Optical properties of polaritons in thin crystal films

Abstract

The dispersion relation for polaritons in a crystal slab of an arbitrary thickness is derived by the quantum Green function method. The equation is reduced to the classical electrodynamics form with an effective dielectric function depending on the crystal thickness. The energy and the radiation damping of polariton modes in thin anthracene crystals are calculated and compared with the experimental values based on the studies of low-temperature luminescence and refractive index dispersion.Die Dispersionsbeziehung fur Polaritonen in einer Kristallplattc beliebiger Dicke wird mittels der Quantenmethode der Greenschen Funktion abgeleitet. Die Gleichung wird auf die Form der klassischen Elektrodynamik mit einer von der Kristalldicke abhiingigen effektiven Dielektrizitiitsfunktion reduziert. Die Energie und die Strahlungsdiimpfung der Polariton-Moden in dunnen Anthrazen-Kristallen werden berechnet und mit den experimentellen Werten verglichen, die auf Untersuchungen der Lumineszenz bei tiefen Temperaturen und der Dispersion des Bechungsindex beruhen.

Exciton–Polariton Dispersion of Thin Anthracene Crystals in the Thickness Range of 3 to 0.1 μm

“…Dispersion curves of the refractive index for E /I b and E 11 a are determined by an analysis of Fabry-Perot interferences in the reflection spectra. Unlike the previous study [9], no evidence for the alteration of the index dispersion has been obtained. The results are discussed in comparison with the previous experiments and a theoretical formula derived by Strashnikova et al [lo].…”

“…In a thin crystal, polariton states are governed by the Fabry-Perot interference condition, and are quantized in the direction normal to the crystal surface. Myasnikov et al [9] and Strashnikova et al [lo] have derived a dispersion relation for such polaritons in a thin crystal slab by using a quantum Green-function method. The equation shows a clear thickness dependence of the refractive index, when the value of d becomes comparable to or less than the wavelength of light that "resonates" with exciton eigenfrequencies.…”

“…They have shown that, in a thin crystal where polariton states are well confined, the refractive index indicates a drastic change from that of the bulk crystals. Experiments on thin crystals of anthracene [9] and CdS [lo, 111 have supported their prediction; when the crystal thickness is decreased down to ~0 . 1 pm, the index begins to drop in the region just below the exciton resonance energy.…”

“…The spectral shape of the interference fringes is governed by the interference condition, and the polariton states become discrete and quantized in the direction normal to the crystal surface. Recently, Myasnikov et al [9] and Strashnikova et al [lo, 111 have derived a dispersion formula for such polaritons theoretically. They have shown that, in a thin crystal where polariton states are well confined, the refractive index indicates a drastic change from that of the bulk crystals.…”

Frequency locking of two TEA CO2lasers utilizing a four-wave interaction in SF6

“…(29) into Eq. (16), and then the electric field strength can also be obtained Figure 3a shows that the curve Ei is similar to the distribution of the light field (proportional to \/|Jfc|||) in the region of k\\ "> 1 X 10~5 m" 1 . As is consistent with the manifestation of the dispersion curves (Fig.…”