Abstract

This study explores two-dimensional binary sub-wavelength diffractive lenses (BSDLs) for implementing long focal depth and high transverse resolution based on the rigorous electromagnetic theory and the finite-difference time-domain method. Focusing performances, such as the actual focal depth, the ratio between the focal depth of the designed BSDL and the focal depth of the conventional sub-wavelength lens and the spot size of the central lobe at the actual focal plane, for different f-numbers, have been studied in the case of TE incidence polarization wave. The rigorous numerical results indicate that the designed BSDLs indeed have long focal depth and high transverse resolution by modulating the binary sub-wavelength characteristic sizes. Because BSDLs have the ability for monolithic integration and can require only single step fabrication, the investigations may provide useful information for BSDLs’ application in micro-optical systems.

©2008 Optical Society of America

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References

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    [Crossref]
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2008 (1)

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

2007 (4)

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek. “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express. 15, 9184–9193 (2007).
[Crossref] [PubMed]

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

2006 (1)

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

2005 (1)

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

2003 (3)

H. Kikuta, H. Toyota, and W. J. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Review,  10, 63–73 (2003).
[Crossref]

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[Crossref]

2002 (1)

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

2001 (3)

S. D. Mellin and G. P. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express. 8, 705–722 (2001).
[Crossref] [PubMed]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

R. Magnusson and M. T. Gale, “Diffractive optics and micro-optics: introduction to the feature issue,” Appl. Opt. 40, 5817–5818 (2001).
[Crossref]

1999 (1)

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A. 16, 1157–1167. (1999).
[Crossref]

1998 (2)

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

E. N. Glytsis, M. E. Harrigan, K Hirayama, and T. K. Gaylord, “Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation,” Appl. Opt. 37, 34–43 (1998).
[Crossref]

1996 (1)

1995 (2)

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).
[Crossref]

J. R. Leger, M. G. Moharam, and T. K. Gaylord, “Feature Issue on Diffractive Optics,” Appl. Opt. 34, 2399–2559 (1995).
[Crossref] [PubMed]

1994 (1)

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A. 11, 1827–1834 (1994).
[Crossref]

1993 (1)

1992 (3)

1991 (1)

1989 (1)

Bará, S.

Collins, J. P.

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

Davidson, N.

Di, S.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

Dong, B.-Z.

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

Espinosa, J.

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

Farn, M. W.

Feng, D.

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

Friesem, A. A.

Gale, M. T.

Gaylord, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, second ed. (McGraw-Hill, New York, 1996).

Gorecki, M.

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[Crossref]

Gracht, J.

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

Grann, E. B.

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A. 11, 1827–1834 (1994).
[Crossref]

Gu, B.-Y.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

Harrigan, M. E.

Hasman, E.

Hayasaka, K.

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

Hirayama, K

Hirayama, K.

Hu, B.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

Illueca, C.

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

Jaroszewicz, Z.

Jin, G. F.

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

Kikuta, H.

H. Kikuta, H. Toyota, and W. J. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Review,  10, 63–73 (2003).
[Crossref]

Kim, H. C.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Kolodziejczyk, A.

Leger, J. R.

Leseberg, D.

Levy, U.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Lin, J.

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

Lin, P.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Liu, J.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

Liu, S.

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

Liu, S.-T.

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

Magnusson, R.

Mait, J. N.

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A. 16, 1157–1167. (1999).
[Crossref]

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

Mas, D.

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

Mathews, S.

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

Mellin, S. D.

S. D. Mellin and G. P. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express. 8, 705–722 (2001).
[Crossref] [PubMed]

Mikula, G.

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek. “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express. 15, 9184–9193 (2007).
[Crossref] [PubMed]

Mirotznik, M. S.

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A. 16, 1157–1167. (1999).
[Crossref]

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

Moharam, M. G.

J. R. Leger, M. G. Moharam, and T. K. Gaylord, “Feature Issue on Diffractive Optics,” Appl. Opt. 34, 2399–2559 (1995).
[Crossref] [PubMed]

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A. 11, 1827–1834 (1994).
[Crossref]

Nezhad, M.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Nishioka, H.

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

Nordin, G. P.

S. D. Mellin and G. P. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express. 8, 705–722 (2001).
[Crossref] [PubMed]

Perez, J.

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

Petelczyc, K.

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek. “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express. 15, 9184–9193 (2007).
[Crossref] [PubMed]

Pommet, D. A.

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A. 11, 1827–1834 (1994).
[Crossref]

Prather, D. W.

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A. 16, 1157–1167. (1999).
[Crossref]

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

Prokopowicz, C.

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[Crossref]

Pustai, D.

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

Sochacki, J.

Sun, X.-D.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

Sypek, M.

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek. “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express. 15, 9184–9193 (2007).
[Crossref] [PubMed]

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[Crossref]

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).
[Crossref]

Taflove, A.

A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

Tomita, H.

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

Toyota, H.

H. Kikuta, H. Toyota, and W. J. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Review,  10, 63–73 (2003).
[Crossref]

Tsai, C. H.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Ueda, K.

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

Wang, S.-Q.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

Wang, Y.-Q.

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

Wil-son, D. W.

Wu, M. X.

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

Yan, Y. B.

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

Yang, G.-Z.

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

Ye, J.

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

Ye, J.-S.

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

Yeshaiahu, F.

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Yu, W. J.

H. Kikuta, H. Toyota, and W. J. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Review,  10, 63–73 (2003).
[Crossref]

Appl. Opt. (6)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. A. (8)

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A. 11, 1827–1834 (1994).
[Crossref]

B.-Z. Dong, J. Liu, B.-Y. Gu, and G.-Z. Yang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A. 18, 1465–1470 (2001).
[Crossref]

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on a rigorous electromagnetic theory,” J. Opt. Soc. Am. A. 19, 2030–2035 (2002).
[Crossref]

J. Lin, J. Liu, J. Ye, and S. Liu, “Design of microlenses with long focal depth based on general focal length function,” J. Opt. Soc. Am. A. 24, 1747–1751 (2007).
[Crossref]

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination,” J. Opt. Soc. Am. A. 24, 512–516 (2007).
[Crossref]

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A. 16, 1157–1167. (1999).
[Crossref]

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A. 15, 1599–1607 (1998).
[Crossref]

U. Levy, M. Nezhad, H. C. Kim, C. H. Tsai, P. Lin, and F. Yeshaiahu, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A. 22, 724–733(2005).
[Crossref]

Opt. Commun. (1)

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).
[Crossref]

Opt. Eng. (1)

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[Crossref]

Opt. Express. (6)

S. D. Mellin and G. P. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express. 8, 705–722 (2001).
[Crossref] [PubMed]

H. Nishioka, H. Tomita, K. Hayasaka, and K. Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express. 14, 7447–7455 (2006).
[Crossref] [PubMed]

D. Feng, Y. B. Yan, G. F. Jin, and M. X. Wu. “Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution,” Opt. Express. 11, 1987–1994 (2003).
[Crossref]

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek. “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express. 15, 9184–9193 (2007).
[Crossref] [PubMed]

D. Mas, J. Espinosa, J. Perez, and C. Illueca. “Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus,” Opt. Express. 15, 17842–17854 (2007).
[Crossref] [PubMed]

M. S. Mirotznik, J. Gracht, D. Pustai, and S. Mathews, “Design of cubic-phase optical elements using subwavelength microstructures,” Opt. Express. 16, 1250–1259 (2008).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Review (1)

H. Kikuta, H. Toyota, and W. J. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Review,  10, 63–73 (2003).
[Crossref]

Other (2)

A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

J. W. Goodman, Introduction to Fourier Optics, second ed. (McGraw-Hill, New York, 1996).

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Figures (8)

Fig. 1.
Fig. 1. A binary sub-wavelength diffractive lens (BSDL) based on Farn method[29] and a continuous profile diffractive lens
Fig. 2.
Fig. 2. Schematic diagram of our rigorous design and analysis process
Fig. 3.
Fig. 3. Binary sub-wavelength profile distribution of BSDLs for different preset focal depth (df=0, 9µm, and 18µm)
Fig. 4.
Fig. 4. Optical field axial intensity distribution of BSDLs(f/0.6) with different preset focal depth df.
Fig. 5.
Fig. 5. Optical field transverse intensity distribution of BSDLs(f/0.6) with different preset focal depth df at the actual focal plane
Fig. 6.
Fig. 6. Propagation plots of the intensity of the electric field of BSDLs (f/0.6) with different preset focal depths: (a) df=18µm, (b) df=9µm, (c) df=0µm.
Fig. 7.
Fig. 7. Optical field axial intensity distribution of BSDLs (f/1.0) with different preset focal depth df.
Fig. 8.
Fig. 8. Optical field transverse intensity distribution of BSDLs(f/1.0) with different preset focal depth df at the actual focal plane

Tables (1)

Tables Icon

Table 1. Focusing characteristics of BSDLs with different preset focal depths for several f-numbers*

Equations (4)

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y ( x ) = n 2 n 1 n 2 ( f 2 + x 2 f m λ ) x m x min ( x m + 1 , D 2 )
f ( x ) = f 0 + df x 2 ( D 2 ) 2
y ( x ) = n 2 n 1 n 2 ( ( f 0 + df x 2 ( D 2 ) 2 ) 2 + x 2 ( f 0 + df x 2 ( D 2 ) 2 ) m λ )
H ( f x ) = exp ( j 2 π y 0 1 cos 2 α λ )

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