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We report frequency-domain degenerate four-wave mixing results on excitons in a semiconductor microcavity in the strong coupling regime. The excitation is kept to the x ͑3͒ limit. The spectral response shows strong polarization dependence. We analyze the data with a new model where the degenerate four-wave mixing process is described as an elastic scattering of two cavity polaritons mediated by the state filling effect and the two-body attractive and repulsive interaction between excitons. From the polarization and detuning dependence, the ratio of the coupling constants of these three terms is uniquely determined. We find that the attractive interaction term and the state filling are the dominant contributions to the nonlinearity. [S0031-9007(97)03813-1] PACS numbers: 71.36. + c, 71.35.Lk The exciton-photon coupled system in a semiconductor microcavity structure is attracting a lot of current interest in both fundamental and applied research [1]. In the strong coupling regime very large normal mode splitting exists which is several orders of magnitude larger than that of the atomic system [2]. Various experimental and theoretical studies have been performed to elucidate the features characteristic to the excitonic system [2-7]. As long as linear optical responses are concerned the semiclassical picture with anomalous dispersion associated with excitons can well explain these features as it was pointed out for the atomic system [8]. In the nonlinear regime, the atom-cavity coupled system shows characteristic features originating from the granular nature of the radiation field [9]. Because of the similarities with the atomic system and ease of integration with the existing semiconductor technology, the exciton-cavity coupled system is expected to be suitable for the fabrication of quantum logic devices. However, the atomic two-level system can be saturated with as little as one photon and shows a large nonlinearity, whereas the excitonic system behaves mostly harmonic in the low density regime. Any deviation from this harmonic behavior is due to the nonideal bosonic nature of excitons. This deviation is essential to photon manipulation. Therefore, elucidation of the nonlinear optical responses of the exciton-cavity coupled system is crucial to the realization of the idea of quantum logic devices.In the conventional scheme of nonlinear optics the nonlinear polarization is evaluated as a higher-order perturbation of the exciton-photon dipole interaction. This framework is not applicable to the strong coupling regime, because the exciton-photon dipole interaction is fully taken into account nonperturbatively in order to form cavity polaritons. Nonlinear responses are described as higher-order scattering of cavity polaritons by the anharmonicities which originate from the fermionic nature and Coulomb interaction of the constituents of the excitons. Nonlinear optical processes of bulk polaritons should also be treated in the same framework. For the bulk case, however, the propagation effects of polaritons bring furt...

Using a 4-mm-long compact silicon-nanowire waveguide, we demonstrated nonlinear-optic effects such as the spectral broadening of optical short pulses due to self-phase modulation and nonlinear transmittance due to two-photon absorption. At a 12 W input power level, we observed a 1.5-π nonlinear phase shift and a strong saturation of optical output power in a sample. We also estimated the third-order nonlinear coefficient n 2 and the two-photon absorption coefficient β, and compared them with those previously reported.

We investigate the quality (Q) factor and the mode dispersion of single-defect nanocavities based on a triangular-lattice GaAs photonic-crystal (PC) membrane, which contain InAs quantum dots (QDs) as a broadband emitter. To obtain a high Q factor for the dipole mode, we modulate the radii and positions of the air holes surrounding the nanocavity while keeping six-fold symmetry. A maximum Q of 17 000 is experimentally demonstrated with a mode volume of V = 0.39(λ/n) 3 . We obtain a Q/V of 44 000(n/λ) 3 , one of the highest values ever reported with QD-embedded PC nanocavities. We also observe ten cavity modes within the first photonic bandgap for the modulated structure. Their dispersion and polarization properties agree well with the numerical results.

We report here the first observation of vacuum Rabi splitting in a single quantum dot (QD) embedded in a H1 photonic crystal nanocavity by photoluminescence measurement. The QD emission was tuned into a cavity mode by controlling the temperature. At the resonance condition, clear anticrossing with a Rabi splitting of ∼124 μeV was observed, where the cavity mode possesses the smallest mode volume V∼0.43(λ/n)3 among strongly coupled QD-cavity systems reported to date.

We experimentally investigated the excitation power dependence of a strongly coupled quantum dot (QD)-photonic crystal nanocavity system by photoluminescence (PL) measurements. At a low-excitation power regime, we observed vacuum Rabi doublet emission at QD-cavity resonance condition. With increasing excitation power, in addition to the doublet, a third emission peak appeared. This observed spectral change is unexpected from conventional atomic cavity quantum electrodynamics. The observations can be attributed to featured pumping processes in the semiconductor QD-cavity system. Solid-state cavity quantum electrodynamics (QED) based on semiconductor quantum dots (QDs) has been intensively studied as a key tool for quantum information processing 1-3 . In these studies, single QDs are often considered as atomic two-level systems 4 . However, recent experiments on coupled QD-cavity systems 5-8 have reported several strange phenomena unexpected from conventional atomic cavity QED. One of the major oddities is the so-called non-resonant coupling, which describes strong photon feeding to the cavity mode from the QDs with large spectral detuning from the cavity resonance. Another peculiarity is triplet emission in the strong coupling regime at the resonance condition where vacuum Rabi doublet emission is expected. Both peculiar observations were first reported by Hennessy et al 5 , and much effort has been made to understand the observations.With regard to the mystery of non-resonant coupling, several groups have been investigating the mechanisms both experimentally 6,7 and theoretically 9,10 . In contrast, with regard to the spectral triplet, detailed studies have not been conducted so far, and there is little knowledge of the mechanism. The effect of pumping processes on strongly coupled QD-cavity systems is also known little even though photoluminescence (PL) measurements, in which collective carriers are injected around and inside the QDs, are a major experimental tool in semiconductor cavity QED. A theoretical model 11,12 considering incoherent pumping on both the QD and the cavity mode has recently been introduced and applied to explain the pumping power dependence of the vacuum Rabi doublet emission 13 ; however, the spectral triplet was outside its scope. Deeper understanding of the peculiar observations is necessary for developing QD-based cavity QED systems for wide application in quantum information technology.In this paper, we studied the excitation power dependence of a strongly coupled QD-cavity system in the resonance condition by micro-PL measurements. With increasing excitation power, a transition from vacuum Rabi doublet to triplet emission was observed. Quantum correlations of the emitted photons were also investigated and the degradation of the quantum nature along with the increment of the third emission peak were observed. The spectral triplet is attributed to featured pumping processes in semiconductor cavity QED systems, including collective carrier injection inside the host material and incohe...

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An electromagnetic (EM) Bloch wave propagating in a photonic crystal (PC) is characterized by the immittance (impedance and admittance) of the wave. The immittance is used to investigate transmission and reflection at a surface or an interface of the PC. In particular, the general properties of immittance are useful for clarifying the wave propagation characteristics. We give a general proof that the immittance of EM Bloch waves on a plane in infinite one-and two-dimensional (2D) PCs is real when the plane is a reflection plane of the PC and the Bloch wavevector is perpendicular to the plane. We also show that the pure-real feature of immittance on a reflection plane for an infinite three-dimensional PC is good approximation based on the numerical calculations. The analytical proof indicates that the method used for immittance matching is extremely simplified since only the real part of the immittance function is needed for analysis without numerical verification. As an application of the proof, we describe a method based on immittance matching for qualitatively evaluating the reflection at the surface of a semi-infinite 2D PC, at the interface between a semiinfinite slab waveguide (WG) and a semi-infinite 2D PC line-defect WG, and at the interface between a semi-infinite channel WG and a semi-infinite 2D PC slab line-defect WG.