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The objective of this research was to investigate the possibility of increasing the useful bandwidth of multilayer mirrors. Mirrors 'constructed' with non-periodically spaced reflecting surfaces were considered. These structures included depth-graded and laterally-graded mirrors as well as those with reflectors located via a log-periodic spacing rule. No enhancement of bandwidth resulted from simulations of simple versions of any of the three non-periodic mirrors. However, certain depth-graded structures did exhibit reflectances essentially the same as from uniform mirrors. Moreover, it was found that some control was possible regarding the location (with respect to energy) of the maximum reflectance peak. Effective bandwidth was increased when composite models were simulated. In two of the cases studied, bandwidth was enhanced by a factor of approximately 3. One model consisted of a depth-graded mirror constructed with three separately defined structures, or blocks. Each block consisted of two layer-pairs repeated three times. Then, the entire 18 layer-pair group was repeated several times. Simulation of this 3 block depth-graded configuration yielded three reflectance peaks, one representative of each depth-graded block. The other configurations resulting in enhanced bandwidth assumed independently constructed mirrors immediately adjacent to each other and sharing the same substrate. Reflectance peaks from each mirror appeared in the response. Both basic models show greatly enhanced effective bandwidths even though the reflectance curves appear as non-overlapping for these specific models. Additionally, these configurations are realizable. Details are contained in the section, DESIGN SIMULATIONS.