Abstract

Performance parameters have been presented that can be used to compare the focusing performance of different optical systems, including the effect of pupil filters. These were originally given for the paraxial case and recently extended to the high-aperture scalar regime. We generalize these parameters to the full vectorial case for an aplanatic optical system illuminated by a plane-polarized wave. The behavior of different optical systems is compared.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (2)

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, Opt. Eng. (Bellingham) 45, 098003 (2006).
[CrossRef]

2005 (1)

2004 (3)

2003 (1)

1994 (2)

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

M. W. Kowarz, Opt. Commun. 110, 274 (1994).
[CrossRef]

1988 (1)

1981 (1)

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

J. Mod. Opt. (1)

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

M. W. Kowarz, Opt. Commun. 110, 274 (1994).
[CrossRef]

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

Opt. Eng. (Bellingham) (1)

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, Opt. Eng. (Bellingham) 45, 098003 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Other (1)

R. K. Luneberg, Mathematical Theory of Optics (U. California Press, 1964).

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Figures (2)

Fig. 1
Fig. 1

(a) Variation in F, the ratio of the intensity at focus to the input power, for aberration-free focusing systems of different types. (b) Variation in F I , the ratio of the intensity at focus to the integrated intensity in the focal plane.

Fig. 2
Fig. 2

Gains, compared with complete scalar spherical illumination, for aberration-free focusing systems of different types: (a) transverse x, (b) transverse y, (c) transverse circular-polarized, (d) axial gains, and (e) polar gains.

Equations (22)

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E x = i k f ( I 0 + I 2 cos 2 ϕ ) ,
E y = i k f I 2 sin 2 ϕ ,
E z = 2 k f I 1 cos ϕ ,
I n = Q ( c ) ( 1 c 1 + c ) n 2 J n ( k ρ 1 c 2 ) exp ( i k z c ) d c .
I 0 = Q ( c ) [ 1 ( k ρ ) 2 4 ( 1 c 2 ) + i k z c 1 2 ( k z ) 2 c 2 ] d c ,
I 1 = Q ( c ) ( 1 c ) k ρ 2 ( 1 + i k z c ) d c ,
I 2 = Q ( c ) ( 1 c ) 2 ( k ρ ) 2 8 d c .
q n = Q ( c ) c n d c ,
I 0 = q 0 + i k z q 1 ( k z ) 2 2 q 2 ( k ρ ) 2 4 ( q 0 q 2 ) ,
I 1 = k ρ 2 ( q 0 q 1 ) + i ( k z ) ( k ρ ) 2 ( q 1 q 2 ) ,
I 2 = ( k ρ ) 2 8 ( q 0 2 q 1 + q 2 ) .
E = 4 Q ( c ) 2 ( 1 + c ) 2 d c .
F = 3 q 0 2 4 E
I total = Q ( c ) 2 c ( 1 + c ) 2 d c ,
Q ( c ) = c ( 1 + c ) 2 2 , cos α < c < 1
F I = 3 q 0 2 16 I total ,
G A = 3 ( q 0 q 2 q 1 2 q 0 2 ) ,
G T = 3 4 [ ( 4 q 0 q 1 2 q 0 q 2 2 q 1 2 ) ( 3 q 0 2 6 q 0 q 1 + q 0 q 2 + 2 q 1 2 ) cos 2 ϕ q 0 2 ] .
G x = 3 4 ( 10 q 0 q 1 3 q 0 q 2 3 q 0 2 4 q 1 2 q 0 2 ) ,
G y = 3 4 ( 3 q 0 2 2 q 0 q 1 q 0 q 2 q 0 2 ) ,
G C = 3 4 ( 4 q 0 q 1 2 q 0 q 2 2 q 1 2 q 0 2 ) .
G P = 2 q 1 ( q 0 q 1 ) q 0 2 .

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