Radius of curvature of Bessel and modified Bessel Gaussian beams

Abstract

We analyze the radius of curvature of Bessel Gaussian (BG) and modified Bessel Gaussian (mBG) beams. The study is based on the results of analytic derivation as well as those of the random phase screen approach. Our results are displayed in graphs as variations of radius of curvature against propagation distance at various settings of beam order, width parameter, source focal length, wavelength, refractive index structure constant. Our findings indicate that mBG beams, in general will have larger radius of curvature values than BG beams. It is further observed that increases in beam order will lead to greater radius of curvatures. Rises in the width parameter will reveal more the differentiations between BG and mBG beams. At small focal lengths, the difference between BG and mBG beams is hardly noticeable. Higher wavelengths will initially cause a reduction in the radius of curvature, but at longer propagation distances, the reverse will happen. Increases in the refractive index structure constant will lead to smaller radius of curvature values. A general agreement is found in comparing the analytic results of BG beams with those of phase screen approach.