  In this work we use the fundamental in quantum optics Jaynes-Cummings model
to study the response of spin $\tfrac12$ chain to a single mode of a laser
light falling on one of the spins, a focused interaction model between the
light and the spin chain. For the spin-spin interaction along the chain we use
the XY model. We report here the exact analytical results, obtained with the
help of a computer algebra system, for the energy spectrum in this model for
chains of up to 4 spins with nearest neighbors interactions, either for open or
cyclic chain configurations. Varying the sign and magnitude of the spin
exchange coupling relative to the light-spin interaction we have investigated
both cases of ferromagnetic or antiferromagnetic spin chains.
