Photon-added one-photon and two-photon nonlinear coherent states
  From the photon-added one-photon nonlinear coherent states $a^{\dagger m}|\alpha,f>$, we introduce a new type of nonlinear coherent states with negative values of $m.$ The nonlinear coherent states corresponding to the positive and negative values of $m$ are shown to be the result of nonunitarily deforming the number states $|m>$ and $|0>$, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of $m$ in detail. Finally we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions. 
Xiao-Guang Wang