volume | PIER Journals

Abstract

The focusing properties of radially polarized hypergeometric Gaussian beam are studied using the Richards-Wolf vectorial diffraction model. Such a polarized beam is decomposed into radial and longitudinal polarization. With a proper combination of the beam order, beam size and imaginary parameter variables, the adjustably confined flat-topped focus and focal hole can be obtained in the focal region. Moreover, we got originality characteristic for the axial intensity distribution of two shaped symmetric light spots. The tight focusing of a hypergeometric Gaussian beam may find applications in data storage, laser drilling, optical trapping, etc.

1. Neves, A. R., A. Fontes, L. Y. De Pozzo, et al. "Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric," Optics Express, Vol. 14, No. 26, 13101-13106, 2006.
doi:10.1364/OE.14.013101 Google Scholar

2. Li, X., Y. Cao, and M. Gu, "Superresolution-focal-volume induced 3.0 Tbytes/disk capacity by focusing a radially polarized beam," Opt. Lett., Vol. 36, 2510-2512, 2011.
doi:10.1364/OL.36.002510 Google Scholar

3. Jeffries, G. D. M., J. S. Edgar, Y. Zhao, J. P. Shelby, C. Fong, and D. T. Chiu, "Using polarization-shaped optical vortex traps for single-cell nanosurgery," Nano. Lett., Vol. 7, 415-420, 2007.
doi:10.1021/nl0626784 Google Scholar

4. Zhao, Y., J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, "Spin-to-orbital angular momentum conversion in a strongly focused optical beam," Phys. Rev. Lett., Vol. 99, 073901, 2007.
doi:10.1103/PhysRevLett.99.073901 Google Scholar

5. Davis, J. A., D. E. McNamara, D. M. Cottrell, and J. Campos, "Image processing with the radial Hilbert transform: Theory and experiments," Opt. Lett., Vol. 25, 99-101, 2000.
doi:10.1364/OL.25.000099 Google Scholar

6. Verhagen, E., L. Kuipers, and A. Polman, "Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence," Optics Express, Vol. 17, No. 17, 14586-14598, 2009.
doi:10.1364/OE.17.014586 Google Scholar

7. Valagiannopulos, C. A. and N. L. Tsitsas, "Field enhancement in a grounded dielectric slab by using a single superstrate layer," Advances in OptoElectronics, Vol. 10, 1-9, 2012.
doi:10.1155/2012/439147 Google Scholar

8. Tsitsas, N. L. and C. A. Valagiannopoulos, "On centrating the electromagnetic power in a grounded dielectric slab excited by an external gaussian beam," International Conference on Mathematical Methods in Electromagnetic Theory, 304-307, 2012. Google Scholar

9. Valagiannopulos, C. A., "Electromagnetic absorption of gaussian beams by a grounded layered structure," Radioengineering, Vol. 22, No. 1, 333-340, 2013. Google Scholar

10. Wolf, E., "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. R. Soc. A, Vol. 253, 349-357, 1959.
doi:10.1098/rspa.1959.0199 Google Scholar

11. Richards, B. and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. A, Vol. 253, 358-379, 1959.
doi:10.1098/rspa.1959.0200 Google Scholar

12. Dorn, R., S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett., Vol. 91, 233901, 2003.
doi:10.1103/PhysRevLett.91.233901 Google Scholar

13. Yang, L., X. Xie, S. Wang, and J. Zhou, "Minimized spot of annular radially polarized focusing beam," Opt. Lett., Vol. 38, 1331-1333, 2013.
doi:10.1364/OL.38.001331 Google Scholar

14. Kitamura, K., K. Sakai, and S. Noda, "Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam," Optics Express, Vol. 18, 4518-4525, 2010.
doi:10.1364/OE.18.004518 Google Scholar

15. Kotlyar, V. V., R. V. Skidanov, S. N. Khonina, and V. A. Soifer, "Hypergeometric modes," Opt. Lett., Vol. 32, 742-744, 2007.
doi:10.1364/OL.32.000742 Google Scholar

16. Karimi, E., G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, "Hypergeometric-Gaussian modes," Opt. Lett., Vol. 32, 3053-3055, 2007.
doi:10.1364/OL.32.003053 Google Scholar

17. Kotlyar, V. V., A. A. Kovalev, R. V. Skidanov, S. N. Khonina, and J. Turunen, "Generating hypergeometric laser beams with a diffractive optical element," Appl. Opt., Vol. 47, 6124-6133, 2008.
doi:10.1364/AO.47.006124 Google Scholar

18. Kotlyar, V. V. and A. A. Kovalev, "Family of Hypergeometric laser beams," J. Opt. Soc. Am. A, Vol. 25, 262-270, 2008.
doi:10.1364/JOSAA.25.000262 Google Scholar

19. Eyyuboglu, H. T. and Y. Cai, "Hypergeometric Gaussian beam and its propagation in turbulence," Opt. Commun., Vol. 285, 4194-4190, 2012.
doi:10.1016/j.optcom.2012.07.020 Google Scholar

20. Youngworth, K. and T. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Optics Express, Vol. 7, 77-87, 2000.
doi:10.1364/OE.7.000077 Google Scholar

21. Zhan, Q. and J. Leger, "Focus shaping using cylindrical vector beams," Optics Express, Vol. 10, 324-331, 2002.
doi:10.1364/OE.10.000324 Google Scholar

22. Lin, J., Y. Ma, P. Jin, G. Davies, and J. Tan, "Longitudinal polarized focusing of radially polarized sinh-Gaussian beam," Optics Express, Vol. 21, 13193-13198, 2013.
doi:10.1364/OE.21.013193 Google Scholar

Dr. Ji Peng

Dr. Zhengye Shan

Dr. Yangsheng Yuan

Dr. Zhifeng Cui

Dr. Wei Huang

Dr. Jun Qu