Spectral anomalies of focused high order Bessel beams in the neighborhood of focus

The spectral behaviors of spatially fully coherent polychromatic high order Bessel beams focused by an aperture lens are studied. It is shown that the spectrum is generally different from that at the aperture, i.e., the spectrum in the neighborhood of focus is proportional to the spectrum at the aperture and a spectral modifier, which depends on the truncation parameter, Fresnel number, position parameter and order number of Bessel beams. Detailed numerical calculation results indicate that the significant spectral changes take place near the geometrical focal plane. It is found that at the critical position ρc (the relative radial coordinate in the observation plane) at which the phase of field is singular, the spectrum is split into two lines, while at a position a little smaller than ρc, the spectrum is redshifted, and at a position a little larger than ρc, the spectrum is blueshifted. The influence of the truncation parameter, Fresnel number and order number on the spectral anomalies is presented.