Near-field: A finite-difference time-dependent method for simulation of electrodynamics on small scales

Abstract

We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yee's method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding.

Communication: Dynamical embedding: Correct quantum response from coupling TDDFT for a small cluster with classical near-field electrodynamics for an extended region

“…Time dependent density functional theory (TDDFT) has been widely used to study quantum effects in plasmonics [5][6][7] that are missing in conventional classical electrodynamics models. [8][9][10] However, TDDFT is expensive so a multiscale approach bridging the molecular and plasmonic scales is needed. [11][12][13] Recently, we developed an embedding electrodynamics approach.…”

“…The electrodynamics of the entire system is calculated by propagating each subsystem (TDDFT for the quantum part and near-field (NF) 10 for the classical part) simultaneously and the common Coulomb potential is evaluated and used at each step. We demonstrate that the resulting atomistic embedding method is successful at mimicking full scale TDDFT for describing the plasmonic response of a Mg slab and the dynamical charge transfer (CT) between an adsorbed H 2 O molecule and substrate.…”

Near-field for electrodynamics at sub-wavelength scales: Generalizing to an arbitrary number of dielectrics

“…If there are no dielectrics (i.e., no semiconductor and insulators) or there is only a single dielectric without vacuum, the Poisson equation can be solved by an FFT (fast-Fouriertransform) convolution integral, as was done in our original NF paper. 21 Dielectrics are ubiquitous however in nanostructures. We therefore extend here NF to include an arbitrary number of dielectrics by solving the Poisson equation using conjugate graa) dxn@chem.ucla.edu.…”

“…Recently we developed the near-field (NF) method, 21 which quantitatively studies electrodynamics of nanostructures at sub-wavelength scales. When the size of the nanostructure is much smaller than the optical wavelength, retardation effects can be neglected.…”

Molecular nanoplasmonics: Self-consistent electrodynamics in current-carrying junctions

“…[1][2][3][4][5][6] The unique optical properties of the surface plasmon-polariton (SPP) resonance, being the very foundation of plasmonics, find intriguing applications in optics of nano-materials, 7-9 materials with effective negative index of refraction, [10][11][12] direct visualization, 13,14 photovoltaics, [15][16][17] single molecule manipulation, [18][19][20] and biotechnology. [21][22][23][24] Theoretical modeling of the optical properties of metal nanostructures is conventionally based on numerical integration of Maxwell's equations, [25][26][27][28][29] although simulations within time-dependent density functional theory appeared recently for small atomic clusters. 30,31 Moreover, current theoretical models are quickly advancing toward self-consistent simulations of hybrid materials: metal/semiconductor nanostructures optically coupled to ensembles of quantum emitters.…”