Implementation of the FDTD method in cylindrical coordinates for dispersive materials: Modal study of C-shaped nano-waveguides

The objective of this work is to develop a code based on the finite difference time domain method in cylindrical coordinates (CC-FDTD) that integrates the Drude Critical Points model (DCP) and to apply it in the study of a metallic C-shaped waveguide (CSWG). The integrated dispersion model allows an accurate description of noble metals in the optical range and working in cylindrical coordinates is necessary to bypass the staircase effect induced by a Cartesian mesh especially in the case of curved geometrical forms. The CC-FDTD code developed as a part of this work is more general than the Body-Of-Revolution-FDTD algorithm that can only handle structures exhibiting a complete cylindrical symmetry. A N-order CC-FDTD code is then derived and used to perform a parametric study of an infinitly-long CSWG for nano-optic applications. Propagation losses and dispersion diagrams are given for different geometrical parameters. •Drude critical points model is successfully implemented in the CC-FDTD algorithm.•The CC-FDTD allows a gain in both memory space and CPU time.•The C-shaped nano-waveguide allows the propagation of the optical signal over quite long distances via the TE10 mode.•The TE10 group velocity of the C-shaped nano-waveguide is low, so the enhancement of a nonlinear effects.•The C-Shaped Aperture Array opens new perspectives for enhanced transmission applications.