Abstract

The dyadic Green’s function (DGF) is applied to examine the effect of focal shift in a spherical microlens with the variation of the numerical aperture for a given Fresnel number when a monochromatic plane wave with x linear polarization is incident on the microlens. By comparing the results based on the method for the vector Kirchhoff diffraction theory [J. Opt. Soc. Am. A 22, 68–76 (2005)], the effect of the spherical aberration on focal shift in a microlens is evaluated, and the influences of NA as well as the spherical aberration on the transverse electric energy density distribution in the focal plane are also investigated. In contrast with other vector formulations of imaging theory, which mainly focus on the focal shift in an aplanatic system, the DGF method is more practical and effective to locate the principal maximum energy density along the normal axis and to study transverse electric energy density distribution, because the actual shape of a microlens and the effects of aberrations are considered.

© 2009 Optical Society of America

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References

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2006 (2)

2005 (2)

2003 (1)

2002 (1)

1999 (1)

1998 (1)

H. Hamam, “A two-way optical interconnection network using a single mode fiber array,” Opt. Commun. 150, 270-276(1998).
[CrossRef]

1996 (1)

C. R. King, L. Y. Lin, and M. C. Wu, “Out-of-plane refractive microlens fabricated by surface micromachining,” IEEE Photonics Technol. Lett. 8, 1349-1351 (1996).
[CrossRef]

1994 (1)

1988 (1)

1982 (1)

Atoda, N.

Chen, J.

Dereux, A.

Fan, Z.

Girard, C.

Guo, H.

Hamam, H.

H. Hamam, “A two-way optical interconnection network using a single mode fiber array,” Opt. Commun. 150, 270-276(1998).
[CrossRef]

Javidi, B.

King, C. R.

C. R. King, L. Y. Lin, and M. C. Wu, “Out-of-plane refractive microlens fabricated by surface micromachining,” IEEE Photonics Technol. Lett. 8, 1349-1351 (1996).
[CrossRef]

Kourogi, M.

Lee, M. B.

Li, Y.

Lin, L. Y.

C. R. King, L. Y. Lin, and M. C. Wu, “Out-of-plane refractive microlens fabricated by surface micromachining,” IEEE Photonics Technol. Lett. 8, 1349-1351 (1996).
[CrossRef]

Martin, O. J. F.

Neville Connell, G. A.

Ohtsu, M.

Popovic, Z. D.

Shin, S. H.

Sprague, R. A.

Tang, T.

Tsutsui, K.

Wang, X.

Wu, M. C.

C. R. King, L. Y. Lin, and M. C. Wu, “Out-of-plane refractive microlens fabricated by surface micromachining,” IEEE Photonics Technol. Lett. 8, 1349-1351 (1996).
[CrossRef]

Yatsui, T.

Zhuang, S.

Appl. Opt. (3)

IEEE Photonics Technol. Lett. (1)

C. R. King, L. Y. Lin, and M. C. Wu, “Out-of-plane refractive microlens fabricated by surface micromachining,” IEEE Photonics Technol. Lett. 8, 1349-1351 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

H. Hamam, “A two-way optical interconnection network using a single mode fiber array,” Opt. Commun. 150, 270-276(1998).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Coordinate system with origin at geometric focus of the microlens.

Fig. 2
Fig. 2

Discretization of the left-half microlens.

Fig. 3
Fig. 3

Focusing geometry at a circular plane.

Fig. 4
Fig. 4

Normalized intensity distribution in the z axis by KDT with different definitions of f. (a)  f KDT is the curvature radius of the spherical wavefront. (b)  f BDW is the distance from center of the aperture to geometric focus.

Fig. 5
Fig. 5

Normalized intensity distribution in the z axis by the DGF and the KDT, with f DGF starting from the right vertex of the lens. (a) Normalized intensity distribution in the z axis by vector KDT. (b) Normalized intensity distribution in the z axis by the DGF method.

Fig. 6
Fig. 6

Comparison of transverse normalized electric energy density in the z = z m plane for the microlens and aplanatic system: (a)  NA = 0.3 ; (b)  NA = 0.5 ; (c)  NA = 0.7 ; and (d)  NA = 0.9 .

Equations (6)

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E ( r i ) = E 0 ( r i ) + k = 1 N p D k G 0 ( r i , r k ) · V ( r k ) E ( r k ) ,
G 0 ( r , r ) = ( I + 1 k 2 ) G 0 ( r , r ) ,
ω ( z ) = W ( z ) W ( 0 ) = E ( 0 , 0 , z ) · E * ( 0 , 0 , z ) E ( 0 , 0 , 0 ) · E * ( 0 , 0 , 0 ) ,
ω z m ( x ) = W z m ( x ) W z m ( 0 ) = E ( x , 0 , z m ) · E * ( x , 0 , z m ) E ( 0 , 0 , z m ) · E * ( 0 , 0 , z m ) ,
ω z m ( y ) = W z m ( y ) W z m ( 0 ) = E ( 0 , y , z m ) · E * ( 0 , y , z m ) E ( 0 , 0 , z m ) · E * ( 0 , 0 , z m ) .
Δ f DGF f DGF = z m f DGF .

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