Fractional Hankel transform gained via non-unitary bosonic operator realization of angular momentum generators

By proposing new non-unitary Bose operator realization of angular momentum generators (J−,J+,J0) and finding that the charge-amplitude entangled states (CAES) introduced in [H.-y. Fan, Phys. Lett. A 313 (2003) 343] carry the representative space of them, we derive the integral kernel of optical fractional Hankel transform (FHT) by calculating the matrix element of exp{iθ(J++J−)} in the CAES.