OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 2 — Feb. 1, 2009
  • pp: 337–341

Ray tracing of an aspherical lens with antireflective subwavelength structured surfaces

Akio Mizutani, Yu Kobayashi, Akira Maruyama, and Hisao Kikuta  »View Author Affiliations

JOSA A, Vol. 26, Issue 2, pp. 337-341 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (650 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A method of ray tracing for an aspherical lens with subwavelength periodic structured surfaces has been developed. The ray tracing in the antireflective subwavelength structure is based on the group velocity of the Bloch wave. Transmittance and phase delay for the surface structure are determined with rigorous coupled wave analysis. Calculated wavefront aberration was smaller than 20 m λ for an aspherical lens with numerical aperture of 0.6. For a lens with a higher numerical aperture, the wavefront aberrations increase drastically.

© 2009 Optical Society of America

OCIS Codes
(220.3620) Optical design and fabrication : Lens system design
(310.1210) Thin films : Antireflection coatings
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

Original Manuscript: June 18, 2008
Revised Manuscript: November 13, 2008
Manuscript Accepted: November 24, 2008
Published: January 28, 2009

Akio Mizutani, Yu Kobayashi, Akira Maruyama, and Hisao Kikuta, "Ray tracing of an aspherical lens with antireflective subwavelength structured surfaces," J. Opt. Soc. Am. A 26, 337-341 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. J. Wilson and M. C. Hutley, “The optical properties of 'moth eye' antireflection surfaces,” Opt. Acta 29, 993-1009 (1982). [CrossRef]
  2. D. H. Raguin and G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154-1167 (1993). [CrossRef] [PubMed]
  3. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24, 1422-1424 (1999). [CrossRef]
  4. H. Toyota, K. Takahara, M. Okano, T. Yotsuya, and H. Kikuta, “Fabrication of microcone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys., Part 2 40, L747-L749 (2001). [CrossRef]
  5. M. Karlsson and F. Nikolajeff, “Diamond micro-optics: microlenses and antireflection structured surface for the infrared spectral region,” Opt. Express 11, 502-507 (2003). [CrossRef] [PubMed]
  6. A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351, 73-78 (1999). [CrossRef]
  7. C. David, P. Haberling, M. Schnierper, J. Sochtig, and C. Zschokke, “Nano-structured anti-reflective surface replicated by hot embossing,” Microelectron. Eng. 61-62, 435-440 (2002). [CrossRef]
  8. Y. Hirai and Y. Tanaka, “Application of nano-imprint lithography,” J. Photopolym. Sci. Technol. 15, 475-480 (2002). [CrossRef]
  9. Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005). [CrossRef]
  10. W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surface,” J. Opt. Soc. Am. A 8, 549-553 (1991). [CrossRef]
  11. R. Brauer and O. Bryngdahl, “Design of antireflection grating with approximated and rigorous method,” Appl. Opt. 33, 7875-7882 (1994). [CrossRef] [PubMed]
  12. E. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695-2703 (1994). [CrossRef]
  13. P. Lalanne and D. L. Lalanne, “Depth dependence of effective properties of subwavelength gratings,” J. Opt. Soc. Am. A 14, 450-458 (1997). [CrossRef]
  14. H. Kikuta, Y. Ohira, H. Kubo, and K. Iwata, “Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit,” J. Opt. Soc. Am. A 15, 1577-1585 (1998). [CrossRef]
  15. M. G. Moharam, “Coupled-wave analysis of two-dimensional gratings,” Proc. SPIE 883, 8-11 (1988).
  16. K. M. Baker, “Highly corrected closed-packed microlens array and moth-eye structuring on curved surface,” Appl. Opt. 38, 352-356 (1999). [CrossRef]
  17. S. Kobayashi, A. Yamaguchi, S. Sumi, M. Higuchi, and Y. Maeno, “Production method of curved-surface metal mold having fine uneven structure and production method of optical element using this metal mold,” PCT/JP2005/005012 (2005) or U.S. Patent Application 10,594,154 (2007).
  18. K. Crabtree and R. A. Chipman, “Subwavelength-grating-induced wavefront aberrations: a case study,” Appl. Opt. 46, 4549-4554 (2007). [CrossRef] [PubMed]
  19. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077-1086 (1995). [CrossRef]
  20. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767 (1997). [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