In-Plane Nonlinear Optical and Transport Properties of Quantum Wells at Terahertz Frequencies

In-plane nonlinear response of quasi-two dimensional degenerate electron gas (Q-2DEG) systems is explored theoretically and experimentally. Calculations of the third order nonlinear susceptibility arising from band nonparabolicity in narrow gap semiconductors, chi_sp{NP }{(3)}, are extended to consider confinement and saturation effects. The calculation of the Q-2DEG chi_sp{NP}{(3) } has a nonmonotonic density dependence and as much as a factor of 5 enhancement over the values for bulk material for sufficiently narrow confinement. The calculations of saturation based on the semiclassical equations of motion, result in predicted saturation fields for nondegenerate narrow gap systems on the order of 5 kV/cm. A phenomenological model for nonlinear response based on energy dependent damping, or relaxation rates is developed, chi _sp{tau}{(3)}.. The quasi-two dimensional systems are realized by InAs/Al_{1-x}Ga _{x}Sb and GaAs/Al_ {0.3}Ga_{0.7} As quantum well structures. A free electron laser (FEL) is used as a source of intense terahertz radiation for the nonlinear transport and optical measurements. Instrumentation and analysis is developed for performing nonlinear optical experiment using a FEL. Third harmonic generation measurements are made to measure the in-plane third order susceptibility of InAs/Al_{1-x}Ga _{x}Sb and rm GaAs/Al _{0.3}Ga_{0.7}As quantum wells, chi^{(3)} , arising from free carrier effects. For modulation doped quantum well structures, chi^ {(3)}'s measured are large at low incident fields, (E_{inc} = 500 V/cm chi^{(3)} ~ 1 esu), and then rapidly decrease with increasing input field strength. The magnitude and field dependence of the measured chi^{(3)} 's is inconsistent with nonparabolicity as the only source of nonlinear response. For unintentionally continuously doped InAs Q-2DEG samples, the chi^ {(3)}'s are smaller (~ .01 esu), have no field dependence, and are in good agreement with the nonparabolicity source of nonlinear response. In order to determine the contribution of the nonlinear response from energy dependent relaxation rates, chi_sp{tau}{(3) }, the energy dependent energy and momentum relaxation rates were measured for the samples InAs/Al _{1-x}Ga_ {x}Sb samples using photoconductivity measurements in the presence of strong DC and AC fields. These measurements show that the main mechanism of energy relaxation in the InAs/Al_{1-x}Ga _{x}Sb samples is LO phonon emission with a LO phonon emission time of 10 +/- 2 ps. This emission time is found to be independent of the drive frequency between DC and 660 GHz. The calculated chi_sp{tau} {(3)} based on these measured relaxation rates was in good agreement with the chi ^{(3)} measured for modulation doped quantum wells. The infrared transmission of the InAs/Al _{1-x}Ga_{x }Sb samples was found to be nonlinear as well. This effect was not due to nonlinear current response, but rather due to an abrupt increase in the charge density with large fields at the plane of the electron gas, by impact ionization. The critical fields for impact ionization for input frequencies of 300-660 GHz were 4-9 kV/cm, a factor of 3 less than their theoretically predicted value, but consistent with earlier measurements of InSb, also a narrow gap semiconductor.