Numerical Simulation (FDTD)

As a first estimation, the behavior of the micro-structured low-e coatings was investigated by way of numerical simulation using the finite difference method in the time domain (FDTD) [3]. The FDTD method uses the difference form of Maxwell’s curl equations

— = Vx H

dt

and

— = -—Vx E,

dt J

where D=rE, є is the relative permittivity and /jo is the vacuum permeability [4].

These difference equations are used to calculate the time dependent development of the electric and magnetic field, iterating the calculation of Maxwell’s equations over many time steps. The frequency dependence is calculated by Fourier transformation into the frequency domain. As the Fourier transform of a small pulse

contains all frequencies, the response of a system to excitation by plane waves of several frequencies can be calculated in one numerical simulation, where the system to be examined is excited by a narrow Gaussian pulse [5].

For the simulations, only the wavelength selectivity of a metal mesh was examined, the influence of the glass substrate on the transmittance or reflectance spectrum was not considered. The mesh consisted of metal cylinders with infinite conductivity, thus being perfectly reflecting (see Figure 5).

The simulation was implemented using periodic boundary conditions, so that dependent scattering of an infinite array of cylinders was calculated.