Simulation of resonance focusing of a piсosecond pulse by a dielectric microcylinder

Time dependence of the parameters of a focal spot when performing the resonance focusing of a plane TE-wave with a dielectric microcylinder (refractive index $n=1.59$) is investigated using the FDTD-method. It is shown that as the picosecond pulse passes through the cylinder, the focus width decreases, whereas the intensity of the focus increases, as does the energy of light accumulated in the cylinder. Following the pulse propagation, a leaking whispering gallery mode is excited within the cylinder, which is matching a round-wire-fiber mode with zero propagation constant. With time the mode energy is leaking. Solving the Helmholtz equation by a finite element method, the best parameters of the focal spot are shown to be achieved for a cylinder of radius $2.1749\lambda$, with the focal spot size at full width at half maximum of intensity being $0.226\lambda$ and the maximum intensity in the focus being $60$ times the incident light intensity, where $\lambda$ is the incident wavelength.