This work examines, both experimentally and theoretically, nonradiative decay processes in a series of substituted naphthalenes. We report single vibronic level fluorescence lifetimes and fluorescence excitation spectra of jet-cooled 2-chloronaphthalene, 1- and 2-fluoronaphthalene and 1- and 2-methylnaphthalene over an energy range of about 0–4000 cm−1 in S1. While the 00 nonradiative rates of these molecules vary by a factor of 30, the energy dependences of the nonradiative rates are quite similar. At low vibrational energies the nonradiative rates depend sensitively on the level excited, but in general they increase with energy. As energy increases, the nonradiative rates become less sensitive to the level excited and eventually become almost independent of vibrational energy. We can qualitatively predict this behavior using a thermodynamic formalism which treats the density of states as an intramolecular entropy and avoids the calculation of vibrational coupling terms. In addition we report the fluorescence lifetime of the S1 vibrationless level of 1-chloronaphthalene, and single vibronic level fluorescence spectra of levels up to 1396 cm−1 in 2-chloronaphthalene. Most of the fluorescence excitation and fluorescence spectra show substantial enhancement of the origin inensity and vibrational mode mixing in S1 compared to naphthalene. We briefly discuss these substituent effects and make some tentative assignments of S1 vibrational levels. We also discuss substituent effects on the 00 fluorescence lifetimes. In particular, the order of magnitude increase in the decay rate of 1-chloronaphthalene relative to 2-chloronaphthalene cannot be explained using CNDO/S calculations.
Beam-shape transformers are used in high-efficiency projectors to match round source beams to rectangular LCD targets. Two common alternative approaches use (1) light-pipes and (2) lenslet arrays. Both approaches outperform the simple overfilling used in simpler systems. We review the two approaches conceptually and develop simple theoretical models which elucidate each approach's trade-offs between uniformity, efficiency, etendue, and compactness. For the light-pipe approach, we develop a detailed analytical theory for idealized, uniform sources, and we compare the predictions to raytrace results. Finally, we compare the two approaches and fmd that the light-pipe approach offers similar performance with higher compactness. The lens array approach, however, may be favored in complex systems where multiple elements already result in long optical trains, or in systems where etendue conservation is not a priority.
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