Polariton lasing by exciton-electron scattering in semiconductor microcavities

In this chapter we address a complex set of optical phenomena linked to the spin dynamics of exciton polaritons in semiconductor microcavities. When optically created, polaritons inherit the spin and dipole moment from the exciting light. Their state can be fully characterized by a so‐called “pseudospin” accounting for both spin and dipole moment orientation. However, from the very beginning of their life in a microcavity, polaritons start changing their pseudospin state under effect of effective magnetic fields of different nature and due to scattering with acoustic phonons, defects, and other polaritons. This makes pseudospin dynamics of exciton polaritons rich and complex. It manifests itself in non‐trivial changes in polarization of light emitted by the cavity versus time, pumping energy, pumping intensity and polarization. During the first years of theoretical research on exciton‐polariton relaxation the polarization has been simply neglected. Later it has been understood that the energy and momentum‐relaxation of exciton polaritons are spin‐dependent. It is typically the case in the regime of stimulated scattering when the spin polarizations of initial and final polariton state have a huge effect on the scattering rate between these states. It appeared that critical conditions for polariton Bose‐condensation are also polarization‐dependent. In particular, the stimulation threshold (i.e. the pumping power needed to have a population exceeding 1 at the ground state of the lower polariton branch) has been experimentally shown to be lower under linear than under circular pumping. These experimental observations have stimulated the theoretical research toward understanding of mutually dependent polarization‐ and energy‐relaxation mechanisms in microcavities. The authors of this chapter have been working on theoretical description of different specific effects of polariton spin‐dynamics in microcavities for years. Here we attempted to put together all fragments and to formulate a general approach to the problem that would allow then to consider a variety of particular cases. We start from reminding the main spin‐relaxation mechanisms known for free carriers and excitons. We then overview the most essential experimental results in this field before to present our original formalism which allowed us to interpret the key experimental findings. We are going to discuss only the strong coupling regime leaving aside all polarization effects in VCSELs. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Condensation of exciton polaritons in semiconductor microcavities takes place despite in-plane disorder. Below the critical density, the inhomogeneity of the disorder limits the spatial extension of the ground state. Above the critical density, in the presence of weak disorder, this limitation is spontaneously overcome by the nonlinear interaction, resulting in an extended synchronized phase. In the case of strong disorder, several non-phase-locked condensates can be evidenced. The transition from a synchronized phase to a desynchronized phase is addressed by sampling the cavity disorder.

Optical technology has proved to be the best choice for the transmission of information at high data rate over long distances. However, the implementation of high-speed, low-energy, all-optical logics in semiconductors represents a formidable challenge due to the intrinsic difficulty of all-optical devices to satisfy the basic system requirements [1]. In particular, cascadability is difficult to obtain in optical systems, and it is assured only if the output of one stage is in the correct form to drive the input of the next stage. In this context, we demonstrate a scheme of all-optical transistor based on exciton polaritons in semiconductor microcavities, which exhibits full connectivity in the same chip plane.

Polariton–polariton scattering and the nonequilibrium condensation of exciton polaritons in semiconductor microcavities

The impact of quantum fluctuations on the properties of quantum well excitons excited inside 0D semiconductor microcavity possessing strong light confinement is analysed. The analysis takes into account the exciton-exciton repulsion and the presence of a reservoir. Analytical solutions are obtained for the generalized Glauber P-function of the system in the adiabatic limit. Destabilization of the homogeneous nonlinear solution belonging to the lower bistability branch in the presence of quantum noise is predicted.

Group III-nitrides have been considered a promising choice for the realization of optoelectronic devices since 1970. Since the first demonstration of the high-brightness blue light-emitting diodes (LEDs) by Shuji Nakamura and coworkers, the fabrication of highly efficient white LEDs has passed successful developments. A serious physical issue still remained, which prevents their use for high power and highly efficient LEDs: the drop of external quantum efficiency (EQE) of III-nitride LEDs when increasing the driving current, the so-called ''efficiency droop'' problem. In order to have a fast expansion to the lighting market, the cost-per-lumen of packaged LEDs must rapidly decrease. This indeed demands for having LED chips operating with high EQE under the high current operation. Besides the industrial interest of III-nitrides, owing to their large direct bandgap, they feature some interesting optical properties such as large exciton binding energy and large oscillator strength of excitons. However, when the carrier density raised in a semiconductor, a transition should occur from an insulating state consisting of a gas of excitons to a conductive electron-hole plasma, that is called the Mott transition. This crossover can drastically affect the optical and electrical characteristics of semiconductors and may, for instance, drive the transition from a polariton laser to a vertical cavity surface-emitting laser. More interestingly, even if biexcitons are frequently seen to dominate the emission of III-nitride heterostructures when the density is raised, no clear experimental report is available on the role of biexcitons in the Mott transition in a two-dimensional (2D) nanostructure. In the first part, the emission properties of high-quality GaN/AlGaN single quantum wells (QWs) at high-carrier densities are examined. They are of crucial importance to provide a deeper insight into the operating conditions of III-nitride based lasers and LEDs, as well as the transition from strong to weak coupling regime of exciton-polaritons in semiconductor microcavities. Employing the same technique then to investigate some InGaN/GaN QWs, the droop signature was investigated comprehensively in both polar and non-polar QWs. Having an accurate estimation of the carrier density in the QWs, the contribution of several non-radiative processes were quantitatively examined. These experiments can indeed provide a deeper insight on the physical phenomena responsible for the efficiency droop in III-nitride LEDs, and can stimulate several theoretical and experimental on this subject. The second part focuses on the transport mechanisms of excitons in ZnO and III-nitride based nano-structures. The transverse movement of donor-bound excitons in a purely bent ZnO microwire as a function of temperature have been investigated, owing to the high spatial, spectral and temporal resolutions of our original time resolved cathodoluminescence system. The movement mechanism was modeled by a hopping process of excitons. Our results pave the way to new experiments allowing to reveal the physics at play at the nanoscale in different materials. However, in case of highly disordered systems, one should take into account more complex considerations, as in the case of InGaN core-shell QW structures studied in the last chapter, the large energy fluctuations prevent excitons to move along the energy gradient at low temperatures.

Static and dynamic responses of excitons in state-of-the-art bulk and epitaxial ZnO are reviewed to support the possible realization of polariton lasers, which are coherent and monochromatic light sources due to Bose condensation of exciton–polaritons in semiconductor microcavities (MCs). To grasp the current problems and to pave the way for obtaining ZnO epilayers of improved quality, the following four principal subjects are treated: (i) polarized optical reflectance (OR), photoreflectance (PR) and photoluminescence (PL) spectra of the bulk and epitaxial ZnO were recorded at 8 K. Energies of PR resonances corresponded to those of upper and lower exciton–polariton branches, where A-, B- and C-excitons couple simultaneously to an electromagnetic wave. PL peaks due to the corresponding polariton branches were observed. Longitudinal–transverse splittings (ωLT) of the corresponding excitons were 1.5, 11.1 and 13.1 meV, respectively. The latter two values are more than two orders of magnitude greater than that of GaAs being 0.08 meV. (ii) Using these values and material parameters, corresponding vacuum-field Rabi splitting of exciton–polaritons coupled to a model MC mode was calculated to be 191 meV, which is the highest value ever reported for semiconductor MCs and satisfies the requirements to observe the strong exciton–light coupling regime necessary for polariton lasing above room temperature. (iii) Polarized OR and PR spectra of an out-plane nonpolar ZnO epilayer grown by laser-assisted molecular beam epitaxy (L-MBE) were measured, since ZnO quantum wells (QWs) grown in nonpolar orientations are expected to show higher emission efficiencies due to the elimination of spontaneous and piezoelectric polarization fields normal to the QW plane. They exhibited in-plane anisotropic exciton resonances according to the polarization selection rules for anisotropically-strained wurzite material. (iv) Impacts of point defects on the nonradiative processes in L-MBE ZnO were studied using time-resolved PL making a connection with the results of positron annihilation measurement. Free excitonic PL intensity at room temperature naturally increased with the increase in nonradiative lifetime (τnr). The value of τnr increased and density or size of Zn vacancies (VZn) decreased with increasing growth temperature (Tg) in heteroepitaxial films grown on a ScAlMgO4 substrate, and the use of homoepitaxial substrates further reduced VZn density. The value of τnr was shown to increase with the decrease in gross density of positively and negatively charged and neutral point defects including complexes rather than with the decrease in VZn density. The results indicate that the nonradiative recombination process is governed not by single point defects, but by certain defects introduced with the incorporation of VZn, such as VZn-defect complexes. As a result of defect elimination by growing the films at high Tg followed by subsequent post-growth in situ annealing, combined with the use of high-temperature-annealed ZnO self-buffer layer, a record long τnr for spontaneous emission of 3.8 ns was obtained at room temperature. By using progressively improving epitaxial growth methods, the polariton laser effect is expected to be observed at room temperature in the near future.

Anisotropic polariton scattering and spin dynamics of cavity polaritons

The concept of Bose–Einstein condensation (BEC) critical temperature and volume are introduced for atomic systems. The possibility of observation of BEC at high temperature due to small mass is discussed considering exciton-polaritons in bulk CuCl, CdSe, and Cu2O, indirect excitons in coupled QWs, and mostly polaritons in semiconductor microcavities, the last system being most effective for observing BEC at room temperature. The dispersion relations of exciton-polaritons for both upper and lower polariton branches, effective masses, scattering processes, and conditions for observing BEC in microcavities are discussed. Experimental results for BEC in such structures, pumping and detection mechanisms, and characteristics are then presented. Novel features of polariton lasers, progress in developing room temperature electrically pumped lasers with structures are then presented. A model for electrically driven polariton laser considering formation and scattering of excitons is developed and a steady state rate equation model is used to obtain useful characteristics.

Exciton-polaritons are hybrid quasiparticles that stem from the strong coupling between microcavity photons and excitons. Their photonic component attributes an extremely small effective mass, while the nonlinear behavior inherited from the excitonic component provides the polaritons with unique physics. Recent progress in room temperature (RT) perovskite microcavities has advocated great promise in robust and nonlinear polaritons. My work concerns the nonlinearity of CsPbBr3 perovskite polaritons towards future optoelectronic applications at room temperature. In chapter 1, I would briefly introduce the backgrounds and basic knowledge of excitons, cavity photon dispersions, exciton polaritons, polariton nonlinearity and CsPbBr3 perovskite. In chapter 2, the experiment setup including CVD, AFM, SEM, EBL, evaporator, and spectroscopy are described. In chapter 3, I present the synthesis and characterization of CsPbBr3 perovskite film. In chapter 4, I demonstrate the first observation of the nonlinear regime of polariton-polariton interaction in perovskite exciton-polaritons. By designing a thick lead halide perovskite microcavity with multiple polariton branches, driven by an exciton-polariton condensation in one polariton branch, we find correlated polariton pairs at high k states in an adjacent branch. In chapter 5, we present an on-chip perovskite polariton parametric oscillator with a low threshold. By designing the lead halide perovskite thin film in a transparent microcavity, under the resonant excitation at a range of angles, the signal at the ground state with long wavelength and the idler at high k state are obtained thanks to the S-shaped polariton dispersion. In chapter 6, I conduct the direct precise measurement of polariton interaction strength in planar all-inorganic perovskite microcavities and enhance the polariton interaction strength value among confined 0D polaritons. In chapter 7, I report the first experimental demonstration of the high order topological polariton corner state lasing. By utilizing a two-dimensional Su–Schrieffer–Heeger (SSH) lattice of coupled perovskite micropillars, the high order topological corner states are obtained in perovskite polaritons, and the robust exciton polariton lasing is achieved at these corner states with low threshold at room temperature. This work drives the exploration of the interplay between the nonlinearity and topology of polaritons in future.

The investigation of exciton-polaritons in semiconductor microcavities operating in the strong-coupling regime is attracting growing interest because of their extraordinary optical properties [1]. Together with the strong excitonic nonlinearities, originating from the Coulomb interaction between excitons, the peculiar dispersion relation of these quasi-particles allows a variety of fundamental effects like optical bistability, low threshold parametric oscillations [2] and formation of robust self-localized states, so-called, cavity polariton solitons (CPSs) [3,4]. It was shown that the inclination of the coherent optical pump (plane wave) endows exciton-polaritons with a kinetic momentum (k x ) along one of the orthogonal directions in the plane of the microcavity. It even allows controlling their dispersion. As a result moving 2D CPSs can exist despite the opposite dispersion signs along (x) and orthogonal (y) to the pump momentum directions [4]. In this contribution we provide theoretical evidence of self-localization of polaritons in the direction orthogonal to the pump tilt (y), which is unusual for the defocusing nonlinearity. We study the formation of 1D CPSs excising due to the parametric four-wave mixing of polaritons.

We consider theoretically the spin relaxation of exciton–polaritons in semiconductor microcavities in the strong coupling regime. The dominant quantum well exciton polarization relaxation mechanism is typically due to the long-range intra-exciton electron–hole exchange. We estimate perturbatively the corresponding contribution for the lower polaritons as a function of the elastic scattering time in analogy to the Dyakonov-Perel model for electron spin relaxation. We find a strong suppression of the polariton spin flip rate due to the electron–hole exchange with respect to the quantum well exciton case.

Condensation of exciton polaritons in planar microcavities with GaAs/AlAs quantum wells in the active area has been studied. It has been found that an increase in the lifetime of polaritons up to ∼10–15 ps when the Q factor of a microcavity exceeds 7000 makes it possible to detect Bose-Einstein condensation of polaritons with a dominant (>90%) photon component. Condensation occurs under thermodynamically nonequilibrium conditions in lateral traps with diameters ∼10 μm formed due to long-range fluctuations of the polariton potential. The violet shift of the polariton emission line at the condensation threshold significantly exceeds the energy of the repulsive interaction between polaritons in the condensate. It has been shown that the shift is mainly due to a decrease in the oscillator strength of bright excitons in lateral traps, caused by the localization of photoexcited long-living dark excitons.

I discuss similitude and differences of spin-orbital effects for electrons in quantum wells with the Rashba coupling and for polaritons in semiconductor microcavities with TE-TM splitting. Contrary to the case of electron, the ground state of polariton in the trap can be non-degenerate and can possess specific polarization structure. For the case of azimuthally symmetric trap and sufficiently strong spin-orbital coupling, the ground state is either radial or azimuthal vortex, depending on the sign of the coupling constant. The effect is strongly enhanced for polaritons trapped in a ring, where even weak TE-TM splitting results in formation of vorticity and definite polarization of the ground state. The Hamiltonian for quasi-1D motion of polaritons in the ring is derived and it is shown the the dispersion of polaritons depend qualitatively on the curvature of the ring.

Polarization modulation reflectance measurements of cavity polaritons in semiconductor microcavities