On the Damping of the Excitonic Polaritons

Abstract

The genera1 properties of the damping constants of polaritons in the two-branch and three-branch models are considered in the framework of the Green's function method. In particular, the expressions for the damping constants of the polaritons in terms of those of the excitons are estaablished.PaCCMOTpeHbI o61me CBOfkCTBa KOHCTaHT 3aTyXaHHR IIOJIRPHTOHOB B AByX H TpeXBeT-JIeHHOn MOAeJIRX B paMaKaX MeTOAa $IYHKqUHEI rpHHa. B YaCTHOCTU YCTaHOBJIeHbI HX BblpameHHR uepe3 KOHCTaHTbI 3aTyXaHHR BKCHTOHOB.

Absorption in dipole-lattice models of dielectrics

“…where q is now a continuous variable over the first Brillouin zone − π a < q < π a . The delta functions in (7) contain terms where q is displaced by an integer number of the reciprocal lattice vector 2π/a. As we are primarily interested in initial fields with λ a, we only consider the j = 0 term at this point.…”

“…where γ = 6V 0 /a 3 and we have omitted reciprocal lattice vector terms present due to (7) for notational brevity. After evaluating the Dirac delta functions, the equations of motion become: where the integration variables have been rescaled to dimensionless values and…”

“…No calculations however are given in [2] for such a model with nonlinear matter interactions. Subsequently Hopfield's suggestion has been followed up in a quantum setting where excitons (the quantized polarization field) are nonlinearly coupled to lattice phonons, the latter providing an effective damping when light interacts with the former [3][4][5][6][7]. A full analysis in the quantum setting is very challenging whereas an appealing aspect of Hopfield's proposal is that it can be carried out classically, much as the textbook motivations [1] for the macroscopic Maxwell equations are classical.…”