We report the laser spectroscopic characterization of bulk
monoclinic Eu3+:Y2O3, which was
prepared by a
high-temperature, high-pressure synthesis method. The bulk
monoclinic phase has sharp spectral lines without
the line broadening and “secondary phase” of
Eu3+:Y2O3 nanocrystals. The
unusual optical properties of site
A in this material have been determined to be intrinsic to the
monoclinic phase and are not a result of surface
effects in the nanocrystals. The 5D0
fluorescence lifetimes are longer in the nanocrystals than in the
bulk
material, indicating that there is no lifetime shortening in the
nanocrystals due to quenching by the proximity
of surface defects.
A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10 Ϫ12 for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0
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