  General concept of Fano resonance is considered so that to show the
possibility of this resonance in space. Using a recently found solution for a
Bessel wave beam impinging a dielectric sphere, we analyze the electromagnetic
fields near a microsphere with different optical size and permittivity values.
We theoretically reveal a spatial Fano resonance when a resonant mode of the
sphere interferes with {an amount of } non-resonant modes. This resonance
results in a giant jump of the electric field behind the sphere impinged by the
first-order Bessel beam. The local minimum of the electromagnetic field turns
out to be noticeably distanced from the rear edge of the microsphere. However,
this is a near-field effect and we prove it. We also show that this effect can
be utilized for engineering a submicron optical trap with unusual and useful
properties.
