An Analog of the Migdal–Kohn Singularity and the Radiation Width of the High-Frequency Branch of the Polariton Spectrum for a Bounded Crystal of the J-Aggregate Type

Dubovsky, O. A.
February 2004
Journal of Experimental & Theoretical Physics;Feb2004, Vol. 98 Issue 2, p240
Academic Journal
The excitation spectra of crystalline ensembles of coherently emitting interacting quantum electric dipole oscillators are investigated. The system of dynamic equations derived for a one-dimensional crystal of the J-aggregate type can be used in various limiting cases for studying optical photons as well as X-ray and gamma quanta. An exact analytic solution to the dispersion equation is obtained for polaritons (mixed states of Frenkel excitons and transverse photons). It is shown that the high-frequency polariton branch with anomalously high radiation broadening has the limiting wave vector corresponding to the spectral edge not because the broadening becomes comparable to the frequency (as was generally accepted earlier), but due to smooth joining of this polariton branch with the other (nonphysical) branch determined from the dispersion equation. At this point, the derivative of the dispersion curve goes to infinity, which is an analog of the well-known Migdal–Kohn singularity in the phonon spectra of metals. It is shown that the low-frequency polariton branch also exhibits slight broadening due to the fact that the proper radiation width is taken into account exactly. © 2004 MAIK “Nauka / Interperiodica”.


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