  A certain class of exact solutions of Einstein Maxwell spacetime in general
relativity is discussed which demonstrates at the level of theory that, when
certain parametric resonance condition is met, the interaction of
electromagnetic field with a gravitational wave will display certain Liapounov
instability and lead to exponential amplification of a gravitational wave train
described by certain Newman-Penrose component of the Weyl curvature. In some
way akin to a free electron laser in electromagnetic theory, by the conversion
of electromagnetic energy into gravitational energy in a coherent way, the
feasibility of generating a pulsed laser like intense beam of gravitational
wave is displayed.
