Modeling the resonance focusing of a picosecond laser pulse using a dielectric microcylinder

Based on the finite-difference time-domain method, we study temporal variations of focal spot parameters when focusing a plane TE wave by use of a dielectric microcylinder with refractive index 1.59. It is shown that as a picosecond (ps) pulse travels through the microcylinder, the focal spot gets tighter, whereas its intensity and the mode energy stored in the microcylinder grow. As a result of the ps-pulse passage, in the cylinder a whispering gallery mode is excited, which is coincident with the mode in a circular wire with zero propagation constant. With time, the mode energy is leaking out. By solving the Helmholtz equation using a finite-element technique we show that in the stationary case, the best focal spot parameters are achieved in a cylinder of radius 2.1749  λ (λ is wavelength): the focal spot size is FWHM=0.226  λ, whereas the maximal intensity in the focus is 60 times the incident light intensity.