Abstract

The propagation and the distribution of the optical near field in nanometallic slits are measured by a near-field scanning optical microscope. The optical near field for the p-polarized wave is confined to the middle of the slit. In contrast, the near field for the s-polarized wave is located at the edges. A simulation by the finite-difference time-domain method verifies that the near-field distribution for the s-polarized wave is due to the propagation of the surface plasmon wave (SPW) at the air-metal surface. The existence of the SPW also accounts for the extraordinary transmittance of s-polarized light, which is one order of magnitude larger than that of p-polarized light.

© 2002 Optical Society of America

1. Introduction

Light propagation in a nanoslit has received much attention recently because of its extraordinary behavior and potential applications in biologic and photonic devices. For example, Tegenfeldt et al. have proposed a new near-field scanner for mapping of moving biomolecules with super spatial resolution [1]. In this scanner, a fixed nanoslit was fabricated on a glass substrate. A laser illuminated the silt from its back and excited the molecules moving above it. With this setup, a resolution of 200 nm for flowing objects was achieved. Ebbesen et al. used a nanoslit with a periodic structure on the exit side [2,3]. They found that the transmitted light emerged from the silt as a beam with a small angular divergence. This finding is especially surprising because it is well known that light diffracts in all directions when it emerges from a nanoslit. In addition, the radiating region is mainly confined to an area with lateral dimensions comparable with the wavelength of the light. To utilize the nanoslits for these novel devices, it is essential to understand the propagation behavior of light transmitting through them. Unfortunately, analytical study of finite-thickness nanoslits is difficult. Previous calculations assumed that the thickness of the metal film was much greater than the wavelength, and the calculations were based on microwave propagation [4]. In that case, only the s-polarized wave was taken into account for its zero cut-off frequency. However, both p-polarized and s-polarized waves can exist in the finite-thickness slit geometry. Furthermore, it is known that a collective oscillation of electrons can propagate several micrometers along the metallic surface when its polarization is orthogonal to the surface. This surface plasmon wave (SPW) will cause extraordinary transmittance of light in nanoscale structures [3]. The finite thickness of metallic film and the effect of SPW make the calculation of nanoslits very complicated despite their simple structure.

In this paper, we propose what we believe to be the first combined use of finite-difference time-domain (FDTD) method [5] and near-field scanning microscopy (NSOM) [6] to study the propagation behavior of light transmitting through a metallic nanoslit. The FDTD method is a powerful tool for simulating the propagation of electromagnetic waves without any assumption in the Maxwell’s equations. The simple slit structure makes the three-dimensional simulation two dimensional. As a result, simulations of the s-polarized wave and the p-polarized wave can be carried out separately. In the meantime, the NSOM is a unique tool for resolving the optical field distribution in the nanoslit without optical diffraction. The combination of both techniques allows us to understand the nanoslit both analytically and experimentally.

2. Experimental setup and measurement results

Figure 1 is a schematic diagram for the setup of a home-made NSOM operating in a collection mode. The incident light is a solid-state diode pump laser (532.5 nm, 5 mW). The light is polarized and focused on the nanoslit fabricated using the electron beam lithography technique. The slit width is 100 nm and the thickness of the metal (aluminum) is 200 nm. A tapered fiber probe, fabricated by the heating and pulling method, is used to collect the light emitted from the nanoslit [7]. The collected light is sent to a photo-multiplier and then to a photo-counter to read the weak optical signals. The tip-sample distance is maintained by using the shear force feedback with an optical detection method [8].

 

Fig. 1. The experimental setup for a collection-mode NSOM

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Figures 2(a) and 2(b) show the topography and NSOM images near the nanoslit. The topography images (left images) show a slit of 100 nm width on the metallic film. The NSOM image for s-polarized light (right image in Fig. 2(a)) has two bright lines at the edges of the slit. In contrast, the NSOM image for p-polarized light (right image in Fig. 2(b)) has a bright line at the middle of the slit. Figure 2(c) shows the propagation of the near-field for s-polarized light. Clearly, the light is concentrated on the slit. It splits into two lobes and decays exponentially along the propagation direction. The decay length is ~ 100 nm. The propagation of p-polarized light is noisy and its far-field intensity is too weak (~1/30 of the s-polarized light) to be imaged.

 

Fig. 2. The measured topographic and NSOM images for 100 nm silt. (a) Topography (left) and s-polarized NSOM image (right). (b) Topography (left) and p-polarized NSOM image (right). (c) The propagation of the optical field for s-polarized light.

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3. Theoretical Simulation

The finite-difference time-domain (FDTD) method is used to simulate light propagation in the near field for a slit structure. The governing Maxwell’s equations for the slit structure are divided into the transverse magnetic (TM) and transverse electric (TE) modes. The TM and TE modes correspond to the s-polarized light and the p-polarized light, respectively. The metallic (Al) film is 200nm thick with a slit width of 100 nm. The refractive indices for the glass and the Al metal are 1.5, -34+8.5i, respectively. A sinusoidal wave with 532.5 nm wavelength is excited from the glass substrate. The area of the simulation domain (2.0 μm × 3.0 μm) is much smaller than the focus spot of the laser used (~ 10 μm in diameter). The amplitude and the phase of the focused field at the focal plane do not vary much in the simulation area. Hence, the incident plane wave approximation is adequate. The results of the simulation in a movie for the intensity distribution of the TE mode (p-polarized) at different calculation time are shown in Fig. 3(a). From this figure, we see that light is reflected by the metal film and only a small fraction can exit. Due to the film thickness, the light is confined to the middle of the slit and very little light can propagate to the far-field. This is the reason why the propagation field of the p-polarized light could not be measured as mentioned previously. Figure 3(b) shows the propagation of s-polarized light, TM mode, in the slit. This figure clearly shows that light propagates via the air-metal interface at the edges, not in the middle of the slit. The light in the air-metal surface is known to be the surface plasmon wave (SPW). The SPW propagates towards the opening of the slit and then radiates from the edge. Thus, the NSOM image in Fig. 2(a) has two bright lines at the edges and the propagation field in Fig. 2(c) has two lobes. Because of the SPW the intensity of s-polarized light is much stronger than that of p-polarized light and, therefore, can be experimentally measured.

 

Fig. 3. Animation of the propagation of light in a 100 nm metallic slit. (a) TE mode (839k) (b) TM mode (856k).

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The SPW is of great importance in the nanometallic structure. As light penetrates a nanostructure, it decays as (D/λ)-4 [9], where λ is the wavelength, D is the aperture length. Because of the existence of SPW, the penetration of light in a periodic nanostructure is greatly enhanced [3]. This enhancement dominates the light distribution in the optical field for structure size much smaller than the wavelength. It still exists even if the structure size is on the same order of magnitude as the wavelength. For example, Fig. 4 shows the topography and NSOM images for a slit 500 nm in width using incident light of wavelength 532.5 nm. For the p-polarized light, only light in the slit is seen in the NSOM image in Fig. 4(b). For the s-polarized light, three distinguishable bright lines are seen in the NSOM image in Fig. 4(a). The central one is the light that penetrates directly through the slit; the other two lines are the SPWs at the edges of the slit. The simulation results by the FDTD method are shown in Fig. 4(c). The p-polarized light in the left of Fig. 4(c) is concentrated at the center of the slit while the s-polarized light has three peaks at the slit. Thus, the simulations are consistent with the measured experimental results.

 

Fig. 4. The measured topographic and NSOM images for 500 nm silt. (a) Topography (left) and s-polarized NSOM image (right). (b) Topography (left) and p-polarized NSOM image (right). (c) The FDTD simulations of the propagated optical field for s-polarized light (left image) and p-polarized light (right image). The dashed white lines indicate where the NSOM measured.

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In conclusion, we have imaged the optical near field in nanoslits. Different polarized light shows quite different near-field distributions in the slit. The optical near-field image shows a bright line for the p-polarized light and two additional peaks at the metallic edges for s-polarized light. These two peaks are due to the propagation of the surface plasmon wave (SPW) at the air-metal surface. It dominates the near-field image when the slit width is much smaller than the wavelength of the light. Furthermore, it causes extraordinary transmittance of light as compared with the p-polarized light.

The work is supported by National Science Council of Taiwan, under the contract no. NSC 91-3112-P-001-004-Y-3.

References and Links

1. J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001). [CrossRef]  

2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]  

4. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, NewYork, 1998).

5. A. Taflove and S. C. Hagness, Computational Electrodynamics : the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

6. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991). [CrossRef]   [PubMed]  

7. G. A. Valaskovic, M. Holton, and G. H. Morrison, “ Parameter control, characterization, and optimization in the fabrication of optical fiber near-field probes,” Appl. Opt. 34, 1215–1228 (1995). [CrossRef]   [PubMed]  

8. P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998). [CrossRef]  

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

References

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  1. J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
    [Crossref]
  2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [Crossref]
  4. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, NewYork, 1998).
  5. A. Taflove and S. C. Hagness, Computational Electrodynamics : the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).
  6. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
    [Crossref] [PubMed]
  7. G. A. Valaskovic, M. Holton, and G. H. Morrison, “ Parameter control, characterization, and optimization in the fabrication of optical fiber near-field probes,” Appl. Opt. 34, 1215–1228 (1995).
    [Crossref] [PubMed]
  8. P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998).
    [Crossref]
  9. H. A. Beth, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [Crossref]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

2001 (1)

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998).
[Crossref]

1995 (1)

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

1944 (1)

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

Austin, R.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Bakajin, O.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Beth, H. A.

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

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Chan, E.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Chan, S. S.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Chou, C.-F.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Cox, E. C.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Duke, T.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Ebbesen, T.W.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Fann, W.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Fann, W. S.

P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998).
[Crossref]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics : the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Holton, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, NewYork, 1998).

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Liou, L.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Morrison, G. H.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics : the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

Tegenfeldt, J. O.

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Trautman, J. K.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Valaskovic, G. A.

Wei, P. K.

P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998).
[Crossref]

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Appl. Opt. (1)

J. Appl. Phys. (1)

P. K. Wei and W. S. Fann, “Tip-sample distance regulation for near-field scanning optical microscopy using the bending angle of the tapered fiber probe,” J. Appl. Phys. 84, 4655–4660 (1998).
[Crossref]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Phys. Rev. (1)

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

Rev. Phys. Lett. (1)

J. O. Tegenfeldt, O. Bakajin, C.-F. Chou, S. S. Chan, R. Austin, W. Fann, L. Liou, E. Chan, T. Duke, and E. C. Cox, “Near-field scanner for moving molecules,” Rev. Phys. Lett. 86, 1378–1381 (2001).
[Crossref]

Sci. Express (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Sci. Express 20, (2002).

Science (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468 (1991).
[Crossref] [PubMed]

Other (2)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, NewYork, 1998).

A. Taflove and S. C. Hagness, Computational Electrodynamics : the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

Supplementary Material (2)

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Figures (4)

Fig. 1.
Fig. 1.

The experimental setup for a collection-mode NSOM

Fig. 2.
Fig. 2.

The measured topographic and NSOM images for 100 nm silt. (a) Topography (left) and s-polarized NSOM image (right). (b) Topography (left) and p-polarized NSOM image (right). (c) The propagation of the optical field for s-polarized light.

Fig. 3.
Fig. 3.

Animation of the propagation of light in a 100 nm metallic slit. (a) TE mode (839k) (b) TM mode (856k).

Fig. 4.
Fig. 4.

The measured topographic and NSOM images for 500 nm silt. (a) Topography (left) and s-polarized NSOM image (right). (b) Topography (left) and p-polarized NSOM image (right). (c) The FDTD simulations of the propagated optical field for s-polarized light (left image) and p-polarized light (right image). The dashed white lines indicate where the NSOM measured.

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