Quasi-scaling of the extinction efficiency of spheres in high frequency Bessel beams

The extinction efficiency Qext of a sphere is defined to be the ratio of its extinction cross section to the area of its profile. For non-dissipative situations Qext reduces to the scattering efficiency. For a sphere centered on the axis of a Bessel beam Qext has a complicated dependence on dimensionless frequency ka and on the conic angle β of the beam, even in the simple case of a rigid sphere. With appropriate scaling using Babinet's principle, however, the dependence reduces approximately to a function of ka sin(β) when ka is large. An example is also shown for a metal shell in water.