Numerical Study on Micro-optical Vortex Generation with the Use of an Achromatic Nanostructured Phase Mask
Main Article Content
Abstract
We present the design and numerical evaluation of an achromatic, nanostructured vortex phase micro-optical mask and a numerical analysis of its optical function to generate fundamental charged optical vortex beams in the visible and near-infrared spectral regions. The nanostructured mask was designed using a pair of thermally compatible commercial glasses, enabling cost-effective production through an adapted stack-and-draw technique. An initial investigation was conducted on 20 μm-thick free-space achromatic vortex phase mask designs. The results confirmed successful vortex beam generation with a fundamental topological charge, with mode-conversion efficiencies reaching 100% at wavelengths of 542 nm and 773 nm. Furthermore, the mask demonstrated the ability to correct chromatic aberration, achieving over 90% mode-conversion efficiency across a broad spectrum (bandwidth of 416 nm) from 504 nm to 920 nm. These results highlight the potential of this achromatic nanostructured vortex mask for integrated broadband vortex beam generation in applications such as optical trapping, high-resolution microscopy, and laser micromachining
Keywords:
Micro-optical vortex, , nano-structurization, achromatic mask
References
[1] Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, X. Yuan, Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities, Light Sci Appl 8 (2019) 1–29. https://doi.org/10.1038/s41377-019-0194-2.
[2] L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys Rev A (Coll Park) 45 (1992) 8185–8189. https://doi.org/10.1103/PhysRevA.45.8185.
[3] M. Padgett, R. Bowman, Tweezers with a twist, Nat Photonics 5 (2011) 343–348. https://doi.org/10.1038/nphoton.2011.81.
[4] A. Kocyigit, K. Cicek, R. Topkaya, X. Cai, Integrated vortex beam emitter device for optical manipulation, Applied Optics, Vol. 59, Issue 10, Pp. 3179-3182 59 (2020) 3179–3182. https://doi.org/10.1364/AO.384838.
[5] M. Yoshida, Y. Kozawa, S. Sato, Subtraction imaging by the combination of higher-order vector beams for enhanced spatial resolution, Opt Lett 44 (2019) 883. https://doi.org/10.1364/ol.44.000883.
[6] K.I. Willig, S.O. Rizzoli, V. Westphal, R. Jahn, S.W. Hell, STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis, Nature (2006). https://doi.org/10.1038/nature04592.
[7] J. Wang, J.Y. Yang, I.M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A.E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat Photonics (2012). https://doi.org/10.1038/nphoton.2012.138.
[8] L. Zhu, A. Wang, J. Wang, Free-space data-carrying bendable light communications, Sci Rep 9 (2019). https://doi.org/10.1038/s41598-019-51496-z.
[9] S. Syubaev, A. Zhizhchenko, A. Kuchmizhak, A. Porfirev, E. Pustovalov, O. Vitrik, Yu. Kulchin, S. Khonina, S. Kudryashov, Direct laser printing of chiral plasmonic nanojets by vortex beams, Opt Express 25 (2017) 10214. https://doi.org/10.1364/oe.25.010214.
[10] Y. Zhang, M. Agnew, T. Roger, F.S. Roux, T. Konrad, D. Faccio, J. Leach, A. Forbes, Simultaneous entanglement swapping of multiple orbital angular momentum states of light, Nat Commun 8 (2017). https://doi.org/10.1038/s41467-017-00706-1.
[11] H.-Y. Tsai, H.I. Smith, R. Menon, Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 25 (2007) 2068. https://doi.org/10.1116/1.2806961.
[12] T. Jankowski, N. Bennis, P. Morawiak, D.C. Zografopoulos, A. Pakuła, M. Filipiak, M. Słowikowski, J.M. López-Higuera, J.F. Algorri, Optical vortices by an adaptive spiral phase plate, Opt Laser Technol 176 (2024) 111029. https://doi.org/10.1016/J.OPTLASTEC.2024.111029.
[13] Y.-H. Kim, C.-Y. Hwang, J.H. Choi, J.-E. Pi, J.-H. Yang, S.-M. Cho, S.-H. Cheon, G.H. Kim, K. Choi, H.-O. Kim, W.-J. Lee, H.-B. Kang, C.-S. Hwang, Development of high-resolution active matrix spatial light modulator, Optical Engineering 57 (2018) 1. https://doi.org/10.1117/1.oe.57.6.061606.
[14] A.S. Ostrovsky, C. Rickenstorff-Parrao, V. Arrizón, Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator, Opt Lett 38 (2013) 534. https://doi.org/10.1364/ol.38.000534.
[15] K. Qu, Q. Jia, N.J. Fisch, Plasma q -plate for generation and manipulation of intense optical vortices, Phys Rev E 96 (2017) 053207. https://doi.org/10.1103/PhysRevE.96.053207.
[16] D.W. Prather, J.N. Mait, M.S. Mirotznik, Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory, JOSA A, Vol. 16, Issue 5, Pp. 1157-1167 16 (1999) 1157–1167. https://doi.org/10.1364/JOSAA.16.001157.
[17] A. Filipkowski, Fabrication and Integration of Nanostructured Optical Devices, 2015.
[18] K. Switkowski, A. Anuszkiewicz, A. Filipkowski, D. Pysz, R. Stepien, W. Krolikowski, R. Buczynski, Formation of optical vortices with all-glass nanostructured gradient index masks, Opt Express 25 (2017) 31443. https://doi.org/10.1364/oe.25.031443.
[19] F. Hudelist, J.M. Nowosielski, R. Buczynski, A.J. Waddie, M.R. Taghizadeh, Nanostructured elliptical gradient-index microlenses, Opt Lett 35 (2010) 130. https://doi.org/10.1364/ol.35.000130.
[20] R. Kasztelanic, H.T. Nguyen, D. Pysz, H. Thienpont, T. Omatsu, R. Buczynski, Free-Form Optical Fiber with a Square Mode and Top-Hat Intensity Distribution, Advanced Science (2024). https://doi.org/10.1002/advs.202402886.
[21] H.T. Nguyen, K. Switkowski, R. Kasztelanic, A. Anuszkiewicz, Optical characterization of single nanostructured gradient index vortex phase masks fabricated by the modified stack-and-draw technique, Opt Commun 463 (2020) 125435. https://doi.org/10.1016/j.optcom.2020.125435.
[22] H.T. Nguyen, B. Le Viet, H.T. Thi, Achromatic nanostructured phase components for micro-optical vortex beam generation, JOSA B, Vol. 42, Issue 6, Pp. 1194-1203 42 (2025) 1194–1203. https://doi.org/10.1364/JOSAB.555732.
[23] CDGM, (n.d.). https://www.cdgmgd.com//database/toWebDatabase.htm?k=Products_Data&url=database (accessed July 30, 2025).
[24] F. Hudelist, R. Buczynski, A.J. Waddie, M.R. Taghizadeh, Design and fabrication of nano-structured gradient index microlenses, Opt Express 17 (2009) 3255. https://doi.org/10.1364/oe.17.003255.
[25] R. Buczynski, A. Filipkowski, B. Piechal, H.T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M.R. Taghizadeh, M. Klimczak, R. Kasztelanic, Achromatic nanostructured gradient index microlenses, Opt Express 27 (2019) 9588. https://doi.org/10.1364/oe.27.009588.
[26] H.T. Nguyen, R. Kasztelanic, A. Filipkowski, D. Pysz, H. Van Le, R. Stepien, T. Omatsu, W. Krolikowski, R. Buczynski, Broadband optical vortex beam generation using flat-surface nanostructured gradient index vortex phase masks, Sci Rep 13 (2023). https://doi.org/10.1038/s41598-023-46871-w.
[27] K. Okamoto, Fundamentals of Optical Waveguides, Fundamentals of Optical Waveguides (2006).
[2] L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys Rev A (Coll Park) 45 (1992) 8185–8189. https://doi.org/10.1103/PhysRevA.45.8185.
[3] M. Padgett, R. Bowman, Tweezers with a twist, Nat Photonics 5 (2011) 343–348. https://doi.org/10.1038/nphoton.2011.81.
[4] A. Kocyigit, K. Cicek, R. Topkaya, X. Cai, Integrated vortex beam emitter device for optical manipulation, Applied Optics, Vol. 59, Issue 10, Pp. 3179-3182 59 (2020) 3179–3182. https://doi.org/10.1364/AO.384838.
[5] M. Yoshida, Y. Kozawa, S. Sato, Subtraction imaging by the combination of higher-order vector beams for enhanced spatial resolution, Opt Lett 44 (2019) 883. https://doi.org/10.1364/ol.44.000883.
[6] K.I. Willig, S.O. Rizzoli, V. Westphal, R. Jahn, S.W. Hell, STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis, Nature (2006). https://doi.org/10.1038/nature04592.
[7] J. Wang, J.Y. Yang, I.M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A.E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat Photonics (2012). https://doi.org/10.1038/nphoton.2012.138.
[8] L. Zhu, A. Wang, J. Wang, Free-space data-carrying bendable light communications, Sci Rep 9 (2019). https://doi.org/10.1038/s41598-019-51496-z.
[9] S. Syubaev, A. Zhizhchenko, A. Kuchmizhak, A. Porfirev, E. Pustovalov, O. Vitrik, Yu. Kulchin, S. Khonina, S. Kudryashov, Direct laser printing of chiral plasmonic nanojets by vortex beams, Opt Express 25 (2017) 10214. https://doi.org/10.1364/oe.25.010214.
[10] Y. Zhang, M. Agnew, T. Roger, F.S. Roux, T. Konrad, D. Faccio, J. Leach, A. Forbes, Simultaneous entanglement swapping of multiple orbital angular momentum states of light, Nat Commun 8 (2017). https://doi.org/10.1038/s41467-017-00706-1.
[11] H.-Y. Tsai, H.I. Smith, R. Menon, Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 25 (2007) 2068. https://doi.org/10.1116/1.2806961.
[12] T. Jankowski, N. Bennis, P. Morawiak, D.C. Zografopoulos, A. Pakuła, M. Filipiak, M. Słowikowski, J.M. López-Higuera, J.F. Algorri, Optical vortices by an adaptive spiral phase plate, Opt Laser Technol 176 (2024) 111029. https://doi.org/10.1016/J.OPTLASTEC.2024.111029.
[13] Y.-H. Kim, C.-Y. Hwang, J.H. Choi, J.-E. Pi, J.-H. Yang, S.-M. Cho, S.-H. Cheon, G.H. Kim, K. Choi, H.-O. Kim, W.-J. Lee, H.-B. Kang, C.-S. Hwang, Development of high-resolution active matrix spatial light modulator, Optical Engineering 57 (2018) 1. https://doi.org/10.1117/1.oe.57.6.061606.
[14] A.S. Ostrovsky, C. Rickenstorff-Parrao, V. Arrizón, Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator, Opt Lett 38 (2013) 534. https://doi.org/10.1364/ol.38.000534.
[15] K. Qu, Q. Jia, N.J. Fisch, Plasma q -plate for generation and manipulation of intense optical vortices, Phys Rev E 96 (2017) 053207. https://doi.org/10.1103/PhysRevE.96.053207.
[16] D.W. Prather, J.N. Mait, M.S. Mirotznik, Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory, JOSA A, Vol. 16, Issue 5, Pp. 1157-1167 16 (1999) 1157–1167. https://doi.org/10.1364/JOSAA.16.001157.
[17] A. Filipkowski, Fabrication and Integration of Nanostructured Optical Devices, 2015.
[18] K. Switkowski, A. Anuszkiewicz, A. Filipkowski, D. Pysz, R. Stepien, W. Krolikowski, R. Buczynski, Formation of optical vortices with all-glass nanostructured gradient index masks, Opt Express 25 (2017) 31443. https://doi.org/10.1364/oe.25.031443.
[19] F. Hudelist, J.M. Nowosielski, R. Buczynski, A.J. Waddie, M.R. Taghizadeh, Nanostructured elliptical gradient-index microlenses, Opt Lett 35 (2010) 130. https://doi.org/10.1364/ol.35.000130.
[20] R. Kasztelanic, H.T. Nguyen, D. Pysz, H. Thienpont, T. Omatsu, R. Buczynski, Free-Form Optical Fiber with a Square Mode and Top-Hat Intensity Distribution, Advanced Science (2024). https://doi.org/10.1002/advs.202402886.
[21] H.T. Nguyen, K. Switkowski, R. Kasztelanic, A. Anuszkiewicz, Optical characterization of single nanostructured gradient index vortex phase masks fabricated by the modified stack-and-draw technique, Opt Commun 463 (2020) 125435. https://doi.org/10.1016/j.optcom.2020.125435.
[22] H.T. Nguyen, B. Le Viet, H.T. Thi, Achromatic nanostructured phase components for micro-optical vortex beam generation, JOSA B, Vol. 42, Issue 6, Pp. 1194-1203 42 (2025) 1194–1203. https://doi.org/10.1364/JOSAB.555732.
[23] CDGM, (n.d.). https://www.cdgmgd.com//database/toWebDatabase.htm?k=Products_Data&url=database (accessed July 30, 2025).
[24] F. Hudelist, R. Buczynski, A.J. Waddie, M.R. Taghizadeh, Design and fabrication of nano-structured gradient index microlenses, Opt Express 17 (2009) 3255. https://doi.org/10.1364/oe.17.003255.
[25] R. Buczynski, A. Filipkowski, B. Piechal, H.T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M.R. Taghizadeh, M. Klimczak, R. Kasztelanic, Achromatic nanostructured gradient index microlenses, Opt Express 27 (2019) 9588. https://doi.org/10.1364/oe.27.009588.
[26] H.T. Nguyen, R. Kasztelanic, A. Filipkowski, D. Pysz, H. Van Le, R. Stepien, T. Omatsu, W. Krolikowski, R. Buczynski, Broadband optical vortex beam generation using flat-surface nanostructured gradient index vortex phase masks, Sci Rep 13 (2023). https://doi.org/10.1038/s41598-023-46871-w.
[27] K. Okamoto, Fundamentals of Optical Waveguides, Fundamentals of Optical Waveguides (2006).