Journal of Atomic and Molecular Physics

Journal of Atomic and Molecular Physics / 2013 / Article

Research Article | Open Access

Volume 2013 |Article ID 451715 | https://doi.org/10.1155/2013/451715

K. Lalithambigai, R. C. Saraswathi, P. M. Anbarasan, K. B. Rajesh, Z. Jaroszewicz, "Generation of Multiple Focal Hole Segments Using Double-Ring Shaped Azimuthally Polarized Beam", Journal of Atomic and Molecular Physics, vol. 2013, Article ID 451715, 4 pages, 2013. https://doi.org/10.1155/2013/451715

Generation of Multiple Focal Hole Segments Using Double-Ring Shaped Azimuthally Polarized Beam

Academic Editor: Mark D. Havey
Received17 Jul 2012
Revised04 Jan 2013
Accepted18 Feb 2013
Published05 Jun 2013

Abstract

We investigated the focusing properties of a double-ring-shaped azimuthally polarized beam tightly focused with a high NA lens and a binary phase filter. We observe that by using 3 belts and 5 belts binary phase filters novel focal patterns including splitting of focal rings and multiring focus are obtained. We also found that a suitably designed phase structure can shift the focal rings along optical axis. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.

1. Introduction

Growing interest in the generation of three-dimensional (3D) optical beams that are dark regions in space surrounded by light is driven by wide ranging applications including dark optical traps for atoms [1], manipulation, guiding and binding of microparticles and biological cells [2], and erase beams for super-resolution fluorescence microscopy [3]. Such beams are also known as twice-closed tubular optical structure (TCTOS) [4], optical bubbles [5], and hollow dark spherical spots [6]. Optical beams with oscillating on-axis intensity due to interference resulting in 3D intensity voids and 3D optical chains were proposed recently for trapping of multiple particles along the beam propagation and for controllable particle delivery [7]. Over the past years, a variety of techniques have been proposed for generating such optical bottle beams for applications in optical tweezers and atom traps [815]. Recently, a subwavelength focal hole (~0.5) with a quite long depth of focus (~48) is achieved near the focus by tight focusing of double-ring-shaped azimuthally polarized beam with high NA lens axicon [16]. In this paper we investigate the focal properties of the tightly focused azimuthally polarized double-ring-shaped beam using 3 belts and 5 belts binary phase filters. We observed that by properly designing the binary phase filters one can achieve many novel focal patterns including splitting of focal rings and generation of multiring structures.

2. Theoretical Work

A schematic diagram of the suggested method is shown in Figure 1. The analysis was performed on the basis of Richards and Wolf’s vectorial diffraction method [17] widely used for high-NA focusing systems at arbitrary incident polarization. In the case of the azimuthally incident polarization, adopting the cylindrical coordinates and and the notations of [18], the electric field in the vicinity of the focal region can be written as Here is relative amplitude, = arcsin () is the maximum aperture angle with () is the numerical aperture, and is the index of refraction between the lens and the sample. denotes the Bessel functions of first order, and the function () describes the amplitude modulation.

For illumination by a double-ring-shaped R-TEM11* beam with its waist in the pupil, this function is given by [19] where is the parameter that denotes the ratio of pupil diameter to the beam diameter and is the generalized Laguerre polynomial. If , the incident azimuthally polarized beam is a double-ring-shaped azimuthally polarized beam.

3. Analysis of Binary Phase Plate

It is seen from (1) that an additional radial electric field component is produced after introducing the phase modulation to the input double-ring-shaped azimuthally polarized beam [20]. Owing to this radial component, the polarization near the focal plane is rather complicated and space variant. We perform the integration of (1) numerically using parameters , , and of the objective is 0.9. Here, for simplicity, we assume that the refractive index and . The effect of phase modulation on the input double-ring-shaped azimuthally polarized beam is evaluated by replacing the function by where for 3 belts binary phase plate (BPP) is given by

For 5-belt binary phase filter,

When a double-ring-shaped azimuthally polarized beam without any phase modulation is tightly focused, a single-ring focal hole pattern is obtained and is shown in Figure 2(a). We observed that the FWHM of the generated focal hole is 0.782 and its corresponding focal depth is 4. Such a focal ring with subwavelength size can be used for stable trapping of single particle with low refractive index [21]. However, to trap two separates such particles and to manipulate them, we need to split this single-ring focal hole structure to a double ring structure. We observed that this is possible by introducing phase modulation to the input double-ring-shaped azimuthally polarized beam through a 3-belt binary phase plate. We optimized the NA of the first, second, and third ring of the 3-belt binary phase plate as NA1 = 0.1, NA2 = 0.25, and = 0.9 for to achieve the above-mentioned task, and the generated focal segment is shown in Figure 2(b). From Figure 2(b), we observed that the single focal hole is splitted into two focal holes, and the FWHM of each focal hole segment is measured as 0.468 and is separated by the distance of 2.8 between them. We observed that the residual intensity that exists between the two rings is only 35% of the total intensity measured at the focal hole. The ring focus altered by the BPP can be used to move the trapped particle from one place to another. We also observed that it is possible to increase the separation distance between the two focal rings by setting NA1 and NA2 of the BPP as 0.2, 0.85 and by tuning , respectively. The corresponding focal hole segment generated is shown in Figure 2(c). From the figure we measured that the FWHM of each focal holes is 0.468 and is axially separated by the distance of 4 between them. We observed that the residual intensity that exists between the two rings is only 33% of the total intensity measured at the focal hole. It is also possible to achieve 3-ring focal hole segment by setting NA1 and NA2 of the BPP as 0.3, 0.775 and by tuning . The corresponding focal hole segment generated is shown in Figure 2(d). From Figure 2(d), we measured that the FWHM of each focal hole is 0.468λ, and each of them is separated by the distance of 2.8. We observed that the residual intensity that exists between the rings is only 31% of the total intensity measured at the focal hole. We observed that by using 5 belts BPP, it is possible to generate double ring focal segments with FWHM of 0.468and are axially separated by a large distance of 9.4as shown in Figure 3(a).

The set of values of NA of BPP optimized to achieve the above-mentioned task is NA1 = 0.34, NA2 = 0.57, NA3 = 0.78, NA4 = 0.85, and = 0.9 for . From Figure 3(b) we also found that it is possible to generate four-ring patterns having almost uniform FWHM of 0.468 and are axially separated by the distance of 2.7 between them by setting NA1 = 0.24, NA2 = 0.354, NA3 = 0.6, NA4 = 0.8, and = 0.9 for . We observed that the residual intensity that exists between the rings is only 30% of the total intensity measured at the focal hole. Thus with the help of liquid crystal-based tunable BPP, it is possible to generate tunable subwavelength focal hole segment with input double-ring-shaped azimuthally polarized beam.

4. Conclusion

In conclusion, we show by vector diffraction theory that the tight focusing of double-ring-shaped azimuthally polarized beam with a high NA lens and tunable BPP, it is possible to generate many novel focal patterns which are potentially useful for optical trapping and manipulation of low refractive index particles.

References

  1. N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” Advances in Atomic, Molecular, and Optical Physics, vol. 48, pp. 99–151, 2002. View at: Google Scholar
  2. T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” Journal of Physics B, vol. 43, Article ID 102001, 2010. View at: Google Scholar
  3. T. Watanabe, Y. Iketaki, T. Omatsu, K. Yamamoto, M. Sakai, and M. Fuji, “Two point separation in super-resolution fluorescence microscope based on up-conversion fluorescence depletion technique,” Optics Express, vol. 11, pp. 3271–3276, 2003. View at: Google Scholar
  4. J. Garcia-Sucerquia, F. F. Medina, and G. Matteucci, “Optical tubular structures produced by diffraction of circular apertures,” Optics and Lasers in Engineering, vol. 42, no. 1, pp. 61–70, 2004. View at: Publisher Site | Google Scholar
  5. W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Optics Communications, vol. 265, pp. 411–417, 2006. View at: Google Scholar
  6. N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam,” Optics Letters, vol. 31, pp. 149–151, 2006. View at: Google Scholar
  7. B. P. S. Ahluwalia, W. C. Cheong, X. C. Yuan et al., “Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids,” Optics Letters, vol. 31, no. 7, pp. 987–989, 2006. View at: Publisher Site | Google Scholar
  8. J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Optics Letters, vol. 25, no. 4, pp. 191–193, 2000. View at: Google Scholar
  9. B. P. S. Ahluwalia, X. C. Yuan, and S. H. Tao, “Transfer of “pure” on-axis spin angular momentum to the absorptive particle using self-imaged bottle beam optical tweezers system,” Optics Express, vol. 12, no. 21, pp. 5172–5177, 2004. View at: Publisher Site | Google Scholar
  10. D. Yelin, B. E. Bouma, and G. J. Tearney, “Generating an adjustable three-dimensional dark focus,” Optics Letters, vol. 29, no. 7, pp. 661–663, 2004. View at: Publisher Site | Google Scholar
  11. J. X. Pu, X. Y. Liu, and S. Nemoto, “Partially coherent bottle beams,” Optics Communications, vol. 252, pp. 7–11, 2005. View at: Google Scholar
  12. L. Isenhower, W. Williams, A. Dally, and M. Saffman, “Atom trapping in an interferometrically generated bottle beam trap,” Optics Letters, vol. 34, no. 8, pp. 1159–1161, 2009. View at: Publisher Site | Google Scholar
  13. P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap,” Optics Letters, vol. 35, no. 13, pp. 2164–2166, 2010. View at: Publisher Site | Google Scholar
  14. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Optics Express, vol. 18, no. 3, pp. 3137–3142, 2010. View at: Publisher Site | Google Scholar
  15. B. Tian and J. Pu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam,” Optics Letters, vol. 36, no. 11, pp. 2014–2016, 2011. View at: Publisher Site | Google Scholar
  16. K. Lalithambigai, P. Suresh, V. Ravi et al., “Generation of sub wavelength super-long dark channel using high NA lens axicon,” Optics Letters, vol. 37, pp. 999–1001, 2012. View at: Google Scholar
  17. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems—II. Structure of the image field in an aplanatic system,” Proceedings of the Royal Society of London A, vol. 253, no. 1274, pp. 358–379, 1959. View at: Google Scholar
  18. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express, vol. 7, no. 2, pp. 77–87, 2000. View at: Google Scholar
  19. K. B. Rajesh, N. V. Suresh, P. M. Anbarasan, K. Gokulakrishnan, and G. Mahadevan, “Tight focusing of double ring shaped radially polarized beam with high NA lens axicon,” Optics & Laser Technology, vol. 43, no. 7, pp. 1037–1040, 2011. View at: Publisher Site | Google Scholar
  20. G. H. Yuan, S. B. Wei, and X.-C. Yuan, “Nondiffracting transversally polarized beam,” Optics Letters, vol. 36, pp. 3479–3481, 2011. View at: Google Scholar
  21. X. Gao, S. Hu, and J. Wang, “Optical manipulation of azimuthally polarized beam altered by phase plate,” IEEE Computer Society, vol. 163, pp. 657–661, 2008. View at: Google Scholar

Copyright © 2013 K. Lalithambigai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Download other formatsMore
 Order printed copiesOrder
Views856
Downloads448
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.