Abstract

We investigate a two-dimensional low F-number dual micro-axilens array with binary structures based on a rigorous electromagnetic theory. The focal characteristics of a binary dual micro-axilens array (BDMA), including axial performances (focal depth and focal shift) and transverse performances (focal spot size and diffraction efficiency), have been analyzed in detail for different F-numbers, different incident polarization (TE and TM) waves, and different distances between micro-axilens. Numerical results reveal that the interference effect of a BDMA is not very evident, which is useful for building a BDMA with a high fill factor, and the focal characteristics of a BDMA are sensitive to the polarization of an incident wave. The comparative results have also shown that the diffraction efficiency of a BDMA will increase and the focal spot size of a BDMS will decrease when the F-number increases, for both TE polarization and TM polarization, respectively. It is expected that this investigation will provide useful insight into the design of micro-optical elements with high integration.

©2011 Optical Society of America

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References

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2010 (3)

R. Stevens and T. Miyashita, “Review of standards for microlenses and microlens arrays,” Imaging Sci. J. 58(4), 202–212 (2010).
[Crossref]

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

K. L. Wlodarczyk, E. Mendez, H. J. Baker, R. McBride, and D. R. Hall, “Laser smoothing of binary gratings and multilevel etched structures in fused silica,” Appl. Opt. 49(11), 1997–2005 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (2)

2006 (1)

2004 (1)

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

2002 (2)

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[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 rigorous electromagnetic theory,” J. Opt. Soc. Am. A 19(10), 2030–2035 (2002).
[Crossref]

2001 (1)

1999 (3)

1998 (1)

1992 (3)

1991 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Astilean, S.

Baker, H. J.

Bará, S.

Brunner, R.

Cambril, E.

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A 16(5), 1143–1156 (1999).
[Crossref]

Chavel, P.

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A 16(5), 1143–1156 (1999).
[Crossref]

Chen, Q. D.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Chen, Y.

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

Chokshi, T. V.

Chronis, N.

Collins, J. P.

Davidson, N.

Dong, B. Z.

Druart, G.

Fan, S. S.

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

Fang, H. H.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Farn, M. W.

Feng, D.

D. Feng, P. Ou, L. S. Feng, S. L. Hu, and C. X. Zhang, “Binary sub-wavelength diffractive lenses with long focal depth and high transverse resolution,” Opt. Express 16(25), 20968–20973 (2008).
[Crossref] [PubMed]

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

Feng, L. S.

Friesem, A. A.

Gu, B. Y.

Guérineau, N.

Haïdar, R.

Hall, D. R.

Hasman, E.

Hu, S. L.

Jaroszewicz, Z.

Jin, G. F.

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

Kattnig, A.

Kolodziejczyk, A.

Lalanne, P.

Launois, H.

Lee, M. S.

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

Liu, J.

Liu, S. T.

Mait, J. N.

McBride, R.

Mendez, E.

Mirotznik, M. S.

Miyashita, T.

R. Stevens and T. Miyashita, “Review of standards for microlenses and microlens arrays,” Imaging Sci. J. 58(4), 202–212 (2010).
[Crossref]

Niu, L. G.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Ou, P.

Pätz, D.

Prather, D. W.

Primot, J.

Rodier, J. C.

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

Ruoff, J.

Sandfuchs, O.

Sauer, H.

Sinzinger, S.

Sochacki, J.

Song, J. F.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Stevens, R.

R. Stevens and T. Miyashita, “Review of standards for microlenses and microlens arrays,” Imaging Sci. J. 58(4), 202–212 (2010).
[Crossref]

Sun, H. B.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Taboury, J.

Tripathi, A.

Wang, J.

Wang, R.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Wlodarczyk, K. L.

Wu, D.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Wu, S. Z.

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

Yan, Y. B.

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

Yang, G. Z.

Ye, J. S.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Zhang, C. X.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

D. Wu, S. Z. Wu, L. G. Niu, Q. D. Chen, R. Wang, J. F. Song, H. H. Fang, and H. B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Imaging Sci. J. (1)

R. Stevens and T. Miyashita, “Review of standards for microlenses and microlens arrays,” Imaging Sci. J. 58(4), 202–212 (2010).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

M. S. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A, Pure Appl. Opt. 4(5), S119–S124 (2002).
[Crossref]

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

Opt. Commun. (1)

D. Feng, Y. B. Yan, G. F. Jin, and S. S. Fan, “Beam focusing characteristics of diffractive lenses with binary subwavelength structures,” Opt. Commun. 239(4-6), 345–352 (2004).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a two-dimensional electromagnetic scattering problem of a binary dual micro-axilens array (BDMA).

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Fig. 2
Fig. 2

Total optical field intensity distribution of BDMA with F-number = 0.3 and space between l = 0.0 μm, for different incident polarization wave: (a) for TE polarization wave, and (b) for TM polarization wave. The red districts indicate high field intensities, and the blue ones indicate low field ones, respectively. The yellow lines are profiles of the BDMA.

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Fig. 3
Fig. 3

Normalized axial intensity distribution of (a) BDMA and (c) continuous profiles; (b) the lateral intensity distribution of (b) BDMA and (d) continuous profiles for different incidence polarization waves (TE polarization and TM polarization). (F-number = 0.3, space between l = 0.0μm).

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Fig. 4
Fig. 4

(a) Focal shift versus distance between of BDMA with F-number = 0.3. (b) Focal depth versus distance between of BDMA with F-number = 0.3. (c) Focal spot size at the real focal plane versus distance between BDMA with F-number = 0.3. (d) Diffraction efficiency versus distance between of BDMA with F-number = 0.3.

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Fig. 5
Fig. 5

Total optical field intensity distribution of BDMA with F-number = 0.3 and space between l = 10.0 μm for different incident polarization waves: (a) TE polarization wave and (b) TM polarization wave. The red districts indicate high field intensities, and the blue ones indicate low field ones, respectively. The yellow lines are profiles of BDMA.

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Tables (2)

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Table 1 Focusing Characteristics of BDMA with Different Distance Between Dual Binary Micro-axilenses for F-numbers 0.3 (Geometrical Length is 3μm)

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Table 2 Focusing Characteristics of BDMA with Different Distance between Dual Binary Micro-axilenses and Different F-numbers (Diameter of Axilens is 10 μm)

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Equations (4)

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∂ E z ∂ t = 1 ε ( ∂ H y ∂ x − ∂ H x ∂ y − σ E z ) , ∂ H x ∂ t = − 1 μ ( ∂ E z ∂ y + σ * H x ) , ∂ H y ∂ t = 1 μ ( ∂ E z ∂ x − σ * H y ) ,
∂ H z ∂ t = − 1 μ ( ∂ E y ∂ x − ∂ E x ∂ y + σ * H z ) , ∂ E x ∂ t = 1 ε ( ∂ H z ∂ y − σ E x ) , ∂ E y ∂ t = − 1 ε ( ∂ H z ∂ x + σ E y ) .
y ( x ± D + l 2 ) = n 2 n 1 − n 2 ( f 2 + x 2 − f − m λ )   ,                                 x m ≤ | x | ≤ min ( x m + 1 , D / 2 )   ,
Δ f = f − y max .

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