Resonant Light Delay in GaN with Ballistic and Diffusive Propagation
T. V. Shubina, Михаил Михайлович Глазов, Alexey A. Toropov, Николай Алексеевич Гиппиус, A -M Vasson, J. Leymarie, Alexey Vitalievich Kavokin, A. Usui, J. Peder Bergman, Galia Pozina, B. Ḿonemar
We report on a strong delay in light propagation through bulk GaN, detected by time-of-flight spectroscopy. The delay increases resonantly as the photon energy approaches the energy of a neutral-donor bound exciton (BX), resulting in a velocity of light as low as 2100 km/s. In the close vicinity of the BX resonance, the transmitted light contains both ballistic and diffusive components. This phenomenon is quantitatively explained in terms of optical dispersion in a medium where resonant light scattering by the BX resonance takes place in addition to the polariton propagation.
We report on a strong delay in light propagation through bulk GaN, detected by time-of-flight spectroscopy. The delay increases resonantly as the photon energy approaches the energy of a neutral-donor bound exciton (BX), resulting in a velocity of light as low as 2100 km/s. In the close vicinity of the BX resonance, the transmitted light contains both ballistic and diffusive components. This phenomenon is quantitatively explained in terms of optical dispersion in a medium where resonant light scattering by the BX resonance takes place in addition to the polariton propagation.
Propagation of light pulses in wide-gap semiconductors, GaN and ZnO, has been studied by time-of-flight spectroscopy. It has been demonstrated that significant light delay exists near an exciton resonance and that this delay is accompanied by pulse distortion and attenuation. Simulation of the pulse shape in the time-energy plane has permitted us to refine excitonic parameters inherent for bulk materials. The time-of-flight studies done over a wide temperature range demonstrate the strong influence of resonant scattering by phonons on the light delay in polar semiconductors. Optical dispersion at exciton resonances in semiconductors results in a delay of light transfer, which is induced by the variation of the group velocity — a phenomenon studied long ago(1-3). Thisdelayhasbeenobservedbytime-of-flightspec- troscopy in different semiconductors (4-6). The current inter- estinsuchretardationisenhancedbecauseitisoneoftheways toobtaintheso-calledslowlight,whichisneededforoptical communication and data processing. Wide-gap semiconduc- tors, like ZnO and GaN, possess strong excitonic resonances thatmakesthemsuitableforsuchapplication. Lightvelocities as low as 6000 km/s in ZnO (4) and 2100 km/s in GaN (5) have been recently measured. In view of these findings, the distortion of a pulse shape has attracted special attention (7). It is worth mentioning that early experiments showed no sig- nificant changes in the shape of a light pulse at the excitonic resonances in GaAs (8) and GaP (9), while the optical dis- persion near the resonances implies a different group velocity and attenuation for the higher- and lower-energy edges of the pulses (10), that inevitably means their distortion in the time- energy plane. The optical pulse modification is also important for a set of optoelectronic devices — high-frequency ones or those, where the light should propagate a long distance. The
Development of all-optical schemes of quantum communication and information processing implies a precise control of photon pulses—in particular, their spectral and temporal characteristics. Therefore “slow light”, propagating with a velocity much lower than the speed of light in vacuum, has been studied intensively in recent years. GaN and related materials are very promising for different applications in nanophotonics and optoelectronics. The advantages of time-of-flight spectroscopy to determine the parameters of bulk semiconductors, as well as investigation of the fine structure of an excitonic spectrum, are presented
Propagation times of optical pulses through a medium near an absorptive resonance with and without spatial dispersion are studied and contrasted. When spatial dispersion is not present, a light pulse is expected to traverse a medium in a time inversely proportional to its group velocity. In a medium with spatial dispersion, where two polariton modes exist (here, bulk GaAs as an example), a similar description is obtained if the losses are such that light propagates primarily in one mode. However, we show that, when the broadening of the resonance (dephasing rate) is below a critical value, a frequency range exists near resonance where the transit times are determined by interference between copropagating polaritons and deviate strongly from expectations based on the group velocities of the polariton branches. When the interference is constructive at the samples end face, the transit times are determined by the average of the inverse group velocities; when it is destructive, we find abrupt transitions between very slow (long positive) and very fast (large negative) transit times. We present quantitative criteria for the resolution of these features and for distortion-free propagation in the spectral vicinity of them. Our analysis puts the well-known slow- and fast-light effects in systems without spatial dispersion into a broader context by illustrating that they are a limiting case of systems with spatial dispersion.
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.
This dissertation presents research on the propagation and manipulation of excitons in GaAs. There are three main aspects to be addressed. In the first part, we provide a comprehensive understanding of the slow- and fast-light propagation based on excitonic resonances. Propagation (or transit) times of optical pulses through a medium near an absorptive resonance with and without spatial dispersion are studied and contrasted. We show that, when the broadening of the resonance (i.e., dephasing rate) is below a critical value, a frequency range exists near resonance where the transit times are determined by interference between co-propagating exciton-polaritons and deviate strongly from expectations based on the group velocities of the individual exciton-polariton branches. Our theory puts the well-known slow- and fast-light effects in systems without spatial dispersion into a broader context by interpreting them as a limiting case of systems with spatial dispersion. An important ingredient of the exciton theory is the light-matter coupling that can be expressed either in terms of the dipole or the momentum matrix elements. We re-examine the validity of a frequently used relation between the interband momentum and dipole matrix elements ('p-r relation') in semiconductors. An additional correction term was obtained when we applied the 'p-r relation' to finite-volume crystals treated with periodic boundary conditions. The correction term does not vanish in the limit of infinite volume. We illustrate this with numerical examples for bulk GaAs and GaAs superlattices. For bulk GaAs, the correction term is found to be always important; while for a GaAs superlattice, the importance of the correction term for the transition depends strongly on the origin of the unit cell.As an example for manipulation of excitons, we consider mechanical deformations of GaAs nanomembranes. The nanomembranes with lateral sizes much larger than their thicknesses exhibit great flexibility in non-planar deformations and thus promise applications in flexible electronic and photonic devices. These non-planar deformations do not fit in the well-established theory for planar deformations induced by lattice mismatch. Our theory relates the general mechanical deformations (planar or non-planar) of nanomembranes to their excitonic spectra, and is numerically evaluated within the average-strain approximation.
Pulse time-of-flight measurements at the heavy exciton resonance in GaAs quantum wells reveal large pulse delays which are dependent on intensity and pulse spectral width. The measured pulse velocities are comparable to those seen in bulk GaAs and are as low as 6.7\ifmmode\times\else\texttimes\fi{}106cm${\mathrm{s}}^{\ensuremath{-}1}$. We obtain quantitative agreement with a simple theory based on hole burning observed in the inhomogeneous exciton line, and we show that the measurements are useful in estimating exciton damping, under certain conditions.