Abstract

The interaction of a tightly focused laser beam with a step function is encountered in optical storage media, scanning microscopy, positioning and aligning systems, and various other applications. A theoretical and experimental investigation provides an improved description of the physical process and indicates the possibility of achieving extreme superresolution suitable for certain applications.

© 1991 Optical Society of America

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References

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  1. H. H. Hopkins, J. Opt. Soc. Am. 69, 4 (1979).
    [Crossref]
  2. G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).
  3. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  4. L. W. Casperson, C. Yeh, Appl. Opt. 17, 1637 (1978).
    [Crossref] [PubMed]
  5. H. D. Betz, Appl. Opt. 8, 1007 (1969).
    [Crossref] [PubMed]

1979 (1)

1978 (1)

1969 (1)

Betz, H. D.

Bouwhuis, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Braat, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Casperson, L. W.

Hopkins, H. H.

Huijser, A.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Pasman, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Schouhamer Immink, K.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Sheppard, C.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

van Rosmalen, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

Wilson, T.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Yeh, C.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Other (2)

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schouhamer Immink, Principles of Optical Disk Systems (Hilger, London, 1985).

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

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Figures (5)

Fig. 1
Fig. 1

Configuration of the step.

Fig. 2
Fig. 2

Illumination of the step by a Gaussian beam moving from the left to the right.

Fig. 3
Fig. 3

Calculated diffraction by a step of λ/2. The horizontal scale is in micrometers over the observation plane, and the vertical scale is normalized to unity for the peak intensity away from the step.

Fig. 4
Fig. 4

Experimental setup. The source is a He–Ne laser, and the image from the CCD camera is processed by a digital computer.

Fig. 5
Fig. 5

Intensity distributions across magnified observed diffraction patterns. (a) q = −0.2 μm, (b) q = 0, (c) q = 0.3 μm.

Equations (11)

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E ( x , y , z ) = E 0 w 0 w ( z ) exp { - r 2 [ 1 w 2 ( z ) + j k 2 R ( z ) ] } × exp ( - j k z ) exp [ j tan - 1 ( z z 0 ) ] ,
w 2 ( z ) = w 0 2 ( 1 + z 2 z 0 2 ) ,
R ( z ) = z + z 0 2 z ,
z 0 = π w 0 2 n λ ,
E ( x , y ) = exp ( - j k D ) j λ D a ˜ T ( x 1 , y 1 ) E 1 ( x 1 , y 1 + q ) × exp { - j k 2 D [ ( x - x 1 ) 2 + ( y - y 1 ) 2 ] } d x 1 d y 1 .
E ( x , y , z = D ) = A - exp ( - B x 1 2 + C x x 1 ) d x 1 × - exp ( - B y 1 2 + C y y 1 ) × exp { - q 2 [ 1 w 2 ( z ) + j k 2 R ( z ) ] } d y 1 ,
A = exp { j [ - k z + tan - 1 ( z z 0 ) ] } w ( z ) ,
B = 1 w 2 ( z ) + j k 2 R ( z ) + j k 2 D ,
C x = x j k D ,
C y = - q 2 w 2 ( z ) + j ( y k D - q k R ) .
E ( x , y , D ) = A 1 - exp [ - B 1 ( x 1 ) 2 + C x 1 x 1 ] d x 1 × - 0 exp [ - B 1 ( y 1 ) 2 + C y 1 y 1 ] d y 1 + A 2 - exp [ - B 2 ( x 1 ) 2 + C x 2 x 1 ] d x 1 × 0 exp [ - B 2 ( y 1 ) 2 + C y 2 y 1 ] d y 1 .

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