Abstract: Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter $\alpha $ the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state $\left| {\beta ,m} \right\rangle _{\rm o} $ (or $\left| {\beta ,m} \right\rangle _{\rm e} )$ is more pronounced when $m$ is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.

Key words: photon-depleted even and odd coherent state, Wigner function, intermediate coordinate-momentum representation, tomogram