Abstract

The common focusing characteristics of a cylindrical microlens with a long focal depth and under a given multiple-wavelength illumination are analyzed based on the boundary element method (BEM). The surface-relief profile of a finite-substrate-thickness microlens with a long focal depth is presented. Its focusing performances, such as the common extended focal depth (CEFD), the spot size, and the diffraction efficiency, are numerically studied in the case of TE polarization. The results show that the CEFD of the microlens increases initially, reaches a peak value, and then decreases with increasing preset focal depth. Two modified profiles of a finite-substrate-thickness cylindrical microlens are proposed for enlarging the CEFD. The rigorous numerical results indicate that the modified surface-relief structures of a cylindrical microlens can successfully modulate the optical field distribution to achieve longer CEFD, higher transverse resolution, and higher diffraction efficiency simultaneously, compared with the prototypical microlens. These investigations may provide useful information for the design and application of micro-optical elements in various multiwavelength optical systems.

© 2007 Optical Society of America

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References

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2001

2000

R. Kant, "Superresolution and increase depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

1997

1996

1992

1991

1985

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic field problems," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

1984

S. Kagami and I. Fukai, "Application of boundary-element method to electro-magnetic field problems," IEEE Trans. Microwave Theory Tech. MTT-32, 455-461 (1984).
[CrossRef]

Bara, S.

Davidson, N.

Dong, B.-Z.

Ersoy, O. K.

Friesem, A. A.

Fukai, I.

S. Kagami and I. Fukai, "Application of boundary-element method to electro-magnetic field problems," IEEE Trans. Microwave Theory Tech. MTT-32, 455-461 (1984).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Gu, B.-Y.

Hasman, E.

Hirayama, K.

Jaroszewicz, Z.

Jin, G.-F.

G.-F. Jin, Y.-B. Yan, and M.-X. Wu, Binary Optics (Chinese Defense Industry Press, 1998, in Chinese).

Kagami, S.

S. Kagami and I. Fukai, "Application of boundary-element method to electro-magnetic field problems," IEEE Trans. Microwave Theory Tech. MTT-32, 455-461 (1984).
[CrossRef]

Kant, R.

R. Kant, "Superresolution and increase depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

Kolodziejczyk, A.

Liu, J.

Mait, J. N.

Miroznik, M. S.

Ohkawa, S.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic field problems," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Prather, D. W.

Sochacki, J.

Wang, J.

Wilson, D. W.

Wu, M.-X.

G.-F. Jin, Y.-B. Yan, and M.-X. Wu, Binary Optics (Chinese Defense Industry Press, 1998, in Chinese).

Yan, Y.-B.

G.-F. Jin, Y.-B. Yan, and M.-X. Wu, Binary Optics (Chinese Defense Industry Press, 1998, in Chinese).

Yang, G.-Z.

Yashiro, K.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic field problems," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Appl. Opt.

IEEE Trans. Antennas Propag.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic field problems," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. Kagami and I. Fukai, "Application of boundary-element method to electro-magnetic field problems," IEEE Trans. Microwave Theory Tech. MTT-32, 455-461 (1984).
[CrossRef]

J. Mod. Opt.

R. Kant, "Superresolution and increase depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

G.-F. Jin, Y.-B. Yan, and M.-X. Wu, Binary Optics (Chinese Defense Industry Press, 1998, in Chinese).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a two-dimensional microlens under illumination of multiple wavelengths.

Fig. 2
Fig. 2

Axial intensity distributions of the model microlenses with aperture D = 60 μ m , preset focal length f = 60 μ m , and three different preset focal depths: (a) δ f = 10 μ m , (b) δ f = 22 μ m , and (c) δ f = 30 μ m . Curve I corresponds to the illuminating wavelength λ 1 = 0.85 μ m , curve II to λ 2 = 1.31 μ m , and curve III to λ 3 = 1.55 μ m . The CEFD is indicated by two vertical bold dashed lines.

Fig. 3
Fig. 3

Variation of the CEFD as a function of the preset focal depth. The considered microlens with the relief-surface depth function h ¯ ( x ) is the same as that in Fig. 2.

Fig. 4
Fig. 4

Dependence of the CEFD on the present focal depth for three microlenses with different relief-surface depth functions: solid curve corresponds to the prototypal surface-relief depth function h ¯ ( x ) , dotted curve to the modified surface-relief depth function h ¯ ( x ) , and dashed curve to the modified surface-relief depth function h ¯ ( x ) .

Fig. 5
Fig. 5

Same as Fig. 2c except for different surface-relief profiles of (a) h ¯ ( x ) and (b) h ¯ ( x ) .

Tables (1)

Tables Icon

Table 1 Comparisons of the Focusing Performances of Microlenses with Different Structural Parameters

Equations (8)

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h ( x , f 0 , λ ) = [ f 2 ( x , f 0 ) + n 1 ( λ ) + 1 n 1 ( λ ) 1 x 2 ] 1 2 f ( x , f 0 ) n 1 ( λ ) + 1 .
f ( x , f 0 ) = f 0 + x 2 R 2 δ f ,
h ¯ ( x ) = 1 2 [ h ( x , f 0 , λ 1 ) + h ( x , f 0 , λ n ) ] .
ϕ 1 ( r 1 ) + Γ [ ϕ 1 ( r Γ ) n ̂ G 1 ( r 1 , r Γ ) p 1 G 1 ( r 1 , r Γ ) n ̂ ϕ 1 ( r Γ ) ] d l = ϕ inc ( r 1 ) ,
ϕ 2 ( r 2 ) + Γ [ ϕ 2 ( r Γ ) n ̂ G 2 ( r 2 , r Γ ) p 2 G 2 ( r 2 , r Γ ) n ̂ ϕ 2 ( r Γ ) ] d l = 0 ,
( θ Γ 2 π 1 ) ϕ ( r Γ ) + Γ [ ϕ ( r Γ ) n ̂ G 1 ( r Γ , r Γ ) G 1 ( r Γ , r Γ ) n ̂ ϕ ( r Γ ) ] d l = ϕ inc ( r Γ ) ,
( θ Γ 2 π ) ϕ ( r Γ ) + Γ [ ϕ ( r Γ ) n ̂ G 2 ( r Γ , r Γ ) G 2 ( r Γ , r Γ ) n ̂ ϕ ( r Γ ) ] d l = 0 ,
G i ( r i , r Γ ) = ( j 4 ) H 0 ( 2 ) ( k i r i r Γ ) , ( i = 1 , 2 ) ,

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