Simulation of focusing femtosecond pulse by ellipsoid, paraboloid, sphere and hemisphere

Numerical simulation of FDTD-method showed that it is not temporarily broadening of pulses and spatial broadening a little more for less short pulse in case of focusing two linearly polarized pulses of 1,24 fs and 2,98 fs (with a plane wavefront and a central wavelength of 532 nm) by silica microspheres with a diameter of 2 µm. In contrast, spatial and temporal broadening of the pulse is in the normal way: a shorter pulse broadens more than less short in the case of by focusing by hemisphere, the paraboloid and ellipsoid (all with maximum cross-section diameter of 2 µm).