Abstract

Using a linearized form of the Kukhtarev equations, we study beam fanning in LiNbO₃ when a Gaussian beam is incident on the crystal in which no hologram has been previously stored. Both steady state and transient solutions are provided. The space charge field is calculated by numerically integrating the charge distribution, which can be found in closed form in the spatial frequency domain. A split-step beam propagation method is thereafter used to analyze the propagation of incident Gaussians of arbitrary widths and radii of curvature through a "thick" sample of the material. Our results clearly show the transient buildup of beam fanning, which is also verified from experiment. In the case of Gaussian beam incidence on a previously stored grating in LiNbO₃, beam fanning is observed in the transient state for both the diffracted and undiffracted light. Once again, this observation is corroborated with theoretical results.

© 1992 Optical Society of America