Abstract

We demonstrate that, under suitable conditions, subwavelength feature variations of an object can affect the corresponding far-field diffraction pattern in a measurable way. We present an experiment in which width variations of less than 1/100 of the wavelength are measured with a slit whose width is 100 times the wavelength. Integral and differential intensity measurements in the far field are fully consistent with standard diffraction theory even in the subwavelength variation regime. In particular, slit modulations of 6 nm with a wavelength of 670 nm are shown to follow theoretical calculations within the experimental sensitivity of 10-5.

© 2002 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  2. T. W. Mayes and B. F. Melton, Am. J. Phys. 62, 397 (1994).
    [CrossRef]
  3. J. A. Lock, Am. J. Phys. 164, 1307 (1996).
    [CrossRef]
  4. M. A. Cervantes, J. Mod. Opt. 146, 255 (1999).
    [CrossRef]
  5. M. Glass, Appl. Opt. 37, 2550 (1998).
    [CrossRef]
  6. O. W. Shih, J. Appl. Phys. 184, 6485 (1998).
    [CrossRef]
  7. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [CrossRef]
  8. J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
    [CrossRef]
  9. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
  10. Blades were obtained by dismantling a BIC razor.
  11. Isaac Newton, Opticks (Dover, New York, 1952).

1999 (2)

M. A. Cervantes, J. Mod. Opt. 146, 255 (1999).
[CrossRef]

J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

1998 (3)

M. Glass, Appl. Opt. 37, 2550 (1998).
[CrossRef]

O. W. Shih, J. Appl. Phys. 184, 6485 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

1996 (1)

J. A. Lock, Am. J. Phys. 164, 1307 (1996).
[CrossRef]

1994 (1)

T. W. Mayes and B. F. Melton, Am. J. Phys. 62, 397 (1994).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Cervantes, M. A.

M. A. Cervantes, J. Mod. Opt. 146, 255 (1999).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Garcia-Vidal, F. J.

J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Glass, M.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Lock, J. A.

J. A. Lock, Am. J. Phys. 164, 1307 (1996).
[CrossRef]

Mayes, T. W.

T. W. Mayes and B. F. Melton, Am. J. Phys. 62, 397 (1994).
[CrossRef]

Melton, B. F.

T. W. Mayes and B. F. Melton, Am. J. Phys. 62, 397 (1994).
[CrossRef]

Newton, Isaac

Isaac Newton, Opticks (Dover, New York, 1952).

Pendry, J. B.

J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Port, J. A.

J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Shih, O. W.

O. W. Shih, J. Appl. Phys. 184, 6485 (1998).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Am. J. Phys. (2)

T. W. Mayes and B. F. Melton, Am. J. Phys. 62, 397 (1994).
[CrossRef]

J. A. Lock, Am. J. Phys. 164, 1307 (1996).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

O. W. Shih, J. Appl. Phys. 184, 6485 (1998).
[CrossRef]

J. Mod. Opt. (1)

M. A. Cervantes, J. Mod. Opt. 146, 255 (1999).
[CrossRef]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

J. A. Port, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Other (4)

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

Blades were obtained by dismantling a BIC razor.

Isaac Newton, Opticks (Dover, New York, 1952).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup: L, 670-nm laser diode; M, mirror with micrometric adjustment; XYZ, piezo stage (100 µm per axis); MC, mechanical rough Z adjust; PZ, Z piezo for slit modulation (2 µm maximum); S, slits, DF, variable diaphragm; FL, Fresnel lens; D, silicon detector.

Fig. 2
Fig. 2

Calculated and experimental intensities. Top, total intensity (solid curve) calculated for the angular aperture and wavelength (±0.0227 rad at 670 nm) and experimental data (filled circles). The experimental data have been normalized to the theoretical data. Bottom, calculated derivative intensity (solid curve) and experimental data with a 100-nm modulation (filled circles) and 6-nm modulation (open circles).

Equations (5)

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

Ix,y,z=4Aab2λ2z2sin2kax/zkax/z2sin2kby/zkby/z2,
Pz= -XX-YYIx,y,zdxdy= 16A2λ2z2-XXsin2kax/zkx/z2dx×-YYsin2kby/zky/z2dy.
Pz=8A2bλz-XXsin2kax/zkx/z2dx.
Pza,X= 8A2abπaSi2kaX/z-8A2bzkπX sin2kaX/z,
dPzda=8A2bπ Si2kaXz.

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