Presented are the results of numerical simulations accomplished to investigate the propagation of electromagnetic excitations in certain types of metal-coated tapered tips terminating SiO2 multimode optical fibres with a subwavelength output aperture. The numerical simulations were initiated in order to enable better interpretation of previously reported experimental results concerning some features of the mesoscopic effect of spectral modulation observed for a broadband light transmitted by such tips. This effect occurs due to the interference between a small number of waveguide modes exiting a metal-coated tip, and the experimental results indicate a possible mode-selective photon-plasmon coupling in the studied tips. To match the experimental conditions, the tips were modelled for the light wavelength of 800 nm as three-layer systems (with the intermediate adhesion Cr layer and the outer layer of Al or Au). However, due to computational restrictions the end of a tip, only 18 μm long (most significant), was modelled. Numerical simulations yielded the dependences of propagation and attenuation constants on the fibre core radius for the most intensive (both photonic and plasmonic) output modes. The pairs of modes most probably contributing to the observed spectral modulation were identified. Although the simulations did not reveal any explicit mode coupling, the imperfections of real tips can cause mode transformations implying possible involvement of more than two modes. The thin (20 nm) Cr layer plays the main role for plasmonic modes generated on its SiO2 interface, which explains the small outer metal layer influence on the observed modal dispersion.
1. Hecht, B., Sick, B., Wild, U. P., Deckert, V., Zenobi, R., Martin, O. J. F., and Pohl, D. W. Scanning near-field optical microscopy with aperture probes: Fundamentals and applications. J. Chem. Phys., 2000, 112, 7761–7774.
https://doi.org/10.1063/1.481382
2. Rähn, M., Pärs, M., Palm, V., Jaaniso, R., and Hizhnyakov, V. Mesoscopic effect of spectral modulation for the light transmitted by a SNOM tip. Opt. Commun., 2010, 283, 2457–2460.
https://doi.org/10.1016/j.optcom.2010.02.010
3. Novotny, L. and Hafner, C. Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function. Phys. Rev. E., 1994, 50, 4094–4106.
https://doi.org/10.1103/PhysRevE.50.4094
4. Palm, V., Rähn, M., and Hizhnyakov, V. Modal dispersion due to photon-plasmon coupling in a SNOM tip. Opt. Commun., 2012, 285, 4579–4582.
https://doi.org/10.1016/j.optcom.2012.07.008
5. Palm, V., Rähn, M., Jäme, J., and Hizhnyakov, V. Excitation of surface plasmons in Al-coated SNOM tips. Proc. SPIE, 2012, 84572S, 1–10.
https://doi.org/10.1117/12.929719
6. Palm, V., Pärs, M., Loot, A., Rähn, M., and Hizhnyakov, V. 2017. On mesoscopic effect of spectral modulation and its potential influence on hyperspectral SNOM imaging results. In Microscopy and imaging science: practical approaches to applied research and education (Méndez-Vilas, A., ed.). Formatex Research Center, 610–619, Badajoz, Spain.
7. Malitson, I. H. Interspecimen comparison of the refractive index of fused silica. J. Opt. Soc. Am., 1965, 55, 1205–1209.
https://doi.org/10.1364/JOSA.55.001205
8. Rakic, A. D., Djurisic, A. B., Elazar, J. M., and Majewski, M. L. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt., 1998, 37, 5271–5283.
https://doi.org/10.1364/AO.37.005271
9. Johnson, P. B. and Christy, R. W. Optical constants of the noble metals. Phys. Rev. B, 1972, 6, 4370–4379.
https://doi.org/10.1103/PhysRevB.6.4370
10. Marcuse, D. Light Transmission Optics. Van Nostrand Reinhold, New York, 1982.
11. Delves, L. M. and Lyness, J. N. A numerical method for locating the zeros of an analytic function. Math. Comp., 1967, 21, 543–560.
https://doi.org/10.1090/S0025-5718-1967-0228165-4
12. Novotny, L. and Hecht, B. Principles of Nano-Optics. Cambridge University Press, New York, 2006.
https://doi.org/10.1017/CBO9780511813535
