  We construct a class of nonlinear coherent states (NLCSs) by introducing a
more general nonlinear function and study their non-classical properties,
specifically the second-order correlation function $g^{(2)}(0)$, Mandel
parameter $Q$, squeezing, amplitude squared squeezing and Wigner function of
the optical field. The results indicate that the non-classical properties of
the new types of even and odd NLCSs crucially depend on nonlinear functions.
More concretely, we find that the new even NLCSs could exhibit the
photon-bunching effect whereas the new odd NLCSs could show photon-antibunching
effect. The degree of squeezing is also significantly affected by the parameter
selection of these NLCSs. By employing various forms of nonlinear functions, it
becomes possible to construct NLCSs with diverse properties, thereby providing
a theoretical foundation for corresponding experimental investigations.
