Abstract

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 20mλ 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

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    [CrossRef]
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2007 (1)

2005 (1)

Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

2003 (1)

2002 (2)

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]

Y. Hirai and Y. Tanaka, “Application of nano-imprint lithography,” J. Photopolym. Sci. Technol. 15, 475-480 (2002).
[CrossRef]

2001 (1)

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]

1999 (3)

1998 (1)

1997 (2)

1995 (1)

1994 (2)

1993 (1)

1991 (1)

1988 (1)

M. G. Moharam, “Coupled-wave analysis of two-dimensional gratings,” Proc. SPIE 883, 8-11 (1988).

1982 (1)

S. J. Wilson and M. C. Hutley, “The optical properties of 'moth eye' antireflection surfaces,” Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Baker, K. M.

Blasi, B.

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]

Brauer, R.

Bryngdahl, O.

Chen, Y.

Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Chipman, R. A.

Crabtree, K.

David, C.

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]

Doll, W.

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]

Dreibholz, J.

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]

Gaylord, T. K.

Glaubitt, W.

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]

Gombert, A.

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]

Grann, E.

Grann, E. B.

Haberling, P.

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]

Hane, K.

Heinzel, A.

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]

Higuchi, M.

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).

Hirai, Y.

Y. Hirai and Y. Tanaka, “Application of nano-imprint lithography,” J. Photopolym. Sci. Technol. 15, 475-480 (2002).
[CrossRef]

Hutley, M. C.

S. J. Wilson and M. C. Hutley, “The optical properties of 'moth eye' antireflection surfaces,” Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Iwata, K.

Kanamori, Y.

Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24, 1422-1424 (1999).
[CrossRef]

Karlsson, M.

Kikuta, H.

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]

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]

Kobayashi, S.

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).

Kubo, H.

Lalanne, D. L.

Lalanne, P.

Li, L.

Maeno, Y.

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).

Moharam, M. G.

Morris, G. M.

Nikolajeff, F.

Ohira, Y.

Okano, M.

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]

Pommet, D. A.

Raguin, D. H.

Rose, K.

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]

Roy, E.

Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Sasaki, M.

Schnierper, M.

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]

Sochtig, J.

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]

Southwell, W. H.

Sporn, D.

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]

Sumi, S.

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).

Takahara, K.

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]

Tanaka, Y.

Y. Hirai and Y. Tanaka, “Application of nano-imprint lithography,” J. Photopolym. Sci. Technol. 15, 475-480 (2002).
[CrossRef]

Toyota, H.

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]

Wilson, S. J.

S. J. Wilson and M. C. Hutley, “The optical properties of 'moth eye' antireflection surfaces,” Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Wittwer, V.

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]

Yamaguchi, A.

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).

Yotsuya, T.

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]

Zschokke, C.

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]

Appl. Opt. (4)

J. Opt. Soc. Am. A (6)

J. Photopolym. Sci. Technol. (1)

Y. Hirai and Y. Tanaka, “Application of nano-imprint lithography,” J. Photopolym. Sci. Technol. 15, 475-480 (2002).
[CrossRef]

Jpn. J. Appl. Phys., Part 2 (1)

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]

Microelectron. Eng. (2)

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]

Y. Kanamori, E. Roy, and Y. Chen, “Antireflection sub-wavelength gratings fabricated by spin-coating replication,” Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Opt. Acta (1)

S. J. Wilson and M. C. Hutley, “The optical properties of 'moth eye' antireflection surfaces,” Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

M. G. Moharam, “Coupled-wave analysis of two-dimensional gratings,” Proc. SPIE 883, 8-11 (1988).

Thin Solid Films (1)

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]

Other (1)

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).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the ray-tracing and electromagnetic analysis for the antireflective SWS coated lens. (a) A cross-section model and (b) the profile of SWS on the lens surface.

Fig. 2
Fig. 2

Ray trace based on the group velocity in the subwavelength structure. RCWA gives the transmittance and phase delay at point B.

Fig. 3
Fig. 3

Solving the group velocity of the Bloch wave in the SWS.

Fig. 4
Fig. 4

(a) Calculated aspherical lens with NA = 0.6 and (b) bell-shaped SWS square-array.

Fig. 5
Fig. 5

Beam shift of IEMT and P- and S-polarized light (obtained from the group velocity of the Bloch wave) with respect to the position of on-axes incident rays.

Fig. 6
Fig. 6

(a) Calculated transmittance and (b) wavefront aberration of the lens with NA = 0.6 with respect to the position of on-axis incident rays. Bare, 1L-AR, and 3L-AR represent uncoated surface, one-, and three-layered conventional antireflective coatings.

Fig. 7
Fig. 7

Calculated aspherical lens with NA = 0.8 .

Fig. 8
Fig. 8

(a) Calculated transmittance and (b) wavefront aberration of the lens with NA = 0.8 with respect to the position of on-axis incident rays. Bare represents an uncoated surface.

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