Spiral light fields in the form of closed curves as generalization of Laguerre–Gaussian beams

In this paper we provide a numerically obtained result for analytical solution for the problem of monochromatic nonparaxial Gaussian beam diffraction by uniform dielectric cylinder, which yields a focal spot outside the cylinder with linear sizes twice less than the diffraction limit in the free space in case of cylinder radius comparable with the wavelength. Although the radius of cylinder is only two times larger than the wavelength, the produced intensity in focal spot is 48 times larger than the maximal intensity of incident Gaussian beam. Two percent deviation from the resonant radius (for a fixed wavelength) causes the focal spot increase in half, and the resulted intensity in focal spot drop to value of 12 times greater than the incident beam intensity. Obtained solution corresponds to the growth of the Bessel function of order 18 coefficient in E-field amplitude Bessel series expansion.