Theoretical realization of three-dimensional nanolattice structure fabrication based on high-order waveguide-mode interference and sample rotation

  • Xiangxian WangEmail author
  • Huan Tong
  • Zhiyuan Pang
  • Jiankai Zhu
  • Xiaoxiong Wu
  • Hua Yang
  • Yunping Qi


A theoretical method of using high-order waveguide-mode interference combined with sample rotation is proposed to fabricate different kinds of three-dimensional nanolattice structures. The lithography sample is assisted by an asymmetric metal-cladding dielectric waveguide structure. High-order waveguide modes can be excited in the photoresist layer by both transverse magnetic and transverse electric polarized light. By utilizing multiple exposures of high-order waveguide-mode interference combined with sample-rotation, various three-dimensional nanolattice structures can be obtained. The resulting optical field distributions are simulated using the finite element method in this study, and sample rotation is expressed by coordinate matrix transformation. As examples, the three-dimensional optical field distributions resulting from fifth-order waveguide-mode interference were simulated with 90° and 60° sample rotations and multiple exposures. The results show that a quasi-cuboid structure with a simple tetragonal arrangement and a quasi-hexagonal structure with a hexagonal close-packed lattice can be obtained. Moreover, the numerical simulation results revealed that the shapes, sizes, arrangements, and periods of the structures can be controlled by the rotation method, photoresist thickness, waveguide modes used for exposure, and so on.


Nanolithography Subwavelength structure Waveguide mode Sample rotation 



This work was supported by the National Natural Science Foundation of China, (Grant No. 61865008), the Undergraduate Innovation Training Program of GanSu province (Grant No. DC2018002) and the Undergraduate Innovation Training Program of Lanzhou University of Technology (Grant No. DC2018004).


  1. Bogaerts, W., Wiaux, V., Taillaert, D., Beckx, S., Luyssaert, B., Bienstman, P.: Fabrication of photonic crystals in silicon-on-insulator using 248-nm deep UV lithography. IEEE J. Sel. Top. Quantum Electron. 8(4), 928–934 (2002)ADSCrossRefGoogle Scholar
  2. Cen, C.L., Lin, H., Huang, J., Liang, C.P., Chen, X.F., Tang, Y.J., Yi, Z., Ye, X., Liu, J.W., Yi, Y.G., Xiao, S.Y.: A tunable plasmonic refractive index sensor with nanoring-strip graphene arrays. Sensors 18, 4489 (2018a)CrossRefGoogle Scholar
  3. Cen, C.L., Chen, J.J., Liang, C.P., Huang, J., Chen, X.F., Tang, Y.J., Yi, Z., Xu, X.B., Yi, Y.G., Xiao, S.Y.: Plasmonic absorption characteristics based on dumbbell-shaped graphene metamaterial arrays. Physica E 103, 93–98 (2018b)ADSCrossRefGoogle Scholar
  4. Chen, J., Tang, C.J., Mao, P., Peng, C., Gao, D.P., Yu, Y., Wang, Q.G., Zhang, L.B.: Surface-plasmon-polaritons-assisted enhanced magnetic response at optical frequencies in metamaterials. IEEE Photon. J. 8, 4800107 (2016a)Google Scholar
  5. Chen, J., Zhang, T., Tang, C.J., Mao, P., Liu, Y.J., Yu, Y., Liu, Z.Q.: Optical magnetic field enhancement via coupling magnetic plasmons to optical cavity modes. IEEE Photon. Technol. Lett. 28, 1529–1532 (2016b)ADSCrossRefGoogle Scholar
  6. Chen, Y.Z., Wang, X.X., Wang, R., et al.: Theoretical study of micro-optical structure fabrication based on sample rotation and two-laser-beam interference. Chin. Phys. B 26(5), 054203-1–054203-5 (2017)ADSGoogle Scholar
  7. Chien, F.S.S., Wu, C.L., Chou, Y.C., Chen, T.T., Gwol, S., Hsieh, W.F.: Nanomachining of (110)-oriented silicon by scanning probe lithography and anisotropic wet etching. Appl. Phys. Lett. 75(16), 2429–2431 (1999)ADSCrossRefGoogle Scholar
  8. Du, H.M., Zhang, L.P., Li, D.G.: THz plasma wave instability in field effect transistor with electron diffusion current density. Plasma Sci. Technol 20, 115001 (2018)CrossRefGoogle Scholar
  9. Feiertag, G., Ehrfeld, W., Freimuth, H., Kolle, H., Lehr, H., Schmidt, M., Sigalas, M.M., Soukoulis, C.M., Kiriakidis, G., Pedersen, T., Kuhl, J., Koenig, W.: Fabrication of photonic crystals by deep x-ray lithography. Appl. Phys. Lett. 71(11), 1441–1443 (1997)ADSCrossRefGoogle Scholar
  10. Gunnarsson, L., Rindzevicius, T., Prikulis, J., Kasemo, B., Kall, M., Zou, S., Schatz, G.: Confined plasmons in nanofabricated single silver particle pairs: experimental observations of strong interparticle interactions. J. Phys. Chem. B 109(3), 1079–1087 (2005)CrossRefGoogle Scholar
  11. Gwyn, C.W., Stulen, R., Sweeney, D., et al.: Extreme ultraviolet lithography. J. Vac. Sci. Technol., B 16(6), 3142–3149 (1998)CrossRefGoogle Scholar
  12. Hassanzadeh, A., Mohammadnezhad, M., Mittler, S.: Multiexposure laser interference lithography. J. Nanophoton. 9, 093067-1–093067-12 (2015)ADSCrossRefGoogle Scholar
  13. Li, D.G., Zhang, L.P., Du, H.M.: The instability of terahertz plasma waves in cylindrical FET. Plasma Sci. Technol (2018). CrossRefGoogle Scholar
  14. Liang, C.P., Niu, G., Chen, X.F., Zhou, Z.G., Yi, Z., Ye, X., Duan, T., Yi, Y., Xiao, S.Y.: Tunable triple-band graphene refractive index sensor with good angle-polarization tolerance. Opt. Commun. 436, 57–62 (2019)ADSCrossRefGoogle Scholar
  15. Liu, G., Yu, M., Liu, Z., Liu, X., Huang, S., Pan, P., Wang, Y., Liu, M., Gu, G.: One-process fabrication of metal hierarchical nanostructures with rich nanogaps for highly-sensitive surface-enhanced Raman scattering. Nanotechnology 26(18), 185702 (2015a)ADSCrossRefGoogle Scholar
  16. Liu, Z.Q., Liu, X.S., Huang, S., Pan, P.P., Chen, J., Liu, G.Q., Gu, G.: Automatically acquired broadband plasmonic-metamaterial black absorber during the metallic film-formation. Appl. Mater. Interfaces 7, 4962–4968 (2015b)CrossRefGoogle Scholar
  17. Liu, C., Su, W.Q., Liu, Q., Lu, X.L., Wang, F.M., Sun, T., Chu, P.K.: Symmetrical dual D-shape photonic crystal fibers for surface plasmon resonance sensing. Opt. Express 26(7), 9039–9049 (2018)ADSCrossRefGoogle Scholar
  18. Lv, J.W., Mu, H.W., Liu, Q., Zhang, X.M., Li, X.L., Liu, C., Jiang, S.S., Sun, T., Chu, P.K.: Multi-wavelength unidirectional forward scattering in the visible range in all-dielectric silicon hollow nanodisk. Appl. Opt. 57(17), 4771–4776 (2018)ADSCrossRefGoogle Scholar
  19. Mohammadnezhad, M., Hassanzadeh, A.: Evanescent field interferometric optical tweezers with rotational symmetric patterns. J. Opt. Soc. Am. B 34(5), 983–989 (2017a)ADSCrossRefGoogle Scholar
  20. Mohammadnezhad, M., Hassanzadeh, A.: Multibeam interferometric optical tweezers. J Nanophoton. 11(3), 036007 (2017b)CrossRefGoogle Scholar
  21. Murukeshan, V.M., Sreekanth, K.V.: Maskless plasmonic lithography for patterning of one- and two dimensional periodic features. Proc. SPIE 7637, 76371G (2015)CrossRefGoogle Scholar
  22. Pang, Z.Y., Tong, H., Wu, X.X., Zhu, J.K., Wang, X.X., Yang, H., Ping, Q.Y.: Theoretical study of multiexposure zeroth-order waveguide mode interference lithography. Opt. Quant. Electron. 50, 335 (2018)CrossRefGoogle Scholar
  23. Qi, Y.P., Zhang, X.W., Zhou, P.Y., Hu, B.B., Wang, X.X.: Refractive index sensor and filter of metal-insulator-metal waveguide based on ring resonator embedded by cross structure. Acta Phys. Sin. 67(19), 197301 (2018)Google Scholar
  24. Shao, H.Y., Chen, C., Wang, J.C., Pan, L., Sang, T.: Metalenses based on the non-parallel double-slit arrays. J. Phys. D Appl. Phys. 50(38), 384001 (2017)ADSCrossRefGoogle Scholar
  25. Su, W.X., Feng, W.J., Cao, Y., Chen, L.J., Li, M.M., Song, C.K.: Porous honeycomb-like carbon prepared by a facile sugar-blowing method for high-performance lithium–sulfur batteries. Int. J. Electrochem. Sci. 13, 6005–6014 (2018)CrossRefGoogle Scholar
  26. Utke, I., Hoffmann, P., Melngailis, J.: Gas-assisted focused electron beam and ion beam processing and fabrication. J. Vac. Sci. Technol., B 26(4), 1197–1276 (2008)CrossRefGoogle Scholar
  27. Wang, B., Chew, A.B., Teng, J.H., Si, G.Y., Danner, A.J.: Subwavelength lithography by waveguide mode interference. Appl. Phys. Lett. 99(15), 151106 (2011)ADSCrossRefGoogle Scholar
  28. Wang, X.X., Zhang, D.G., Chen, Y.K., Zhu, L.F., Yu, W.H., Wang, P., Yao, P.J., Ming, H., Wu, W.W., Zhang, Q.J.: Large area sub-wavelength azo-polymer gratings by waveguide modes interference lithography. Appl. Phys. Lett. 102(3), 031103 (2013)ADSCrossRefGoogle Scholar
  29. Wang, X.X., Wang, X.D., Yang, H., Ye, S., Yu, J.: Study of surface relief-gratings lithography of epoxy-based bisazobenzene polymer BP-2A-35-CN. J. Funct. Mater. 6, 20132–20135 (2015)Google Scholar
  30. Wang, R., Wang, X.X., Yang, H., Ye, S.: Theoretical investigation of adjustable period sub-wavelength grating inscribed by TE0 waveguide modes interference lithography. Acta Phys. Sin. 65(9), 094206 (2016)Google Scholar
  31. Wang, R., Wang, X.X., Yang, H., Qi, Y.P.: Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph. Chin. Phys. B 26(2), 024202 (2017a)ADSCrossRefGoogle Scholar
  32. Wang, X.X., Wang, R., Yang, H., Qi, Y.P.: Inscription of sub-wavelength gratings with different periods based on asymmetric metal-cladding dielectric waveguide structure. Optik 140, 261–267 (2017b)ADSCrossRefGoogle Scholar
  33. Wang, X.X., Wu, X.X., Chen, Y.Z., Bai, X.L., Pang, Z.Y., Yang, H., Qi, Y.P., Wen, X.L.: Investigation of wide-range refractive index sensor based on asymmetric metal-cladding dielectric waveguide structure. AIP Adv. 8, 105029 (2018)ADSCrossRefGoogle Scholar
  34. Wang, X.X., Pang, Z.Y., Tong, H., Wu, X.X., Bai, X.L., Yang, H., Wen, X.L., Qi, Y.P.: Theoretical investigation of subwavelength structure fabrication based on multi-exposure surface plasmon interference lithography. Results Phys. 12, 732–737 (2019)ADSCrossRefGoogle Scholar
  35. Wei, Z.Q., Zhou, Z.K., Li, Q.Y., Xue, J.C., Falco, A.D., Yang, Z.J., Zhou, J.H., Wang, X.H.: Flexible nanowire cluster as a wearable colorimetric humidity sensor. Small 13, 1700109 (2017)CrossRefGoogle Scholar
  36. Yan, Y.X., Yang, H., Zhao, X.X., Li, R.S., Wang, X.X.: Enhanced photocatalytic activity of surface disorder-engineered CaTiO3. Mater. Res. Bull. 105, 286–290 (2018)CrossRefGoogle Scholar
  37. Yang, L., Wang, J.C., Yang, L.Z., Hu, Z.D., Wu, X.J., Zheng, G.G.: Characteristics of multiple Fano resonances in waveguide-coupled surface plasmon resonance sensors based on waveguide theory. Sci. Rep. 8, 2560 (2017)ADSCrossRefGoogle Scholar
  38. Ye, Y.C., Yang, H., Zhang, H.M., Jiang, J.L.: A promising Ag2CrO4/LaFeO3 heterojunction photocatalyst applied to photo-Fenton degradation of RhB. Environ. Technol. (2018). CrossRefGoogle Scholar
  39. Yu, M., Huang, Z., Liu, Z., Chen, J., Liu, Y., Tang, L., Liu, G.: Annealed gold nanoshells with highly-dense hotspots for large-area efficient Raman scattering substrates. Sens. Actuator B-Chem. 262, 845–851 (2018)CrossRefGoogle Scholar
  40. Zhang, X.W., Qi, Y.P., Zhou, P.Y., Gong, H.H., Hu, B.B., Yan, C.M.: Refractive index sensor based on fano resonances in plasmonic waveguide with dual side-coupled ring resonators. Photon. Sens. 8(4), 367–374 (2018)ADSCrossRefGoogle Scholar
  41. Zhao, Q., Yang, Z.J., He, J.: Fano resonances in heterogeneous dimers of silicon and gold nanospheres. Front. Phys. 13(3), 13780 (2018a)CrossRefGoogle Scholar
  42. Zhao, X.X., Yang, H., Li, S.H., Cui, Z.M., Zhang, C.R.: Synthesis and theoretical study of large-sized Bi4Ti3O12 square nanosheets with high photocatalytic activity. Mater. Res. Bull. 107, 180–188 (2018b)CrossRefGoogle Scholar
  43. Zheng, C.X., Yang, H.: Assembly of Ag3PO4 nanoparticles on rose flower-like Bi2WO6 hierarchical architectures for achieving high photocatalytic performance. J. Mater. Sci.: Mater. Electron. 29(11), 9291–9300 (2018)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Xiangxian Wang
    • 1
    Email author
  • Huan Tong
    • 1
  • Zhiyuan Pang
    • 1
  • Jiankai Zhu
    • 1
  • Xiaoxiong Wu
    • 1
  • Hua Yang
    • 1
  • Yunping Qi
    • 2
  1. 1.School of ScienceLanzhou University of TechnologyLanzhouChina
  2. 2.College of Physics and Electronic EngineeringNorthwest Normal UniversityLanzhouChina

Personalised recommendations