Photon-added coherent states as nonlinear coherent states

The states \alpha, m), defined as (a) over cap dagger(m)\alpha] up to a nor malization constant and where m is a non-negative integer, are shown to be the eigenstates of f((n) over cap, m)(a) over cap where f((n) over cap, m) is a nonlinear function of the number operator (n) over cap. The explicit f orm of f((n) over cap, m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of the state \alpha, m]. The eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states \m] and \0] respectivel y.