Spatial Fano resonance of a dielectric microsphere impinged on by a Bessel beam

Using a recently found solution for a Bessel wave beam impinginga sphere, practically suitable for optically large dielectric spheres, we analyzethe electromagnetic fields near a substantial sphere for different sphere sizes andpermittivity. We theoretically reveal a Fano resonance when a resonant mode ofthe sphere interferes with an amount of all other modes. This resonance results ina giant amplification of the longitudinal electric field component in a substantialarea noticeably shifted to free space behind the microsphere. We prove that thisspatial Fano resonance is a near-field effect, though the maximum can be distancedup to {\lambda}/2 from the sphere and its effective length can be close to {\lambda}.