Abstract

Focal shift of the converging spherical wavefront light diffracted by a circular aperture is numerically studied with the method of calculating the vector diffractive field by using Borgnis potentials given in Part I [J. Opt. Soc. Am. A 23, 872 (2006) ]. The quantitative dependence of the focal shift on the geometric parameters is discussed. The focal shift is mainly determined by the Fresnel number (Nf) on the geometric focusing plane of the converging light, and an empirical formula between the fractional focal shift and the Fresnel number is deduced for Nf<2. The focal shift of the same geometry is also studied on the basis of the scalar Rayleigh theory of diffraction, and its comparison with and difference from the result of our method are presented.

© 2006 Optical Society of America

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References

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    [CrossRef]
  4. T. D. Visser and S. H. Wiersma, "Diffraction of converging electromagnetic waves," J. Opt. Soc. Am. A 9, 2034-2047 (1992).
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    [CrossRef]
  8. I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
    [CrossRef]
  9. D. A. Fletcher, K. E. Goodson, and G. S. Kino, "Focusing in microlenses close to a wavelength in diameter," Opt. Lett. 26, 399-401 (2001).
    [CrossRef]
  10. T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
    [CrossRef]
  11. J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
    [CrossRef]
  12. M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
    [CrossRef]
  13. X. E. Wang, Z. Z. Fan, and T. T. Tang, "Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture using Borgnis potentials. I. General theory," J. Opt. Soc. Am. A 23, 872-877 (2006).
    [CrossRef]
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  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

2006 (1)

2005 (2)

2004 (1)

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[CrossRef]

2003 (2)

Y. Li, "Focal shift in small-Fresnel-number focusing systems of different relative aperture," J. Opt. Soc. Am. A 20, 234-239 (2003).
[CrossRef]

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

2001 (1)

1998 (1)

J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

1995 (1)

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

1992 (1)

1987 (1)

1984 (1)

A. S. Dementev and D. P. Domarkene, "Diffraction of converging spherical waves by a circular aperture," Opt. Spectrosc. 56, 532-534 (1984).

1981 (1)

Atoda, N.

J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergammon, 1964).

Dementev, A. S.

A. S. Dementev and D. P. Domarkene, "Diffraction of converging spherical waves by a circular aperture," Opt. Spectrosc. 56, 532-534 (1984).

Domarkene, D. P.

A. S. Dementev and D. P. Domarkene, "Diffraction of converging spherical waves by a circular aperture," Opt. Spectrosc. 56, 532-534 (1984).

Erkkila, J. H.

Fan, Z. Z.

Fletcher, D. A.

Garavaglia, M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Goodson, K. E.

Ichimura, I.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Kino, G. S.

D. A. Fletcher, K. E. Goodson, and G. S. Kino, "Focusing in microlenses close to a wavelength in diameter," Opt. Lett. 26, 399-401 (2001).
[CrossRef]

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Kunz, R. R.

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

Li, Y.

Maeda, F.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Nakano, T.

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[CrossRef]

J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

Ooki, H.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Osato, K.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Owa, H.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

Rogers, M. E.

Rothschild, M.

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

Shima, T.

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[CrossRef]

Sinta, R. F.

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

Switkes, M.

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

Tang, T. T.

Tominaga, J.

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[CrossRef]

J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

Torroba, R.

Visser, T. D.

Wang, X. E.

Wiersma, S. H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergammon, 1964).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with an Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

J. Vac. Sci. Technol. B (1)

M. Switkes, R. R. Kunz, M. Rothschild, and R. F. Sinta, "Extending optics to 50 nm and beyond with immersion lithography," J. Vac. Sci. Technol. B 21, 2794-2799 (2003).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

A. S. Dementev and D. P. Domarkene, "Diffraction of converging spherical waves by a circular aperture," Opt. Spectrosc. 56, 532-534 (1984).

Proc. SPIE (2)

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, and G. S. Kino, "High density optical disk system using a solid immersion lens," in Proc. SPIE 2514, 176-181 (1995).
[CrossRef]

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergammon, 1964).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (10)

Fig. 1
Fig. 1

Model of a converging light diffracted by a circular aperture.

Fig. 2
Fig. 2

Contour lines of Fresnel number N f related to aperture radius Λ and z 0 .

Fig. 3
Fig. 3

Distributions of the electric energy density of the diffracted converging light on plane y = 0 in geometries of θ = 30 ° and (a) Λ = 250 λ or (b) Λ = 5 λ .

Fig. 4
Fig. 4

Distributions of the electric energy density along the optical axis of the diffracted converging light of θ = 30 ° by circular apertures of different radii.

Fig. 5
Fig. 5

Distributions of the electric energy density of the diffracted converging light on plane y = 0 in geometries of Λ = 100 λ and (a) z 0 = 100 λ or (b) z 0 = 5000 λ .

Fig. 6
Fig. 6

Relationship between the fractional focal shift F s f and the Fresnel number N f for apertures of different radii.

Fig. 7
Fig. 7

Same as Fig. 6 but for the region of N f < 2.0 .

Fig. 8
Fig. 8

Fitting curve for the relationship between F s f and N f .

Fig. 9
Fig. 9

Relationship between the fractional focal shift F s f and the Fresnel number N f for apertures of different radii based on the Rayleigh theory of diffraction.

Fig. 10
Fig. 10

Comparison of the relationships between the fractional focal shift F s f and the Fresnel number N f based on the vector and scalar diffractive theories for Λ = 10 λ .

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

E ( r , φ , z ) = j k ω ϵ R exp ( j k R ) [ cos φ z 2 R 2 e r + sin φ e φ + r z cos φ R 2 e z ] ,
H ( r , φ , z ) = j exp ( j k R ) R 2 ( z sin φ e r + z cos φ e φ r sin φ e z ) ,
R = r 2 + z 2 ,
N = Λ 2 λ z ,
N f = Λ 2 λ z 0 .
W e ( x , y , z ) = ϵ 0 E ( x , y , z ) 2 4 ,
w e ( x , y , z ) = E ( x , y , z ) 2 E ( 0 , 0 , 0 ) 2 .
Λ = 100 λ , z 0 = 5000 λ .
U ( P ) = exp ( j k s 0 ) S Σ K ( S ) U 0 ( S ) exp [ j k ( s s 0 ) ] s d S ,
s d = s e s 0 ,
s 0 = R 0 z p ,
s e = ( R 0 2 + z p 2 2 R 0 z p cos θ ) 1 2 = ( R 0 2 + z p 2 2 z p z 0 ) 1 2 .
s d T λ .
( R 0 2 + z p 2 2 z p z 0 ) 1 2 R 0 + z p T λ .
z p R 0 [ 1 + Λ 2 T λ z 0 ( 1 + 1 + ( Λ z 0 ) 2 ) ] 1 .
z p m R 0 = [ 1 + N f T ( 1 + 1 + ( Λ z 0 ) 2 ) ] 1 .
z p m R 0 = [ 1 + Λ c T λ ( 1 + 1 + c 2 ) ] 1 .
z p m R 0 = [ 1 + Λ 2 T λ ( z 0 + z 0 2 + Λ 2 ) ] 1 .
F s f = F s R 0 ,
F s f = F s Λ 2 + z 0 2 .
F s f = 0.1216 + 0.87372 * e N f 1.19378 .
F ( r , φ , z ) = exp ( j k R ) R ,
F ( r ) = S Λ F ( r ) G ( r , r ) z d s ,
G ( r , r ) = G 0 ( r , r ) G 0 ( r img , r ) .

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