Nonuniform Bragg holograms with complex refractive index

Abstract

It has been known for years that the bandwidth of typical Bragg-Lippmann holograms, based on dichromated gelatin (DCG) and PVA-based polymers, is much broader1 than could be expected based on the fully uniform Kogelnik theory. Indeed the typical holographic processing is highly nonuniform, particularly in the z direction; thus both fundamental parameters of Kogelnik’s theory; the coupling constant and off-Bragg parameter, become functions of the z coordinate.1 This fact constitutes the basis for the more general theory based on the well-known (from quantum mechanics) WKB approximation.1 On the other hand, it became evident that the analysis of UV and XUV holograms2 requires the introduction of both a complex bias refractive-index and refractive-index modulation. Unfortunately, the elegant analytic model based on the WKB method does not hold for highly nonuniform Kogelnik parameters. Such a situation, however, is quite typical in DCG holography where an experimental hologram bandwidth can easily exceed 100 nm, while the theoretical bandwidth, based on Kogelnik’s theory, can still be below 20 nm. Therefore, the generalization in both directions, high-grating constant vertical nonuniformity and complex refractive index, is necessary.