Impact of the apex of an elongated dielectric tip upon its light absorption properties
Introduction
The interaction of light with elongated objects is widely involved in a variety of fields ranging from human vision to the most state-of-the-art technology. More specifically, the laser light absorption by nanoscale semiconducting cones has recently gained attention owing to its relevance to metrology and, in particular, to the laser-assisted atom probe tomography (APT) technique [1]. In this context, it has been observed that conical silicon tips exposed to high-fluence infrared (IR) and green illumination exhibit sharply localized holes, indicative of enhanced coupling and preferential absorption at well-defined locations along the cone axis. A recently developed approximate Mie theory for conical particles demonstrates that the holes observed on IR-irradiated tips result from local Mie resonances in cross sections with specific radii [2]. However, this theory cannot explain the location and high spatial frequency of the ripples observed on green-irradiated tips. In this paper, we show that the latter ripples are a consequence of the light coupling through the tip apex and we use this observation to study its impact on the absorption capabilities of the tip. This paper is structured as follows. First, we discuss how the Mie theory developed in [2], which considers conical particles but neglects the impact of the apex, applies to green irradiation. We then investigate the additional contribution of a hemispherical apex to the optical properties of the conical tip.
Section snippets
Light interaction with a conical tip
According to the theory developed in [2], a conical particle interacts with light incident normally to its symmetry axis z as a mere stack of cylinders with a varying radius. As shown on the left of Fig. 1 for a transverse-magnetic (TM) incident wave of amplitude E0 and wavelength λ0 = 515 nm (green), the coupling of light into a silicon cone varies strongly along its axis as a result of the varying local radius R(z). For specific values of the local radius, local Mie resonances indeed enhance the
Impact of the tip apex
Although the low-contrast spots observed far away from the apex of the green-irradiated Si tip of Fig. 1 are well accounted for by Mie theory, the periodic ripples appearing in close proximity to the tip apex cannot be attributed to Mie resonances, their spatial frequency along the tip axis being too high. The theory developed in [2] indeed neglects the contribution of the apex of the conical particle to its optical coupling properties. This approximation is, however, only valid for wavelengths
Conclusion
To conclude, the impact of the apex on the light absorption properties of an elongated tip can be understood in the following manner. On the one hand, if the λ0/(2nRapex) ratio is large, the apex does not contribute to the coupling with light. If, on the other hand, the incident wavelength is commensurate with the apex radius, light can be coupled into the apex and excite guided modes of the dielectric shank. While propagating away from the apex along the tip shank, the magnitude of these modes
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