Efficiency of volume phase reflection holograms recorded in an attenuating medium

The effect of attenuation when recording a volume phase hologram has been treated by a number of authors who neglect the effect of the varying average permittivity. It is shown here that such a variation, and the consequent violation of the Bragg conditions, leads to lower efficiency, the effect being more detrimental for greater attenuation and greater beam ratio. The mathematical solution is obtained with the aid of a generalisation of the coupled wave approach from which a set of numerical results is derived.