We consider a problem for the Bessel equation of integer order with complex physical and spectral parameters in the boundary condition. The spectral parameter occurs quadratically in the boundary ...condition. The basis property of the eigenfunction system is studied.
The subject of this paper is microlasers with the emission spectra determined by the whispering gallery modes. Owing to the total internal reflection of light on the sidewalls, a high Q-factor is ...achieved until the diameter is comparable to the wavelength. The light emission predominantly occurs in the plane of the structure, which facilitates the microlaser integration with other elements. We focus on microdisk lasers with various types of the In(Ga)As quantum dots (QDs). Deep localization of charge carriers in spatially separated regions suppresses the lateral diffusion and makes it possible to overcome the undesirable effect of non-radiative recombination in deep mesas. Thus, using conventional epitaxial structures and relatively simple post-growth processing methods, it is possible to realize small microlasers capable of operating without temperature stabilization at elevated temperatures. The low sensitivity of QDs to epitaxial and manufacturing defects allows fabricating microlasers using III-V heterostructures grown on silicon.
We consider a problem for the zero-order Bessel equation with complex-valued physical and spectral parameters in the boundary condition. The spectral parameter is squared in the boundary condition. ...We study the basis property for the system of eigenfunctions.
The Gellerstedt eigenvalue problem with homogeneous boundary conditions on interior characteristics is studied. We prove that the eigenfunction system of this problem is a Riesz basis in the
L
2
...space in the elliptic domain.
Gain saturation in a semiconductor optical amplifier with an array of quantum dots is studied analytically and by numerical simulation on the basis of an analysis of rate equations. It is shown that, ...at a moderate injection level, the saturation power increases in proportion to the current density, and then reaches its maximum value, limited by the rate of carrier delivery to the ground state and by the number of quantum dots interacting with photons. Expressions are proposed that allow explicit description of the dependence of the saturation power on current and its relationship with the internal parameters of the active region.
We prove that the homogeneous Neumann–Gellerstedt problem with data on internal characteristics has a nontrivial solution under the Frankl matching condition on the line where the equation changes ...type.
The paper addresses the completeness of perturbed systems of sines and cosines with non-integer indices and, moreover, complex, in the space of Lebesgue-integrable functions. The criteria for the ...variation from the integer value have been found such that sine and cosine systems are complete.
Two boundary value problems in which one of the conditions is nonlocal and contains a real parameter are studied for an equation of mixed type in a half-strip. Sufficient conditions for the unique ...solvability of these problems are obtained under some restrictions on the parameter.
Abstract
In complex organizational systems in which there is asymmetry of information, an important element of effective work is equal access to objective statistics. Because of the benefits to one ...of the parties in such systems, key elements of effective management and making the right decisions, it is necessary to develop independent approaches. The developed approach makes it possible to assess risks in various situations and with various interactions within the system, and also allows you to recreate the missing information for decision-making from open statistical databases. The key element of the developed approach is the use of self-organizing Kohonen neural networks, which make it possible to classify objects based on the reconstructed information. The importance of the correct grouping of system objects makes it possible to recommend a management decision with greater accuracy. The developed approach allows you to reduce uncertainty (risk), and, as a result, reduce losses and maximize profits.
We demonstrate a record low threshold current density of 250 A/cm
2
in a quantum dot microdisk laser with a 31-μm diameter operating at room temperature in continuous wave regime without temperature ...stabilization. This low threshold current density is very close to the transparency current density estimated in broad-area edge-emitting lasers made of the same epitaxial wafer.
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