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physica status solidi (b)

The Origin of Third‐Order Optical Nonlinearity in Exciton Systems

Teruya Ishihara

Published May 1, 1990• 8 citations
Publisher

Abstract

Abstract The third‐order optical nonlinearity is estimated to be −10−4 e. s. u. at the exciton resonance in PbI2 evaporated films from the population oscillation effect. Such a large nonlinearity cannot be explained if the system is regarded as independent oscillators. The origin of the third‐order nonlinearity is examined in the density matrix formalism. The observed large nonlinearity is shown to come from the exciton‐exciton interaction.

DOI
10.1002/pssb.2221590143

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Abstract The third‐order optical nonlinearity is estimated to be −10−4 e. s. u. at the exciton resonance in PbI2 evaporated films from the population oscillation effect. Such a large nonlinearity cannot be explained if the system is regarded as independent oscillators. The origin of the third‐order nonlinearity is examined in the density matrix formalism. The observed large nonlinearity is shown to come from the exciton‐exciton interaction.
Excitonic nonlinearity in wide-gap semiconductors has a strong possibility that we can realize efficient ultrafast optical interactions. Recently, we have observed very large third-order nonlinear phase shift in ZnSe layers grown by MBE on GaAs substrate [1], The third-order nonlinear susceptibility at exciton resonance is more than 10–2 esu at 10 K. Because of the biaxial strain, the valence band splits into a heavy- and a light-hole branches at Γ point [2]. To clarify the intrinsic nature of excitonic nonlinearity, the materials which are free from such strain are preferable. In this report, we present our experiments on excitonic nonlinearity using ZnSe homoepitaxial layers which are free from the strain effects [3], and discuss the origin of enhanced nonlinearity at exciton resonance in ZnSe.
We here propose a new procedure to derive a general expression of the third-order susceptibility valid for any semiconductor Hamiltonian. It relies on our theory for composite exciton many-body effects which is quite appropriate to this problem since all optical nonlinearities in semiconductors come from exchange scatterings with the virtual excitons coupled to photons. Our expression of χ (3) is sample volume free, as physically expected. It also contains a Pauli term (exchange without Coulomb) which is missed by all bosonized exciton approaches. This term, dominant at large detuning, is a direct manifestation of the exciton composite nature.
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.
We present a novel heterodyne‐detected four‐wave mixing technique, which determines the third‐order nonlinear polarization in phase and amplitude by spectral interferometry. It allows us to measure the resonant transient four‐wave mixing of single localized excitons, both frequency and time‐resolved. In the signal, the strength of the coupling between two probed exciton transitions is directly observable. Applying a strong optical pump pulse, we observe optical Rabi oscillations of the exciton polarization. Observing decay of the third‐order polarization after the pump pulse, we can exclude the presence of signi£cant excitation‐induced dephasing.
We theoretically investigated optical third-order nonlinearity of a coherently coupled exciton-plasmon hybrid system under a strong control field with a weak probe field. The analytic formulas of exciton population and effective third-order optical susceptibility of the hybrid of a metal nanoparticle (MNP) and a semiconductor quantum dot (SQD) were deduced. The bistable exciton population and the induced bistable nonlinear absorption and refraction response were revealed. The bistability region can be tuned by adjusting the size of metal nanoparticle, interparticle distance and intensity of control field. Our results have perspective applications in optical information processing based on resonant coupling of exciton-plasmon.
A semi parabolic quantum well model to study the third order optical nonlinearities was proposed. A concise formulation of the third harmonic generation was presented. Using a compact density matrix approach, the extremely large third order nonlinearities were obtained. The reason is the possibility of tuning independently the frequency of the semi parabolic potential and the triply resonance effect. The value of | χ (3) max (3 ω )| is as high as 2.7×10 -12 (m/V) 2 at 10.7 μm.