It is theoretically investigated the generation of higher harmonics of two-dimensional and three-dimensional terahertz electromagnetic beams in nonlinear crystals. The attention is paid to crystalline paraelectrics li...It is theoretically investigated the generation of higher harmonics of two-dimensional and three-dimensional terahertz electromagnetic beams in nonlinear crystals. The attention is paid to crystalline paraelectrics like SrTiO<sub>3</sub> under the temperatures 60 - 200 K, these crystals possess the cubic nonlinearity. The bias electric field is applied to provide the dominating quadratic nonlinearity. The initial focusing of the beams not only increases the efficiency of generation of higher harmonics, but alto makes possible to select maxima of different higher harmonics at some distances from the input. At lower temperatures the nonlinearity behaves at smaller input amplitudes, whereas at higher temperatures the harmonic generation can be observed at higher frequencies up to 1.5 THz. In three-dimensional beams the peak amplitudes of higher harmonics can be bigger than in two-dimensional beams, but the ratios of these peak values to the maximum values of the focused first harmonic are smaller than in two-dimensional beams.展开更多
The nonlinear waves of terahertz (THz) range are investigated in the paraelectric crystals SrTiO<sub>3</sub> at the temperatures ~77 K. The frequency dispersion is important there. In the absence of a bias...The nonlinear waves of terahertz (THz) range are investigated in the paraelectric crystals SrTiO<sub>3</sub> at the temperatures ~77 K. The frequency dispersion is important there. In the absence of a bias electric field the dominating nonlinearity is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability (MI) of long input pulses, whereas in the transverse direction MI is absent. There exists a possibility to generate the regular sequences of short THz pulses due to MI in bounded SrTiO<sub>3</sub> crystals. The focusing of input long pulses reduces the threshold of MI, increases the output amplitudes of the short pulses, and provides more stable generation of the short pulses. It is investigated the frequency multiplication of THz electromagnetic radiation in bounded paraelectric SrTiO<sub>3</sub> when a bias electric field is applied. The dominating nonlinearity is quadratic there. The frequency dispersion and the transverse width of the input wave beams affect the generation of higher harmonics. It is possible to select the certain numbers of higher harmonics by means of the optimum length of the crystal, by the width of the beam of the input first harmonic, and by the focusing of the input first harmonic.展开更多
The superheterodyne amplification of electromagnetic waves is investigated when the resonant three-wave interaction of two electromagnetic waves with the space charge wave occurs in the waveguides nitride <em>n&...The superheterodyne amplification of electromagnetic waves is investigated when the resonant three-wave interaction of two electromagnetic waves with the space charge wave occurs in the waveguides nitride <em>n</em>-GaN, <em>n</em>-InN films-dielectric. The amplification of SCW waves due to the negative differential conductivity is investigated in nitride <em>n</em>-GaN, <em>n</em>-InN films at the frequencies <em>f</em> ≤ 400 GHz in the lower part of the terahertz (THz) range. The electromagnetic waves are either in the upper part of THz range or in the optical range. The superheterodyne amplification is considered in two geometries, the collinear one in which the three interacting waves travel in the same direction and the anti-collinear geometry where the second electromagnetic wave propagates in the opposite direction. The preferences and drawbacks of each geometry are pointed out. The finite width of space charge waves leads to decrease of increments of amplification.展开更多
Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the...Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrödinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.展开更多
文摘It is theoretically investigated the generation of higher harmonics of two-dimensional and three-dimensional terahertz electromagnetic beams in nonlinear crystals. The attention is paid to crystalline paraelectrics like SrTiO<sub>3</sub> under the temperatures 60 - 200 K, these crystals possess the cubic nonlinearity. The bias electric field is applied to provide the dominating quadratic nonlinearity. The initial focusing of the beams not only increases the efficiency of generation of higher harmonics, but alto makes possible to select maxima of different higher harmonics at some distances from the input. At lower temperatures the nonlinearity behaves at smaller input amplitudes, whereas at higher temperatures the harmonic generation can be observed at higher frequencies up to 1.5 THz. In three-dimensional beams the peak amplitudes of higher harmonics can be bigger than in two-dimensional beams, but the ratios of these peak values to the maximum values of the focused first harmonic are smaller than in two-dimensional beams.
文摘The nonlinear waves of terahertz (THz) range are investigated in the paraelectric crystals SrTiO<sub>3</sub> at the temperatures ~77 K. The frequency dispersion is important there. In the absence of a bias electric field the dominating nonlinearity is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability (MI) of long input pulses, whereas in the transverse direction MI is absent. There exists a possibility to generate the regular sequences of short THz pulses due to MI in bounded SrTiO<sub>3</sub> crystals. The focusing of input long pulses reduces the threshold of MI, increases the output amplitudes of the short pulses, and provides more stable generation of the short pulses. It is investigated the frequency multiplication of THz electromagnetic radiation in bounded paraelectric SrTiO<sub>3</sub> when a bias electric field is applied. The dominating nonlinearity is quadratic there. The frequency dispersion and the transverse width of the input wave beams affect the generation of higher harmonics. It is possible to select the certain numbers of higher harmonics by means of the optimum length of the crystal, by the width of the beam of the input first harmonic, and by the focusing of the input first harmonic.
文摘The superheterodyne amplification of electromagnetic waves is investigated when the resonant three-wave interaction of two electromagnetic waves with the space charge wave occurs in the waveguides nitride <em>n</em>-GaN, <em>n</em>-InN films-dielectric. The amplification of SCW waves due to the negative differential conductivity is investigated in nitride <em>n</em>-GaN, <em>n</em>-InN films at the frequencies <em>f</em> ≤ 400 GHz in the lower part of the terahertz (THz) range. The electromagnetic waves are either in the upper part of THz range or in the optical range. The superheterodyne amplification is considered in two geometries, the collinear one in which the three interacting waves travel in the same direction and the anti-collinear geometry where the second electromagnetic wave propagates in the opposite direction. The preferences and drawbacks of each geometry are pointed out. The finite width of space charge waves leads to decrease of increments of amplification.
文摘Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrödinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.
