  We theoretically introduce a new kind of non-Gaussian state-----Laguerre
polynomial excited coherent states by using the multiphoton catalysis which
actually can be considered as a block comprising photon number operator. It is
found that the normalized factor is related to the two-variable Hermite
polynomials. We then investigate the nonclassical properties in terms of
Mandel's Q parameter, quadrature squeezing, second correlation, and the
negativity of Wigner function (WF). It is shown that all these properties are
related to the amplitude of coherent state, catalysis number and unbalanced
beam splitter (BS). In particular, the maximum degree of squeezing can be
enhanced as catalysis number and keeps a constant for single-photon catalysis.
In addition, we examine the effect of decoherence by Wigner function, which
show that the negative region, characteristic time of decoherence and structure
of WF are affected by catalysis number and unbalanced BS. Our work provides a
general analysis about how to prepare theoretically polynomials quantum states.
