A Non‐Singular, Field‐Only Surface Integral Method for Interactions between Electric and Magnetic Dipoles and Nano‐Structures

Abstract

With the development of condensed-matter physics and nanotechnology, attention has turned to the fields near and on surfaces that result from interactions between electric dipole radiation and mesoscale structures. It is hoped that studying these fields will further the understanding of optical phenomena in nano-optics, quantum mechanics, electromagnetics, and sensing using solid-state photon emitters. Here, a method for implementing dynamic electric and magnetic dipoles in the frequency domain into a non-singular field-only surface integral method is described. It is shown that the effect of dipoles can conveniently be described as a relatively simple term in the integral equations, which fully represents how they drive the fields and interactions. Also, due to the non-singularity, this method can calculate the electric and magnetic fields on the surfaces of objects in both near and far fields with the same accuracy, which makes it an ideal tool to investigate nano-optical phenomena. The derivation of the framework is given and tested against a Mie theory alike formula. Some interesting examples are shown involving the interaction of dipoles with different types of mesoscale structures including parabolic nano-antennas and gold probes.

Fluorescence profile of a nitrogen-vacancy center in a nanodiamond

“…In Fig. 17, we showed the electromagnetic fields obtained by the asymptotic approximations detailed in Section A, and compared them with the results gotten by the in-house built field only surface integral method [35]. Good agreement has been found between the results…”

“…Here we show large variations in NV fluorescence by performing theoretical modelling of the fluorescence of of a point defect in spherical nanodiamonds as a function of nanodiamond size and the defect position within the crystal. To explore the effect of geometry on emission, we treat the NV phonon structure by a set of electric dipoles with fixed energy spacing and emission probabilities [29,30], and the electromagnetic fields within and outside the diamond are calculated via Mie theory [31][32][33][34] which were also validated by the numerical solver [35].…”

Efficient sunlight promoted nitrogen fixation from air under room temperature and ambient pressure via Ti/Mo composites

“…Numerical simulations via the field-only surface integral method [54][55][56][57][58] were also carried out to study the interactions between light and the synthesized TMCx photocatalytic particles to further confirm that TMCx can be an effective and efficient material for photocatalyst. The focus of the calculation is the absorption cross section of a TMCx photocatalytic particle which represents how much energy from the sunlight can be utilized by such a particle.…”

Efficient photocatalytic nitrogen fixation from air under sunlight via iron-doped WO3

“…The numerical modelling was performed to investigate the absorption and surface charge distribution of a single 0.25Fe-WO3 photocatalytic particle under the illumination of sunlight in water by using the field-only surface integral method [47][48][49][50][51]. As shown in Figure 12c, the typical morphology of our synthesized 0.25Fe-WO3 photocatalytic particle is a hexagon disk with irregular bumps on the particle surface.…”