Sharp resonant focusing of light by a dielectric cylinder with square cross-section and cube

In this paper a research on conditions for resonance excitation in a homogeneous dielectric cylinder with square cross-section is conducted using a FDTD-method. It is shown that in a cylinder with square cross-section resonant modes similar to whispering gallery modes can be excited, which allows one to reduce the transverse dimensions of the focal spot. FDTD method demonstrates an acceptable accuracy of the resonant mode detection. A similar result is obtained for a cube on a dielectric substrate: it is possible to achieve the reduction of the transverse dimensions of the focal spot by changing the corresponding cube size.