Abstract

A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.

© 2006 Optical Society of America

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References

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    [CrossRef]
  7. 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]
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    [CrossRef]
  9. J. Tominaga, T. Nakano, and N. Atoda, "An approach for recording and readout beyond the diffraction limit with a Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
    [CrossRef]
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    [CrossRef]
  12. X. E. Wang, Z. Z. Fan, and T. T. Tang, "Vector near-field calculation of scanning near-field optical microscopy probes using Borgnis potentials as auxiliary functions," J. Opt. Soc. Am. A 22, 1263-1273 (2005).
    [CrossRef]
  13. K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer-Verlag, 1998).
  14. A. Vainstein, Electromagnetic Waves (Soviet Radio Press, 1957) (in Russian).
  15. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (Science Press, 2000).

2005

2004

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

2003

2001

1998

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

1995

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

1987

1984

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

1981

Atoda, N.

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

Canale, R. P.

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (Science Press, 2000).

Chapra, S. C.

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (Science Press, 2000).

Dementev, A. S.

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

Erkkila, J. H.

Fan, Z. Z.

Fletcher, D. A.

Garavaglia, M.

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]

Li, D.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer-Verlag, 1998).

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 a 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.

Shima, T.

T. Nakano, T. Shima, and J. Tominaga, "Readout process analysis of super-RENS disk," in Proc. SPIE 5380, 328-335 (2004).
[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 a Sb thin film," Appl. Phys. Lett. 73, 2078-2080 (1998).
[CrossRef]

Torroba, R.

Vainstein, A.

A. Vainstein, Electromagnetic Waves (Soviet Radio Press, 1957) (in Russian).

Visser, T. D.

Wang, X. E.

Wiersma, S. H.

Zhang, K.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer-Verlag, 1998).

Appl. Opt.

Appl. Phys. Lett.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Opt. Spectrosc.

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

Proc. SPIE

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

Other

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer-Verlag, 1998).

A. Vainstein, Electromagnetic Waves (Soviet Radio Press, 1957) (in Russian).

S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (Science Press, 2000).

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Figures (8)

Fig. 1
Fig. 1

Model of the diffraction at an aperture.

Fig. 2
Fig. 2

Cartesian, cylindrical, and spherical coordinates.

Fig. 3
Fig. 3

Distribution of the real part (solid curves) and absolute value (dashed curves) of Borgnis potentials in the aperture along the x axis. (a) U and (b) its z derivative U z .

Fig. 4
Fig. 4

(a) Absolute value (solid curve) and argument (dashed curve) of the r component of electric field E r in the aperture along the x axis calculated from the Borgnis potentials and (b) their deviation from theoretic values.

Fig. 5
Fig. 5

Distribution of the real part (solid curves) and absolute value (dashed curves) of Borgnis potentials on the diffractive apertured diaphragm. (a) U along the x axis and (b) the z derivative of V ( V z ) along the y axis.

Fig. 6
Fig. 6

Gray plots of Borgnis potentials on the focusing plane of the converging input wave. (a) U and (b) V .

Fig. 7
Fig. 7

Gray plots of components of the electric field on the focusing plane of the converging input wave. (a) E r , (b) E φ , (c) E z .

Fig. 8
Fig. 8

Distribution of the electric energy density on the focusing plane of the converging input wave.

Equations (34)

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E r = 2 U ( r , φ , z ) r z j ω μ r V ( r , φ , z ) φ ,
E φ = 2 U ( r , φ , z ) r φ z + j ω μ V ( r , φ , z ) r ,
E z = ( 2 z 2 + k 2 ) U ( r , φ , z ) ,
H r = 2 V ( r , φ , z ) r z + j ω ϵ r U ( r , φ , z ) φ ,
H φ = 2 V ( r , φ , z ) r φ z j ω ϵ U ( r , φ , z ) r ,
H z = ( 2 z 2 + k 2 ) V ( r , φ , z ) ,
( 2 + k 2 ) { U V } = 0 .
c F ( r ) = S c + S Λ [ G ( r , r ) F ( r ) z F ( r ) G ( r , r ) z ] d s ,
c = { 1 2 P on S c or S Λ 1 otherwise } ,
2 G ( r , r ) + k 2 G ( r , r ) = δ ( r r ) ,
G ( r , r ) = 1 4 π exp ( j k r r ) r r = 1 4 π exp ( j k r 2 + r 2 2 r r cos ( φ φ ) + ( z z ) 2 ) r 2 + r 2 2 r r cos ( φ φ ) + ( z z ) 2 ,
E ( r , θ , φ ) = e θ j k sin θ exp ( j k r ) ( ω ϵ r ) ,
H ( r , θ , φ ) = e φ j sin θ exp ( j k r ) r ,
E ( r , θ , φ ) = e θ j k sin θ exp ( j k r ) ( ω ϵ r ) ,
H ( r , θ , φ ) = e φ j sin θ exp ( j k r ) r .
x = r cos θ = r cos φ , y = r sin θ sin φ = r sin φ , z = r sin θ cos φ = z .
e φ = cos φ e y sin φ e z ,
e θ = sin θ e x cos θ sin φ e y + cos θ cos φ e z .
e x = cos φ e r sin φ e φ , e y = sin φ e r + cos φ e φ .
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 = r 2 + z 2 .
U ( r , φ , z ) = U ( r , z ) cos φ = U ( r , z ) [ exp ( j φ ) + exp ( j φ ) ] 2 ,
V ( r , φ , z ) = j V ( r , z ) sin φ = V ( r , z ) [ exp ( j φ ) exp ( j φ ) ] 2
2 U ( r , z ) r z + ω μ V ( r , z ) r = j k z 2 exp ( j k R ) ω ϵ R 3 ,
U ( r , z ) r z + ω μ V ( r , z ) r = j k exp ( j k R ) ω ϵ R ,
2 V ( r , z ) r z ω ϵ U ( r , z ) r = z exp ( j k R ) R 2 ,
V ( r , z ) r z ω ϵ U ( r , z ) r = z exp ( j k R ) R 2 .
F z = z 0 = exp ( j k R ) R 2 n a n r n ,
F ( r ) 2 + S c [ G ( r , r ) F ( r ) z F ( r ) G ( r , r ) z ] d S = S Λ [ G ( r , r ) F ( r ) z F ( r ) G ( r , r ) z ] d S ,
E r S c = 0 , E φ S c = 0 , H z S c = 0 .
V S c = 0 , U z S c = 0 .
U ( r ) 2 S c [ U ( r ) G ( r , r ) z ] d S = S Λ [ G ( r , r ) U ( r ) z U ( r ) G ( r , r ) z ] d S ,
S c [ G ( r , r ) V ( r ) z ] d S = S Λ [ G ( r , r ) V ( r ) z V ( r ) G ( r , r ) z ] d S .

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