Compact flattop laser beam shaper using vectorial vortex Wen Cheng,* Wei Han, and Qiwen Zhan Electro-Optics Program, University of Dayton, 300 College Park, Dayton, Ohio 45469, USA *Corresponding author:
[email protected] Received 18 March 2013; revised 13 May 2013; accepted 14 May 2013; posted 15 May 2013 (Doc. ID 187243); published 26 June 2013
In this paper, we demonstrate a compact flattop beam shaper to realize two-dimensional flattop focus through generating a second order full Poincaré beam. Liquid crystal material is used in the device as the voltage-dependent birefringent material to provide appropriate phase retardation modulation. The beam shaper is fabricated and tested. Experimental results show that high quality flattop profiles can be obtained with steep edge roll-off. The tolerance of different input beam sizes of the beam shaper is also verified in the experimental demonstration. © 2013 Optical Society of America OCIS codes: (140.3300) Laser beam shaping; (160.3710) Liquid crystals; (260.1960) Diffraction theory; (260.5430) Polarization; (230.6120) Spatial light modulators. http://dx.doi.org/10.1364/AO.52.004608
1. Introduction
Laser beams with flattop profiles are often desired in many applications including lithography, laser/ material processing, medical treatment, and national security [1–3]. One common way to generate such uniform power distribution is the conversion from a Gaussian laser source by the use of a flattop laser beam shaper. Several types of beam shaper have been proposed and manufactured that utilized refractive or diffractive optical devices with spatially homogeneous polarization as the input [4–7]. Flattop shaping techniques with spatially variant polarization that require appropriate phase retardation modulation also have been proposed and demonstrated recently [8–10]. Liquid crystal (LC) material, which has been widely used in electro-optics devices such as spiral phase plate and LC cell structures [11,12], is a popular choice to provide such a phase modulation. In our previous work [13], we proposed and experimentally demonstrated the method of generating two-dimensional flattop focusing with the second 1559-128X/13/194608-05$15.00/0 © 2013 Optical Society of America 4608
APPLIED OPTICS / Vol. 52, No. 19 / 1 July 2013
order full Poincaré (FP) beams by using a LC spatial light modulator (SLM). FP beams are a new class of beams whose cross sections contain all polarization states on the Poincaré sphere, which has been proposed and studied recently [14]. The second order FP beam is a beam whose states of polarization within the beam cross-section span the entire surface of the Poincaré sphere twice. By linearly superimposing horizontally (x-) polarized fundamental Gaussian (LG00 ) and vertically (y-) polarized second order Laguerre Gaussian (LG02 ) beams, a second order FP beam can be generated. When focused with a low numerical aperture (NA) lens, the x-polarized LG00 produces a solid spot while the y-polarized LG02 contributes a concentric donut shape distribution. With appropriate relative weighting between these two orthogonally polarized components and optimal imaging distance, a flattop profile with good intensity uniformity and steep edge roll-off had been realized in the reported work. The SLM served well for the purpose of proof-of-principle demonstration. However, the LC SLM itself is expensive and bulky, making it unrealistic for practical beam shaping applications. The LC based cell structure would be a good alternative in this situation because of its compactness, low cost, and high efficiency.
Fig. 1. Phase pattern loaded into SLM for second order FP beam generation: (a) continuous phase (0–2π) and (b) four-level quantized phase. (The four-level phase is 0, 0.5π, π, and 1.5π).
2. Working Principles of LC Beam Shaper
In our proposed technique, LC SLM was used for the second order FP beam generation. The phase pattern that was loaded onto SLM is shown in Fig. 1(a). Embedded in the phase pattern are two phase functions, generating second order FP beam and a lens function to achieve a defocusing effect to overcome the size mismatch of LG00 and LG02 mode. For practical implementation purpose, the phase has to be quantized for potential beam shaper design. A four-level phase quantization process [Fig. 1(b)] has been successfully verified, both theoretically and experimentally using LC SLM [15]. This four-level quantized phase pattern can be realized with a LC based birefringent wave plate whose optic axis depends on an externally applied electric field. The LC beam shaper cell structure we propose consists of a LC layer sandwiched by two pieces of indium tin oxide (ITO) coated glass (25 × 25 × 1.1 mm from Cytodiagnostics). The thickness of the coated ITO layer is around 30 nm. The illustration of the proposed cell structure is shown in Fig. 2. In order to obtain a pure phase modulation and avoid amplitude or polarization modulation, the directors of LC molecules need to be homogeneously aligned (untwisted). In other words, the rubbing directions of two ITO glasses are parallel. The LC device becomes a wave plate that features a voltagedependent birefringence. Therefore, the incident light would experience ordinary and extraordinary refractive indices for orthogonally polarized components. For light polarized along the directors of LC molecules (extraordinary light), the desired phase pattern would be imposed onto the beam through engineering the voltage distribution on the ITO glass. Meantime, for light polarized in the orthogonal direction (ordinary light), the wave front does not change in distribution except for a piston phase. As mentioned above, the desired second order FP beam can be generated through the superposition of orthogonally polarized LG00 and LG02 beam. As
in the proposed LC device, the second order FP beam will be generated by the superposition of both extraordinary and ordinary components. After being focused by a lens, the extraordinary field will become a donut-like Laguerre–Gaussian field while the ordinary field remains a Gaussian shape. By introducing a defocus function to match the sizes of intensity distribution of both beams, flattop can be achieved by directly superimposing the intensity patterns at optimal imaging plane. To realize the design proposed in Fig. 2, the ITO electrode on one piece of the glass is lithographically patterned into eight spiral-shaped regions that are shown in Fig. 3. Every four contiguous regions realize a 2π linear phase change with properly chosen driving voltages. Therefore, the entire design will impose a 2 × 2π phase modulation around the center of the design to generate LG02 beam. Adjacent regions are separated by a 100 μm insulation gap (blue areas shown in Fig. 3) where ITO is removed from glass substrate. The entire spiral pattern has a 10 μm narrow annular gap near the outer edge
Fig. 2. Illustration of the proposed beam shaper cell structure. 1 July 2013 / Vol. 52, No. 19 / APPLIED OPTICS
4609
Phase Retardation 2 π∆nd/ λ
15
X: 0.7 Y: 11.12
10 X: 1.3 Y: 6.659
5
0 0
1
2 3 4 Liquid Crystal Driving Voltage (V)
5
6
Fig. 4. Phase retardation versus LC driving voltage with cell thickness of 12 μm. Fig. 3. Illustration of proposed ITO electrode patterning. (Blue lines) 100 μm insulated gap where ITO is removed.
of the structure. Since the resistance of ITO is inversely proportional to the width, the narrow gap behaves like a large resistance. The width of each gap is carefully designed to be the same so that each spiral region of the ITO patterning is connected to the adjacent one through a fixed resistance. When external voltage is applied to the patterned ITO glass with the other unpatterned ITO coated glass grounded, a linear voltage drop will be present across each four spiral regions on the ITO layer. In other words, the design becomes a circuit with equal resistances in series so that evenly spaced driving voltages can be obtained on the spiral regions. By choosing an appropriate input voltage range where the phase retardation change of 2π is linearly proportional to the driving voltage, the LC cell structure would be able to realize 2π phase change with four contiguous spiral regions or 2 × 2π with the entire design. 3. Fabrication of LC Beam Shaper
Nematic LC mixture E7 from Merck is chosen in this design. The plot of the retardation 2πdΔn∕λ of the 12 μm thick LC cell with respect to the applied voltage of the LC cell is shown in Fig. 4. d is the thickness of the LC cell structure and λ is the wavelength of the laser beam. Δn is the birefringence of the chosen LC material, which is 0.21 for 633 nm illumination. Since a linear voltage drop is required for a 2π phase change, voltage drops of 0.7, 0.9, 1.1, and 1.3 V are chosen to be applied on each contiguous spiral region. Proper photolithography and chemical etching recipes are experimentally developed to remove ITO from substrate for specific areas (blue gaps shown in Fig. 3). Four gold pads at the bottom of the sample with slim gold trails are deposited to apply external input voltage. The lithographically patterned piece (Fig. 5) 4610
APPLIED OPTICS / Vol. 52, No. 19 / 1 July 2013
Fig. 5. Fabricated ITO electrodes with detailed structure viewed under a white light interferometer. Dark slits are the areas where ITO layer (∼30 nm) is removed.
is then rubbed and combined with another piece of ITO coated glass to form the beam shaper cell structure. LC material E7 is then filled into the cell structure with two 12 μm spacers placed between the two pieces to control the cell thickness. The experimental setup to test the performance of the beam shaper sample is schematically illustrated in Fig. 6. A half-wave plate is placed in front of the sample in order to adjust the relative weighting between the two orthogonally polarized components. The beam shaper is properly mounted and connected to a designed circuit where the voltage drop from 1.3 to 0.7 V is supplied for four contiguous spiral regions accurately. A lens with 400 mm focal length is used to bring the generated FP beam near the focal plane.
Fig. 6. Experimental setup of testing the performance of the beam shaper. Laser: linearly polarized HeNe laser; Iris: adjust the input beam size; HW: half-wave plate; CCD: Spiricon camera.
(a) 1 1 0.8
0.8 0.6
0.6
0.4
0.4
0.2 0 -200
0.2 0
200
x ( µ m)
-200
0
200
0
y ( µ m)
(b) Fig. 7. Flattop profile (a) 2D view and (b) 3D view obtained by testing the fabricated beam shaper.
One CCD (Spiricon) camera is translated to find the optimal position for high quality flattop profile. 4. Results and Discussion
A flattop beam profile with input beam size of 6 mm has been obtained with steep edge roll-off (Fig. 7). The flattop profile diameter is about 107 μm. The calculated β value is 3.18. The β value is defined to provide a relationship between the desired flattop beam size and the diffraction-limited beam size: β
p 2 2π r0 y0 ; λf
(1)
where r0 is the 1∕e2 intensity radius of the incident Gaussian beam and y0 is the half width of the desired output flattop profile. In our case, the small β value indicates the significant role that diffraction plays. The conversion efficiency of the beam shaper is measured as 76%, which is defined as the ratio of output power with and without the fabricated beam shaper. The loss of conversion efficiency may be due to the reflection caused by index mismatch between multiple interfaces such as air-to-glass, glass-to-ITO, and ITO-to-LC. The patterned ITO electrode with complex fine features may cause scattering and diffraction loss as well. Further improvement can be done by putting index matching LC molecules for ITO layer and depositing AR coating layer onto the front and back sides of the beam shaper to increase transmission. In our proposed beam shaper design, a spatially variant polarization-based technique is utilized.
Fig. 8. 3D flattop profile and corresponding line scan of two different input beam diameters: (a) 5 mm and (b) 6.5 mm.
One advantage of this technique is that the two orthogonally polarized component of the incident laser beam would propagate separately without interfering with each other. Moreover, the desired phase modulation does not require any information about input beam size. As a result, flattop profiles can be achieved with different input beam sizes by slightly adjusting the relative weighting between two orthogonal components and finding optimal image distance. Flattop profiles of two different input beam sizes of 5 and 6.5 mm are shown in Fig. 8 to illustrate this feature. The associated flattop size is 137 and 98 μm, respectively. And the β values are calculated to be 3.73 and 3.15, respectively. 5. Conclusions
In summary, we demonstrate a compact flattop beam shaper to realize two-dimensional flattop beam focusing through generating the second order FP beam. A LC based beam shaper cell structure has been designed, fabricated, and tested. Experimental results show that high quality flattop profile can be obtained with steep edge roll-off. The tolerance of the proposed beam shaper to different beam sizes shaper is also verified in the experimental demonstration. The proposed and experimentally verified LC beam shaper has the potential to become a promising candidate for compact and low-cost flattop beam shaping in areas such as laser processing/machining, lithography, and medical treatment. 1 July 2013 / Vol. 52, No. 19 / APPLIED OPTICS
4611
The authors gratefully thank Dr. Andrew M. Sarangan and Dr. Rola Aylo from the University of Dayton for their discussion and helps during the fabrication process. W. Cheng has been supported in part by the University of Dayton Office for Graduate Academic Affairs through the Graduate Student Summer Fellowship Program. References 1. F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000). 2. L. A. Romero and F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996). 3. O. Homburg and T. Mitra, “Gaussian-to-top-hat beam shaping: an overview of parameters, methods, and applications,” Proc. SPIE 8236, 82360A (2012). 4. C.-Y. Han, Y. Ishii, and K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983). 5. X. Tan, B. Y. Gu, G. Z. Yang, and B. Z. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995). 6. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488–5499 (2000).
4612
APPLIED OPTICS / Vol. 52, No. 19 / 1 July 2013
7. S. Zhang, G. Neil, and M. Shinn, “Single-element laser beam shaper for uniform flat-top profiles,” Opt. Express 11, 1942–1948 (2003). 8. B. Hao and J. Leger, “Polarization beam shaping,” Appl. Opt. 46, 8211–8217 (2007). 9. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009). 10. J. Dai and Q. Zhan, “Beam shaping with vectorial vortex beams under low numerical aperture illumination condition,” Proc. SPIE 7062, 70620D (2008). 11. Q. Wang, X. W. Sun, and P. Shum, “Generating doughnutshaped beams with large charge numbers by use of liquid-crystal spiral phase plates,” Appl. Opt. 43, 2292–2297 (2004). 12. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27, 1351–1353 (2002). 13. W. Han, W. Cheng, and Q. Zhan, “Flattop focusing with full Poincaré beams under low numerical aperture illumination,” Opt. Lett. 36, 1605–1607 (2011). 14. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincare beams,” Opt. Express 18, 10777–10785 (2010). 15. W. Cheng, W. Han, and Q. Zhan, “Generation of flattop focusing with second order full Poincaré beams,” Proc. SPIE 8130, 81300D (2011).
