Three-level filter for increased depth of focus and Bessel beam generation
نویسندگان
چکیده
A novel axially-symmetric filter for increasing focal depth and generating an approximation to a Bessel beam is proposed. It consists of an array of rings of strength –1,0 and 1. The design is based on an analytic solution, and combines high resolution in the transverse direction with good efficiency. One presented design increases the depth of focus compared with a standard lens by more than 30 times, with a very flat axial intensity distribution over this range. Effects of discretization are discussed. Various different approaches to increasing depth of focus are compared, to put the new design into perspective. © 2012 Optical Society of America OCIS Codes: (050.1220) Apertures; (050.1940) Diffraction; (070.2580) Paraxial wave optics; (110.6980) Transforms; (350.6980) Transforms. References and links 1. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photon. Rev. 4(4), 529–547 (2010). 2. J. H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954). 3. J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A Math. Phys. Sci. 248(1252), 93–106 (1958). 4. G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 3 18, 1–10 (1841). 5. J. W. S. Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872). 6. G. C. Steward, “IV Aberration diffraction effects,” Phil. Trans. Roy. Soc. London Ser. A 225(626-635), 131–198 (1926). 7. E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66(2), 145–149 (1953). 8. B. J. Thompson, “Diffraction by semitransparent and phase annuli,” J. Opt. Soc. Am. 55(2), 145–149 (1965). 9. G. Yang, “An optical pickup using a diffractive optical element for a high-density optical disc,” Opt. Commun. 159(1-3), 19–22 (1999). 10. H. F. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40(31), 5658–5662 (2001). 11. E. R. Dowski, Jr. and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34(11), 1859–1866 (1995). 12. C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2(4), 105–112 (1978). 13. J. Durnin, “Exact solutions for nondiffracting beams. I. the scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). 14. C. J. R. Sheppard, “Binary phase filters with a maximally-flat response,” Opt. Lett. 36(8), 1386–1388 (2011). 15. C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, “Three-zone pupil filters,” Opt. Commun. 281(14), 3623–3630 (2008). 16. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987). 17. A. J. Cox and J. D’Anna, “Constant-axial-intensity nondiffracting beam,” Opt. Lett. 17(4), 232–234 (1992). 18. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). 19. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). 20. M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–168. 21. R. Boivin and A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta (Lond.) 27, 857 (1980). 22. C. J. R. Sheppard and Z. S. Hegedus, “Axial behaviour of pupil plane filters,” J. Opt. Soc. Am. A 5(5), 643–647 (1988). #172811 $15.00 USD Received 17 Jul 2012; revised 23 Aug 2012; accepted 23 Aug 2012; published 19 Nov 2012 (C) 2012 OSA 3 December 2012 / Vol. 20, No. 25 / OPTICS EXPRESS 27212 23. Y. S. Xu, J. Singh, C. J. R. Sheppard, and N. G. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007). 24. V. F. Canales, J. E. Oti, and M. P. Cagigal, “Three-dimensional control of the focal light intensity distribution by analytically designed phase masks,” Opt. Commun. 247(1-3), 11–18 (2005). 25. Z. Bouchal, J. Wagner, and M. Olivik, “Bessel beams in the focal region,” Opt. Eng. 34(6), 1680–1688 (1995). 26. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007). 27. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011). 28. C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43(3), 525–536 (1996). 29. M. R. Foreman, S. S. Sherif, P. R. T. Munro, and P. Török, “Inversion of the Debye-Wolf diffraction integral using an eigenfunction representation of the electric fields in the focal region,” Opt. Express 16(7), 4901–4917 (2008). 30. T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009). 31. J. Wang, W. Chen, and Q. W. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express 18(21), 21965–21972 (2010). 32. H. F. Wang, L. Shi, B. Luk`yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008). 33. C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, “Bessel beams: Effects of polarization,” Opt. Commun. 282(24), 4647–4656 (2009). 34. X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010). 35. C. J. R. Sheppard and S. Rehman, “Highly convergent focusing of light based on rotating dipole polarization,” Appl. Opt. 50(22), 4463–4467 (2011).
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