An axially symmetric three-dimensional finite element method model is applied to investigate the electromagnetic field distribution in the vicinity of a silver coated glass tip. Under radially polarized illumination, a strongly enhanced field located at the apex of the tip is found due to the constructive interference of surface plasmon propagating at the air/silver interface. The enhancement factor and surface plasmon resonance excitation are analyzed systematically. The optimal condition for field enhancement is investigated through the exploration of different taper angles of the tip and the illumination geometry. The numerical studies show that a significantly enhanced localized electromagnetic field with a full-width-half-maximum of 10 nm is obtainable with 632.8 nm optical excitation.
© 2007 Optical Society of America
Near field scanning optical microscope (NSOM) is one type of scanning probe microscopes (SPM) that can provide optical information with spatial resolution beyond the diffraction limit . Combined with various feedback techniques, NSOM can offer topographical and optical information simultaneously and has found many applications in the characterization of sub-wavelength structures and devices. Most widely used NSOM probes are metallic coated tapered glass fiber with the end left uncoated to form a nanometric aperture. These probes typically have extremely low throughput due to small taper angles and aperture sizes. The resolution of apertured NSOM, determined by the size of the aperture and tip-sample distance, is generally limited to about 50 nm ∼ 100 nm. The spatial resolution cannot be reliably increased further due to technical obstacles such as weak detectable signal, large background scattering noise and rigorous tip-sample distance control [1, 2].
To overcome the drawback of apertured NSOM, various field-enhanced NSOM techniques using apertureless metallic probes were developed. Most of these techniques utilized field enhancement effect arising from surface plasmon excitation or localized free electrons similar to the electrostatic lightning-rod effect . Surface plasmon, a group oscillation of free electrons, can be generated at the dielectric/metal interface due to the interaction of metal with the incident light. The excited surface plasmon waves can propagate to the apex of sharply pointed structures, producing a strongly enhanced field that may be used as a nanoscale near field light source. The enhancement factor strongly depends on both the structure of the probe tip and polarization state of the incident light. Most theoretical and experimental investigations of apertureless NSOM use linearly polarized external illumination, which has the critical problem of large far field background noise [4–7].
In order to eliminate the background noise, apertureless NSOM probes using fully metal-coated axially symmetric dielectric structures under radially polarized internal light illumination were proposed and studied [8–13]. Radially polarized beam is one type of cylindrical vector beams, which are solutions of Maxwell equations that obey radially symmetry both in amplitude and polarization. The generation and application of radially polarized beam have stimulated continuous interests [14–20]. Using radially polarized beam, the focal spot size can be much smaller than the diffraction limit of focused spatially homogeneously polarized beams such as linear polarized beam and circularly polarized beams [14–16].
When a radially polarized light is injected into the axially symmetric fully coated apertureless NSOM probe, the induced surface plasmon will converge toward the end of the tip and interfere constructively because of the rotational symmetry of the input polarization and the probe. Consequently, a strong field enhancement can be realized. Bouhelier et al. studied this field enhancement using a multiple multipole method, where the radial polarization was mimicked by placing an electric dipole parallel to the probe at the center of the input port . In contrary, if a spatially homogeneously polarized light is coupled into the probe, the surface plasmon excitation will cancel out at the apex of the tip because the opposed sides on the probe surface have opposite charges. Hence, there is no field enhancement in this case. In this paper, we will use a finite element method model to quantitatively solve the electromagnetic field distribution at the vicinity of the tip. With an axially symmetric three-dimensional model, we numerically investigate the field distribution and the field enhancement factor. Surface plasmon resonance excitation at the surface of thin silver film will be shown. A full-width-half-maximum (FWHM) spot size smaller than 10 nm can be realized with 632.8 nm excitation. From our simulations, we also found that the enhancement factor strongly depends on the illumination spot size and the probe structure.
2. Three-dimensional finite element modeling structure
The probe structure to be modeled is illustrated in Fig. 1. A radially polarized beam is focused by an objective lens towards the bottom of a hemispherical solid immersion lens (SIL), where a sharp conical shape tip is fabricated at the center. The SIL and the tip are not to scale to illustrate the details of the probe. The bottom of SIL and the entire tip are coated with thin silver film in order to form an apertureless probe and eliminate the strong far field background signal.
A finite element method (FEM) is applied to investigate the field enhancement in the vicinity of the silver coated tip. Numerical simulation was performed with COMSOL, a commercial FEM software package. Three-dimensional axial symmetry geometry was applied to model the tapered tip as well as the illumination. Since both the structure and the illumination are axisymmetric, there are only variations in the radial (r) and vertical (z) directions and no dependence in the angular (θ) direction. One can then solve a quasi two-dimensional problem in the r-z plane instead of the full three-dimensional problem, which saves considerable amount of memory and computational time.
In the model, the SIL material was chosen to have a dielectric constant of εr=2.2 at the excitation wavelength of 632.8 nm. The domain of calculation for the tip is chosen to be 1.2 μm in the r-direction and 3.86 μm in the z-direction. The tip has a half cone angle of 16.4° and a radius of curvature of 20 nm. The entire tip is coated with 50 nm thin silver film, and the radius of curvature of the silver film at the apex is set to be 5 nm. The dielectric constant of silver is chosen to be -15.8779 - 1.0765i . The input radially polarized beam is modeled as
where r is the radial coordinate, and w is the beam waist of the focused incident light at the bottom of the SIL. In the following simulations, the beam waist is chosen to be 0.4 μm. In the FEM model, axial symmetry boundary condition is applied to the symmetry axis of the probe structure. Continuity boundary conditions are used for the dielectric/metal and metal/air boundaries. Electric field boundary is used to specify the radial polarization as the input to the probe. A scattering boundary condition of COMSOL is chosen for the outer boundary to simulate an open boundary. After carefully setting the maximum finite element mesh sizes, the field distribution within the whole domain of calculation can be solved rigorously.
3. Simulation results for field enhancement and spot size
Figure 2 shows the logarithmic 2-D and 3-D plots of electric energy density distribution in the vicinity of the tip. From the plots, we can see that the surface plasmon propagates along the air/silver interface and constructively interfere at the tip apex, leading to strong localized field. The distributions for the radial (Er) and longitudinal (Ez) field components are shown in Fig. 3. The propagation of these components is also illustrated by the movie clips shown in Fig. 3. Please notice that the color scale for the movies has been intentionally saturated in order to illustrate the details of the propagation.
Due to the rotational symmetry of both the illumination and the tip, there is no transverse electric field along the symmetry axis. From the movie, we can clearly see the propagation of surface plasmon towards the end of the tip. A high field enhancement at the tip apex is observed due to the constructive interference of the surface plasmon. In this case, the electric energy enhancement is about 102,400, corresponding to an electric field enhancement of about 320. The value of the enhancement is given by the ratio between the field amplitude at the end of the tip and the incoming field peak amplitude. The spot size of the strong localized field is analyzed through calculating the FWHM of the electric energy density distribution at different distances from the tip. The results are shown in Fig. 4. The FWHMs of 6.0 nm, 13.3 nm and 21.4 nm are calculated at distances of 0 nm, 5 nm and 10 nm from the tip apex, respectively.
4. Effects of taper angle and illumination spot size
We further explored different taper angles of the tip and illumination spot sizes and found that the enhancement factor has strong dependence on these parameters. In order to seek for the optimal taper angle for maximum field enhancement, we numerically studied the enhancement factor for different half cone angles with the same illumination spot size. The results of this study are shown in Fig. 5. The relationship between the enhancement and taper angles exhibits a strong oscillating nature, which means that the enhancement factor is very sensitive to the tip taper angle. Though the field enhancement is sensitive to the taper angle, in practice, we can choose an angle range with relatively higher field enhancement to design the tip. For example, according to Fig. 5, field enhancement factor higher than 50 is generally obtainable for half taper angles ranging from 15° to 19°. Thus it would make sense to select 17° as the desired half taper angle to fabricate the tip. It should be pointed out that, although at certain angles the enhancement factors are very low, they are always higher than one, which means the field is still enhanced.
In addition to the tip cone angle, another study was also carried out to investigate the effects of the illumination spot size on the field enhancement. Figure 6 shows the relationship between the electric field enhancement factor and spot size w with the same half taper angle of 16.4°. It is found that there is an optimal spot size of about 0.68 μm for this tip cone angle. This relationship indicates that, given a fabricated tip with fixed cone angle, we may be able to conveniently maximize the enhancement effect by adjusting the size of the focal spot through controlling the aperture of the objective lens. For example, for the minimal field enhancement occurs at 20° half cone angle shown in Fig. 5, we found the field enhancement factor can be increased to 50 by increasing the spot size from 0.4 μm to 1 μm. The dependence of field enhancement on taper angle and the illumination spot size could be explained by the differences in coupling efficiencies between the guided modes and plasmonic modes . However, the details of the physical explanation are subject to further studies.
When radially polarized beam is coupled into a conic shape apertureless near field scanning optical microscope tip, the entire beam is TM polarized with respect to the dielectric/metal interface. Surface plasmon excited by the TM polarized light propagates toward the end of the tip and interferes constructively due to the rotational symmetry of both the geometry structure and the polarization state of illumination. A 3-D finite element method is applied to investigate the surface plasmon excitation at the dielectric/metal interface and the field enhancement at the end of the tip. The field distribution with FWHM of as small as 10 nm and intensity enhancement of five orders of magnitude can be achieved with 632.8 optical excitation. From our simulations, we also found that the enhancement factor strongly depends on the probe tip structure and illumination spot size. Local field enhancement at the end of the metal-coated tip may find important near field scanning optical microscopy applications such as near-field Raman microscopy [22,23], surface enhanced Raman scattering (SERS)  and fluorescence imaging  etc.
Weibin Chen is supported by the Dayton Area Graduate Studies Institute (DAGSI) Research Fellowship. The authors are thankful for this support.
References and links
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 251,1468–1470 (1991). [CrossRef] [PubMed]
5. R. Fikri, D. Barchiesi, F. H′Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method,” Opt. Commun. 221,13–22 (2003). [CrossRef]
6. R. Bachelot, F. H′Dhili, and D. Barchiesi et. al. “Apertureless near-field optical microscopy: A study of the local tip field enhancement using photosensitive azobenzene-containing films,” J. Appl. Phys. 94,2060–2072 (2003). [CrossRef]
7. A. Tarun, M. Daza, N. Hayazawa, Y. Inouye, and S. Kawata, “Apertureless optical near-field fabrication using an atomic force microscope on photoresists,” Appl. Phys. Lett. 80,3400–3402 (2002). [CrossRef]
9. W. Chen and Q. Zhan, “Optimal plasmonic focusing with radial polarization,” Proc. SPIE ,6450,64500D (2007). [CrossRef]
10. H. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology 17,3105–3110 (2006). [CrossRef]
11. F. Keilmann, “Surface-polariton propagation for scanning near-field optical microscopy application,” J. Microsc. 194,567–570 (1999). [CrossRef]
12. L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dändliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett. 83,584–586 (2003). [CrossRef]
13. N. A. Janunts, K. S. Baghdasaryan, Kh.V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253,118–124 (2005). [CrossRef]
18. N. Passilly, R. Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” J. Opt. Soc. Am. A 22,984–991 (2005). [CrossRef]
19. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10,324–331 (2002). [PubMed]
21. E. D. Palik, Handbook of Optical Constants of Solids, page 356 (Academic Press, 1998).
22. A. Hartschuh, N. Anderson, and L. Novotny, “Near-field Raman spectroscopy using a sharp metal tip,” J. Microsc. 210,234–240 (2002). [CrossRef]
23. T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. kawata, “Application of tip-enhanced microscopy for nonlinear Raman spectroscopy,” Appl. Phys. Lett. 84,1768–1770 (2004). [CrossRef]
25. T. J. Yang, G. A. Lessard, and S. R. Quake, “An apertureless near-field microscope for fluorescence imaging,” Appl. Phys. Lett. 76,378–380 (2000). [CrossRef]