Abstract
Tight focusing properties of axially symmetric polarized beams with fractional orders are studied theoretically based on vector diffraction theories. The mathematical expressions of focused fields are derived, which can be used to calculate the amplitude, phase and polarization distributions of focused fields. Simulation results are further shown, and many interesting patterns of focused fields are presented, which may find some potential applications in optical trapping, microscopy, near-field optics and so on. In addition, the influences of system parameters including numerical-aperture of objective lens, the beam filling factor and the beam waist factor on focused fields are analyzed, which provide more flexible modulation of focused field patterns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bomzon, Z., Kleiner, V., Hasman, E.: Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings. Appl. Phys. Lett. 79, 1587–1589 (2001)
Chen, H., Hao, J., Zhang, B., Xu, J., Ding, J., Wang, H.: Generation of vector beam with space-variant distribution of both polarization and phase. Opt. Lett. 36, 3179–3181 (2011)
Huang, K., Shi, P., Cao, G., Li, K., Zhang, X., Li, Y.: Vector-vortex Bessel-Gauss beams and their tightly focusing properties. Opt. Lett. 36, 888–890 (2011)
Maurer, C., Jesacher, A., Furhapter, S., Bernet, S., Ristch-Marte, M.: Tailoring of arbitrary optical vector beams. New J. Phys. 9, 78 (2007). doi:10.1088/1367-2630/9/3/078
Rashid, M., Maragò, O.M., Jones, P.H.: Focusing of high order cylindrical vector beams. J. Opt. A Pure Appl. Opt. 11, 065204 (2009). doi:10.1088/1464-4258/11/6/065204
Richards, B., Wolf, E.: Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System. Proc. Roy. Soc A 253, 358–379 (1959)
Stalder, M., Schadt, M.: Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters. Opt. Lett. 21, 1948–1950 (1996)
Wang, X., Ding, J., Ni, W., Guo, C., Wang, H.: Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Opt. Lett. 32, 3549–3551 (2007)
Youngworth, K.S., Brown, T.G.: Focusing of high numerical aperture cylindrical vector beams. Opt. Express 7, 77–87 (2000)
Zhan, Q.: Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 1–57 (2009)
Zhou, Z., Zhu, L.: Parallel confocal microscopy using high-order axially symmetric polarized beams. Microsc. Res. Tech. 78, 302–308 (2015a)
Zhou, Z., Zhu, L.: Multiple optical trapping based on high-order axially symmetric polarized beams. Chin. Phys. B 24, 028704 (2015b). doi:10.1088/1674-1056/24/2/028704
Zhou, Z., Tan, Q., Jin, G.: Focusing of high polarization order axially symmetric polarized beams. Chin. Opt. Lett. 7, 938–940 (2009)
Zhou, Z., Tan, Q., Zhu, L., Yang, C.: Near-field multiple optical trapping using high order axially symmetric polarized beams. Opt. Appl. 43, 287–296 (2013)
Zhou, Z., Hu, Z., Zhu, L.: Interferometric generation of high order vector beams using an adjustable cat-eye cavity laser. Opt. Quant. Electron. 47, 2241–2247 (2015)
Acknowledgments
The work was supported by National Natural Science Foundation of China (Nos. 61108047 and 61475021), Beijing Natural Science Foundation (No. 4152015), the Program for New Century Excellent Talents in University, China (No. NCET-13-0667) and Beijing Top Young Talents Support Program (CIT&TCD201404113).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Zhou, Z., Zhu, L. Tight focusing of axially symmetric polarized beams with fractional orders. Opt Quant Electron 48, 44 (2016). https://doi.org/10.1007/s11082-015-0260-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-015-0260-9