We proposed a formalism enables us to describe accurately the interaction between the electromagnetic field and linear as well as nonlinear polarizations from a quantum well in a microcavity, considering on the same footing either true guided modes or Fabry-Perot quasi-modes. We showed that stable pulses propagating along quantum wells in such a microcavity can be sustained by cavity modes for two kinds of nonlinear mechanisms at different time scales. The first mechanism is ultrafest two-level unharmonicity leading to the self-induced transparency for 2π-pulses. In this case, we could derive soliton velocity as well as other pulse characteristics and compare them to bulk ones. We found pulse energies in the picojoule range. We gave some hint of the advantages of quantum wells and possible ways to flexibly design a system in view of given pulse requirements. The second mechanism is the slower third-order nonlinearity. In this case the linear polarizability of the quantum well giving rise to the so-called vacuum Rabi splitting has to be included and new split models have to be obtained before nonlinearity is taken into account. The obtainmnet of the soliton solution is found to depend critically on the sign and magnitude of the curvature of the new dispersion relation for which suggestive examples are given. In view of experiments, laser pulses for self-induced transparency seem available. For Kerr nonlinearity, the detailed effect of inhomogeneity on splitting and linewidth has to be studied in more detail to evaluate the potential of this mechanisms in novel systems for soliton generation.
We proposed a formalism enables us to describe accurately the interaction between the electromagnetic field and linear as well as nonlinear polarizations from a quantum well in a microcavity, considering on the same footing either true guided modes or Fabry-Perot quasi-modes. We showed that stable pulses propagating along quantum wells in such a microcavity can be sustained by cavity modes for two kinds of nonlinear mechanisms at different time scales. The first mechanism is ultrafest two-level unharmonicity leading to the self-induced transparency for 2π-pulses. In this case, we could derive soliton velocity as well as other pulse characteristics and compare them to bulk ones. We found pulse energies in the picojoule range. We gave some hint of the advantages of quantum wells and possible ways to flexibly design a system in view of given pulse requirements. The second mechanism is the slower third-order nonlinearity. In this case the linear polarizability of the quantum well giving rise to the so-called vacuum Rabi splitting has to be included and new split models have to be obtained before nonlinearity is taken into account. The obtainmnet of the soliton solution is found to depend critically on the sign and magnitude of the curvature of the new dispersion relation for which suggestive examples are given. In view of experiments, laser pulses for self-induced transparency seem available. For Kerr nonlinearity, the detailed effect of inhomogeneity on splitting and linewidth has to be studied in more detail to evaluate the potential of this mechanisms in novel systems for soliton generation.
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.
The authors develop and apply a novel group-theoretical approach for studying the coherent dynamics of ultrashort pulse propagation in nonlinear optical waveguides and passive semiconductor microresonators. The resonant nonlinearity is modeled by a degenerate three-level system of saturable absorbers in order to allow for a two-dimensional medium polarization. The resulting Maxwell-pseudospin equations are solved in the time domain using the finite-difference time-domain method. Conditions of onset of the self-induced transparency (SIT) regime of propagation are investigated. Numerical evidence of multidimensional solitons localized both in space and in time is given for the planar optical waveguides. Pattern formation and cavity SIT-soliton formation are demonstrated for a passive semiconductor microcavity filled with saturable absorbers.
We examine theoretically the transparency of electromagnetic pulses through an infinite one-dimensional array of coupled optical microcavities uniformly filled with superconducting qubits-one per cavity. Two types of hybrid matter-light waves, i.e., polaritons and self-induced transparency solitons, govern the transparency of electromagnetic radiation in these media. The spectrum of linear excitations, i.e., polaritons, consists of two branches separated by a relatively wide forbidden band. In the nonlinear regime, the dispersion relation of the carrier wave is determined by soliton width that is controlled by the reciprocal qubit frequency. The separate dispersion curves lie within the polariton forbidden band. Soliton transparency requires that the carrier wave frequency exceeds a threshold value; the latter depends strongly on the pulse width. We find that for pulses with widths ranging from ultrashort to an intermediate limit, the threshold is of the order of the gap frequency value in the photon spectrum. For wider pulses, the threshold frequency gradually decreases to values that are toward the edge of the polariton lower band, provided the soliton width is larger than a critical value. In the overcritical regime, the bandgap appears in the spectrum of the soliton carrier wave, while a twin transparency window appears in the soliton pulse dispersion law. A possible experimental observation of the predicted effects within the proposed setup would be of interest in understanding the properties of self-induced transparency in general and applications in the design of quantum technological devices.
Electromagnetic induced transparency (EIT) in condensed media, especially in a semiconductor, is attractive for nonlinear applications, because of its high density, compactness, and flexibility in artificial design. However, fast relaxation time and fermionic character of electrons obstructs the realization of EIT in semiconductor materials. We propose a resonant parametric conversion scheme which is applicable to the semiconductor quantum well (QW) microcavity (MC) exciton system. Because of its large oscillator strength, the semiconductor QW MC excitons show the large vacuum Rabi splitting which can be larger than the phase relaxation broadening of the media. It is found that when the coupling strength of the MC mode and the medium transition is larger than any other Rabi frequency and relaxation rate, the nonlinear susceptibility term becomes dominant compared to the linear susceptibility term.
We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.
Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.