Near finite difference time domain

Krug, J.T., E.J. Sanchez, and X.S. Xie. 2002. Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation. 7. Chem. Phys. 116 10895-10901. 

N. Farahat, W. Yu, and R. Mittra, A fast near-to-far-field transformation in body of revolution finite-difference time-domain method, IEEE Trans. Antennas Propag., vol. 51, no. 9, pp. 2534-2540, Sep. 2003.doi 10.1109/TAP.2003.816360... 

Figure 16. Schematic for finite-difference, time-domain (FDTD) calculations of fluorescent molecule behavior in near-field microscopy. The aperture diameter is 96 nm. The calculation is performed on a two-dimensional 300 x 300 grid of 1.2 nm square cells. The arrangement of f,-, and H points are shown in the zoom-in inset. A horizontal point dipole is placed at the center of the cell with the four surrounding H. points driven sinusoidally in the simulation. Molecular emission characteristics are evaluated as a function of the lateral displacement d and the tip molecule gap h. Adapted from Ref. 25.

The inter-particle distance dependence of the near-field coupling would therefore reflect the distance decay of the near-field itself. In other words, each particle senses the near-field due to the other particle. By varying the distance of the other particle and monitoring the LSPR response, the spatial profile of the near-field can be deduced. The plot of the LSPR red-shift as a function of inter-particle gap (surface-to-surface separation) shows a much more rapid decay of the near-field than predicted by the dipolar model. This is because the dipolar model does not take into account the multipolar interactions between the particles, which become increasingly important at smaller and smaller inter-particle gaps. Plasmon coupling is therefore a multipolar interaction and its true distance-dependence can be quantitatively reproduced only by a complete treatment that includes all modes of interaction (dipolar, quadrupolar, octupolar). Computational electrodynamics methods such as discrete dipole approximation (DDA) (see Chapter 2) and finite-difference-time-domain (FDTD), which include a full multipolar treatment in addition to finite-size retardation effects, fit experimental trends well. 

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