Polaritons In Quantum Wells Research Articles

Layer-resolved absorption of light in arbitrarily anisotropic heterostructures

We present a generalized formalism to describe the optical energy flow and spatially resolved absorption in arbitrarily anisotropic layered structures. The algorithm is capable of treating any number of layers of arbitrarily anisotropic, birefringent, and absorbing media and is implemented in an open access computer program. We derive explicit expressions for the transmitted and absorbed power at any point in the multilayer structure, using the electric field distribution from a 4 $\times$ 4 transfer matrix formalism. As a test ground, we study three nanophotonic device structures featuring unique layer-resolved absorption characteristics, making use of (i) in-plane hyperbolic phonon polaritons, (ii) layer-selective, cavity-enhanced exciton absorption in transition metal dichalcogenide monolayers, and (iii) intersubband-cavity polaritons in quantum wells. Covering such a broad spectral range from the far-infrared to the visible, the case studies demonstrate the generality and wide applicability of our approach.

Strong and weak coupling limits in optics of quantum well excitons

A transition between the strong (coherent) and weak (incoherent) coupling limits of resonant interaction between quantum well (QW) excitons and bulk photons is analyzed and quantified as a function of the incoherent damping rate ${\ensuremath{\gamma}}_{x}$ caused by exciton-phonon and exciton-exciton scatterings. For confined QW polaritons, a second, anomalous, ${\ensuremath{\gamma}}_{x}$-induced dispersion branch arises and develops with increasing ${\ensuremath{\gamma}}_{x}$. In this case, the strong-weak coupling transition is attributed to ${\ensuremath{\gamma}}_{x}={\ensuremath{\gamma}}_{x}^{\mathrm{tr}}$ or ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}}_{x}^{\mathrm{tr}}$, when the intersection of the normal and damping-induced dispersion branches occurs either in ${{k}_{\ensuremath{\parallel}},\mathrm{Im}[\ensuremath{\omega}],\mathrm{Re}[\ensuremath{\omega}]}$ coordinate space (in-plane wave vector ${k}_{\ensuremath{\parallel}}$ is real) or in ${\ensuremath{\omega},\mathrm{Im}[{k}_{\ensuremath{\parallel}}],\mathrm{Re}[{k}_{\ensuremath{\parallel}}]}$ coordinate space (frequency $\ensuremath{\omega}$ is real), respectively. For the radiative states of QW excitons, i.e., for radiative QW polaritons, the transition is described as a qualitative change of the photoluminescence spectrum at grazing angles along the QW structure. We show that the radiative corrections to the QW exciton states with in-plane wave vector ${k}_{\ensuremath{\parallel}}$ approaching the photon cone, i.e., at ${k}_{\ensuremath{\parallel}}\ensuremath{\rightarrow}{k}_{0}=({\ensuremath{\omega}}_{0}\sqrt{{\ensuremath{\epsilon}}_{b}})∕(\ensuremath{\hbar}c)$ (${\ensuremath{\epsilon}}_{b}$ is the background dielectric constant), are universally scaled by the energy parameter ${({\ensuremath{\Gamma}}_{0}^{2}{\ensuremath{\omega}}_{0})}^{1∕3}$ with ${\ensuremath{\Gamma}}_{0}$ the intrinsic radiative width and ${\ensuremath{\omega}}_{0}$ the exciton energy at ${k}_{\ensuremath{\parallel}}=0$, rather than diverge. Similarly, the strong-weak coupling transition rates ${\ensuremath{\gamma}}_{x}^{\mathrm{tr}}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}}_{x}^{\mathrm{tr}}$ are also proportional to ${({\ensuremath{\Gamma}}_{0}^{2}{\ensuremath{\omega}}_{0})}^{1∕3}$. The numerical evaluations are given for a GaAs single quantum well with realistic parameters: ${\ensuremath{\Gamma}}_{0}=45.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{eV}$ and ${({\ensuremath{\Gamma}}_{0}^{2}{\ensuremath{\omega}}_{0})}^{1∕3}\ensuremath{\approx}1.5\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$.

Optical spectroscopy of a semi-insulating GaAs/AlGaAs multiple quantum well system near double exciton–polariton and Bragg resonance

We studied optical reflection (OR) and contactless electroreflection (CER) from a periodic system of multiple GaAs/AlGaAs quantum wells (QWs). The QW width was 15 or 20 nm and the barriers were 104 nm thick. In this system the electromagnetic resonance of Bragg reflection occurs at the frequency that coincides or is close to the frequency of the exciton–polariton resonance in the wells. The optical measurements were made at various temperatures, angles of the light incidence and polarization. The optical reflection spectra have been found to be a result of the interplay of three different contributions, namely (i) the reflection from the air/semiconductor interface, (ii) the Bragg reflection due to periodic modulation of the background indices of refraction being different for the wells and barriers and (iii) the resonant reflection from the periodic system of exciton–polaritons in quantum wells. The latter contribution was separately studied by CER technique in the spectral range covering ground states of the heavy-hole and light-hole excitons. A quantitative analysis of the experimental CER line shape has been done along with quantum-mechanical calculations, which revealed the characteristic energies and broadening parameters for different exciton–polariton levels. In particular, the systems of four and 32 QWs exhibit spectral features with the characteristic broadening of 1.8 meV and 2.2 meV at 17 K, respectively. By comparison with theoretical calculations we discuss the radiative and non-radiative contributions to the total broadening.

Theory of propagation and scattering of exciton–polaritons in quantum wells

A novel semi-classical theory of exciton–polaritons in quantum wells (QWs) is presented. Time-resolved coherent optical spectra of QWs are described by the light coupling with ensembles of localised quantum dot-like exciton states. The ratio between reflection and resonant Rayleigh scattering (RRS) intensity gives a direct measure of the density of these excitonic dots. Good agreement with experimental data on time-resolved angle-dependent reflection and RRS from a GaAs single QW is achieved.

Quantum theory of the interaction of quantum-well excitons with electromagnetic waveguide modes.

We investigate the influence of the dielectric mismatch between barrier material and well material on the properties of excitonic polaritons in quantum wells. A quantum theory of the interaction between quantum-well excitons and dielectric waveguide eigenmodes is presented and polariton dispersion, radiative decay rate, and polariton eigenstates are obtained. The modifications as compared to previous theories are mainly a photonlike dispersion of the upper polariton branch for energies above the excitonic resonance as well as a finite imaginary part of the exciton self-energy for all values of ${\mathit{Q}}_{\mathrm{\ensuremath{\parallel}}}$. This theory can easily be extended to a description of structures with a more complicated profile of the dielectric constant.

Squeezed polaritons in confined systems

We discuss the statistical properties of polaritons in quantum wells embedded in a microcavity. In particular we evaluate the amount of squeezing of confined exciton polaritons in a GaAs quantum well. The limit of a large cavity is also considered.

Quantum theory of excitonic polaritons in quantum wells

We derive the Hamiltonian which describes in second quantization the interaction of quantum-well excitons with photons and obtain by solving the corresponding quantum-mechanical equations of motion the dispersion relations for localized and resonant polaritons as well as the lifetime for the resonant modes. The results are compared with those obtained by Andreani et al. and Tassone et al. who instead solved Maxwell's equations.

Resonant and surface polaritons in quantum wells

We show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectorkII: those atkII ω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofkII. Numerical results are obtained for GaAs-Ga1−xAlxAs and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature.