The electronic states in the laser-dressed hexagonal and cubic Al[Formula: see text]Ga[Formula: see text]N/GaN single quantum wells are calculated using the effective mass equation. The hexagonal single quantum well contains an internal electric field due to spontaneous and piezoelectric polarizations. The effective mass equation is solved by the finite difference method. The energy levels in both cubic and hexagonal laser-dressed wells are found to increase with increase in laser dressing as the effective well widths in both the wells increase. The intersubband energy spacing between first excited state and ground state increases in the cubic quantum well, whereas it decreases in the hexagonal well due to the presence of internal electric field in it. Using the compact density matrix method with iterative procedure, first-, second- and third-order nonlinear optical susceptibilities in the laser-dressed quantum well are calculated taking only two levels. While the susceptibilities in the hexagonal well are found to get red shifted, the susceptibilities in the cubic well are blue shifted.
Long-wavelength plasma frequencies have been obtained in the modified random phase approximation (RPA) and plasmon-pole approximation (PPA) methods for both quantum and classical plasmas in fractional-dimensional space. The dynamical local-field factor is included in the dielectric function. Comparison of the plasma frequencies in these methods shows that both RPA and PPA methods are quite accurate in finding plasma frequencies. Although the contribution of the dynamical local-field factor to the quantum plasma frequency is quite significant, it vanishes for the classical plasma. While the quantum plasma is undamped in the collective excitation regime, the classical plasma is damped in this regime.
The dielectric function for electron gas with parabolic energy bands is derived in a fractional dimensional space. The static response function shows a good dimensional dependence. The plasma frequencies are obtained from the roots of the dielectric functions. The plasma dispersion shows strong dimensional dependence. It is found that the plasma frequencies in the low dimensional systems are strongly dependent on the wave vector. It is weakly dependent in the three dimensional system and has a finite value at zero wave vector.
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