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Journal of the Physical Society of Japan

Non-Linear Polaritons by Frenkel Excitons

Masahiro Inoue

Published Dec 1, 1974• 14 citations
Publisher

Abstract

By using the model of two level atoms and the boson description of the Frenkel excitons, the dispersion relation of the polariton for intense radiation field is investigated. It is shown that the quenching effect of the dipole moment and the effect of the exciton-exciton interaction modify the dispersion curve significantly. The possibility of the self-induced transparency of a pulse wave is examined by taking into account the polariton effect, and a negative answer is obtained.

DOI
10.1143/jpsj.37.1560

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Soviet Journal of Quantum Electronics•Jul 31, 1977•0 citations
By using the model of two level atoms and the boson description of the Frenkel excitons, the dispersion relation of the polariton for intense radiation field is investigated. It is shown that the quenching effect of the dipole moment and the effect of the exciton-exciton interaction modify the dispersion curve significantly. The possibility of the self-induced transparency of a pulse wave is examined by taking into account the polariton effect, and a negative answer is obtained.
The present paper has the dual purposes. As the first purpose, it is demonstrated that the boson description of Wannier excitons introduced in the preceding paper is suitable also to discussion of non-linear coherent interaction of Wannier excitons with the radiation field. The second purpose is to discuss the possibility of self-induced transparency due to Wannier excitons on the basis of the boson description by making clear the difference between a two-level atomic system and a system of excitons which can propagate in a crystal as polariton. As a result, stable pulse propagation of the radiation field is shown to be prevented by the polariton effect of excitons.
A formal, regorous theory of Frenkel excitons interacting with an external electromagnetic field is doveloped within the framework of a two-level-atom model in which the dipole approximation is employed in describing the atom-field (taken as a c-number) interaction. The model exciton Hamiltonian is shown to be identical in form with the Heisenberg model Hamiltonian for S=1/2 spins with anisotropic long-range exchange interactions. Instead of treating excitons as a non-ideal Bose gas, atomic polarization operators and level population defference are taken up as two fundamental quantities to describe Frenkel excitons. A pair of equations satisfied by these two quantities are derived. It is shown that Frenkel excitons are generally expressed as quantum-mechanical nonlinear polarization waves, the nonlinearity being characterized by the level population. A discussion is given on the interrelationship between such polarization waves and those derivable from the classical Drude-Lorentz model. With the aid of several approximation procedures similar to those employed in nonlinear optics, a set of equations describing nonlinear exciton-photon coupled modes are derived. Brief discussion is given on the eigenfrequencies of nonlinear Frenkel excitons and nonlinear polaritons. The existence of nonlinear exciton-photon coupled modes whose properties are different from those of polariton modes is suggested.
Polariton effect quenches not only the possibility of Bose-Condensation but also of the self-induced transparency of single direct excitons . Here, as to bi-excitons which are not suffered from this negative effect due to polariton, we propose the direct and coherent excitation of Bose-condensed bi-excitons by giant two-photon absorption due to bi-excitons. Then we discuss the possibility of superradiance of Bose-condensed bi-excitons created by this method and the possibility of self-induced transparency associated with giant two-photon transition due to these bi-excitons.
For pt.I see ibid., vol.10, p.425 (1977). The effect of spatial dispersion or exciton formation on the steady propagation of a coherent light pulse in a dielectric medium is studied. The optical Bloch equation for a lattice of atomic dipoles coupled to one another by an exchange-type interaction is solved simultaneously with the Maxwell equation by the method of power-series expansion developed in the preceding paper. Two kinds of pulse solutions are obtained in general: one propagating by the medium of the radiation field and the other by excitation transfer between atomic dipoles. The former solution is SIT-like in the short pulse limit, but a polariton-soliton or a standing wave of non-linear polariton if the pulse width is long. The latter is an exciton-soliton containing little photon component. When the pulse width is extremely long, there appears a polariton-soliton of a new type in which the two propagation mechanisms are mixed. It is found that the spatial dispersion prevents the polariton-soliton solutions from existing in a certain frequency range. This effect is explained on the basis of the functional behavior of the dispersion relation of the non-linear polariton.