试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解     

两种新型芴类衍生物的三光子吸收特性研究

研究了两种新型芴类衍生物9，9_二（2_乙基已基）_2，7_二咔唑_9H_芴（简记为DCZF）和9 ，9_二（2_乙基已基）_2，7_二（2_（4_甲氧基）苯_2，1_乙烯基）芴（简记为BMOSF）在N ，N_二甲基甲酰胺（DMF）中的线性吸收和单光子荧光行为，并用脉冲宽度为38ps，重复 频率为10 Hz的1064 nm Nd：YAG脉冲激光研究了两种化合物的三光子吸收性质.结果表明： 两种新材料的最大线性吸收峰分别位于330和380nm，吸收区域覆盖了270—420 nm波段. 两种化合物的荧光带位于蓝_紫区，中心波长为369和442 nm，都具有较小的斯托克斯位移. 化合物DCZF和BMOSF的三光子吸收系数分别为γ_DCZF=678×10^{- 20} cm3/W²和γ_BMOSF=592×10^-20 cm³/W². 同时， 两种新材料还表现出明显的三光子吸收光限幅效应，当入射光强分别为8和6GW/cm²时，非线性透过率分别达到30%和45%. 关键词： 芴类衍生物 三光子吸收 光限幅 非线性透过率     

Directed segregation in compartmentalized bi-disperse granular gas

A bi-disperse granular gas in an asymmetrical two-compartment system is studied experimentally.The presence of asymmetry within the range of our experimental parameters results in a directed segregated state and a directed clustering state.This deterministic system does not depend on the initial conditions.A modified flux model based on Lohse’s flux model for bi-disperse granular gases is derived.The modified flux model explains qualitatively the experimental results.     

Multi-linear Variable Separation Approach to Solve a (2+1)-Dimensional Generalization of Nonlinear Schrödinger System

By using a Bäcklund transformation and the multi-linear variable separation approach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinear Schrödinger system. The new “universal” formula is defined, and then, rich coherent structures can be found by selecting corresponding functions appropriately.     

Nonlinear Squeezed States and Multiplication Rule of Nonlinear Squeezing Operators Gained via Nonlinear Coherent State Representation and IWOP Technique

Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.     

Ultrafast Saturable Absorption of Core/Shell Colloidal Quantum Dots

Ultrafast saturable absorption (SA) materials that are capable of blocking the optical absorption under strong excitation have extensive applications in photonic devices. This work presents core/shell colloidal quantum dots (CQDs) which have the quantized energy levels, excellent band gap tunability, and possess significant SA performance. When the band gap is close to the pump pulse energy, the CQDs show significant resonant SA response. At the same excitation conditions, the core/shell CQDs dispersions show better SA response than graphene dispersions, and comparable to the recently reported molybdenum disulfide. The carrier dynamics of the SA of the CQDs is analyzed systematically. The research has also found that the two‐photon absorption of the CQDs show nearly cubic power law of the band gap, while the SA performance keeps almost the same in the nonresonant regime. Further, superior passive Q‐switched laser behavior is observed using the CQDs as a saturable absorber. The results directly reveal the physical processes of this basic problem and broaden the applications of CQDs in photonic devices.     

1.5-MHz repetition rate passively Q-switched Nd:YVO_4 laser based on WS_2 saturable absorber

A transmission-type tungsten disulfide(WS_2)-based saturable absorber(SA) is fabricated and applied to passively Q-switched Nd:YVO_4 laser.The WS_2 nanosheets are deposited on a quartz substrate by the vertical evaporation method.By inserting the WS2 SA into the plano-concave laser cavity,we achieve 153-ns pulses with an average output power of1.19 W at 1064 nm.To the best of our knowledge,both of them are the best results among those obtained by the Q-switched solid-state lasers with WS_2-based absorbers.The repetition rate ranges from 1.176 MHz to 1.578 MHz.As far as we know,it is the first time that MHz level Q-switched pulses have been generated in all solid state lasers based on low-dimensional materials so far.     

用于CARS激发源的全光纤飞秒脉冲谱压缩

进行了基于光纤预啁啾和自相位调制的多模/单模组合式全光纤啁啾谱压缩研究.提出利用多模光纤模式估计群速度色散均值的方法,并将该估计值作为啁啾参量分析的计算参数,仿真计算了50/125μm折射率渐变多模光纤的群速度色散均值及其与单模光纤在不同长度比值下的光谱压缩效果.采用三种折射率渐变多模光纤进行实验,对比分析了折射率渐变多模光纤的芯径大小及其与单模光纤的长度比值对光谱压缩效果的影响.实验结果表明使用50/125μm折射率渐变多模光纤获得光谱最大压缩比为5.796,谱宽为2.243 nm,与理论仿真一致;使用105/125μm折射率渐变多模光纤,可进一步提高压缩比至152.941,输出谱宽为0.085 nm的光脉冲.将此脉冲用于相干反斯托克斯拉曼散射光谱探测,理论光谱分辨率可达1.386 cm~(-1).     

Analysis of detection limit to time-resolved coherent anti-Stokes Raman scattering nanoscopy

In the implementation of CARS nanoscopy, signal strength decreases with focal volume size decreasing. A crucial problem that remains to be solved is whether the reduced signal generated in the suppressed focal volume can be detected. Here reported is a theoretical analysis of detection limit （DL） to time-resolved CARS （T-CARS） nanoscopy based on our proposed additional probe-beam-induced phonon depletion （APIPD） method for the low concentration samples. In order to acquire a detailed shot-noise limited signal-to-noise （SNR） and the involved parameters to evaluate DL, the T-CARS process is described with full quantum theory to estimate the extreme power density levels of the pump and Stokes beams determined by saturation behavior of coherent phonons, which are both actually on the order of ~ 109 W/cm2. When the pump and Stokes intensities reach such values and the total intensity of the excitation beams arrives at a maximum tolerable by most biological samples in a certain suppressed focal volume （40-nm suppressed focal scale in APIPD method）, the DL correspondingly varies with exposure time, for example, DL values are 103 and 102 when exposure times are 20 ms and 200 ms respectively.     

Quasiprobability distributions of a new kind of even and odd nonlinear coherent states

Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states (EONLCS) are investigated. The results show that the distributions of the new even nonlinear coherent states (NLCS) are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.