Large Magnetostatic Field Research Articles

Phase conjugation in weakly piezoelectric magnetized semiconductor-plasmas

The occurrence of optical phase conjugation via stimulated Brillouin scattering (OPC-SBS) in weakly piezoelectric III–V semiconductor plasmas subjected to a large magnetostatic field under off-resonant transition regime has been explored theoretically. The reflectivity of the phase conjugate wave is dependent upon the Brillouin susceptibility and can be significantly enhanced through n-type doping of the crystal and the simultaneous application of a magnetostatic field. Moreover, the threshold pump intensity required for the occurrence of SBS in the crystal with finite optical attenuation can be considerably diminished through proper selection of the doping concentration and magnetostatic field. Consequently, OPC-SBS becomes a possible tool in phase-conjugate optics even under not-too-high power laser excitation by using doped n-type semiconductors kept under the influence of a large magnetostatic field. Numerical estimates made for n-InSb crystal at 77 K duly irradiated by a nanosecond pulsed 10.6 µm CO2 laser reveal that high OPC-SBS reflectivity can be achieved at excitation intensities below the optical damage threshold if the semiconductor crystal is used as an optical waveguide with an interaction length of a few millimetres.

Optical phase conjugation via stimulated Brillouin scattering in magnetoactive doped semiconductors.

The occurrence of optical phase conjugation via stimulated Brillouin scattering (OPC-SBS) in bulk semiconducting crystals under the off-resonant transition regime has been investigated theoretically, the crystal being immersed in a large magnetostatic field. The model is based upon the coupled-mode approach and incorporates the effect of pump absorption through the first-order (i.e., linear) induced polarization. The linear dispersion is found not to affect the reflectivity of the phase-conjugate Stokes-shifted Brillouin mode. The reflectivity of the image radiation is dependent upon the Brillouin susceptibility and can be significantly enhanced through n-type doping of the crystal and the simultaneous application of a large magnetostatic field. Moreover, the threshold of the pump intensity required for the occurrence of SBS in the crystal with finite optical attenuation can be considerably diminished through a suitable choice of the excess carrier concentration and the magnetic field. Consequently, OPC-SBS becomes a possible tool in phase-conjugate optics even under not-too-high-power laser excitation by using moderately doped n-type semiconductors kept under the influence of large magnetostatic field. Numerical estimates made for InSb crystal at 77 K duly irradiated by nanosecond pulsed 10.6-\ensuremath{\mu}m ${\mathrm{CO}}_{2}$ laser show that high OPC-SBS reflectivity can be achieved at pump intensities below the optical damage threshold if the crystal is used as an optical waveguide with relatively large interaction length (L\ensuremath{\sim}3 mm).

Effect of magnetostatic field on the second-order optical susceptibility of III-V semiconductors

An analytical investigation of the application of a large magnetostatic field on the second-order optical susceptibility χ(2) in III-V semiconductors like GaAs and InSb is reported. The model is based upon the parity indefiniteness of the electron wave functions in crystals lacking inversion symmetry. The generalized force and the electronic dipole moment operators are accordingly taken to be 2×2 matrices with all elements being finite. We have followed perturbation technique for the density matrix. The magnetostatic field renormalizes the transition frequency and sharpens the density of states. Both the resonant as well as nonresonant three-wave parametric interactions have been discussed. Numerical estimates made for InSb crystal under resonant regime reveal considerable enhancement in the real part of χ(2) even at moderately low magnetic field while the imaginary part exhibits a near saturation behavior. Under nonresonant laser excitation, both χ(2)r and χ(2)i rise very sharply with magnetic field for effective cyclotron frequency ωc≤ω0−ωg, ω0 and ωg being the pump and crystal band-gap frequencies, respectively. Quite interestingly, χ(2)r and χ(2)i decay almost exponentially to very low values at ωc>2(ω0−ωg).

Nonlinear Landau absorption in III-V semiconductors near the fundamental absorption edge.

Analytical investigations have been made of nonlinear Landau absorption in important III-V semiconductors such as GaAs, GaSb, InSb, and InAs which have been irradiated by suitable lasers of photon energies (\ensuremath{\Elzxh}\ensuremath{\omega}) nearly equal to the band-gap energies (\ensuremath{\Elzxh}${\ensuremath{\omega}}_{g}$) in the presence of a large magnetostatic field. A coherent radiation-exciton interaction model has been used for the direct allowed transitions between the n=0 Landau subbands. The result obtainable for linear magnetoabsorption using the present model agrees very well with that obtained in the 1960's using a completely different approach. The effective nonlinear Landau absorption ${\ensuremath{\alpha}}^{\mathrm{nonlin}({B}_{0})}$ has been studied by examination of the imaginary part of the third-order optical susceptibility. The contributions from the higher-order susceptibilities have been neglected. The Wannier-Mott exciton wave function \ensuremath{\psi}(0) is found to play a very important role in the nonlinear Landau absorption processes as it occurs in the fourth power in the expression for ${\ensuremath{\alpha}}^{\mathrm{nonlin}({B}_{0})}$. For near-band-gap resonant excitation in the true continuum with \ensuremath{\Elzxh}(\ensuremath{\omega}-${\ensuremath{\omega}}_{g}$) less than the crystal exciton rydberg, \ensuremath{\Vert}\ensuremath{\psi}${(0)}^{2}$\ensuremath{\Vert}\ensuremath{\gg}1 and its contribution must be recognized under this regime. The renormalization of the crystal band gap due to the exciton rydberg and the light shift has also been discussed.

Stimulated Brillouin scattering of transversely polarized electromagnetic waves in magnetoactive moderately piezoelectric semiconductor plasmas

AbstractAn analytical investigation is made of the stimulated Brillouin scattering of a large amplitude, transversely polarized, electromagnetic pump wave produced by both, an electron‐plasma wave and acoustical phonon vibrations in a magnetoactive n‐type moderately piezoelectric semiconductor. Using the hydrodynamical model of plasma, the general dispersion relation is obtained in the presence of a large magnetostatic field applied at an arbitrary angle θ to the direction of propagation of the pump wave. The analysis is applied to both the cases of isotropic (B0 = 0) and magnetoactive (B0 ± 0) plasmas. The threshold electric field necessary for the onset of Brillouin instability and the growth rate of the unstable Brillouin mode well above the threshold are studied. It is concluded that the threshold pump amplitude as well as the growth rate are strongly dependent on the orientation of the magnetostatic field with respect to the directions and magnitudes of the wave vectors k and k1 of the acoustic and scattered electromagnetic waves, respectively.

Effect of Magnetostatic Field on the Stimulated Raman Scattering of Transversely Polarized Electromagnetic Waves and Raman Instability in Semiconductor Plasmas

AbstractThe stimulated Raman scattering of a large amplitude transversely polarized electromagnetic pump wave from both, the electron plasma wave and the molecular vibrations produced at a frequency equal to that of transverse optical phonon, is investigated in an n‐type semiconductor plasma. The general dispersion relation is obtained considering only the Stokes' component of the scattered electromagnetic wave in the presence of a large magnetostatic field applied at an arbitrary angle to the direction of propagation of the pump wave. The analysis is applied to both the cases of isotropic (B0 = 0) and magnetoactive (B0 ± 0) plasmas. The threshold electric field necessary for the onset of Raman instability and the growth rate of the unstable mode well above the threshold is studied. It is concluded that the threshold pump amplitude as well as the growth rate have strong dependence on the orientation of the magnetostatic field with respect to the wave vectors k, k1 and its magnitude.

Stimulated Raman scattering in a magnetoactive piezoelectric semiconductor

The stimulated Raman scattering of a large-amplitude, transversely polarized, electromagnetic pump wave from both the electron plasma wave and the molecular vibrations produced at a frequency equal to that of transverse optical phonon has been investigated in an n-type piezoelectric semiconductor. The general dispersion relation has been obtained considering only the Stoke’s component of the scattered electromagnetic wave in the presence of a large magnetostatic field applied at an arbitrary angle ϑ to the direction of propagation of the pump wave. The analysis has been applied to both cases of isotropic (B0 = 0) and magnetoactive (B0≠0) plasmas. The threshold electric field necessary for the onset of Raman instability and the growth rate of the unstable Raman mode well above the threshold have been studied. It is concluded that the threshold pump amplitude as well as the growth rate are strongly dependent on the orientation of the magnetostatic field with respect to the wave vectors k, k1 and its magnitude.

Parametric conversion of an electron plasma wave into an electromagnetic wave in a piezoelectric semiconductor

The possibility of the excitation of an electromagnetic wave as a consequence of the nonlinear coupling between an electron plasma wave and an acoustic wave in an inhomogeneous piezolectric semiconductor plasma has been analyzed. The nonlinear interaction results in the parametric amplification of acoustic waves. The dispersion relation for such a parametric instability is obtained using a hydrodynamic model of an inhomogeneous semiconductor plasma; it is solved to study the threshold electric field necessary for the onset of instability and the growth rate of the unstable mode well above the threshold as a function of the magnitude of an externally applied magnetostatic field. The numerical analysis has been made for the typical case of n-InSb at 77 K. The threshold electric field is appreciably lowered by the application of a large magnetostatic field, and the growth rate of the unstable mode is found to be 104 times more in a magnetoactive (B0≠0) semiconductor than in an isotropic ( B0=0) crystal.

Resonance cones in non‐Maxwellian plasmas

Properties of resonance cones in non‐Maxwellian plasmas are examined and compared with those in Maxwellian plasmas. The dispersion relations and the potential of a point charge in a current‐carrying non‐Maxwellian plasma with a beamlike or a long flat tail of the electron distribution functions are investigated with the approximation of a large magnetostatic field. In the case of a beam, when the beam velocity is well above the thermal velocities of the beam and bulk electrons, the Cerenkov instability occurs. In this case the wave number spectrum k∥ > ω/νb becomes unstable, where νb is the beam velocity, ω is the frequency, and k∥ is the wave number parallel to the magnetic field. The Cerenkov instability causes strong radiation near a conical surface called the Cerenkov cone. When νb is not very large, the Cerenkov cone angle is found to be considerably smaller than the resonance cone angle, thus there are two distinct angles corresponding to the Cerenkov and resonance cones, where the radiation peaks. The Cerenkov cone peak grows with increasing distance from the source, while the resonance cone peak decays. For the situations when the resonance cone peak is not affected by the Cerenkov instability, we have compared the angular shifts of the resonance cone peaks caused by the same current in Maxwellian and non‐Maxwellian plasmas. This comparison throws light on the resonance cone technique for measuring magnetic field‐aligned currents in plasmas. It is found that a long flat tail to the bulk electron distribution function gives a characteristic split to the resonance cone peak in the downstream of the electron flow, an observation of this split can be used as an indication of the existence of the long tail.

Modulational instability of a laser beam in a piezoelectric semiconductor

Using a hydrodynamic model of a homogeneous plasma, the modulational instability of a laser beam has been studied when the laser beam interacts nonlinearly with a low-frequency transverse acoustic wave in the presence of a transverse magnetostatic field in a heavily doped n-type piezoelectric semiconductor. The instability results in the parametric amplification of the acoustic wave. The threshold electric field necessary for the onset of instability in the absence as well as in the presence of the magnetostatic field and the corresponding growth rates have been obtained analytically. The numerical analysis made for n-InSb at 77 K shows that the necessary laser field can be obtained by irradiating the crystal with a 10.6-μm CO2 laser. A large magnetostatic field lowers the threshold laser field appreciably.

Radiation From an Oscillating Source Moving Through a Dispersive Medium With Particular Reference to the Complex Doppler Effect

The complex Doppler effect is analyzed from the time behavior of the radiation field of an oscillating source traversing a dispersive medium. The effect is calculated for the case where an oscillating electric dipole is moving uniformly through an ionized gas permeated by an infinitely large magnetostatic field. It is found that the radiation field can be split into a number of waves, each having characteristics of its own, and that the number of waves changes with time. The group velocity of each individual wave is shown to play an important role in the physical mechanism of the effect.

On the propagation of waves in an electromagnetic elastic solid

The coupling of electromagnetic and elastic waves is considered from the standpoint of linear elasticity and a linearized electromagnetic theory. The problem of plane waves traveling through a uniform magnetostatic field is considered and couplings of the waves are studied. An investigation of the same problem for a uniform electrostatic field shows that the usual plane waves propagate without any change in their phase velocities but that the mechanical waves are accompanied by small fluctuating electromagnetic fields. The problem of the vibration of a free infinite elastic plate in a large magnetostatic field is examined under the assumption that the resulting electromagnetic fields are quasistationary. Frequency equations are obtained for both symmetric and antisymmetric vibrations and the damping caused by the field for both the first two symmetric and antisymmetric modes is obtained as a linear correction to the usual free plate frequencies.

Electromagnetic Radiation from an Electric Dipole in a Cold Anisotropic Plasma

The general solution to the problem of monochromatic radiation from an electric dipole in a magnetically biased, cold, tenuous plasma is presented. It is found that, generally, several waves exist in the radiation zone, traveling in different directions with different indices of refraction. For certain ranges of the plasma, gyro, and operating frequencies, the field becomes very large in certain directions compared with that in other directions, producing highly directive radiation characteristics. In general, the expression for the field is quite complicated although several special cases are treated which yield simple solutions. For high operating frequency it is found that the radiation pattern is identical to the isotropic case although a Faraday rotation takes place. Solutions are given for low and very low frequencies which place in evidence the guiding nature of the magnetostatic field. For the case of a large magnetostatic field it is shown that only two waves exist and that the time-average power flow is purely radial.