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We have constructed a mathematical model of an intracavity difference-frequency generator based on a dual-wavelength semiconductor disk laser in the form of a time-delay dynamic system. Steady-state lasing (the equilibrium state of the dynamic system), its stability, and also transient dynamics after switching on the primary optical pump source are investigated. It is shown that the equilibrium state is stable in a wide range of parameters, which is of interest for possible applications of such a generator.

Context. The problem of automation of the generation of natural and anthropogenic landscapes is considered. The subject of the research is methods of procedural generation of landscapes that quickly and realistically visualize natural and anthropogenic objects taking into account different levels of detail. Objective. The goal of the work is to improve the rendering quality and efficiency of the procedural generation process of landscape surfaces at any level of detail based on the implementation of the developed method. Method. The proposed method of visualization involves the construction of a natural landscape using Bezier curves and surfaces and manual editing of individual segments; use of software agents that are responsible for individual steps of generating anthropogenic objects; adaptation of anthropogenic objects to the characteristics of natural landscapes; containerization of three-dimensional objects, which is used in various steps to organize the storage and loading of objects efficiently. A generated heightmap based on the Perlin noise algorithm is used to construct surfaces on individual segments of the natural landscape. Landscape processing software agents are used to unify the design of algorithms for creating and processing information about anthropogenic objects. Correct application operation and error resistance is guaranteed due to the inheritance of a specific interface by all implementations of agents. Containerization with two-level caching ensures the efficiency of display detailing. Results. The developed method is implemented programmatically, and its efficiency is investigated for different variants of input data, which to the greatest extent determine the complexity of visualization objects. Conclusions. The conducted experiments confirmed the efficiency of the proposed algorithmic software and its viability in practice in solving problems of automated landscape generation. Prospects for further research include improvement and expansion of the algorithms for procedural landscape generation, functionality complication of manual visualized object processing, and division of individual objects into separate hierarchies of containers.

Deceleration of terahertz plasma waves (plasmons) in tapered graphene-insulator-graphene heterostructure is studied. It is shown that the plasmon energy velocity can become several times smaller as compared to that near the taper apex.

In this paper, the possibility of synthetic-aperture radar operation is considered not only for ground targets, but also for air ones. An analytical expression of the two-dimensional radar portrait function of a moving air target is obtained, a mathematical model of a two-dimensional radar portrait of a moving single air target, made in the Matlab environment, is presented.

Cognitive radio systems aim to solve the issue of spectrum scarcity through implementation of dynamic spectrum management and cooperative spectrum access. However, the structure of such systems introduced unique types of vulnerabilities and attacks, one of which is spectrum sensing data falsification attack (SSDF). In such attacks malicious users provide incorrect observations to the fusion center of the system, which may result in severe quality of service degradation and interference for licensed users. In this paper we investigate this type of attacks and propose a combined approach to their mitigation. On the first step a reputational method is used to isolate the initially untrustworthy nodes, on the second step specialized q-out-of-m fusion rule is utilized to mitigate the remains of attack. In this paper we present theoretical analysis of the proposed combined method.

Weak plasmon modes in periodic structures with a two-dimensional electron gas without an inversion center are studied theoretically. The asymmetry of the electric field and Fourier harmonics of weak plasmon modes can lead to the excitation of a travelling plasmon by an electromagnetic wave normally incident on the structure and to the appearance of nonlinear effects leading to the rectification of the incident radiation. The low radiation damping of weak plasmon modes can be used to increase the efficiency of terahertz plasmon amplifiers.

The diffusion pumping of graphene by optical plasmons, propagating in metal, and separated from the graphene by a semiconductor layer has been investigated theoretically. It is shown that pumping of graphene with optical plasmons provides maximum negative terahertz conductivity of graphene at a lower (approximately by 25%) pumping power compared to a diffusion pumping of graphene with optical radiation.

The transformation of electromagnetic wave into propagating plasmon in periodical dual-grating-gated graphene with asymmetric unit cell structure is theoretically investigated. The conditions of cancelling the transmission of the electromagnetic wave through the graphene structure and Fabry-Perot blocking the reflection are applied. We found out optimal unit cell asymmetry for maximum transformation incident wave into plasmon modes with the wavevectors multiplied the inverse length of the structure period.

The multi-mode transient power characteristics of an intracavity difference-frequency generator is described. The reason for unattainability of single-mode emission in the device without an additional frequency-selective element (e.g., a Fabry- Perot etalon) is clarified. It is shown that the dynamics of a shortwavelength emission (pump) results mainly from the nonlinear optical interaction, while that of the longer-wavelength optical fields (signal and idler) depends on selectivity of the etalon.

The amplification of terahertz plasmons in a pair of parallel active graphene monolayers is studied theoretically. The plasmon wave in a symmetric double-layer graphene structure splits into two branches with a symmetric and an antisymmetric distribution of tangential to graphene component of the electric field across the plane of symmetry of the structure. It is shown that, normalized to the wavelength, the terahertz plasmon amplification factor of the symmetric mode in the double-layer graphene structure could be greater than that in a single graphene layer by four orders of magnitude.

Amplification of plasma waves in shielded graphene with inverted energy distribution of charge carriers is investigated theoretically. It is shown that graphene shielding allows one to increase an amplification factor of terahertz plasmons in several times compared to the case of amplification of unshielded plasmons due to strong field confinement of the shielded plasmons near graphene.

We study the optical near- and mid-infrared pumping of the heterostructure based on graphene with a black-As layer. This layer serves for the optical generation and cooling of the electron-hole pairs to be injected into the graphene layer. Due to the cooling of the electron-hole pairs, their energy in the case of the absorbing-cooling layer with the optimized thickness can be close to the energy gap of the black-As layer. Owing to a relatively narrow energy gap of the black-As layer Δ G, the energy of the injected electron-hole pairs can be smaller than the energy of optical phonons in in graphene (ℏ ω 0≃0.2 eV. This can provide the formation of the cold electron-hole plasma in the graphene-layer that is beneficial for achieving of the interband population inversion and the interband terahertz lasing. The obtained results can be used for the optimization of the terahertz lasers with the optical pumping.

Nanofocusing and deceleration of terahertz plasma waves in tapered metal-insulator-graphene heterostructure is studied theoretically. It is shown that, choosing an appropriate value of taper length for given values of the taper angle and the Fermi energy in a doped or gated graphene, the plasma wave energy density value in the vicinity of the taper apex exceeds its value in the taper inlet cross-section by tens of percent in spite of the Drude losses in graphene. The plasma wave decelerates while moving toward taper apex and its energy velocity becomes several times smaller as compared to that in the taper inlet cross-section.

The influence of nonlinear optical interaction in a semiconductor dual-wavelength vertical-external-cavity surface-emitting laser on the main parameters of dual-wavelength radiation and lasing in the long-wavelength part of the mid-IR range, obtained in this laser as a result of nonlinear wave mixing, is investigated. An increase in the pump power leads to saturation of the short-wavelength lasing intensity and to a more rapid rise in the long-wavelength lasing intensity in comparison with the linear increase in lasing intensity in these regions in the absence of nonlinear interaction. Under the conditions of nonlinear interaction, the carrier concentration in the active layers is not stabilised near the lasing threshold but changes with an increase in the pump intensity and provides the corresponding gain in the laser active region, thus maintaining steadystate lasing. Some ways for modifying the laser active region in order to obtain the most efficient lasing in the mid-IR range are proposed.

The parameters of middle-IR radiation (λ ∼ 17 μm) generated as a result of the intracavity nonlinear optical interaction in a semiconductor dual-wavelength vertical-external-cavity surface emitting laser operating in a pulsed regime have been numerically analyzed. The dependence of the peak output radiation power on the length of the nonlinear crystal has been studied for various values of the loss factor.

A mathematical model of a dual-wavelength vertical-external-cavity surface-emitting laser (VECSEL) is formulated with the distribution of optical pumping and generated fields over the beam cross sections taken into account. Dynamic regimes are mapped using the 'pump power — cavity round-trip time' plane. The map comprises regions of cw generation, periodic oscillation, quasiperiodic and chaotic oscillations of the radiation intensity and the carrier density in the active regions of the laser. It is shown that when the reflection coefficient of the external cavity is increased, the regions of complex dynamics in the maps become narrower. Using numerical methods the spatio-temporal dynamics of a dualwavelength VECSEL is analysed in the regime of quasi-periodic oscillations.

The stability of the stationary state and periodic oscillations of the radiation intensity of the dual-wavelength vertical external cavity surface-emitting laser is analyzed. It is demonstrated that the stationary state is always stable for the laser with independent active areas that contain quantum dots of different depths. A map of dynamic regimes with the values of parameters that correspond to the cw lasing, periodic oscillations of intensity, and complicated dynamics (quasi-periodic or chaotic regimes) is constructed for the laser with coupled active areas. The dynamics of the laser radiation in the quasi-periodic regime is numerically simulated. It is demonstrated that relatively slow variations in the amplitude with characteristic times of several or several tens of microseconds are typical of the short laser pulses that are formed at time intervals of tens of picoseconds. The period of the pulse train is approximately equal to the round-trip time of the external laser cavity.

The steady-state stability of a dual-wavelength vertical-external-cavity surface-emitting laser has been analyzed. It is shown that, in the laser with independent active regions containing quantum wells (QWs) of different depths, this state is always stable. The increment of growth and the frequency of oscillations of small deviations from the steady state are determined in the presence of coupling between the active regions, which is caused by the absorption of short-wavelength radiation in deep QWs. In the region of violation of the steady-state stability, the generation proceeds in the form of short pulses, with the almost simultaneous excitation of the optical fields at both frequencies.

The effect of pump wave reflections on the carrier generation rate and uniformity of carrier population in quantum wells (QWs) of a dual-wavelength vertical-cavity surface-emitting laser has been numerically analyzed. The laser’s active region has been described within a mathematical model allowing any number of QWs and arbitrary distribution of carrier generation rate. It is shown that the optimal arrangement of blocking layers in the active region of a dual-wavelength vertical-cavity surface-emitting laser allows one to obtain a very uniform QW population. It is established that pump wave reflections significantly affect the local carrier generation rate and, therefore, the distribution of excited carriers in the laser structure.

A nonlinear-optical conversion process in a dual-wavelength vertical-external-cavity surface-emitting laser that leads to the generation of difference-frequency radiation in the long-wavelength part of the mid-infrared range (∼17.7 μm) is analyzed numerically. The nonlinear crystal of GaAs is incorporated in the output-coupler mirror and, at the same time, is placed in a Fabry-Perot cavity tuned to the difference frequency. It is shown that the dependence of the nonlinear-conversion efficiency on the GaAs crystal thickness exhibits a pronounced resonance behavior and that the peak power of the radiation in the mid-infrared range can be as high as a few milliwatts with the parameters of the laser and the optical pump readily attainable experimentally.

The dependence of a critical current at which a virtual cathode (VC) is formed in an electron beam on the retarding electric field and the external focusing magnetic field have been studied. It is shown that, as the retarding field exceeds a certain threshold value, both stationary and nonstationary (oscillating) VCs can form in the interaction space.

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.

The power of microwave generation in a nonrelativistic electron beam with virtual cathode formed in a static retarding electric field (low-voltage vircator system) has been studied experimentally and by means of numerical simulation within the framework of a one-dimensional theory. The limits of applicability of the one-dimensional theory have been experimentally determined., Comment: 4 pages, 2 figures

The structure of the Bragg reflectors in a vertical-cavity laser in which three-wave nonlinear mixing is used to generate the emission in the mid-infrared spectral region is optimized. It is shown that the reflection band of the Bragg reflectors can be broadened appreciably in comparison with conventional quarter-wavelength reflectors formed of the same pair of materials. Using this approach, it becomes possible to produce a laser with nonlinear frequency conversion based on the lattice-related nonlinearity in a GaAs/AlGaAs system; this laser emits in the region of

A method for controlling the polarization characteristics of the radiation of a dual-wavelength vertical external cavity surface-emitting laser (VECSEL) is proposed. It is shown that a retarder of a special kind used as a part of the laser cavity allows the excitation of laser radiation with components in nearly mutually transverse polarization planes.

Optical excitation of a semiconductor structure comprising two nonidentical quantum wells (QWs) separated by barriers absorbing the pump radiation has been numerically simulated. It is shown that the equalization of populations in the QWs can be achieved in two ways: (i) shift of the deeper QW to a region of weak carrier generation and (ii) introduction of a blocking layer preventing the transport of carriers.

A novel scheme of the compact intracavity singly-resonant optical parametric oscillator (OPO) pumped by a semiconductor disk laser is presented. The cavity of the device is shared between the laser's optical field (the pump of the OPO) and the signal radiation emitted by the OPO. The length of the cavity doesn't exceed 10 mm that should hopefully favor for a single mode operational regime without any frequency selective elements (e.g. Fabry-Perot etalons). By estimation, the idler wavelength could be tuned over a few percents in the mid-infrared range (~ 17 μm) as the primary pump power is changed.

Parameters of mid-infrared pulsed radiation (∼17.1 µm) being emitted due to intracavity nonlinear optical frequency conversion in the dual-wavelength vertical external-cavity surface-emitting laser are analyzed. Nonlinear optical frequency conversion is supposed to be realized in the quasi-phase-matched crystal. The dependence of peak pulse power at the wavelength corresponding to the mid-infrared range on the nonlinear crystal length at various values of a loss factor is obtained.

The mathematical model of a dual-wavelength emission from a vertical external cavity surface-emitting laser taking into account the transverse distribution both of optical fields and pump carrier flux density is built. Spatio-temporal dynamics of charge carriers and photons is analyzed. It is shown that the most pronounced optical hole-burning can be observed near the optical axis of the laser.

The map of dynamic regimes of a dual-wavelength vertical external cavity surface-emitting laser is built. The areas of continuous wave operation as well as of time-periodic, quasi-periodic and chaotic operation can be marked out in the map. A possible explanation of quite different laser behavior in those area is given.

The effect of focusing magnetic field on the critical current of electron beam is numerically analyzed. The observable behavior of the critical current is caused by competitive dynamics of longitudinal and transversal electron motion in the drift tube.

Investigations of quantum fields in the de Sitter space have a long history (a bibliography of studies made up to 1981 can be found in the monograph of [i]). Being a curved sPace with maximal symmetry, the de Sitter space makes it possible to construct explicitly a quantum theory of free fields and also some models of interacting fields and investigate effects associated with the influence of the gravitational field on quantum processes. The de Sitter space is an example of a manifold that possesses an event horizon -the cosmological horizon. In the behavior of quantum fields in this space there is an organic intertwining of thermal effects (due to the finiteness of the Hawking temperature [2] associated with the cosmological horizon) with the effects of acceleration and curvature. It is no surprise that problems of quantum field theory in de Sitter space, which are of fundamental interest, have long attracted attention. In recent years a new stimulus to such investigations has been given by the appearance of the theory of an inflationary universe [3,4].