OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 25 — Dec. 6, 2010
  • pp: 26245–26258

Guidelines for 1D-periodic surface microstructures for antireflective lenses

Thomas Søndergaard, Jesper Gadegaard, Peter Kjær Kristensen, Thøger Kari Jensen, Thomas Garm Pedersen, and Kjeld Pedersen  »View Author Affiliations

Optics Express, Vol. 18, Issue 25, pp. 26245-26258 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (2248 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Antireflective properties of one-dimensional periodically microstructured lens surfaces (refractive index 1.5) are studied with the Green’s function surface integral equation method, and design guidelines are obtained. Special attention is given to the requirement of having practically all incident light transmitted in the fundamental transmission diffraction order. The effect of the presence of higher transmission diffraction orders is studied to determine if such more easily fabricated structures will be useful. The decrease of optimum fill factor of a periodic array of subwavelength ridges with structure period is explained as a waveguiding effect. Near-fields are calculated illustrating standing-wave interference and waveguiding effects for ridge structures, and adiabatic field transformation for tapered structures, including evanescent near-fields in in- and out-coupling regions. The antireflective properties of tapered geometries are considered for a wide range of angles of light incidence. It is found that while the reflection can be very small this rarely implies high transmission into the fundamental transmission diffraction order when higher-order transmission diffraction orders exist. This leads to the guideline that for visible and normally incident light the surface structure period should not be larger than ~300 nm, and a smaller period is needed in the case of oblique light incidence.

© 2010 OSA

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(220.3630) Optical design and fabrication : Lenses
(220.4000) Optical design and fabrication : Microstructure fabrication
(240.6700) Optics at surfaces : Surfaces
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

Original Manuscript: September 10, 2010
Revised Manuscript: October 29, 2010
Manuscript Accepted: November 15, 2010
Published: December 1, 2010

Thomas Søndergaard, Jesper Gadegaard, Peter Kjær Kristensen, Thøger Kari Jensen, Thomas Garm Pedersen, and Kjeld Pedersen, "Guidelines for 1D-periodic surface microstructures for antireflective lenses," Opt. Express 18, 26245-26258 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Bäumer, ed., Handbook of Plastic Optics 2nd edition (Wiley-VCH Verlag GmbH & Co. KGaA, 2010).
  2. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33(13), 2695–2706 (1994). [CrossRef] [PubMed]
  3. T. K. Gaylord, W. E. Baird, and M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25(24), 4562–4567 (1986). [CrossRef] [PubMed]
  4. E. N. Glytsis and T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31(22), 4459–4470 (1992). [CrossRef] [PubMed]
  5. M. E. Motamedi, W. H. Southwell, and W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31(22), 4371–4376 (1992). [CrossRef] [PubMed]
  6. D. H. Raguin and G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32(7), 1154–1167 (1993). [CrossRef] [PubMed]
  7. D. H. Raguin and G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32(14), 2582–2598 (1993). [CrossRef] [PubMed]
  8. A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Bläsi, A. Heinzel, D. Sporn, W. Döll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999). [CrossRef]
  9. M. Niggemann, M. Glatthaar, A. Gombert, A. Hinsch, and V. Wittwer, “Diffraction gratings and buried nano-electrodes – architectures for organic solar cells,” Thin Solid Films 451–452, 619–623 (2004). [CrossRef]
  10. C. David, P. Häberling, M. Schnieper, J. Söchtig, and C. Zschokke, “Nano-structured anti-reflective surfaces replicated by hot embossing,” Microelectron. Eng. 61–62(1-4), 435–440 (2002). [CrossRef]
  11. C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, and A. Tünnermann, “Broadband antireflective surface-relief structure for THz optics,” Opt. Express 15(3), 779–789 (2007). [CrossRef] [PubMed]
  12. J. Zhu, Z. Yu, G. F. Burkhard, C.-M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009). [CrossRef]
  13. Y. Wang, F. Hu, Y. Kanamori, T. Wu, and K. Hane, “Large area, freestanding GaN nanocolumn membrane with bottom subwavelength nanostructure,” Opt. Express 18(6), 5504–5511 (2010). [CrossRef] [PubMed]
  14. C.-H. Sun, W.-L. Min, N. C. Linn, P. Jiang, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91(231105), 3 (2007). [CrossRef]
  15. H. L. Chen, K. T. Huang, C. H. Lin, W. Y. Wang, and W. Fan, “Fabrication of sub-wavelength antireflective structures in solar cells by utilizing modified illumination and defocus techniques in optical lithography,” Microelectron. Eng. 84(5-8), 750–754 (2007). [CrossRef]
  16. D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proc. Biol. Sci. 273(1587), 661–667 (2006). [CrossRef] [PubMed]
  17. U. Schulz, “Wideband antireflection coatings by combining interference multilayers with structured top layers,” Opt. Express 17(11), 8704–8708 (2009). [CrossRef] [PubMed]
  18. U. Schulz, P. Munzert, R. Leitel, I. Wendling, N. Kaiser, and A. Tünnermann, “Antireflection of transparent polymers by advanced plasma etching procedures,” Opt. Express 15(20), 13108–13113 (2007). [CrossRef] [PubMed]
  19. A. Kaless, U. Schulz, P. Munzert, and N. Kaiser, “NANO-motheye antireflection pattern by plasma treatment of polymers,” Surf. Coat. Tech. 200(1-4), 58–61 (2005). [CrossRef]
  20. S. Walheim, E. Schäffer, J. Mlynek, and U. Steiner, “Nanophase-separated polymer films as high-performance antireflection coatings, ” Science 283(5401), 520–522 (1999). [CrossRef] [PubMed]
  21. M. S. Park, Y. Lee, and J. K. Kim, “One-Step Preparation of Antireflection Film by Spin Coating of Polymer/Solvent/Nonsolvent Ternary System,” Chem. Mater. 17(15), 3944–3950 (2005). [CrossRef]
  22. B. G. Prevo, E. W. Hon, and O. D. Velev, “Assembly and characterization of colloid-based antireflective coatings on multicrystalline solar cells,” J. Mater. Chem. 17(8), 791–799 (2007). [CrossRef]
  23. H. Jiang, K. Yu, and Y. Wang, “Antireflective structures via spin casting of polymer latex,” Opt. Lett. 32(5), 575–577 (2007). [CrossRef] [PubMed]
  24. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi 244(10), 3448–3462 (2007) (b). [CrossRef]
  25. D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14(1), 34–43 (1997). [CrossRef]
  26. J. Jin, The Finite Element Method in Electromagnetics, Wiley, New York, 2nd ed., (2002).
  27. G. Kobidze, B. Shanker, and D. P. Nyquist, “Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056702 (2005). [CrossRef] [PubMed]
  28. D. Van Orden and V. Lomakin, “Rapidly Convergent Representations for 2D and 3D Green's Functions for a Linear Periodic Array of Dipole Sources,” IEEE Trans. Antenn. Propag. 57(7), 1973–1984 (2009). [CrossRef]
  29. T. Søndergaard and S. I. Bozhevolnyi, “Surface-plasmon polariton resonances in triangular-groove metal gratings,” Phys. Rev. B 80(195407), 9 (2009). [CrossRef]
  30. M. V. Klein, and T. E. Furtak, Optics, second edition (John Wiley & Sons, New York, 1986).
  31. D. E. Aspnes, “Local-field effects and effective-medium theory: A microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982). [CrossRef]
  32. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]
  33. L. Novotny, and B. Hecht, Principles of Nano-Optics (Cambridge university press, New York 2006).
  34. R. Haïdar, G. Vincent, N. Guérineau, S. Collin, S. Velghe, and J. Primot, “Wollaston prism-like devices based on blazed dielectric subwavelength gratings,” Opt. Express 13(25), 9941–9953 (2005). [CrossRef] [PubMed]
  35. P. Lalanne, “Waveguiding in blazed-binary diffractive elements,” J. Opt. Soc. Am. A 16(10), 2517–2520 (1999). [CrossRef]
  36. S. F. Monaco, “Reflectance of an Inhomogeneous Thin Film,” J. Opt. Soc. Am. 51(3), 280–282 (1961). [CrossRef]
  37. M. J. Minot, “Single-layer, gradient refractive index antireflection films effective from 0.35 to 2.5 μ,” J. Opt. Soc. Am. 66(6), 515–519 (1976). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited