A monochromatic recursive convolution finite-difference time-domain algorithm and its application in simulation of arrays of metal nano-particles

A special class of finite-difference time-domain (FDTD) algorithm, called recursive convolution (RC) FDTD, is developed to simulate metals in visible domain. Conventionally, RC-FDTD is implemented for pulsed light sources. This requires that the analytical model of permittivity should fit the handbook permittivities (derived from experimental measurements) closely over broadband of wavelengths. This is not an easy task and the choice of a particular model depends on the metal being simulated. We developed a monochromatic version of RC-FDTD. This algorithm uses the 1st order Drude model to evaluate the convolution operation needed to make FDTD stable for metals for which the real part of permittivity is negative. Unlike the conventional RC-FDTD, the Drude parameters are computed at each wavelength of the incident light using the corresponding handbook value of permittivity. Hence, this version of RC-FDTD allows us to use the handbook permittivity values at all wavelengths of operation. Here, we study the dependence of localized surface plasmon resonance (LSPR) properties of arrays of nano-particles on the shape, size and number of particles in the array and the interparticle distance. We compute the extinction spectra of linear nano-particle arrays using the RC-FDTD method. For such arrays, the peak of the extinction spectra shifts toward the longer wavelengths as the interparticle distance decreases.