Strong and weak coupling limits in optics of quantum well excitons

Abstract

A transition between the strong ͑coherent͒ and weak ͑incoherent͒ coupling limits of resonant interaction between quantum well ͑QW͒ excitons and bulk photons is analyzed and quantified as a function of the incoherent damping rate ␥ x caused by exciton-phonon and exciton-exciton scatterings. For confined QW polaritons, a second, anomalous, ␥ x -induced dispersion branch arises and develops with increasing ␥ x . In this case, the strong-weak coupling transition is attributed to ␥ x = ␥ x tr or ␥ x tr , when the intersection of the normal and damping-induced dispersion branches occurs either in ͕k ʈ ,Im͓͔ ,Re͓͔͖ coordinate space ͑in-plane wave vector k ʈ is real͒ or in ͕ ,Im͓k ʈ ͔ ,Re͓k ʈ ͔͖ coordinate space ͑frequency is real͒, 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 ʈ approaching the photon cone, i.e., at Ϸ1.5 meV.

Dispersion and decay rate of exciton-polaritons and radiative modes in transition metal dichalcogenide monolayers

“…On the contrary, the nonperturbative solution, displayed in Fig. 2(c), shows a maximum for the decay rate close to the light line, after which the rate abruptly drops to γ 0 , as it is typical for TE-polarized modes [32]. Please note that in all dispersion plots, such as Figs.…”

“…This set of equations allows us to investigate the general properties of the electromagnetic modes of the system from a simple and analytical model. As it has been stressed in previous work [32], it is crucial to note that the very same characteristic equations nonperturbatively describe both polaritonic (i.e., spatially confined) and radiative (i.e., spatially diverging) states. The distinction between the two families of modes lies in the complex out-of-plane wave vectors k zj = (ε j ω 2 /c 2 − k 2 ) 1/2 in the two extremal semi-infinite layers (j = 1,2).…”

“…Assuming a temporal and spatial dependence for the field of the form E ∝ e i(k ·r +ik zj |z|−ωt) , modes with Im k zj 0 and Re k zj 0 represent exponentially decaying polaritonic states, whereas modes with Im k zj < 0 and Re k zj > 0 correspond to exponentially diverging radiative states. The remaining cases represent unphysical modes with Im ω > 0, which must be excluded on grounds of energy conservation for passive media [32,33]. The classification of the modes according to the sign of the real and imaginary parts of k z is summarized in Fig.…”

“…As it has been pointed out in the case of semiconductor quantum wells for both interband [32] and intersubband [33,34] transitions, coherence plays an essential role for the formation of the exciton-polariton. In the presence of an additional nonradiative decay channel, whose existence is to be expected in any realistic system, the dispersion and the characteristics of the exciton-polariton are not only quantitatively but also qualitatively affected by the magnitude of the incoherent losses.…”

Strong and ultrastrong coupling with free-space radiation

“…1b) and the properties of the system cannot be described using a perturbative treatment of the light-matter interaction 13 .…”