Abstract
The tight focusing properties of an azimuthally polarized Bessel Gaussian beam phase modulated by annular Walsh function filter is studied numerically by vector diffraction theory. It is observed that upon suitable optimization of order and annular obstruction ratio of an annular Walsh function filter, one can generate multiple sub wavelength scale optical tubes (optical holes) with super long focal depth. Such a focal system is usable for Nano-lithography, particle trapping and transportation, as well as confocal and STED microscopy, microstructure fabrication etc.
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References
Andrews, H.C.: Computer Techniques in Image Processing (Academic, NewYork, 1970)
Ashkin, J.M., Dziedzic, J.E., Bjorkholm, Chu, S.: Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986). https://doi.org/10.1364/OL.11.000288
Beauchamp, K.G.: Walsh Functions and Their Applications (Academic, NewYork, 1985)
Bokor, N., Iketaki, Y., Watanabe, T., Fujii, M.: Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent micro bead. Opt. Express. 13(26), 10440 (2005). https://doi.org/10.1364/opex.13.010440
Calatayud, A., Ferrando, V., Giménez, F., Furlan, W.D., Saavedra, G., Monsoriu, J.A.: Fractal square zone plates. Opt. Commun. 286, 42–45 (2013). https://doi.org/10.1016/j.optcom.2012.09.002
Charles, J.W., Prabakaran, K., Rajesh, K.B., Pandya, H.M.: Generation of sub wavelength super long dark channel using azimuthally polarized annular multi-Gaussian beam. Opt. Quant. Electron. 46(8), 1079–1086 (2013). https://doi.org/10.1007/s11082-013-9827-5
Chojnacki, J., Eggeling, C.: Super-resolution fluorescence microscopy studies of human immunodeficiency virus. Retrovirology (2018).https://doi.org/10.1186/s12977-018-0424-3
Choudhary, D., Mossa, A., Jadhav, M., Cecconi, C.: Bio-molecular applications of recent developments in optical Tweezers. Biomolecules. 9, 23 (2019). https://doi.org/10.3390/biom9010023
Daria, V.R., Rodrigo, P.J., Glückstad, J.: Dynamic array of dark optical traps. Appl. Phys. Lett. 84(3), 323–325 (2004). https://doi.org/10.1063/1.1642752
De, M., Hazra, L.N.: Walsh functions in problems of optical imagery. Opt. Acta. 24, 221–234 (1977a). https://doi.org/10.1080/713819531
De, M., Hazra, L.N.: Real-time image restoration through Walsh filtering. Opt. Acta. 24, 211–220 (1977b). https://doi.org/10.1080/713819540
Fu, M., Wade, G., Ning, J., Jakobs, R.: On Walsh filtering method of decoding CPM signals. IEEE Commun. Lett. 8, 345–347: (2004). https://doi.org/10.1109/LCOMM.2004.828184
Gahagan, K.T., Swartzlander, G.A.: Optical vortex trapping of particles. Opt. Lett. 21, 827–829 (1996). https://doi.org/10.1364/OL.21.000827
Gahagan, K.T., Swartzlander, G.A.: Trapping of low-index microparticles in an optical vortex. J. Opt. Soc. Am. B. 15, 524–534 (1998). https://doi.org/10.1364/JOSAB.15.000524
Gahagan, K.T., Swartzlander, G.A.: Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap. J. Opt. Soc. Am. B 16, 533–537 (1999)
Gao, D., Ding, W., Nieto-Vesperinas, M., et al.: Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects. Light Sci Appl. 6, e17039 (2017). https://doi.org/10.1038/lsa.2017.39
Gould, T.J., Burke, D., Bewersdorf, J., Booth, M.J.: Adaptive optics enables 3D STED microscopy in aberrating specimens. Opt. Express. 20(19), 20998 (2012). https://doi.org/10.1364/oe.20.020998
Hao, X., Antonello, J., Allgeyer, E.S., Bewersdorf, J., Booth, M.J.: Aberrations in 4Pi Microscopy. Opt. Express. 25(13), 14049 (2017). https://doi.org/10.1364/oe.25.014049
Harmuth, H.F.: Transmission of Information by Orthogonal Functions (Springer-Verlag, 1972), p. 31. https://doi.org/10.1007/978-3-642-61974-8$4
Hazra, L.N., Banerjee, A.: Application of Walsh function in generation of optimum apodizers. J. Opt. 5, 19–26 (1976)
Hazra, L.N.: A new class of optimum amplitude filters. Opt. Commun. 21, 232–236 (1977). https://doi.org/10.1016/0030-4018(77)90270-x
Hazra, L.N.: Walsh filters in tailoring of resolution in microscopic imaging. Micron. 38, 129–135 (2007). https://doi.org/10.1016/j.micron.2006.07.003
Jinyong Lin, L., Shao, SufangQiu, X., Huang, M., Liu, Z., Zheng, D., Lin, Y., Xu, Z., Li, Y., Lin: Rong Chen, and Shangyuan Feng.Application of a near-infrared laser tweezers Raman spectroscopy system for label-free analysis and differentiation of diabetic red blood cells. Biomed. Opt. Express. 9, 984–993 (2018). https://doi.org/10.1364/BOE.9.000984
Khonina, S.N., Ustinov, A.V.: Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams. ISRN Optics 2013, 1–6 (2013). https://doi.org/10.1155/2013/185495
Klar, T.A., Jakobs, S., Dyba, M., Egner, A., Hell, S.W.: Fluorescence microscopy with diffraction resolutionbarrier broken by stimulated emission. Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210: (2000). https://doi.org/10.1073/pnas.97.15.8206
Lalithambigai, K., Anbarasan, P.M., Rajesh, K.B.: Effect of complex phase plate on tight focusing of azimuthally polarized double ring shaped beam. Optik - International Journal for Light and Electron Optics. 125(15), 4047–4050 (2014). https://doi.org/10.1016/j.ijleo.2014.03.002
Lalithambigai, K., Anbarasan, P.M., Rajesh, K.B.: Creation of super-length optical tube by phase modulated azimuthally polarized beam with multi-zone phase filter. Optik. 126(5), 554–557 (2015). https://doi.org/10.1016/j.ijleo.2015.02.009
Liu, U.Q., Yu, L., Ma, Z.C., Chen, Q.D.: Silicon three-dimensional structures fabricated by femtosecond laser modification with dry etching. Appl. Opt. 56, 2157–2161 (2017). https://doi.org/10.1364/AO.56.002157
Liu, J., Li, Z.: Controlled Mechanical Motions of Micro particles in Optical Tweezers. Micromachines. 9(5), 232, (2018). https://doi.org/10.3390/mi9050232
Machado, F., Ferrando, V., Giménez, F., Furlan, W.D., Monsoriu, J.A.: Multiple-plane image formation by Walsh zone plates. Opt. Express. 26, 21210–21218 (2018). https://doi.org/10.1364/OE.26.021210
Mandelbrot, B.B.: The Fractal Geometry of Nature: (Freeman, 1982)
Mohanty, S.K., Verma, R.S., Gupta, P.K.: Trapping and controlled rotation of low-refractive-index particles using dual line optical tweezers. Appl. Phys. B. 87(2), 211–215 (2007). https://doi.org/10.1007/s00340-007-2617-7
Mukherjee, P., Hazra, L.N.: Farfield diffraction properties of annular Walsh filters. Adv. Opt. Technol. 2013, 360450 (2013). https://doi.org/10.1155/2013/360450
Mukherjee, P., Hazra, L.N.: Self-similarity in radial Walsh filters and axial intensity distribution in the farfield diffraction pattern. J. Opt. Soc. Am. A. 31(2), 379–387 (2014a). https://doi.org/10.1364/JOSAA.31.000379
Mukherjee, P., Hazra, L.N.: Self-similarity in the farfield diffraction patterns of annular Walsh filters. Asian J. Phys. 23(4):543–560 (2014b)
Mukherjee, P., Hazra, L.N.: Self-similarity in transverse intensity distributions in the far field diffraction pattern of radial Walsh filters. Adv. Opt. (2014c). https://doi.org/10.1155/2014c/352316
Neuman, K.C., Block, S.M.: Optical trapping. Rev. Sci. Instrum. 75(9), 2787–2809: (2004). https://doi.org/10.1063/1.1785844
Neupane, B., Chen, F., Sun, W., Chiu, D.T., Wang, G.: Tuning donut profile for spatial resolution in stimulated emission depletion microscopy. Rev. Sci. Instrum. 84(4), 043701 (2013). https://doi.org/10.1063/1.4799665
Nussenzveig, H.M.: Cell membrane biophysics with optical tweezers. Eur. Biophys. J. 47, 499–514 (2018). :https://doi.org/10.1007/s00249-017-1268-9
Peng, F., Yao, B., Yan, S., Zhao, W., Lei, M.: Trapping of low-refractive-index particles with azimuthally polarized beam. J. Opt. Soc. Am. B. 26, 2242–2247 (2009). https://doi.org/10.1364/JOSAB.26.002242
Rui, G., Wang, Y., Wang, X., Gu, B., Cui, Y.: Trapping of low-refractive-index nanoparticles in a hollow dark spherical spot. J. Phys. Commun. 2(6), 065015 (2018). https://doi.org/10.1088/2399-6528/aaccd1
Saavedra, G., Furlan, W.D., Monsoriu, A.: Fractal zone plates. Opt. Lett. 28, 971–973 (2003). https://doi.org/10.1364/OL.28.000971
Uozumi, J., Sakurada, Y., Asakura, T.: Fraunhofer diffraction from apertures bounded by regular fractals. J. Mod. Opt. 42, 2309–2322 (1995). https://doi.org/10.1080/09500349514552001
Walsh, J.L.: A closed set of normal orthogonal functions. Am. J. Math. 45, 5–24 (1923)
Wang, T., Kuang, C., Hao, X., Liu, X.: Focusing properties of cylindrical vector vortex beams with high numerical aperture objective. Optik. 124(21), 4762–4765 (2013). https://doi.org/10.1016/j.ijleo.2013.01.070
Wu, M., Ling, D., Ling, L., et al.: Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers. Sci Rep. 7, 42930 (2017). https://doi.org/10.1038/srep42930
Xu, J., Jiang, L., Zhu, H., Liu, L., Hu, J., Wang, H., Zhuang, S.: Experimental generation and observation of a super-resolution optical tube. J. Innov. Opt. Health Sci. 09, 1641002 (2016). https://doi.org/10.1142/s1793545816410029
Xue, Y., Kuang, C., Li, S., Gu, Z., Liu, X.: Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy. Opt. Express. 20(16), 17653 (2012). https://doi.org/10.1364/oe.20.017653
Youngworth, K.S., Brown, T.G.: Focusing of high numerical aperture cylindrical-vector beams. Opt. Express. 7, 77–87 (2000). https://doi.org/10.1364/OE.7.000077
Yu, Y., Zhan, Q.: Creation of identical multiple focal spots with prescribed axial distribution. Sci. Rep. 5, 14673 (2015a). https://doi.org/10.1038/srep14673
Yu, Y., Zhan, Q.: Generation of uniform three-dimensional optical chain with controllable characteristics. J. Opt. 17(10), 105606 (2015b). https://doi.org/10.1088/2040-8978/17/10/105606
Yu, Y., Huang, H., Zhou, M., Zhan, Q.: Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps. Opt. Commun. 407, 398–401 (2018) https://doi.org/10.1016/j.optcom.2017.09.075
Zhu, L., Sun, M., Zhu, M., Chen, J., Gao, X., Ma, W., Zhang, D.: Three-dimensional shape-controllable focal spot array created by focusing vortex beams modulated by multi-value pure-phase grating. Opt. Express. 22, 21354–21367 (2014). https://doi.org/10.1364/OE.22.021354
Zunino, L., Garavaglia, M.: Fraunhofer diffraction by Cantor fractals with variable lacunarity. J. Mod. Opt. 50, 717–727 (2003). https://doi.org/10.1080/09500340210130084
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Thiruarul, D., Rajesh, K.B., Lavanya, M. et al. Generation of ultra-long multiple optical tubes using annular Walsh function filters. Opt Quant Electron 52, 396 (2020). https://doi.org/10.1007/s11082-020-02507-1
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DOI: https://doi.org/10.1007/s11082-020-02507-1