  We report the close form expressions of the photon number statistics for a
generalized coherent state and a generalized photon-added coherent state, which
are shown to be crucial for proposing a variety of quantum scissor operations.
The analytically obtained distributions are also capable of predicting the
precise laser intensity windows for realizing a variety of quantum scissors.
Truncating a photon added state overcomes the selection rule of obtaining the
lower order Fock states. Photon addition also enables us to obtain a higher
order Fock state in a lower order superposition. The importance of circular
geometry is also demonstrated for engineering such quantum scissors.
