NONLINEAR COMBINATIONS OF GRATINGS IN BI12SIO20 - THEORY AND EXPERIMENTS

Multiple optical interference patterns generate phase gratings in Bi12 SiO20 as a result of the photorefractive effect. Because of the nonlin ear response of the space-charge field to the optical interference pat tern, these primary gratings interact and cause the formation of addit ional gratings at frequencies that are combinations of the primary gra ting frequencies. Only the diffusion regime is considered in the prese nt investigation. In our setup, two primary gratings are induced as th e result of interference among one reference and two closely situated object beams. The interference between the two object beams leads to a negligible photorefractive grating, because the photorefractive Bi12S iO20 crystal cannot respond to the corresponding large fringe spacing. We show theoretically that nonlinear combinations of gratings are int roduced through this third interference pattern even though the corres ponding grating itself is absent. We obtain analytical expressions for the fundamental frequency components of the space-charge field in the special case of a weak reference beam. In the general case, the frequ ency components of the space-charge field are calculated numerically b y the use of Fourier transforms and are incorporated into the coupled- wave equations. The optical beam propagation method is then used for s olving these equations numerically. The effect is probed in a three-wa ve mixing experiment that uses a sinusoidal phase modulation on one of the object beams to control the grating strength. With this technique one of the gratings is specifically canceled out, and the relative ch ange of the diffraction efficiency in the remaining grating is measure d. It is shown that nonlinear combinations of gratings may cause relat ive changes of more than 35% in the diffraction efficiency. The theore tical predictions are in excellent agreement with our experimental res ults and the cross talk observed in dynamic optical interconnects.