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Physical review. B, Condensed matter

Optical nonlinearities due to excitonic molecules: Optical Stark effects and phase conjugation

Eiichi Hanamura

Published Oct 15, 1991• 15 citations
Publisher

Abstract

Large, nonlinear-optical phenomena are shown theoretically to be observable under nearly two-photon resonant pumping of the excitonic molecule (EM), e.g., in a CuCl crystal. When the exciton polariton (EP) is resonantly pumped into the EM, they are hybridized with each other and show optical Stark splitting. These splittings can be observed, respectively, as a sharp dip in the reflection spectrum and two-photon absorption spectrum due to the EM. We can also clarify how these splittings change into the blueshifts and redshifts of the EP and the EM as functions of the pump frequency and power. The generation of the phase-conjugated wave is shown also to be enhanced under two-photon resonant pumping of the EM. Some characteristics about pump-probe frequency and polarization dependences are also clarified. We have also derived the effective Hamiltonian of the exciton and the EM from the first-principles equation of motion for the exciton coupled with that of the EM. This Hamiltonian has made possible the theoretical analysis of these nonlinear-optical phenomena.

DOI
10.1103/physrevb.44.8514

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Large, nonlinear-optical phenomena are shown theoretically to be observable under nearly two-photon resonant pumping of the excitonic molecule (EM), e.g., in a CuCl crystal. When the exciton polariton (EP) is resonantly pumped into the EM, they are hybridized with each other and show optical Stark splitting. These splittings can be observed, respectively, as a sharp dip in the reflection spectrum and two-photon absorption spectrum due to the EM. We can also clarify how these splittings change into the blueshifts and redshifts of the EP and the EM as functions of the pump frequency and power. The generation of the phase-conjugated wave is shown also to be enhanced under two-photon resonant pumping of the EM. Some characteristics about pump-probe frequency and polarization dependences are also clarified. We have also derived the effective Hamiltonian of the exciton and the EM from the first-principles equation of motion for the exciton coupled with that of the EM. This Hamiltonian has made possible the theoretical analysis of these nonlinear-optical phenomena.
The phase-conjugation in crystalline CuCl has been studied at 1.6 K. It has been found that the two-photon resonance of the Γ1\varGamma_{1}Γ1​-excitonic molecule and the one-photon resonance of the Γ5\varGamma_{5}Γ5​-exciton contribute to the generation of the phase-conjugated wave. Each contribution has been separated spectroscopically by adjusting the polarization configuration of the incident fields adequately and has been compared qualitatively with the theory. The efficiency of the phase-conjugated reflection has become maximum at around the two-photon resonance of the excitonic molecule, 3.186 eV and has been ∼1% at the maximum.
This Letter presents for the first time the observation of the resonant optical Stark effect in a semiconductor. The excitonic system of Cu2{\mathrm{Cu}}_{2}Cu2​O is well suited to the investigation of this effect because of its rather large binding energy and well-resolved resonances at low temperatures. The mixing between the 1S1S1S and 2P2P2P excitons by the electric field of a tunable high-power CO2{\mathrm{O}}_{2}O2​ laser leads to drastic changes in the one-photon spectrum around the 2P2P2P absorption line. Even details of the line shape are consistently described in terms of the frequency-dependent nonlinear susceptibility.
This dissertation presents investigations of fundamental optical nonlinearities in semi-conductor microstructures. Two distinct effects are studied. In the first part the excitonic optical Stark effect in InGaAs and GaAs multiple quantum-well structures is investigated by means of pump-probe spectroscopy. For nonresonant excitation below the excitonic transition the direction of the shift of the resonance depends on the polarization of the pump and probe pulses. In particular, for anti-circular polarization a surprising red-shift is observed. For resonant excitation, induced absorption energetically above and below the exciton transition and bleaching of the resonance is found. Experiments using both resonant and nonresonant excitation reveal the importance of bound and unbound two-exciton states in absorption changes of the 1s heavy-hole exciton resonance. It is found that higher-order Coulomb contributions determine the intensity as well as the time dependence of the differential excitonic absorption. In addition, the influence of light-hole excitons is analyzed. It is shown that the direction of the optical Stark shift for nonresonant excitation depends also sensitively on the heavy-hole to light-hole splitting and the detuning of the pump pulse. For very high pump intensities and nonresonant excitation the absorption is split when a circularly polarized pump and a linearly polarized probe beam are used. For co-circular excitation traces of hyper-Raman gain are observed. In the second part of this dissertation, the nonlinear optical response of semiconductor microcavities in the nonperturbative regime is studied in resonant single-beam transmission and pump-probe experiments. In both types of experiment, a pronounced third transmission peak lying spectrally between the two normal modes is observed. Its dependence on the probe intensity, pump intensity, pump-probe delay, exciton-cavity detuning and pump detuning is investigated. For single-beam transmission, the energy of the third peak parallels the position of the cavity resonance. It is more pronounced for circularly polarized excitation and lasts longer than the two normal modes. For pump-probe experiments, the third peak increases with decreasing probe intensity and increasing pump intensity. Its energy is close to the low-energy side of the pump spectrum and virtually unaffected by the cavity-exciton detuning. The appearance of the third peak requires temporal overlap of pump and probe pulses. The origin of this complex nonlinearity is the quantum nature of light, which induces intraband polarizations in the presence of a coherent driving field and a finite carrier density. It is found that the coupling of the intraband polarizations via guided modes to the polarization of the fundamental longitudinal mode is responsible for the third transmission peak. A fully quantized theory reproduces the experimental observations.
We measured the transient reflection spectra induced by infrared light for a CuCl single crystal using pump-probe spectroscopy. A Stark shift of the 1 s exciton was observed using light with a near resonant energy between the 1 s and 2 p exciton levels. The amount of energy shift due to the Stark effect was obtained from the absorption spectra calculated using the Kramers–Kronig transform. We investigated the energy shift of 1 s excitons with respect to the excitation density. This is the first published report on the Stark effect of 1 s exciton associated with the internal energy levels of the excitons in CuCl crystal.