Abstract

We present an experimental study on the diffraction of light by an aperture small compared with the wavelength. The aperture is illuminated by laser light guided in a metal-clad tapered optical fiber. We investigate different orientations of the aperture in the plane: normal to the cleaved plane, oblique to the cleaved plane, and off-center. We measure the far-field, two-dimensional intensity distributions of the diffracted light as functions of angle coordinates θ and ϕ in a full half-space for various polarization states and analyze the patterns by using low-order multipole fields. We also examine the near- and far-field effects of placing small periodic corrugations near the aperture, focusing on the role of surface-wave excitations. We measure the near-field intensity distributions near the aperture with a near-field scanning optical microscope and discuss their relation to the far-field diffracted fields.

© 2001 Optical Society of America

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References

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  1. M. Ohtsu, H. Hori, Near-Field Nano-optics (Kluwer Academic, New York, 1999).
  2. M. Paesler, P. Moyer, Near-Field Optics (Wiley, New York, 1996).
  3. D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
    [CrossRef]
  4. C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
    [CrossRef]
  5. R. E. English, N. George, “Diffraction from a small square aperture: approximation aperture fields,” J. Opt. Soc. Am. A 5, 192–199 (1988).
    [CrossRef]
  6. H. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  7. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1974), Sect. 9.5, p. 405.
  8. L. Novotny, D. W. Pohl, R. Regli, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
    [CrossRef]
  9. L. Novotny, D. W. Pohl, B. Hecht, “Scanning near-field optical probe with ultrasmall spot size,” Opt. Lett. 20, 970–972 (1995).
    [CrossRef] [PubMed]
  10. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
    [CrossRef] [PubMed]
  11. R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
    [CrossRef]
  12. C. Obermuller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
    [CrossRef]
  13. D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
    [CrossRef]
  14. S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
    [CrossRef]
  15. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1974), Chap. 16.
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, Singapore, 1996), Chap. 9.
  17. See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
    [CrossRef]

2000 (2)

S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
[CrossRef]

1999 (1)

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
[CrossRef]

1997 (1)

R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
[CrossRef]

1996 (2)

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
[CrossRef]

1995 (2)

C. Obermuller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

L. Novotny, D. W. Pohl, B. Hecht, “Scanning near-field optical probe with ultrasmall spot size,” Opt. Lett. 20, 970–972 (1995).
[CrossRef] [PubMed]

1994 (1)

1988 (1)

1954 (1)

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

1944 (1)

H. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Bethe, H.

H. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Bouwkamp, C. J.

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Chavez-Pirson, A.

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
[CrossRef]

Decca, R. S.

R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
[CrossRef]

Drew, H. D.

R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
[CrossRef]

Empson, K. L.

R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
[CrossRef]

English, R. E.

George, N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, Singapore, 1996), Chap. 9.

Hecht, B.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

L. Novotny, D. W. Pohl, B. Hecht, “Scanning near-field optical probe with ultrasmall spot size,” Opt. Lett. 20, 970–972 (1995).
[CrossRef] [PubMed]

Hori, H.

M. Ohtsu, H. Hori, Near-Field Nano-optics (Kluwer Academic, New York, 1999).

Inouye, Y.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1974), Sect. 9.5, p. 405.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1974), Chap. 16.

Jung, S. T.

S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
[CrossRef]

Karrai, K.

C. Obermuller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Lee, Y. H.

S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
[CrossRef]

Mononobe, S.

See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
[CrossRef]

Moyer, P.

M. Paesler, P. Moyer, Near-Field Optics (Wiley, New York, 1996).

Novotny, L.

Obermuller, C.

C. Obermuller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Ohtsu, M.

See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
[CrossRef]

M. Ohtsu, H. Hori, Near-Field Nano-optics (Kluwer Academic, New York, 1999).

Paesler, M.

M. Paesler, P. Moyer, Near-Field Optics (Wiley, New York, 1996).

Pohl, D. W.

Regli, R.

Saiki, T.

See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
[CrossRef]

Shin, D. J.

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
[CrossRef]

S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
[CrossRef]

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
[CrossRef]

Appl. Phys. Lett. (4)

R. S. Decca, H. D. Drew, K. L. Empson, “Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope,” Appl. Phys. Lett. 70, 1932–1934 (1997).
[CrossRef]

C. Obermuller, K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

S. T. Jung, D. J. Shin, Y. H. Lee, “Near-field fiber tip to handle high input power more than 150 mW,” Appl. Phys. Lett. 77, 2638–2640 (2000).
[CrossRef]

See, for instance, T. Saiki, S. Mononobe, M. Ohtsu, “Tailoring a high-transmission fiber probe for photon scanning tunneling microscope,” Appl. Phys. Lett. 68, 2612–2614 (1996).
[CrossRef]

J. Microsc. (1)

D. J. Shin, A. Chavez-Pirson, Y. H. Lee, “Diffraction of circularly polarized light from near-field optical probes,” J. Microsc. 194, 353–359 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Phys. Rev. (1)

H. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Phys. Rev. Lett. (1)

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Other (5)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1974), Sect. 9.5, p. 405.

M. Ohtsu, H. Hori, Near-Field Nano-optics (Kluwer Academic, New York, 1999).

M. Paesler, P. Moyer, Near-Field Optics (Wiley, New York, 1996).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1974), Chap. 16.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, Singapore, 1996), Chap. 9.

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Figures (8)

Fig. 1
Fig. 1

(a) Fabrication procedure for the subwavelength-sized aperture in a metal plane. (b) Experimental setup for near-field measurements. (c) Experimental setup for far-field measurements. LD and PMT denote laser diode and photomultiplier, respectively.

Fig. 2
Fig. 2

Aperture on a normally cleaved metal plane. (a), (b) Far-field diffraction patterns obtained with 810-nm light. The arrows indicate the polarization direction. (c) SEM picture of the aperture. The bar is 600 nm. (d) Multipole model with the coefficients listed in Table 1. (e) Cross sections along the dotted lines in (b) and (d). The squares are the data and the solid curves are from the multipole model. (f), (g) Far-field diffraction patterns obtained with 488-nm light. The arrows indicate the polarization direction. (h) Multipole model with the coefficients listed in Table 2. (i) Cross sections along the dotted lines in (g) and (h). The squares are data, and the solid curves are from the multipole model.

Fig. 3
Fig. 3

Aperture in an obliquely cleaved metal plane. (a)–(f) Far-field diffraction patterns obtained with 810-nm light. The arrows indicate the polarization direction. (f) Circular polarization. (g) SEM picture and the geometry of the aperture structure. The bar is 1 μm. Note the definition of the polar angle, θ. (h) Total throughput as a function of the polarization direction. The letters a–e indicate the figures in (a)–(e). (i), (j) Far-field diffraction patterns obtained with 488-nm light. The arrows indicate the polarization direction. (k), (l) Multipole model with the coefficients listed in Table 3. (m) Cross sections along the dotted lines in (i) and (k). The squares are data, and the solid curves are from the multipole model. The data and the fitting curve along the polarization direction are shifted upward for clarity.

Fig. 4
Fig. 4

Aperture offset from the center of the tapered waveguide. (a) SEM picture of the aperture. The bar is 1 μm. Note the scratches in the horizontal direction. (b) Far-field diffraction pattern from the aperture. The arrow indicates the polarization direction. Note the fringes due to the surface scratches. (c) Replica of (b) in a contour plot to ensure the polarization direction of the diffraction pattern.

Fig. 5
Fig. 5

Aperture in a corrugated metal plane. Far-field diffraction patterns with 810-nm light [(a)–(c)] and 488-nm light [(d)–(f)]. The arrows indicate the polarization direction. (a), (d) Linear polarization normal to the surface scratches. (b), (e) Enhanced interference fringes in (a) and (d), respectively. (c), (f) Linear polarization parallel to the surface scratches. (g) SEM picture of the aperture. The bar is 200 nm. (h) Topography obtained by shear-force detection. The bar is 2 μm. The arrow indicates the location of the aperture.

Fig. 6
Fig. 6

Reconstructed near-field patterns. The arrows indicate the polarization direction. (a) 810 nm, linear polarization normal to the surface scratches, (b) 810 nm, linear polarization along the scratches, (c) 488 nm, linear polarization normal to the scratches, and (d) 488 nm, linear polarization along the scratches. Each image size is 10×10 μm.

Fig. 7
Fig. 7

(a)–(d) Near-field images of linearly polarized light from a small aperture. The intensity scales are adjusted to show the weak sidelobes. The arrows indicate the polarization direction. (e) Topography obtained by shear-force detection. The aperture is located at the center of the image, and the bright point is a dust particle. Excluding the dust particle, the darkest (brightest) regions correspond to 0 nm (25 nm). (f) SEM picture of the aperture. The bars in (e) and (f) are 1 μm long. All images except (f) have the same magnification and orientation.

Fig. 8
Fig. 8

Radiation patterns of the decomposed multipole fields.

Tables (3)

Tables Icon

Table 1 Normalized Coefficients of Multipoles (l, m) [Figs. 2(d) and 2(e) ]

Tables Icon

Table 2 Normalized Coefficients of Multipoles (l, m) [Figs. 2(h) and 2(i) ]

Tables Icon

Table 3 Normalized Coefficients of Multipoles (l, m) [Figs. 3(k) and 3(m) ]

Equations (17)

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θ=π(x2+y2)1/2,
ϕ=arg(x+yi).
Fnf(x)=dΩ cos θ[Iff(θ, ϕ)]1/2[Iffsm(θ, ϕ)]1/2×exp[-ik(R-nˆ  x)],
ElmM=hl(1)(kr)Xlm(θ, ϕ),BlmM=- ik ×ElmM,
BlmE=hl(1)(kr)Xlm(θ, ϕ),ElmE=ik ×BlmE,
θ11=143πexp (iϕ),ϕ11=143π i cos θ exp (iϕ),
θ21=145πcos θ exp (iϕ),
ϕ21=145πi cos 2θ exp (iϕ),
θ31=1167π32+52cos 2θexp (iϕ),
ϕ31=1167π i14cosθ+154cos 3θexp (iϕ),
θ41=1329π92cos θ+72cos 3θexp (iϕ),
ϕ41=1329π i (cos 2θ+7 cos 4θ)exp (iϕ).
Iθ(θ, ϕ)=l,m(-i)l+1[aM(l , m)θlm(θ, ϕ)+aE(l, m)ϕlm(θ, ϕ)]2,
Iϕ(θ, ϕ)=l,m(-i)l+1[aM(l, m)ϕlm(θ, ϕ)-aE(l, m)θlm(θ, ϕ)]2,
θl-1(θ, ϕ)=θl1(θ, ϕ)*,ϕl-1(θ, ϕ)=ϕl1(θ, ϕ)*,
aM(l, -1)=(-1)l+1aM(l, 1)*,
aE(l, -1)=(-1)l+1aE(l, 1)*.

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