Abstract

A theoretical model is established using Rayleigh-Sommerfeld diffraction theory to describe the diffraction focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing, and continuous-relief diffractive optical elements with a design wavelength of 441.6nm and a F-number of F/4 are fabricated and measured to verify the validity of the diffraction focusing model. The measurements made indicate that the spot size is 1.75µm and the diffraction efficiency is 70.7% at the design wavelength, which coincide well with the theoretical results: a spot size of 1.66µm and a diffraction efficiency of 71.2%.

© 2007 Optical Society of America

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Corrections

Mingguang Shan and Jiubin Tan, "Modeling focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing: errata," Opt. Express 16, 11680-11681 (2008)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-15-11680

References

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    [CrossRef]
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    [CrossRef]
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2007 (1)

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

2006 (2)

2004 (2)

2003 (1)

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

2000 (2)

I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000).
[CrossRef]

F. Yong-Qi, N. Kok Ann Bryan, and O. Shing, "Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling," Opt. Express 7, 141-147 (2000).
[CrossRef] [PubMed]

1998 (2)

1997 (1)

1995 (3)

M. Rossi, R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995).
[CrossRef] [PubMed]

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995).
[CrossRef]

1994 (1)

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Akihito, I.

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

Ammer, T.

I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000).
[CrossRef]

Chan, K.F.

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

Delen, N.

Ehbets, P.

M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995).
[CrossRef]

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

Fan, S.

Feng, D.

Feng, Z.

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

Gale, M. T.

T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, "Analysis and optimization of fabrication of continuous-relief diffractive optical elements," Appl. Opt. 37, 4069-4079 (1998).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Gil, D.

Herzig, H. P.

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995).
[CrossRef]

M. Rossi, R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995).
[CrossRef] [PubMed]

Hessler, T.

Hirai, Y.

Hooker, B.

Jin, G.

Kallioniemi, I.

I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000).
[CrossRef]

Kikuta, H.

Kok Ann Bryan, N.

Korolkov, V. P.

Kuittinen, M.

M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995).
[CrossRef]

Kunz, R. E.

Liu, J.

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Mei, W.

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

Menon, R.

Nasyrov, R. K.

Okano, M.

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Rossi, M.

I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000).
[CrossRef]

T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, "Analysis and optimization of fabrication of continuous-relief diffractive optical elements," Appl. Opt. 37, 4069-4079 (1998).
[CrossRef]

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

M. Rossi, R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995).
[CrossRef] [PubMed]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Schutz, H.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Shan, M.G.

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Shimansky, R. V.

Shing, O.

Smith, H. I.

Tan, J. B.

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Yamamoto, K.

Yan, Y.

Yang, R.

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

Yong-Qi, F.

Yotsuya, T.

Zhang, H.

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Zhao, C.G.

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Appl. Opt. (5)

J. Microlithogr. Microfabr. Microsyst. (1)

R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995).
[CrossRef]

I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000).
[CrossRef]

J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007).
[CrossRef]

Opt. Eng. (2)

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Opt. Express (1)

Other (1)

M. T. Gale, "Direct writing of continuous-relief elements," in Micro-Optics-Elements, Systems, and Applications, H. P. Herzig, ed., (Taylor & Francis, London, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

AFM image of DOE with continuous relief

Fig. 2.
Fig. 2.

Schematic diagram of experimental set-up

Fig. 3.
Fig. 3.

Experimental results: (a) CCD image of focused spot (b) Intensity profile

Fig. 4.
Fig. 4.

Comparison of experimental results with theoretical results and ideal design results

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

φ 0 ( r ) = 2 π p m + 2 π ( n 0 1 ) λ 0 c r 2 1 + 1 ( K + 1 ) c 2 r 2 , r m r r m + 1
φ c ( r ) = φ s ( r ) I ( r )
φ s ( r ) = φ 0 ( r ) n = δ ( r n r s ) = n = φ 0 ( n r s ) δ ( r n r s )
I ( r ) = I 0 exp ( 2 r 2 ω 2 )
φ c ( r ) = I 0 n = [ 2 π p m + 2 π ( n 0 1 ) λ 0 c ( n r s ) 2 1 + 1 ( K + 1 ) c 2 ( n r s ) 2 ] exp [ 2 ( r n r s ) 2 ω 0 2 ]
U 1 ( x 1 , y 1 ) = F 1 { F [ U 0 ( x , y ) exp [ i φ c ( x , y ) ] ] H ( v x , v y ) }
H ( v x , v y ) = { exp [ i 2 π z 12 1 λ 2 v x 2 v y 2 ] 1 λ 2 v x 2 v y 2 > 0 0 otherwise
I c ( x 1 , y 1 ) = U 1 ( x 1 , y 1 ) 2
η = 0 r FWHM I c ( r 1 ) r 1 d r 1 0 I c ( r 1 ) r 1 d r 1

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