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Monolayer fluctuations in the thickness of a semiconductor quantum well (QW) lead to the formation of spectrally resolved excitons located in the narrower, average, and thicker regions of the QW. Whether or not these excitons are coherently coupled via Coulomb interaction is a long-standing debate. We demonstrate that different types of disorder potential govern coherent coupling among excitons, and the coupling strength can be quantitatively measured using optical two-dimensional Fourier transform spectroscopy. Strong coherent coupling occurs between certain types of excitons but is missing between other types of excitons because the distinctive nature of excitons results in different spatial overlap. Our finding may be applicable to other disordered systems, such as photosynthesis and conjugated polymers, where exciton coupling plays a critical role in determining charge and energy transfer.

Exciton inter- and intra-actions in a GaAs/AlGaAs quantum well (QW) and quantum dot (QD) ensemble are studied using optical two-dimensional Fourier transform spectroscopy. We measure population dynamics for times up to 300 ps and temperatures up to 50 K and observe biexponential decay for both QW and QD excitons, strong QW $\ensuremath{\rightarrow}$ QD relaxation, and weak QD $\ensuremath{\rightarrow}$ QW activation. The population dynamics are modeled using a system of rate equations that incorporate radiative and nonradiative decay, coupling between bright and dark exciton states, and QW $\ensuremath{\leftrightarrow}$ QD coupling. The fast decay rates are attributed to exciton-bound hole spin flips between optically active and inactive states and are similar for the QW and QDs, indicating excitons are weakly localized in the QDs. The QW $\ensuremath{\rightarrow}$ QD relaxation rate increases with temperature, and QD $\ensuremath{\rightarrow}$ QW excitation is observed at temperatures $\ensuremath{\geqslant}$35 K.

Using optical two-dimensional Fourier transform spectroscopy, we report temperature- and excitation-density-dependent measurements of the homogeneous linewidth of the exciton ground-state transition in a single layer of interfacial GaAs quantum dots (QDs). We show that the homogeneous linewidth increases nonlinearly with temperature from 6 to 50 K and that the thermal broadening is well described by an activation term and offset. The absence of a phonon-activation peak in the two-dimensional spectra reveals that elastic scattering of excitons with acoustic phonons via virtual transitions between the ground and excited states significantly contributes to the thermal broadening. We find that the combination of increasing virtual activation energy and exciton-phonon coupling strength with decreasing QD size results in greater thermal broadening for excitons localized in smaller QDs. The homogeneous linewidth also exhibits a strong excitation-density dependence and is shown to increase linearly as the photon density increases from $2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{12}$ photons pulse${}^{\ensuremath{-}1}$ cm${}^{\ensuremath{-}2}$ at 6 K. This trend is attributed to strong coupling of excitons within the same QD and is independent of the quantum-well exciton population density.

The effective nonlinear optical absorption coefficient ${\ensuremath{\beta}}_{\mathrm{eff}}$ is measured for $20\text{\ensuremath{-}}\mathrm{nm}$-thick Au films at $630\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ as a function of pulse width. The $z$-scan measurements show that ${\ensuremath{\beta}}_{\mathrm{eff}}$ increases from $6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ to $6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{cm}\phantom{\rule{0.2em}{0ex}}{\mathrm{W}}^{\ensuremath{-}1}$ as the pulse width is varied from $0.1\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}5.8\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$. To help interpret this $\ensuremath{\sim}100\ifmmode\times\else\texttimes\fi{}$ increase, differential transmission and reflectivity measurements are performed using $775\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ pump and $630\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ probe pulses. All experiments are simulated with a two-temperature model for electrons and lattice. The pulse width dependence of ${\ensuremath{\beta}}_{\mathrm{eff}}$ is consistent with thermal smearing of $d$-band to conduction-band transitions, with ${\ensuremath{\beta}}_{\mathrm{eff}}$ arising from changes in the linear $(\mathrm{Im}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\chi}}^{(1)})$ absorption coefficient.

${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ waveguides with one-dimensional dual-period patterning, consisting of a short period lattice of semiconductor stripes with periodically placed defects, are investigated by surface coupling reflectivity. Defect states, characterized by flat dispersions and enhanced optical density in the defect region, are observed within an energy gap arising from the short period modulation of the structure. When the defect width is incommensurate with the short period, strong additional features due to band folding are observed. The experimental spectra and dispersions are found to be in very good agreement with the predictions of scattering-matrix calculations.