispersion. The small birefringence in quartz is not adequate for BPM, therefore the crystal has been characterized as a non-phase-matchable NLO material. Another phase-matching scheme called quasi-phase matching (QPM) needs periodic modulation of the nonlinear optical coefficient to compensate for the mismatch, and was originally proposed by Armstrong et al. [4]. Although the QPM scheme enables us to make a flexible design with new degrees of freedom in patterning [5], it is essential to transfer a design pattern to a physical modulated structure in some way. An interesting periodic structure was demonstrated by alternating crystal orientation in bonded quartz substrates [6], but the interface reflection caused relatively high transmission loss, limiting SHG performance as an NLO device.
On the other hand, successful wavelength conversion has been reported by QPM in ferroelectric crystals such as lithium niobate [7,8], lithium tantalate [9,10], and potassium niobate [11] while modulation of the nonlinear optical coefficient was obtained by electric-field poling [12–14]. These devices extend laser wavelength range where coherent light covering from UV to mid infrared is synthesized. Although those devices can be implemented by field poling, the intrinsic band edge around 300 nm prohibits wavelength conversion to vacuum UV (VUV).
VUV lasers with a wavelength shorter than 200 nm are required in industry. For example, ArF excimer gas lasers emitting at 193 nm are used extensively in various applications such as ultrafine lithography, eye surgery, and micro machining. Much effort is underway for an all-solid-state 193 nm source, where most of the works involves sum-frequency generation (SFG) to reach 193 nm. One of the difficulties is that BPM SHG from 386 to 193 nm is not possible in conventional borate NLO crystals; one exception is the crystal KBe2BO3F2 (KBBF) phase-matchable in SHG [15]. Unfortunately its layered crystal structure makes it difficult to grow the crystal thicker than 3 mm, thus limiting the efficiency.
This paper reviews the periodic modulation of the nonlinearity by spatial patterning of a twin structure in quartz and its application to NLO. A unique technique with twinning [16–18] opens a window of opportunity for QPM in non-ferroelecric crystals. At the 50th anniversary year of nonlinear optics, the nonlinear-optics pioneer-crystal quartz returns to the foreground with QPM VUV emission at 193 nm [19].
2. Material properties of crystal quartz
Quartz belongs to the crystallographic symmetry point group 32, having non-zero nonlinear coefficients such as d11 and d12. Although the nonlinear coefficients are 100 times smaller than those of the ferroelectric family, as shown in Table 1 , the damage threshold of quartz is >100 times higher, which means that the crystal can handle >100 times higher peak power, compensating for the lower nonlinear coefficient. One should note that nonlinear coefficient is surely compensated for by high peak power driving, or strong confinement in cavity/waveguide [20] as shown in our efficient waveguide [21,22], but this is never the case for the damage threshold. High damage resistance is actually equivalent to high nonlinearity if high power operation is assumed.
Table 1. Comparison between Conventional Ferroelectrics and Quartz for QPM
Crystal quartz has a phase transition point at 573°C and two equivalent twin states coexist below the transition temperature (Fig. 1 ). When we apply the mechanical stress in the low-temperature phase, one twin state flips to another leading to an X -> -X axis conversion, because twins are connected by a two-fold axis along Z. The crystal possesses nonlinear coefficient d11 and d12, whose sign therefore can be reversed by the external stress. At the phase transition point of the crystal, the required stress reaches zero allowing low-stress switching at high temperature. Here we theoretically analyze twin behaviour in elastic simulation. For theoretical analysis of twinning, the elastic energy was calculated for the 2nd-order ferrobielastic effect [23].
The required stress for flipping (coercive stress) depends on the crystal orientation and temperature. The Gibbs free energy difference between twins ΔG, is described when the stress σ is applied normal to the crystal surface as
where sijkl is the tensor component of the elastic compliance and σij the tensor component of the applied stress. Twinning occurs when ΔG is negative and exceeds the critical value. Equation (1) could be expressed with respect to the crystallographic angle theta’θ’ as,where σ0 is stress normal to the surface. Figure 2(a) shows the crystal orientation and configuration of a twin structure in a device. Wafer cut angle theta’θ’ is defined as an angle between the surface normal and the Y axis. The coercive stress is predicted by the calculated elastic energy at various temperatures, derived from the measured temperature-dependent coercive stress [24]. Figure 2(b) plots the calculated coercive stress and SHG efficiency as a function of cut angle theta’ θ’. As the angle theta’ increases the coercive stress steeply decreases, nevertheless at the sacrifice of the efficiency. Conversion efficiency is expressed as, where Pω and P2ω denote power of fundamental and SH light, λω fundamental wavelength in vacuum, nω and n2ω refractive indices of fundamental and SH light, ε0 electric permittivity in vacuum, c speed of light, L device length, and h(B, ξ) Boyd-Kleinmann focusing parameter, which is 1.068 in optimum focusing. The effective nonlinear coefficient deff corresponds to (2/π)d11 or (2/π)d12(cos θ’)2 for input polarization parallel to X axis or normal to the top surface. As the Y axis inclined, input light component projected to the Y axis monotonically decreases and deff for d12 interaction is reduced. The conventional cut angle theta θ used in quartz oscillator, is connected by. Since a twin growth has a preferential direction, a parameter range of θ’ is actually limited as shown in the next section. Here we have chosen a crystal angle of 5 deg., to limit efficiency reduction to 1% for d12-based interaction.
Fig. 2 a) Crystal orientation and twin configuration. b) Coercive stress and efficiency with respect to crystal orientation.
3. Device fabrication
We developed a hydraulic-ram-based apparatus with two heater blocks for applying stress as illustrated in Fig. 3(a) . The crystal is sandwiched and pressed with polished heater plates at high temperature. A real-time imaging system was installed to monitor the twinning process, using crossed polarizers and an incoherent light source, a light-emitting diode [25]. Besides the expected growth along the Z axis as reported in previous literature [23], preferential growth was also observed along the Y direction and reported for the first time [26]. To achieve high-aspect ratio (depth/width) in twinning, which is suitable for a bulk NLO device, a crystal is cut with its Y face rotated by a small angle as mentioned above (θ’ = 5 deg). The substrate has a thickness of 0.5-1.0 mm and the X faces are polished for in situ observation.
Fig. 3 a) Stress application to surface-stepped quartz at high temperature, b) Quartz substrate surface-patterned by mechanical dicing or dry etching.
In the preliminary experiments, periodical steps were defined by mechanical dicing to modify surface stress with a period of 125 µm (Fig. 3(b)). Figures 4(a) -4(c) shows the evolution of twins under a stress of 160 MPa at 375°C. Twins grow from the top surface and propagate to the bottom. Twin propagation becomes isotropic at high temperature (> 400°C), leading to the difficulty of high-aspect ratio, even though the nucleation density of twins are high. We kept the bottom surface at 100°C to suppress unwanted non-patterned twins from the bottom surface and limit the twin nucleation only to the top surface. Successful twin control was achieved with a high aspect ratio and a clear periodical twin structure was obtained for a 125 µm period. One should note that the material has a phase transition point of 573°C where the required stress decreases to zero. We can therefore adjust the coercive stress by changing the process temperature.
To obtain stress contrast on the surface with the finer patterns, the periodic steps were defined by reactive-ion etching. Stress normal to the surface was applied through computer-controlled air piston. Twin depth along the Y axis was controlled by the temperature of the nonpatterned surface. An accuracy of 0.5% in temparature was required for producing a fine structure with a period of 17.8 μm. Figure 5 is a photograph captured by real-time imaging system. A substantially uniform periodicity is observed in the crosssectional picture for a mechanical stress of around 110 MPa. The twins penetrated almost the entire substrate thickness of 800 μm, which indicates an aspect ratio (depth of single polarity-inverted region / period) of 88. Occasional individual twins exhibit remarkable aspect ratios of several hundred. The control becomes more delicate when a number of twins are fabricated at the same time. Currently obtainable aspect ratio for periodic twins is 110, which is already comparable with ferroelectric domains.
To achieve 193 nm VUV, periods finer than 10 µm are essential. For short-pitch twinning, pulsed stress was applied with a rise time less than 0.2 sec, reaching approximately 100-200 MPa at 350°C. Twins however become less stable, presumably due to the increased elastic energy stored in denser twin walls. A stress maintaining module was therefore, elaborated to realize stable VUV emission.
Here we have devised a mechanical module for suppression of backswitching (Fig. 6 ). After fabricating microfine twins at high temperature, heater blocks are cooled down to room temperature while the stress is maintained. The module has a built-in stress-maintaining function, to maintain the structured twins even after releasing the force of the air piston. Uniform stress distribution was achieved with an accurate control of the stress magnitude. The stabilized fine structure with a 9.6 µm period corresponds to 5th order QPM SHG for 193 nm emission.
4. Nonlinear optical results
For designing quartz-based QPM device, it is crucial to find appropriate refractive index dispersion as is the case in ferroelectric-based one. Several devices with different twin periods were prepared, and QPM SHG wavelengths were measured by a tunable Ti:sapphire laser. Of the several dispersion equations reported for crystal quartz, the one of reference [27] matches well the experimental data (filled circles in Fig. 7 ).
Fig. 7 Wavelength dependence of required period for 1st-order QPM SHG: solid curve: calculated by dispersion equation [27], black circle: measured by Ti:sapphire laser.
UV SHG was performed at room temperature with a nonlinear coefficient d11 or d12. Pulsed 532 nm green light from a doubled Nd:YVO4 laser (rep. rate: 3 kHz, pulse width: 60 nsec, maximum average power: 2 W) was launched into the twinned quartz with 11.9 µm period. The twin structure, made visible in Fig. 8(a) by etching in hydrofluoric acid, had a relatively short interaction length of 0.7 mm. Through second-order-QPM SHG, a deep-UV power of 2.2 mW was generated at 266 nm using 1840 mW of green pump power as shown in Fig. 8(b) [28]. It would be worth mentioning at this point that more than two-fold improvement of SHG conversion efficiency would be possible for the same length of QPM structure if the duty cycle were optimized for second-order QPM.For VUV generation, infrared emission from a Ti:sapphire laser (rep. rate: 76 MHz, pulse width: < 3 psec, max. average power: 200 mW) was first frequency-doubled with LiB3O5 (LBO) and then launched into QPM quartz as a fundamental light at 386 nm. The fundamental beam was almost collimated with a Boyd-Kleinmann focusing parameter ξ of 0.083 (horizontal) and 0.5 (vertical), being asymmetric due to walk-off in LBO. For 9.6 μm period the peak efficiency was obtained exactly at the design QPM wavelength of 193.4 nm based on the reported Sellmeier equation [27]. Multiple peaks were observed in the QPM spectrum (VUV power versus UV pump wavelength), indicating inadequate uniformity of the fabricated structure. The highest efficiency was attained at 193.9 nm, corresponding to normalized conversion efficiency of 2.4x10−4 (%/W). QPM SHG performance was plotted in Fig. 9 and a VUV power of 70 µW was generated from 180 mW fundamental power. Although the module prevents us from checking a twin structure by a conventionally-used acid etching, the estimated twinned length was yet around 1-2 mm based on the real-time image. Our stress-application equipment covers up to 10 cm device length, but even uniform stress induces asymmetric twins in the devices due to the anisotropic nature of a crystal quartz. We currently searching optimum configuration to extend the length of twin structures. Device performance will be improved by more accurate control of the twinning process for an appropriate duty ratio, improved uniformity, and a sufficiently large interaction length. Once SHG devices converting UV radiation at 386 nm to VUV radiation at 193 nm with adequate efficiency become available, they will likely displace complicated sum-frequency-generation-based multiple wavelength conversion systems [29]. All-in-line cascaded SHG devices are likely to result in more compact VUV sources.
5. Conclusion
In this paper we have reviewed the principles of twin control and recent progress for QPM structures in crystal quartz. Precisely-controlled twin structures were demonstrated with a high aspect ratio by mechanical stress application. The periodic twin structure enabled unprecedented quasi-phase matching for VUV second-harmonic generation. Our method will be able to open a window to twin-controlled devices even in other crystal families, holding promise for the future development of sophisticated piezoelectric devices.
In celebration of the 50th anniversary of NLO, we presented the shortest emission wavelength, 193 nm, ever obtained with solid-state QPM technology. Crystal quartz, groundbreaking material in the field, returns to the foreground with the twinning technology. We sincerely hope this example of twinned QPM can be extended to other non-ferroelectric materials. The SHG device paves a road to an all-solid-state VUV laser, which would be a more practical alternative to a gas-based ArF excimer laser.
Half a century ago NLO was entirely in the realm of basic research and real-world applications were only possible in the dreams of researchers. Today, after significant technological progress lead to dramatic increases in efficiency and phase-matching flexibility, NLO has impact in the real world in the realm of light sources. In the future, NLO is likely to become more popular and more sophisticated thanks to continued expansion in flexibility of QPM technology.
Acknowledgments
The research of S.K. was partially supported by the Grant-in-Aid for Exploratory Research of the Japanese Ministry of Education, Science, Sports and Culture (No. 23360037). We appreciate Prof. Martin M. Fejer of Stanford University and Prof. Takunori Taira of Inst. for Molecular Science for early-stage overall discussions and Prof. Yoshiaki Uesu of Waseda University and Prof. Roger Route for thoughtful comments on twin control.
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