We study the Gauss kernels for a class of (2+1)-dimensional linear Schrödinger equations with potential functions. The relationship between the Lie point symmetries and Gauss kernels for the Schrödinger equations is established. It is shown that a classical integral transformation of the Gauss kernel can be generated by a proper Lie point symmetry admitted by the equation. Then we can recover the Gauss kernels for the Schrödinger equations by performing the inverse integral transformation.

We investigate the two-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with different external potentials. In the absence of external potential or in the presence of harmonic potential, the number of localized nonlinear waves is associated not only with the boundary condition but also with the singularity of inhomogeneous cubic-quintic nonlinearities; while in the presence of periodic external potential, the periodic inhomogeneous cubic-quintic nonlinearities, together with the boundary condition, support the periodic solutions with an arbitrary number of circular rings in every unit. Our results may stimulate new matter waves in high-dimensional Schrödinger equations with spatially modulated nonlinearities.

We propose an efficient multi-particle entanglement generation protocol using a quantum dot and optical micro-cavity coupled system. Multi-electron spins may become entangled by the interaction between the electrons and the single photons. The entanglement success probability relies on the coupling strength and the cavity leakage, which is also discussed.

With the improvement of the accuracy of atomic frequency standard and satellite navigation, the high-resolution phase comparison method is necessary. Using the phase synchronous detection principle, a super-high resolution phase comparison method between frequency standards is proposed based on the greatest common factor frequency, phase group processing and a common frequency source and so on. This method is mainly dependent on the stability of the common frequency standard and its frequency. The ±1 count error can be eliminated effectively. Therefore, higher than 1 ps resolution can be easily reached with a simple instrument. Experimental results show higher than 10⁻¹⁵/h precision can be obtained in the long-term frequency standard comparison and the measuring precision can reach 10⁻¹⁷ for several days of comparison.

We successfully label-free and real-time detect the capture processes of human immunoglobulin G (IgG)/goat anti-human IgG and mouse IgG/goat anti-mouse IgG antigen-antibody pairs with different concentrations using the oblique-incidence reflectivity difference (OIRD) method, and obtain the interaction kinetics curves and the interaction times. The experimental results prove that the OIRD method is a promising technique for label-free and real-time detection of the biomolecular interaction processes and achieving the quantitative information of interaction kinetics.

Production of positron-electron (e⁺e⁻) pairs in an intense laser pulse is investigated by solving the Dirac equation with analytical and numerical methods. We observe that the probability of the pair production will firstly decrease slowly as the pulse length τ becomes shortened. Then it will increase until τ is reduced to the Compton time τ_c=ħ/(m_ec)≈1.29×10⁻²¹ s and finally decrease exponentially to zero. Hence, for a prominent pair production, we not only require that the electric field strength should be higher than the the Schwinger critical value E_cr=m²c³/(eħ)≈1.32×10¹⁶ V/cm, but also that the pulse duration τ should be larger than τ_c. The latter is shown to be related to momentum requirement for the transition. For fields with different pulse lengths, the phase and chirp influences upon the pair production are also explored.

We investigate the radiative dileptonic decays B_s→l⁺l⁻γ (l=e, μ and τ) in the framework of the topcolor-assisted technicolor (TC2) model. The contributions of the new particles predicted by this model to the branching ratios and the forward-backward asymmetry (A_FB) of these decays are considered. It is found that the values of their branching ratios are greater than the standard model (SM) predictions by several times up to one order of magnitude and |A_FB| can also be enhanced by several times in a wide range of the parameter space.

The photodetachment of a hydrogen negative ion (H⁻) near a partially reflecting surface with a spherical shape is investigated by a theoretical imaging method. Analytical expressions for the detached electron flux and total photodetachment cross section are derived. It is found that two parameters, i.e. curvature radius r_c and reflection parameter K, control the photodetachment spectra. Furthermore, these parameters can be used for the classification, identification and revelation of minor details like curvature of different types of surfaces.

An experiment setup for narrow linewidth superradiant laser based on the mechanism of an active optical clock is proposed with optical lattice trapped ⁴⁰Ca. We obtain the threshold pumping rate analytically and deduce the linewidth of the superradiant laser in a bad cavity regime. The proposed laser has an extremely narrow linewidth at millihertz level and a power level of order 10⁻⁹ W.

The first experimental comparison between the actively and passively Q-switched intracavity optical parametric oscillators (IOPOs) at 1.57 µm driven by a small-scale diode-pumped Nd:YVO₄ laser are thoroughly presented. It is found that the performances of the two types of IOPOs are complementary. The actively Q-switched IOPO features a shorter pulse duration, a higher peak power, and a superior power and pulse stability. However, in terms of compactness, operation threshold and conversion efficiency, passively Q-switched IOPOs are more attractive. It is further indicated that the passively Q-switched IOPO at 1.57 µm is a promising and cost-effective eye-safe laser source, especially at the low and moderate output levels. In addition, instructional improvement measures for the two types of IOPOs are also summarized.

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge–Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.

Bragg gratings are inscribed in an all-solid photonic bandgap fiber by use of femtosecond laser irradiation. Dual-peak structure is observed in the transmission spectrum of the induced grating, which is formed by the coupling between the forward-propagating fundamental core mode and the backward-propagating core mode or supermode. Sensing characteristics of the device are investigated experimentally by employing strain and temperature tests, and similar behavior is obtained for both resonant peaks. The strain and temperature sensitivities are 0.968pm/μϵ and 12.01pm/°C, and 0.954pm/μϵ and 12.04pm/°C, for the two peaks, respectively. This device would find potential applications in real optical fiber sensing without extra reference gratings.

A novel setup of saturated absorption spectroscopy (SAS) is presented. It is based on laser reflections at surfaces of a sample vapor cell. It only needs one cell and one photodiode and is more compact than conventional setups of SAS. Its spectrum is similar to a conventional SAS. The frequency stabilization performance of an external-cavity diode laser with this setup is investigated. A frequency stability of 1.1×10^-11 is achieved at an averaging time of 60 s in the Allen variance measurements.

We investigate the optical Kerr effect of SrTiO₃ (STO) crystal, of which the nonlinear response time was measured to be less than 200 fs, while the nonlinear refractive index is estimated to be 2.16×10^-15 cm²/W. Using the optical Kerr gate (OKG) technique with an STO crystal as the Kerr medium, we obtain narrow-bandwidth and symmetric gated spectra from a supercontinuum generated in distilled water by a femtosecond laser. The experimental results show superiority compared with the gated spectra obtained using OKG with CS₂ as the Kerr medium, demonstrating that STO crystal is a promising OKG medium.

The generalized nonlinear Schrödinger equation, which describes the evolution of dual steady-state optical solitons in a cold three-state medium, is written as the Hamiltonian symplectic structure. The symplectic method is applied to investigate evolution of dual steady-state optical solitons. By adjusting the initial pulses, the saturation parameter variables and the distances of optical solitons, the different behaviors of dual steady-state optical solitons are analyzed.

High-power quantum cascade lasers (λ=4.6 µm ) working in continuous wave (cw) up to 90°C are presented. The material was grown by solid-source molecular beam epitaxy and processed into narrow conventional ridge geometry without lateral regrowth. High cw output power of 850 mW at 10°C and more than 200 mW at 90°C were obtained with threshold current densities of 1.34 and 2.47 kA/cm², respectively, for a high-reflectivity-coated 12-µm -wide and 3-mm-long laser.

We report the nonlocal imaging of an object by conditional averaging of the random exposure frames of a reference detector, which only sees the freely propagating field from a thermal light source. A bucket detector, synchronized with the reference detector, records the intensity fluctuations of an identical beam passing through the object mask. These fluctuations are sorted according to their values relative to the mean, then the reference data in the corresponding time-bins for a given fluctuation range are averaged, to produce either positive or negative images. Since no correlation calculations are involved, this correspondence imaging technique challenges our former interpretations of "ghost" imaging. Compared with conventional correlation imaging or compressed sensing schemes, both the number of exposures and computation time are greatly reduced, while the visibility is much improved. A simple statistical model is presented to explain the phenomenon.

We present a micro-gravity experimental study of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component of the vibrating direction when dividing particles along the vibration direction into several bins. This feature does not exist in the molecular gas. We further study the hydrodynamic profiles of pressures p and temperatures T in positive and negative components, such as p_y⁺ and p_y⁻ and T_y⁺ and T_y⁻, in accordance with the sign of velocity components of the vibrating direction. Along vibration direction, granular media are found to be not only inhomogeneous and anisotropic, but also different greatly in positive and negative components. Energy equipartition breaks down in this case.

Numerical simulations of unsteady cavitating flow around a NACA66-mod hydrofoil were performed using the partially-averaged Navier–Stokes method with different values of the resolution control parameters (f_k=1.0–0.2, f_ϵ=1). With decreasing f_k, the predicted cavitating flow becomes unsteady as the time-averaged turbulent viscosity at the rear part of the attached cavity is gradually reduced. For f_k=0.9 and 0.8, the cavity becomes unstable and its length dramatically expands and shrinks, but the calculation fails to predict the vapor cloud shedding behavior observed experimentally. With smaller f_k less than 0.7, the cloud shedding behavior is simulated numerically and the predicted cavity shedding frequency increases. With f_k=0.2, the whole cavitating flow evolution can be reasonably reproduced including the cavity growth/destabilization observed previously. The re-entrant flow along the suction surface of the hydrofoil is the main trigger to cause the vapor cloud shedding. The wall pressure along the hydrofoil surface oscillates greatly due to the dynamic cavity shedding. Comparing the simulations and experiments, it is confirmed that for the PANS method, resolution control parameters of f_k=0.2 and f_ϵ=1 are recommended for numerical simulations of unsteady cavitating flows. Thus, the present study shows that the PANS method is an effective approach for predicting unsteady cavitating flow over hydrofoils.

Bi₄Si₃O₁₂ (BSO) is an excellent scintillation crystal, and is becoming the desirable candidate for dual-readout calorimeters in high-energy physics. In this work, high quality BSO crystals are successfully grown by the modified Bridgman method. For the first time, its mechanical and thermal properties are investigated and compared with those of the famous scintillation crystal Bi₄Ge₃O₁₂ (BGO). The Vickers hardness and fracture toughness of BSO crystal are higher than those of BGO crystal. Its specific heat, thermal diffusivity and thermal conductivity are measured to be 0.319 J⋅gK^-1, 1.54 mm²⋅s^-1 and 3.29 W⋅m^-1K^-1 at 298 K, respectively. The average thermal expansion coefficient is calculated to be 7.07×10^-6 K^-1 from 300 to 1173 K. Compared with BGO crystal, BSO crystal possesses larger specific heat, thermal conductivity and smaller thermal expansion. These results indicate that BSO crystals possess better mechanical and thermal properties, which will benefit its practical applications.

In terms of first-principles investigation of H-tungsten (W) interaction, we reveal a generic optimal electron density mechanism for H on W(110) surface and at a vacancy in W. Both the surface and vacancy internal surface can provide a quantitative optimal electron density of ∼0.10 electron/ų for H binding to make H stability. We believe that such a mechanism is also applicable to other surfaces such as W(100) surface because of the (100) surface also providing an optimal electron density for H binding, and further likely actions on other metals.

The complex dielectric permittivity (ϵ^∗=ϵ'-jϵ") and ac conductivity (σ_ac) of Au/SnO₂/n-Si (MOS) structures are studied using capacitance (C) and conductance (G(ω)) measurements in a wide temperature range of 125–400 K for six different frequency values. It is observed that the C and G(ω) values decrease with the increasing frequency, while they increase with the increasing temperature. The observed nature of the C is due to the inability of the dipoles to orient in a rapidly varying electric field. The experimental values of the dielectric constant ϵ', dielectric loss ϵ", loss tangent tanδ and σ_ac are found to be strong functions of frequency and temperature. The values of the ϵ' and ϵ" are found to decrease with the increasing frequency and increase with the increasing temperature. The σ_ac is found to increase with the increasing frequency and temperature. Activation energy (E_a), from the Arrhenius plot, is studied to discuss the conduction mechanism in a MOS structure.

We report the ab initio calculations of transport behaviors of an azobenzene molecular device which is similar to the experimental configurations. The calculated results show that the transport behaviors of the device are sensitive to the molecule-electrode distance and the currents will drop rapidly when the molecule-electrode distance changes from 1.7 Åto 2.0 Å. More interestingly, the negative differential resistance behavior can be found in our device. Nevertheless, it is not the inherent property of an azobenzene molecular device but an effect of the molecule-electrode distance. Detailed analyses of the molecular projected self-consistent Hamiltonian states and the transmission spectra of the system reveal the physical mechanism of these behaviors.

Indium tin oxide (ITO) nanoparticles are synthesized by the two-degradation sulfide and liquid-phase co-precipitation method under the given conditions with solutions of InCl₃⋅4H₂O and SnCl₄⋅5H₂O in the presence of ethylendyamine. The sample powders were characterized by x-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses after heat treatments. The SEM results show that the size of the ITO particles prepared by the co-precipitation method is decreased to 100 nm, whereas the size of the ITO prepared by degradation of sulfide increases to 1 µm after heat treatment. The XRD results reveal that the size of crystallite ITO particles is increased with increasing annealing temperature. Finally the intensity ratio of I₄₀₀/I₂₂₂ has an increase of 29.07% for ITO prepared by the co-precipitation method.

We investigate the transport properties through magnetic superlattices with asymmetric double-barrier units in monolayer graphene. In N-periodic asymmetric double-barrier units, there is (N−1)-fold resonant peak splitting for transmission, but the splitting is (2N−1)-fold in N-periodic symmetric units. The transmission depends not only on the value of incident wavevectors but also on the value and the direction of transverse wavevectors. This renders the structure's efficient wavevector filters. In addition, the conductance of standard electrons with a parabolic energy spectrum is suppressed more strongly than that of Dirac electrons, whereas the resonances are more pronounced for Dirac electrons than for standard ones.

We report that a metal-dielectric-metal cavity with a perforated top metallic film shows a remarkable polarization-selective collimation effect through reflection on the perforated film. According to simulations, such plasmonic cavities can achieve nearly perfect absorption (R<1.5%) of a transverse magnetic (TM) wave at an optimized incident angle while nearly perfect reflection (R∼100%) at normal incidence. A very wide incident angle range (approximately 15^°–65^°) is found to exhibit a high absorption ratio exceeding over 70%. In contrast, for a transverse electric (TE) wave, the plasmonic cavities remain highly reflective (R∼100%) regardless of the incident angles. We elucidate that this polarization- and angle-dependent behavior arises from an even-order (N=2) horizontal Fabry–Pérot (FP) resonant mode inside the plasmonic cavity. This effect may find potential applications for angle filtering of polarized divergent light beams in optics.

Low density ZnO nanorods are grown by modified chemical vapor deposition on silicon substrates using gold as a catalyst. We use high resolution photoluminescence spectroscopy to gain the optical properties of these nanorods in large scale. The as-grown samples show sharp near-band-gap luminescence with a full width at half maximum of bound exciton peaks at about 300 µeV, and the ratio of ultraviolet/yellow luminescence larger than 100. Highly spatial and spectral resolved scanning electron microscope-cathodoluminescence is performed to excite the ZnO nanorods in single rods or different positions of single rods with the vapour-solid growth mechanism. The bottom of the nanorod has a 3.31-eV luminescence, which indicates that basal plane stacking faults are related to the defects that are created at the first stage of growth due to the misfit between ZnO and Si.

We develop a miniaturized chamber installed on a tandetron accelerator into which negative ions of small carbon clusters are transported. Negative clusters C₁⁻− C₁₀⁻ are obtained with beam currents of 1–10⁴ nA at energies of 10–20 keV. C₂⁻ beams of 0.2 µA are used to directly deposit carbon films on SiO₂/Si substrates. Formation of ultrathin carbon films are demonstrated by Raman scattering, which reveals the evolution of the graphitic peak (1550 cm⁻²) with deposition time.

Gate-recessed AlGaN/GaN metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs) on sapphire substrates are fabricated. The devices with a gate length of 160 nm and a gate periphery of 2×75 µm exhibit two orders of magnitude reduction in gate leakage current and enhanced off-state breakdown characteristics, compared with conventional HEMTs. Furthermore, the extrinsic transconductance of an MOSHEMT is 237.2 mS/mm, only 7% lower than that of Schottky-gate HEMT. An extrinsic current gain cutoff frequency f_T of 65 GHz and a maximum oscillation frequency f_max of 123 GHz are deduced from rf small signal measurements. The high f_max demonstrates that gate-recessed MOSHEMTs are of great potential in millimeter wave frequencies.

Airbrush spray deposition is applied to fabricate a bilayer heterojunction solar cell based on P3HT/PCBM. This solar cell device shows an open-circuit voltage of 0.36 V, a short circuit current density of 6.76 mA/cm², a conversion efficiency of 0.74%, and a fill factor of 30.4%. The results demonstrate that airbrush spray deposition is an effective method to fabricate multilayer or other complex polymer-based organic solar cells. Although spin-coated bulk heterojunction devices have better performance than the airbrushed ones, the airbrush is indeed feasible as a low-cost yet simple process. It is noteworthy that such preliminary results of the airbrush spray solar cell is unoptimized and thus its performance can be further improved with the development of this technology. Furthermore, this method itself has huge potential as it can be used for other polymer-based organic thin film devices.