ISSN 1063-7850, Technical Physics Letters, 2007, Vol. 33, No. 2, pp. 176–179. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © T.Yu. Bagaeva, V.V. Popov, N.J.M. Horing, 2007, published in Pis’ma v Zhurnal Tekhnicheskoœ Fiziki, 2007, Vol. 33, No. 4, pp. 79–86.
176
Radiative polaritons in two-dimensional (2D) exci-
tonic systems have been theoretically studied [1–7] and
experimentally observed in structures with quantum
wells [8, 9]. The theoretical approach adopted in [1–5]
was based on perturbation theory. According to this a
quasi-continuous spectrum of photons in the surround-
ing medium (barrier) is represented by eigenwaves in a
hypothetical Fabry–Perot resonator, as its dimensions
increase to infinity. In this case, the total field of a
polariton mode in the barrier represents a superposition
of the incident and outgoing plane electromagnetic
waves. Within the framework of this approach, the dis-
persion branches of radiative polaritons terminate on
the surface of a light cone corresponding to the medium
surrounding the 2D excitonic system. The frequency of
radiative polaritons is practically independent of their
wavevectors and, hence, the frequency of light emitted
as a result of the radiative decay of polaritons is inde-
pendent of the emission angle. The systems with rela-
tively weak exciton–photon coupling are quite ade-
quately described by perturbation theory, but this the-
ory can fail to describe the systems with strong
exciton–photon coupling.
Another theory [6, 7] employed a self-consistent
electrodynamic approach that was based on the repre-
sentation of a light field in the surrounding medium in
the form of an outgoing inhomogeneous plane electro-
magnetic wave satisfying the radiation condition at
infinity. In this case, the field of each radiative polariton
mode at a fixed moment of time increases in space with
the distance from the excitonic layer and decays with
time at a fixed point [6]. The dispersion branches of
radiative polariton modes enter the slow-wave region
on the dispersion plane (i.e., go beyond the light cone)
and terminate at the points corresponding to a zero rate
of the radiative decay of these modes. The dispersion of
radiative excitonic polaritons near the light cone is
much stronger than that predicted by perturbation the-
ory, which must lead to a strong angular dependence of
the frequency of light emitted at grazing angles.
It should be emphasized that both approaches are
mathematically correct and differ only in the condition
at infinity. Indeed, perturbation theory in fact employs
the condition of finiteness of the light field at infinity,
whereas the self-consistent approach [6, 7] employs the
radiation condition. However, the particular behavior of
the electromagnetic field at infinity in real physical sit-
uations is not as important, since this field cannot reach
infinity during a finite observation time. Therefore, a
more adequate approach to the excitation of exciton–
polariton modes in a 2D excitonic system is necessary,
which would include an analysis of the initial condi-
tions.
This Letter describes an analysis of the nonstation-
ary excitation of exciton–polariton modes by obliquely
incident light pulses in a 2D excitonic system. The
problem is solved using the formalism of Green’s ten-
sor (dyadic) function.
Consider a 2D excitonic system (material layer) sit-
uated in the plane z = 0 of an infinite medium possess-
ing permittivity ε
h
. The response of the material is
Temporal Dynamics of Radiative Polariton Modes
in a Two-Dimensional Excitonic Layer
T. Yu. Bagaeva
a,
*, V. V. Popov
a
, and N. J. M. Horing
b
a
Institute of Radio Engineering and Electronics (Saratov Branch), Russian Academy of Sciences,
Saratov, 410019 Russia
b
Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken,
NJ 07030, USA
* e-mail: bagaeva@info.sgu.ru
Received September 11, 2006
Abstract—Nonstationary polariton modes excited by light pulses in a two-dimensional excitonic system have
been theoretically studied using Green’s tensor function. It is shown that the electromagnetic response contains
inhomogeneous radiative polariton modes, which correspond to the complex poles of Green’s function. An
analysis of the nonstationary polariton response eliminates the discrepancy that previously existed between two
different approaches to the description of radiative polariton modes in two-dimensional excitonic systems.
PACS numbers: 73.20.Mf, 71.36.+c, 78.67. De, 78.47.+p
DOI: 10.1134/S1063785007020253