Nonlinear optical switching matrix

We show that nonlinear directional couplers with variable coupling coefficients can be used to compose a special kind of switching matrix. The switching matrix can be controlled by the signal itself or by a strong pump. Light routing is realized by adjustment of the power of the signal or the pump. Because light routing is based on the optical Kerr effect, ultrafast routing is possible.     

Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.     

Minimal switching voltage for magnetization reversals in asymmetric nanorings

Micromagnetic simulations based on the Landau–Lifshitz–Gilbert equation are presented to study spin-polarized current induced magnetization switching in asymmetric nanoring-shaped magnetic tunnel junctions. The results show that in a nanoring with an intermediate eccentric distance S, the critical switching voltage V_C reaches the minimum whose magnitude is less than half of the voltage for a symmetric nanoring. In addition to the spin-transfer torque, the current induced Ampère field is found to play a crucial part in the switching process. Analysis is given to explain the existence of such an energy valley that leads to the minimal voltage.     

Theoretical investigation on the threshold value of stimulated Brillouin scattering in terms of laser intensity

The threshold value of stimulated Brillouin scattering (SBS) was investigated theoretically basing on a new concept of real gain length (RGL). It shows that for ideal steady-state SBS or ideal transient SBS, the threshold values are both constants and the later is five orders of magnitude larger than the former. Under general conditions, whether steady-state SBS or transient SBS will occur is determined by RGL. The SBS occurred in a long material may not be steady-state SBS.     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval

As an important iteration, the Mann and Ishikawa iteration has extensive application in fixed point theory. In 1991, David Borwein and Jonathan Borwein proved the convergence of the Mann iteration on a closed bounded interval in their paper. In this paper, we will extend their result to an arbitrary interval and to the Ishikawa iteration, indicating the necessary and sufficient condition for the convergence of Ishikawa iteration of continuous functions on an arbitrary interval.     

Metal plasmon enhanced europium complex luminescence

The plasmon enhanced luminescence of a rare-earth complex Tris(6, 6, 7, 7, 8, 8, 8-heptafluoro-2, 2-dimethyl-3, 5-octanedionato) europium (Eu(fod)₃) was investigated. A polyvinyl alcohol (PVA) thin film was successfully adopted as a spacer to separate the Eu complex from the silver island film (SIF), and five-fold enhancement of the radiative decay rate of the Eu complex on SIF was demonstrated based on the luminescence intensity and lifetime measurement. Investigation of the distance dependent luminescence indicates that 7 nm is an optimal distance for SIF enhanced Eu luminescence. Plasmon enhanced rare-earth luminescence based on an organic film spacer would find potential applications in plasmon enhanced organic light emitting diode (OLED) devices.     

Best linear unbiased prediction for linear combinations in general mixed linear models

The general mixed linear model can be written as . In this paper, we mainly deal with two problems. Firstly, the problem of predicting a general linear combination of fixed effects and realized values of random effects in a general mixed linear model is considered and an explicit representation of the best linear unbiased predictor (BLUP) is derived. In addition, we apply the resulting conclusion to several special models and offer an alternative to characterization of BLUP. Secondly, we recall the notion of linear sufficiency and consider it as regards the BLUP problem and characterize it in several different ways. Further, we study the concepts of linear sufficiency, linear minimal sufficiency and linear completeness, and give relations among them. Finally, four concluding remarks are given.     

Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones

The paper analyzes the rate of local convergence of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under the constraint nondegeneracy condition and the strong second order sufficient condition, we demonstrate that the sequence of iterate points generated by the augmented Lagrangian method locally converges to a local minimizer at a linear rate, whose ratio constant is proportional to 1/τ with penalty parameter τ not less than a threshold . Importantly and interestingly enough, the analysis does not require the strict complementarity condition. Supported by the National Natural Science Foundation of China under Project 10771026 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.