We want to make the best use of the mesoscopic or macroscopic transition dipolemornent of excitons by controling the size and dimension of the materials. First, the semiconductor microcrystallites embedded in insulators or glasses are shown to have the mesoscopic transition dipolemoment of excitons1 . As a result, the exciton in CuC1 microcrystallite with the radius 80 A superradiatively decays in 100 pico-second2. Futhermore, the exciton-exciton interaction and the decay and relaxation of the exciton work effectively in deviating the excitons in the microcrystallite from ideal bosons and this system shows the large third-order optical susceptibility"3 of an order of iO esu when we assume the 0.1% packing of the CuC1 microcrystallites. These predictions have been confirmed expriment ally4'5. Second, the two-dimensional excitons in quantum wells can superradiatively decay in the direction perpendicular to the surfaces2 . This brings about the quick response and the deviation of the excitons from ideal bosons at the same time. The latter effect as well as the two-dimensional macroscopic enhancement of the exction transition dipolemoment enhance the third-order optical susceptibility3. Both the superradiative decay rate and increase as does the coherent length, which is inversely proportional to the square root of the exciton line width6.
Excitons are sometimes trapped at impurities in crystals and at defects on interfaces in the confined systems, such as quantum wells and microcrystallites embedded in a host matrix. We discuss these trapping effects on the third-order optical polarization under nearly resonant pumping of the exciton. First we predict an enhancement of ${\mathrm{\ensuremath{\chi}}}^{(3)}$(\ensuremath{\Omega};\ensuremath{\Omega},-\ensuremath{\Omega},\ensuremath{\Omega}) by a factor ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\ensuremath{\rightarrow}\mathit{T}}$/${\mathrm{\ensuremath{\Gamma}}}_{\mathit{T}\ensuremath{\rightarrow}\mathit{g}}$ multiplicatively on that enhanced by the large excitonic dipole moments. Here ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\ensuremath{\rightarrow}\mathit{T}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{T}\ensuremath{\rightarrow}\mathit{g}}$ are, respectively, the rate at which the exciton is trapped and the decay rate of the trapped electron into the ground state. In many cases, ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\ensuremath{\rightarrow}\mathit{T}}$ is much larger than ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{T}\ensuremath{\rightarrow}\mathit{g}}$ so that a large enhancement of ${\mathrm{\ensuremath{\chi}}}^{(3)}$ is expected. Second, the four-wave mixing spectrum \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)}$(2${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\Omega}}}_{2}$;${\mathrm{\ensuremath{\Omega}}}_{1}$,-${\mathrm{\ensuremath{\Omega}}}_{2}$,${\mathrm{\ensuremath{\Omega}}}_{1}$)\ensuremath{\Vert} under two beams ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$ is shown to consist of three hierarchical structures as a function of ${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\Omega}}}_{2}$, i.e., the sharpest spike around ${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\Omega}}}_{2}$=0 with the linewidth \ensuremath{\Vert}${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\Omega}}}_{2}$\ensuremath{\Vert}=${\mathrm{\ensuremath{\Gamma}}}_{\mathit{T}\ensuremath{\rightarrow}\mathit{g}}$, the steep shoulder with the center also at ${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\Omega}}}_{2}$=0 and the width ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}}$ (the exciton decay rate), and the wide structure with the width ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\mathit{g}}$ around ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{1\mathit{s}}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{1\mathit{s}}$. Here ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\mathit{g}}$ is the relaxation rate of the exciton polarization and \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{1\mathit{s}}$ the lowest exciton energy. Third, the differential transmission spectrum is found to show the strong absorption saturation peak or the sharp induced absorption dip as a function of pump-probe detuning ${\mathrm{\ensuremath{\Omega}}}_{2}$-${\mathrm{\ensuremath{\Omega}}}_{1}$, depending upon the pump frequency ${\mathrm{\ensuremath{\Omega}}}_{1}$ relative to the exciton peak ${\mathrm{\ensuremath{\omega}}}_{1\mathit{s}}$.
Excitonic superradiance has been predicted to induce a rapid decay rate of coherently excited excitons in thin quantum wells and microspheres. In this paper we revisit this problem and derive the enhancement factor of the radiative decay due to superradiant effects. In a GaAs quantum well, the excitonic superradiant radiative decay can be roughly 320 times faster than the decay of a free electron-hole pair. The exciton decay rate depends strongly on the lateral size of the wave function when the size is smaller than the inverse of the wave vector of the emitted light. In a GaAs quantum well this corresponds to a distance of \ensuremath{\approxeq}365 \AA{}. Therefore, it is predicted that localization and elastic phonon scattering may lead to decay rates substantially smaller than that predicted for an ideal quantum well. It is also shown that if the quantum well is placed inside a microcavity, the decay rate can be enhanced even further since the cavity modifies the available density of radiation states in a way that matches the superradiant emission. It is predicted that in a matched dielectric cavity the decay rate can be enhanced by an additional factor of 100, but that inhomogeneous broadening may in practice limit the possible enhancement.
The study of the nonlinear optical response of excitons in semiconductors is important for both scientific and technological applications. Although the nonlinear optical properties of bulk semiconductors and heterostructures have been studied for almost three decades, with most of the research focusing on heterostructures, the mechanisms leading to the nonlinearities in these systems are not completely understood. Determining these mechanisms and developing a theoretical picture which describes the most dominant effects remains a challenge and an active area of study. Although optical interactions in semiconductors is a genuine many-body problem, a description of this system similar to the optical Bloch equations used in atomic studies has shown some success, but more work is needed to make this model complete. Experimental work, particularly in the bulk system uncomplicated by the interface disorder present in heterostructures, will provide the guidance to extend this formalism. In this dissertation, the frequency domain resonant nonlinear optical response of excitons in bulk gallium arsenide at low density is studied to gain insight into the dominant mechanisms leading to the response, as well as the dynamics of the nominally three-dimensional excitonic system. Specifically, the nonlinear response was probed with differential transmission (DT) and four-wave mixing (FWM) experiments, which measure to lowest order the third-order susceptibility, $\chi\sp{(3)}.$ Using these various tools, three specific areas were studied and the results will be presented. First, the role of the biexciton, the state of two bound excitons, in determining the bulk nonlinear response was explored. The observation of a red-shifted nonlinear resonance suggests the importance of this state at moderate densities. Second, a new response, characterized by a resonant increase in exciton absorption induced by optical pumping with initial superlinear growth and a transition to behavior described by simple line broadening with increased pump intensity, was studied in detail. A model considering increased polariton absorption with increased exciton-exciton interactions explains these effects. Finally, nonlinear optical spectroscopy was used to study exciton transport, where near-ballistic behavior was revealed. The effect of exciton transport, thermalization and radiative recombination on the nonlinear optical response was explored.
The enhancement of /spl chi//sup (3)/(-/spl omega/;/spl omega/,-/spl omega/,/spl omega/) and switching rate has been confirmed under resonant pumping of coherent excitons. We propose theoretically the following nonlinear optical responses of the exciton: (1) Superradiance of Frenkel excitons and excitonic n-strings; (2) Frenkel and Wannier excitons show different characteristics of the third-order optical responses /spl chi//sup (3)/(-/spl omega/;/spl omega/,-/spl omega/,/spl omega/); (3) Generation of phase-conjugated wave shows singular spectrum near mobility edge of the exciton in a bulk crystal.>