Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective functions using SGLD accelerated by variance reductions. Moreover, we prove an ergodicity property of the SGLD scheme, which gives insights on its potential to find global minimizers of nonconvex objectives.

Influence of proximity effects in electron-beam lithography on the optical properties of planar photonic-crystal waveguidesMany optoelectronic devices include multidimensional ͑grayscale͒ semiconductor structures such as diffractive optical elements ͑DOE's͒, blazed gratings, and photonic band gap ͑PBG͒ crystals. Their performance is known to be highly sensitive to dimensional accuracy of features in the multidimensional structure. Therefore, it is essential to have a tight control of the feature size in the fabrication process. Grayscale electron͑e͒-beam lithography enables a single step lithographic process for fabrication of such multidimensional structures and therefore has several advantages over using a binary lithographic process multiple times. As the feature size decreases, proximity effect in the e-beam lithographic process can make dimensions of the written features in a device substantially different from the ideal ones so that performance of the device is significantly degraded. In this paper, an efficient dose control scheme for grayscale e-beam lithography, which attempts to minimize the difference between the spatial exposure distribution and the ''shape'' of a multidimensional structure, is described along with results from an extensive computer simulation.

In recent years, the laser phosphor technology is becoming a mainstream one in the industry of projection display. In this paper, we first review the development of different light source technologies used in projectors. Thereafter, we review the evolution of our laser phosphor technology and then present its latest progress-RGB laser phosphor.

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