Mode competition in multi-core fiber amplifier

3D beam propagation numerical code and a newly developed optical mode solver were implemented for studies on the recently experimentally realized Yb fiber amplifier with 7-core hexagonal structure. It was found that the launched seven single-frequency beams matched with the cores converge to a wave field with permanently diminishing space beating patterns, but the result is sensitive to phases of separate beams. Namely, at a spread of phases of individual beams within a few tenths of radian, the convergence of the wave field to the in-phase mode is observed, while at phases random spread on the order of π the out-of-phase mode is dominating. Such behavior is observed at strong gain saturation in the cores. Both effects take place even if the guiding index of the cores fluctuates within a limited range. The mode solver predicts that the in-phase mode has the minimal small signal gain, and the gain of the out-of-phase mode is maximal one. This fact proves that there is no strict correlation between modal gains and amplification in strong saturated multi-core fiber. The smaller core index step significantly improves the convergence of the amplified radiation to the in-phase mode. An approach to the waveguide structure tailoring is described which assures the single in-phase mode stability.     

P3-支配图哈密尔顿性的两个充分条件

在文献[3]中介绍了一个新的图类-P3-支配图.这个图类包含所有的拟无爪图,因此也包含所有的无爪图.在本文中,我们证明了每一个点数至少是3的三角形连通的P3-支配图是哈密尔顿的,但有一个例外图K1,1,3.同时,我们也证明了k-连通的(k≥2)的P3-支配图是哈密尔顿的,如果an(G)≤k,但有两个例外图K1,1,3 and K2,3.     

Synthesis of nonlinear control systems invariant under perturbations

For nonlinear control systems with perturbations, we consider the problem of synthesis of perturbation-invariant characteristics (invariant functions) with the use of feedbacks. The existence of invariant functions is related to a decomposition of the control system for which the quotient system is independent of perturbations. We present conditions for the existence of such quotient systems, which are certain systems of partial differential equations. The synthesizing controls are found from these equations.     

Tomographic Representation of Electrocardiogram Signals

We consider signals of an arbitrary nature in the tomographic representation and compare their tomographic representation and the fractional Fourier transform. Also we illustrate how to apply the tomograms and the identical Radon transform for processing medical electrocardiogram (ECG) signals. The first results obtained show that, in contrast to routine Fourier analysis, the Radon transform revealed additional information for patients with early signs of ischemic heart disease (IHD) compared to healthy persons.     

Kupfer

Ohne Zusammenfassung     

Polyalkoxybenzenes from plant raw materials 1. Isolation of polyalkoxybenzenes from CO2 extracts of Umbelliferae plant seeds

For the search for a domestic natural source of allylpolyalkoxybenzenes and development of an effective process for their isolation, CO₂ extracts of several varieties of parsley, dill, celery, caraway, and nutmeg were analyzed systematically for the first time by GC/MS and GLC techniques. The varieties with high contents of myristicin, elemicin, allyltetramethoxybenzene, apiol, and dillapiol were identified. The conditions of CO₂ extraction for obtaining concentrates with minimum contents of the distillation residues were selected. Using high performance fractional distillation, polyalkoxyallylbenzenes with 98–99% purity were isolated from the concentrates on a pilot unit. By isomerization of some allylbenzenes followed by ozonolysis under specially selected conditions, apiol-and dillapiolaldehydes were obtained in 75–80% yields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2364–2371, December, 2007.     

Modeling of vertical external cavity semiconductor laser with MQW resonant structure

Numerical model is developed for modeling pulsed operation of a vertical external cavity semiconductor laser (VECSEL) with a resonant gain structure. Properties of optical modes for compound resonator formed by Bragg reflector, chip boundary and external spherical mirror were studied. For above threshold operation carrier density in each of quantum wells (QW) obeys non-linear diffusion equation with a source supplied by electron-hole pairs generated in barrier layers by pump radiation or fast electron beam. A new iteration procedure for round-trip operator evaluation was developed, which provides linear growth of computation time with the number of QWs. Results of numerical simulations are reported for a VECSEL comprising 25 QW in resonant configuration and the output spherical mirror with curvature radius 3 cm. Variation of distance to the external mirror is found to result in notable changes in power and optical quality of the output beam. The decisive role of gain and index non-linearity in these changes is identified. A range of values of distance to external mirror is found where iterative procedure does not converge. In another range, the resulting solution depends on the initial conditions for the iteration procedure.