Volume Bragg gratings (VBGs) are important holographic optical elements in many spectral systems. Using multiple volume gratings, whether multiplexed or arranged sequentially, provides advantages to many types of systems in overall efficiency, dispersion performance, flexibility of design, etc. However, the use of multiple gratings---particularly when the gratings are multiplexed in a single holographic optical element (HOE)---is subject to inter-grating coupling effects that ultimately limit system performance. Analyzing these coupling effects requires a more complex mathematical model than the straightforward analysis of a single volume grating. We present a matrix-based algorithm for determining diffraction efficiencies of significant coupled waves in these multiplexed grating holographic optical elements (HOEs). Several carefully constructed experiments with spectrally multiplexed gratings in dichromated gelatin verify our conclusions. Applications of this theory to broad- and narrow-band systems are explored in detailed simulations. Broadband systems include spectrum splitters for diverse-bandgap photovoltaic (PV) cells. Volume Bragg gratings can serve as effective spectrum splitters, but the inherent dispersion of a VBG can be detrimental given a broad-spectrum input. The performance of a holographic spectrum splitter element can be improved by utilizing multiple volume gratings, each operating in a slightly different spectral band. However, care must be taken to avoid inter-grating coupling effects that limit ultimate performance. We explore broadband multi-grating holographic optical elements (HOEs) in sandwiched arrangements where individual single-grating HOEs are placed in series, and in multiplexed arrangements where multiple gratings are recorded in a single HOE. Particle swarm optimization (PSO) is used to tailor these systems to the solar spectrum taking into account both efficiency and dispersion. Both multiplexed and sandwiched two-grating systems exhibit performance improvements over single-grating solutions, especially when reduced dispersion is required. Dispersion performance can be further improved by employing more than two VBGs in the spectrum splitter, but efficiency is compromised by additional cross-coupling effects. Narrow-band applications of the multi-grating theory include spectral beam combining (SBC) systems. SBC systems utilizing multiple VBGs must be carefully analyzed to maximize channel density and efficiency, and thus output radiance. This analysis grows increasingly difficult as the number of channels in the system increases, and heuristic optimization techniques (e.g. PSO) are again useful tools for exploring the limits of these systems. We explore three classes of multi-grating SBC systems: "cascaded" where each grating adds a new channel to the system in sequence, "sandwiched" where several individual gratings are placed together and all channels enter the system at the same facet, and "multiplexed" where all of the gratings occupy the same holographic optical element (HOE). Loss mechanisms differ among these three basic classes, and the optimization algorithm shows that the highest channel density for a given minimum efficiency and fixed operating bandwidth is achieved for a cascaded-grating system. The multiplexed-grating system exhibits the lowest channel density under that same constraints but has the distinct advantage of being realized by a single HOE. For a particular application, one must weigh channel density and efficiency versus system complexity when choosing among these basic classes of SBC system. Additionally, one may need to consider the effects of finite-width input beams. As input beam radius is reduced, angular clipping effects begin to dominate over spectral interference and crosstalk effects, limiting all three classes of SBC systems in a similar manner.
University of Minnesota Ph.D. dissertation. May 2015. Major: Electrical/Computer Engineering. Advisor: James Leger. 1 computer file (PDF); x, 115 pages.
Multiplexed Volume Bragg Gratings in Narrow- and Broad-band Spectral Systems: Analysis and Application.
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