We study the number of edges in the inhomogeneous random graph when vertex weights have an infinite mean and show that the number of edges is O(n log n).Central limit theorems for the number of edges are also establis...We study the number of edges in the inhomogeneous random graph when vertex weights have an infinite mean and show that the number of edges is O(n log n).Central limit theorems for the number of edges are also established.展开更多
We report the observation of electric field induced random lasing in a dye doped liquid crystal system. This was achieved by using a liquid crystal host with negative dielectric anisotropy doped with laser dye PM 597 ...We report the observation of electric field induced random lasing in a dye doped liquid crystal system. This was achieved by using a liquid crystal host with negative dielectric anisotropy doped with laser dye PM 597 in a 75 μm cell with a homeotropic alignment layer. In the absence of an applied field, only amplified spontaneous emission was observed since the liquid crystal orientation was uniform. However, application of a field resulted in a fieldinduced planar-like configuration with local nonuniformity in liquid crystal orientation. This led to random lasing in the energized state(voltage greater than a transition threshold). The onset of lasing occurs by application of either a spatially homogenous or a spatially inhomogeneous electric field across the liquid crystal. The characteristics of the emission spectra as a function of different(i) dye concentration and(ii) applied voltage were investigated using nanosecond pulsed laser excitation at 532 nm. The effects of using an inhomogeneous field were compared to the use of a homogenous field and reported. It is shown that the spatial configuration can be used to alter the emission spectra of the system. The work is used to suggest a new configuration, referred to here as"reverse mode," for liquid crystal-based random lasers. This new configuration may provide additional avenues for their use in commercial devices.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11671373)。
文摘We study the number of edges in the inhomogeneous random graph when vertex weights have an infinite mean and show that the number of edges is O(n log n).Central limit theorems for the number of edges are also established.
文摘We report the observation of electric field induced random lasing in a dye doped liquid crystal system. This was achieved by using a liquid crystal host with negative dielectric anisotropy doped with laser dye PM 597 in a 75 μm cell with a homeotropic alignment layer. In the absence of an applied field, only amplified spontaneous emission was observed since the liquid crystal orientation was uniform. However, application of a field resulted in a fieldinduced planar-like configuration with local nonuniformity in liquid crystal orientation. This led to random lasing in the energized state(voltage greater than a transition threshold). The onset of lasing occurs by application of either a spatially homogenous or a spatially inhomogeneous electric field across the liquid crystal. The characteristics of the emission spectra as a function of different(i) dye concentration and(ii) applied voltage were investigated using nanosecond pulsed laser excitation at 532 nm. The effects of using an inhomogeneous field were compared to the use of a homogenous field and reported. It is shown that the spatial configuration can be used to alter the emission spectra of the system. The work is used to suggest a new configuration, referred to here as"reverse mode," for liquid crystal-based random lasers. This new configuration may provide additional avenues for their use in commercial devices.
