We have studied two-photon nonlinear optical effects arising in a microcavity geometry from resonant two-photon absorption or second-harmonic generation. The transmission spectrum of the cavity is shown to depend on light intensity according to a simple two-level picture with an intensity-dependent coupling: at resonance the system exhibits a two-photon Rabi splitting. The absorption spectrum of a weak probe beam in a pumped cavity is found to strongly depend on pump intensity and detuning; the resulting effect is a sort of two-photon analogue of the usual optical Stark effect. For moderate pump intensities a two-level picture with a pump-dependent coupling can account for the main results, while at higher intensities new unexpected features show up; in particular, we predict the appearance of gain in well-determined spectral regions due to hyper-Raman processes. Finally, we have shown how the coupling coefficients appearing in our formalism can be obtained from a detailed knowledge of the material and geometrical properties of a specific system. For illustrative purposes, we have estimated the required light intensities using realistic data for a GaAs-based semiconductor microcavity.
We have studied two-photon nonlinear optical effects arising in a microcavity geometry from resonant two-photon absorption or second-harmonic generation. The transmission spectrum of the cavity is shown to depend on light intensity according to a simple two-level picture with an intensity-dependent coupling: at resonance the system exhibits a two-photon Rabi splitting. The absorption spectrum of a weak probe beam in a pumped cavity is found to strongly depend on pump intensity and detuning; the resulting effect is a sort of two-photon analogue of the usual optical Stark effect. For moderate pump intensities a two-level picture with a pump-dependent coupling can account for the main results, while at higher intensities new unexpected features show up; in particular, we predict the appearance of gain in well-determined spectral regions due to hyper-Raman processes. Finally, we have shown how the coupling coefficients appearing in our formalism can be obtained from a detailed knowledge of the material and geometrical properties of a specific system. For illustrative purposes, we have estimated the required light intensities using realistic data for a GaAs-based semiconductor microcavity.
We have investigated resonant two-photon absorption and second harmonic generation in a microcavity geometry. In a single beam arrangement, the transmission depends on the intensity according to a simple two-level picture with an intensity-dependent coupling; at resonance, in particular, the system exhibits a two-photon Rabi splitting. In a pump and probe arrangement, the presence of the strong incident pump beam substantially modifies the absorption spectrum of the weak probe beam: for moderate pump intensities the behaviour can be interpreted as a two-photon version of the well-known optical Stark effect. At higher intensities, more complicated hyper-Raman processes take place, which give also rise to gain in well-determined spectral regions. Finally, we have shown how the non-linear coupling coefficient appearing in the model Hamiltonian is related to the material constants and geometrical parameters of a specific microcavity configuration.
Recently, several research groups have reported investigations of vacuum-field Rabi splittings (VRS) in the linear response of strongly coupled semiconductor microcavities [1-4]. We have previously reported on the dynamics of time-domain vacuum Rabi oscillations, which are most easily understood in the framework of cavity exciton-polaritons, in which the in-plane momentum k|| is conserved [2], so that at each k|| a single cavity mode interacts with only a single mode of the electromagnetic field (Jaynes-Cummings model). In high Q semiconductor microcavities, the strong coupling between two-dimensional excitons and planar distributed- Bragg-reflector cavity modes results in several-meV splittings observable in the reflectivity or absorption spectrum. In the low excitation regime, the VRS is independent of light intensity incident on the cavity, since the vacuum-Rabi frequency exceeds the externally-driven Rabi frequency (in which case the Jaynes-Cummings model is equivalent to the linear dispersion of the coupled exciton-cavity system). As the incident light intensity is increased, two different effects may be expected to contribute to the nonlinear response. First, as long as the excitonic absorption is equivalent to a two-level system, higher-lying states of the Jaynes-Cummings ladder might be observable. Second, at high intensity phase-space filling and Coulomb screening of the exciton states results in a reduced oscillator strength which leads to a reduced VRS; this effect has no analogue in the case of atom-cavity systems. In this paper, we apply several ultrafast nonlinear techniques to investigate the nonlinear response of semiconductor microcavities.
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.
Nonlinear optical phenomena in both semiconductor microcavities and sodium vapor are investigated. Systems displaying atomic and excitonic coupling are studied in detail in order to unravel underlying physical principles. Possible applications for these systems are evaluated where appropriate. Normal-mode coupling (NMC) in a semiconductor microcavity is achieved when a narrow-linewidth quantum well exciton resonance is coincident with the cavity mode of a high-finesse microcavity. This interaction leads to a double-peaked spectrum in either transmission, reflection, or photoluminescence (PL). The high-quality microcavities studied here at liquid-Helium temperatures reveal intensity dependent behavior that has not previously been observed. Nonlinear saturation of the exciton leads to a spectral broadening of the excitonic absorption without a significant loss in oscillator strength. This results in a reduction of the two transmission peaks with almost no change in the splitting between the peaks. Such behavior is easily explained using phenomenological nonlinear dispersion theory. In this nonlinear regime, the luminescence from the microcavity shows a gradual transition from the nonperturbative regime of NMC to lasing with increasing excitation. The observed behavior is explained by density-dependent changes in both the transmission of the microcavity and the bare-exciton emission, rather than a boson-condensation of excitons which has been previously proposed. An intermediate-finesse microcavity also modifies the emission distribution from a bulk-semiconductor at room temperature. Angularly resolved emission spectra and quantum efficiency measurements show the PL is strongly dependent on the reflectivity of the microcavity. Unfortunately, the enhancement in the decay rate of excitons due to high-reflectivity mirrors seen previously by our group does not result in an increased quantum efficiency. High-gain optical-wavefront amplification in atomic sodium vapor is demonstrated via both the three-photon effect and stimulated Raman scattering (SRS). In both cases, single-pass weak-field gain of nearly 400 is achieved with only 800 mW of pump power near 589 nm. In the case of SRS, phase preservation of the amplified wavefront, which is necessary in adaptive imaging applications, is also demonstrated.
The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, (omega) , is in resonance between two subbands in the conduction band. The probe light of the frequency (Omega) falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband (Omega) -light absorption spectra are related to the critical points of the bands, rearranged by the (omega) - light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond (Omega) -light pulses following each other with the delay time, (tau) d. The dependence of energy, absorbed from the second pulse, on the (tau) d value is calculated. Under the (omega) -pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/(omega) R or oscillations with the frequency approximately (omega) R, where (omega) R is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the (Omega) -light pulse.
The biexciton optical Stark-effect under resonant pumping between the exciton and biexciton levels is studied theoretically. The probabilities of biexciton two-photon absorption of a weak probe light and of one-photon biexciton-exciton transition are calculated. The optical Stark splitting manifests itself in two-photon biexciton absorption through two absorption peaks spaced 2 (Omega) apart. Omega is the Raby frequency. In the luminescence spectrum due to biexciton-exciton one-photon transition three luminescence maxima appear which are shifted with respect to the luminescence maximum in the case without pumping.