Binding energies of the lowest two s-symmetric impurity states and linear, third order nonlinear, and total optical absorption coefficients corresponding to the 1s -> 2s transitions for electrons in a Morse quantum well are investigated. Influence of a non-resonant intense laser field is considered for different values of the structure parameter, impurity position, and laser field intensity. In order to find the eigenvalues and eigenfunctions of the unbound electron confined within the Morse quantum well under the intense laser field, the time independent Schrodinger equation is solved by using the effective mass and parabolic band approximations. The impurity binding energy is determined by means of a variational procedure, using hydrogen-like trial wave functions, and the optical response is treated with the use of a two-level approach in the density matrix expansion. Our results show that it is possible to design suitable devices described by a Morse-like confinement pattern in the desired wavelength by changing the mentioned parameters.