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From the photon-added one-photon nonlinear coherent states $a^{\daggerm}|\alpha,f>$, we introduce a new type of nonlinear coherent states withnegative values of $m.$ The nonlinear coherent states corresponding to thepositive and negative values of $m$ are shown to be the result of nonunitarilydeforming the number states $|m>$ and $|0>$, respectively. As an example, westudy the sub-Poissonian statistics and squeezing effects of the photon-addedgeometric states with negative values of $m$ in detail. Finally we investigatethe photon-added two-photon nonlinear coherent states and find that they arestill the two-photon nonlinear coherent states with certain nonlinearfunctions.Comment: 12 pages, 2 figure

Photon-added one-photon and two-photon nonlinear coherent states