Results are presented for Floquet calculations of photodetachment rates from a one-dimensional model atom irradiated by intense laser light. Light-induced quasibound states are found to originate from the movement of poles of the multichannel scattering matrix on the Riemann energy surface. The appearance of new bound states of the negative Hydrogen ion, recently predicted, is related to the motion of resonance poles that correspond to autoionising states in the absence of the field. A number of pole trajectories, leading to light-induced states, are discussed for the one-dimensional model atom. The Floquet method allows one to represent the wave function of a quantum system in a laser field, as an infinite sum of harmonic basis functions. In any practical calculation this infinite sum must be truncated. The consequences of representing the wave function, via the Floquet method, by a finite sum of harmonics is addressed. An illustration of these consequences is made by way of a number of representative calculations performed on a one-dimensional model atom. Results are presented of calculations performed to determine the influence of a laser field, of low to moderate intensity, upon the partial and total photodetachment rates of the negative Hydrogen ion, H(^-). Using the R-matrix Floquet method, a study is undertaken into the detachment of an electron from the ion, via multiphoton transitions through one of several autodetaching resonances of the ion. The discussion focuses on the influence of the laser field upon auto detaching pathways. It is found that the laser may induce structure into the continuum that does not exist in the absence of the laser field, or, conversely, may suppress field-free structure. In the latter case, the suppression of structure is related to the appearance of laser-induced degeneracies.