arXiv subjects

Songhao Liu

Publications and source records attributed to Songhao Liu.

6 recordsLinked to original sources

arXiv2026

Cram\'er-type moderate deviation for double index permutation statistics

We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation results and are insufficient to capture the optimal convergence rates for some relatively sparse DIPS. Our result overcome these limitations: it not only recover the optimal convergence rates for classical DIPS, such as the Mann-Whitney-Wilcoxon statistic, but also extend to sparse statistics, including the number of descents in permutations and Chatterjee's rank correlation coefficient, for which previous approaches do not apply. To prove this result, we establish a Cram\'er-type moderate deviation of normal approximation for bounded exchangeable pairs. Compared with existing results, our theorem requires more easily verifiable conditions.

math.PR↗

arXiv2024

New Upper bounds for KL-divergence Based on Integral Norms

In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches between the convergence of density functions in terms of $L^1$ and $L^2$ norms. Furthermore, we endeavor to apply our newly derived upper bounds to the analysis of the rate theorem of the entropic conditional central limit theorem.

math.PR↗

arXiv2020

Nonvolatile, reconfigurable and narrowband mid-infrared filter based on surface lattice resonance in phase-change GeSbTe

We propose a nonvolatile, reconfigurable, and narrowband mid-infrared bandpass filter based on surface lattice resonance in phase-change material Ge2Sb2Te5 (GST). The proposed filter is composed of a two-dimensional gold nanorod array embedded in a thick GST film. Results show that when GST transits from the amorphous state to the crystalline state, the narrowband reflection spectrum of the proposed filter is tuned from 3.197 {\mu}m to 4.795 {\mu}m, covering the majority of the mid-infrared regime, the peak reflectance decreases from 72.6% to 25.8%, and the corresponding Q-factor decreases from 19.6 to 10.3. We show that the spectral tuning range can be adjusted by varying the incidence angle or the lattice period. By properly designing the gold nanorod sizes, we also show that the Q-factor can be greatly increased to 70 at the cost of relatively smaller peak reflection efficiencies, and that the peak reflection efficiency can be further increased to 80% at the cost of relatively smaller Q-factors. We expect this work will advance the engineering of GST-based nonvalatile tunable surface lattice resonances and will promote their applications especially in reconfigurable narrowband filters.

physics.optics↗

arXiv2016

Optical gears in a nanophotonic directional coupler

Gears are rotating machines, meshing with each other by teeth to transmit torque. Interestingly, the rotating directions of two meshing gears are opposite, clockwise and counterclockwise. Although this opposite handedness motion has been widely investigated in machinery science, the analogue behavior of photons remains undiscovered. Here, we present a simple nanophotonic directional coupler structure which can generate two meshing gears of angular momentum (AM) of light, optical gears. Due to the abrupt phase shift effect and birefringence effect, the AM states of photons vary with the propagation distance in two adjacent waveguides of the coupler. Thus, by the choice of coupling length, it is able to obtain two light beams with opposite handedness of AM, confirming the appearance of optical gears. The full control in the handedness of output beams is achieved via tuning the relative phase between two orthogonal modes at the input ports. Optical gears thus offer the possibility of exploring light-matter interactions in nanoscale, opening up new avenues in fields of integrated quantum computing and nanoscale bio-sensing of chiral molecules.

physics.optics↗

arXiv2013

Study on the Fermi level of microstructured Silicon with impurities introduced by chalcogenides and their affect on solar cell efficiency

Microstructured Silicon, which is obtained by irradiating the surface of a Silicon wafer with femtosecond laser pulses under certain circumstances, has unusual optical properties such as the strong absorption of light with wavelength from 0.25μm to 17μm. So it holds great promise in the intermediate band solar cell (IBSC). Some articles have discussed the electronic structure associating with simple substitutional impurities in Silicon introduced by chalcogenides. And on this basis, after high temperature annealing treatment, we establish the mode of impurity levels of microstructured Silicon introduced by sulfur and oxygen. Using generalized statistics of multi-level,we analyze the probability of electronic in all local energy levels and the relationship among Fermi level, temperature and the density of impurities. Then the theoretical conversion efficiency of the corresponding IBSC is discussed with the Detailed Balance Theory. And the issue of making high efficiency solar cells based on femtosecond laser microstructured Silicon is discussed in detail.

cond-mat.mtrl-sci↗

arXiv2007

An integral gated mode single photon detector at telecom wavelengths

We demonstrate an integral gated mode single photon detector at telecom wavelengths. The charge number of an avalanche pulse rather than the peak current is monitored for single-photon detection. The transient spikes in conventional gated mode operation are canceled completely by integrating, which enables one to improve the performance of single photon detector greatly with the same avalanche photodiode. This method has achieved a detection efficiency of 29.9% at the dark count probability per gate equal to 5.57E-6/gate (1.11E-6/ns) at 1550nm.

physics.optics↗