In order to model the spectroscopic and scattering properties of a quantum system, we propose and explore a new absorbing complex-type optical potential based on a combination of cosine functions. This function provides a high degree of smoothness to joint with a physical real-type potential. The capabilities of this function are investigated in terms of its effect on otherwise freely evolving quantum dynamics. We use our open-source programs to implement the Fourier Grid method with the Optimizer package (in Matlab), freely available at https://sourceforge.net/projects/optimizer-sovkov/ https://sourceforge.net/projects/optimizer-sovkov/. Keywords: quantum dynamics; damping boundary conditions; optical potential; Fourier Grid method; spectroscopy of ultracold ensembles.