Optics Communications 290 (2013) 115–117
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Adaptive beam shaper based on a single liquid crystal cell Michael Zenou a, Mitya Reznikov b,n, Michael Manevich b, Joseph Varshal b, Yuriy Reznikov c, Zvi Kotler a a b c
New Technologies Group, Corp R&D, Orbotech Ltd., Yavne 81101, Israel Micro&Nano Technology Center, Lev Institute-JCT, Jerusalem 91160, Israel Department of Crystals, Institute of Physics of National Academy of Science of Ukraine, Kyiv 03028, Ukraine
a r t i c l e i n f o
Article history: Received 12 August 2012 Received in revised form 9 October 2012 Accepted 10 October 2012 Available online 31 October 2012
We describe a method allowing rapid transformation of a Gaussian input laser beam into a variety of beam proﬁles such as top-hat and ring-shaped. A liquid crystal cell with a simple binary phase structure was designed and prepared using microlithographic processes. The new design provides an electrically tunable, variable mode, beam shaping device with millisecond response time (ton 5 ms and toff 35 ms). & 2012 Elsevier B.V. All rights reserved.
Keywords: Gaussian beam Liquid crystal Beam shaper Adaptive optics
1. Introduction Diffractive optical elements (DOEs) are commonly used for the transformation of a Gaussian beam to a speciﬁc target shape such as ﬂat-top proﬁle [1–4]. Refractive optical designs have also been shown to provide even higher quality single shape transformations [5,6]. Such laser beam shaping elements are important components of modern optical systems. For example, top-hat beam proﬁles are used extensively in laser micromachining applications in order to increase process quality and efﬁciency [7,8]. Other proﬁles, such as the doughnut-shaped one, are used for trapping small particles [9,10]. However, in many cases it is advantageous to have adaptive control on the laser beam proﬁle. This allows for the possibility to dynamically change the ﬁnal intensity distribution to meet speciﬁc intensity proﬁles to ﬁt a given application . One approach to adaptive, tunable beam shaping is using a Spatial Light Modulator (SLM)  with its capacity to locally control the phase of each pixel of the device. The SLM can provide a rather large range of possibilities from adaptive lenses and multi-beam splitters to top-hat beam shapers [7,13,14]. In many cases, however, the diversity offered by an SLM is not needed. In laser machining, for example, one might only be interested in radial symmetry beam proﬁles such as Gaussian, top-hat and doughnutshaped. In this paper we demonstrate a possibility to replace the complex and expensive SLM construction with a single LC cell, for certain beam shaping applications. The proposed adaptive
Corresponding author. E-mail addresses: [email protected]
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0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.10.018
single-cell LC-based DOE device can provide a continuous transition from an incoming beam shape proﬁle to a few pre-designed shapes by applying a speciﬁc voltage across the cell.
2. Device description The liquid crystal cell (Fig. 1) is made of two glass substrates: the ﬁrst one is conventional plain glass and the second one is designed with a binary micro-structure on its surface facing the ﬁrst substrate. The binary structure is prepared using photolithography and precision glass wet etching (Fig. 2). Both glass substrates are coated with thin-ﬁlm ITO electrodes and aligning polyimide (PI) layers that are unidirectionally rubbed before ﬁlling of the cell. The gap between substrates is controlled by spacers (either polymer rods or speciﬁcally prepared glass ‘‘thresholds’’ at the edges of the substrate with a micro-structure). The cell is ﬁlled with the nematic liquid crystal 5CB in the isotropic phase with subsequent slow cooling to the nematic phase. The cell shows homogeneous alignment in the direction of PI rubbing. The LC molecules are aligned along the rubbing direction of the alignment layer when no voltage is applied to the cell. The LC refractive index in this case is n(V¼0) ¼1.72 and as the LC molecules start to re-orient under the effect of the electric ﬁeld, the refractive index changes. The refractive index decreases as the applied voltage increases until the LC reaches an almost homeotropic state (LC molecules are parallel to the electric ﬁeld and normal to the substrate surface) where it approaches a minimal value of n ¼1.51 . Thus the refractive index changes from a
M. Zenou et al. / Optics Communications 290 (2013) 115–117
Fig. 1. Device consists of two principal layers, a binary diffractive structure layer in blue and a homogeneous layer of nematic LC in grey; (top) 3D representation and (bottom) cross section. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)
Fig. 3. Calculated beam proﬁle as a function of n2(V). For system parameters see the text.
Table 1 Parameters of the DOE device. Thickness of binary structure [mm] Type of liquid crystal LC refractive index range Thickness of LC cell [mm] Applied voltage range [V]
Fig. 2. Schematic structure of adaptive LC DOE device.
maximal value at V¼ 0 to a minimum one at the homeotropic state (corresponding to a high applied voltage). By changing the applied voltage it is possible to continuously change the intensity proﬁle. By spanning the voltage range one can get a desired output intensity proﬁle: a ﬂat-top, ring-like, or a hot-point.
3. Theory and design The present device design has four parameters: the disk radius, R0, the ring internal and external radii, R1 and R2 respectively, and the binary structure height, h. The phase shift imposed on the incoming beam is deﬁned by the refractive index n1 of the substrate and the tunable refractive index n2(V) of the LC. The phase shift as a function of voltage is given by ( n1 h, r oR0 and R1 o r o R2 2p jðV,rÞ ¼ : ð1Þ n R0 o r oR1 and r 4 R2 l 2 ðVÞh, Varying the parameter h is equivalent to changing the refractive index of the liquid crystal, n2(V), which is voltage dependent and tunable. This is clearly seen from the formula describing the optical phase change
DjðV Þ ¼
ðn2 ðV Þn1 Þh:
By varying the applied voltage V, it is possible to ﬁne-tune and compensate for any possible change or to compensate for tolerances in the step height and thereby restore any required beam shape. In this sense the device can be said to be robust to variations in step height. If one combines a converging lens with a DOE device, a collimated input Gaussian beam is transformed at the focal plane into a desired beam shaped intensity distribution. This effect is explained by the Fraunhofer diffraction theory . Due to the circular symmetry of the problem, the ﬁnal shape of the beam is given by the zero order Hankel transform of the transmission
2.5 5CB 1.51–1.72 4–25 0–2
function. Consider, for example, the special case where the binary step structure has a height h ¼ l/2Dn, which indicates a phase shift of p rad. Here the transform gets a rather simple form with the intensity proﬁle at focal plane given by Z R2 Z R0 GBS 0 kÞ ¼ G0 kÞ2 dr rJ 0 ðkrÞGðrÞ2 dr rJ 0 ðkrÞGðrÞ: ð2Þ 0
Here G (k) is the Hankel transform of the input Gaussian and J0 is the zero order Bessel function. Eq. (2) describes an optimal tophat proﬁle when a proper choice of the disc and ring diameters is made. In Fig. 3 we show the calculated intensity proﬁles for different voltage values across the cell. The cell parameters are as follows: R0 ¼0.5 mm, R1 ¼0.9 mm, R2 ¼1.2 mm, h¼2.5 mm and n1 ¼ 1.45. The input beam is a Gaussian with waist of 1.3 mm at a wavelength of 532 nm. The voltage scan results in a refractive index (n2) change from 1.6 to 1.68. Accordingly the beam shape at the focal plane changes gradually from ring-like to top-hat and back to Gaussian. We have chosen a speciﬁc set of parameters to allow such a transition from ring to top-hat shape in the fabricated device.
4. Experimental We summarize the relevant parameters of the dynamic beam shaper LC cell in Table 1. The laser source is a frequency doubled passively Q-switched Nd:YAG laser with high beam quality, M2o1.2. The 2.6 mm wide collimated beam is linearly polarized in the plane of the nematic LC director. The DOE-LC cell was fabricated with the parameters as described above corresponding to the data in Fig. 3. The laser beam traversing the cell is then focused by a plano-convex lens (focal length of 400 mm) and the resulting intensity proﬁle is analyzed by a beam proﬁler (Spiricon SP620U). Sinusoidal voltage at 10 kHz is applied to the cell with the voltage amplitude spanning the range from 0 V to 2 V. Fig. 4 depicts typical beam proﬁles obtained at different values of applied voltage. The voltage amplitudes were chosen to demonstrate
M. Zenou et al. / Optics Communications 290 (2013) 115–117
Fig. 4. Measured beam proﬁles at the focal plane for different applied voltages: (a)V ¼0 V; (b)1.3 V; (c) 1.5 V and (d) 2 V.
transition from Gaussian to a ring (V¼1.3 V), then to a top-hat (V¼1.5 V) and ﬁnally at 2 V to a proﬁle showing peak intensity on top of ﬂat pedestal. In all cases there is good correspondence with the calculated results. The cell response time was determined by measuring intensity of light passing the LC cell placed between crossed polarizers. The direction of the polarizer was set at an angle of 451 to the LC cell rubbing direction. Light intensity was registered by a fast photodiode behind the analyzer. The time dependence of the light behind the analyzer was reconstructed to give the time dependence of the LC phase retardation, from which the characteristic time of LC director rotation was obtained . This technique was used to measure both ON- and OFF-times. All the physical information about the LC cell is in the OFF-time value, which depends on the cell gap, viscosity and elastic constants of the LC. ON-time depends on the OFF-time and the amplitude of the applied voltage. For the cell gap of 4 mm, OFF-time of the LC beam shaper device was 35 ms. ON-time for the same cell and the applied voltage of 5 V was 4.5 ms.
5. Conclusions We have designed and built an adaptive beam shaper based on a special binary DOE embedded in a liquid crystal cell. Such a device can be used for fast dynamic modiﬁcation of an input Gaussian laser beam into various output beam proﬁles at the focal plane. Speciﬁcally, transformations to top-hat and ring-like proﬁles were shown. This general concept can serve other beam shaper designs. This tunable LC based device can potentially serve well in other phase forming applications, such as generating reconﬁgurable high ˜as et al. . intensity optical spikes as described recently by Ban
Acknowledgment This work was supported by Grant no. 43826 from the Ministry of Industry of the State of Israel, Program ‘‘Liquid Crystal Devices for Laser Micromachining’’. Authors would also like to thank Matt Worden for help in the preparation of the manuscript. References  R. Saint-Denis, N. Passilly, M. Laroche, T. Mohammed-Brahim, K. Ait-Ameur, Applied Optics 45 (2006) 8136.  W.B. Veldkamp, C.J. Kastner, Applied Optics 21 (1982) 345.  W.B. Veldkamp, Applied Optics 21 (1982) 3209.  J. Cordingley, Applied Optics 32 (1993) 2538.  J.A. Hoffnagle, C.M. Jefferson, Applied Optics 39 (2000) 5488.  S. Zhang, G. Neil, M. Shinn, Optics Express 11 (2003) 1942. ¨  G. Raciukaitis, E. Stankevicius, P. Gecys, M. Gedvilas, C. Bischoff, E. Jager, ¨ U. Umhofer, F. Volklein, Proceedings of LPM 11 (2010) 10–96.  R.J. Beck, J.P. Parry, A. Waddie, W.N. Macpherson, N.J. Weston, J.D. Shephard, D.P. Hand, Proceedings of LPM 11 (2010) 10–34. ¨  P.J. Rodrigo, V.R. Daria, J. Gluckstad, Optics Express 12 (2004) 1417.  D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, T. Tschudi, Optics Letters 27 (2002) 1351.  W. Zhao, P. Palffy-Muhoray, Applied Physics Letters 63 (12) (1993) 1613.  T.-C. Poon, R. Juday, T. Hara, Applied Optics 37 (1998) 7471.  J. Liang, R.N. Kohn Jr., M.F. Becker, D.J. Heinzen, Applied Optics 49 (2010) 1323.  F. Dickey, S.G. Holswade, Laser Beam Shaping—Theory and Techniques, Marcel Dekker, New York, USA, 2000.  Shin-Tson Wu, Deng-Ke Yang, Fundamentals of Liquid Crystal Devices, Wiley, West Sussex, England, 2006, (Chapter 6).  J. Goodman, Introduction to Fourier Optics. Roberts and Company Publishers, New York, USA, 2004. (Chapter 5).  L.M. Blinov, V.G. Chigriniov, Electrooptic Effects in Liquid Crystal Materials, Springer-Verlag, 1993. ˜ as, D. Palima, J. Gluckstad, ¨  A. Ban Optics Express 20 (2012) 9705.