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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spontaneous emission rates of a single-impurity molecule in dependence on its orientation in biaxial host crystal

Inna Rebane

Published Aug 3, 2005• 1 citation

Abstract

The spontaneous emission rate (SER) of a single impurity molecule for the electric dipole transition has been found in the case where the birefringence of a host crystal is taken into account. SER depends on the orientation of the dipole moment with respect to the principal axes of the dielectric (permittivity) tensor of the host crystal and on the principal refractive indices of the crystal. We use the model where the average electromagnetic field in the crystal is classical and effective electric field vectors at the site of the impurity molecule are found for the interstitial impurity which is located in the center of the crystal cell. The results of calculations for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl) are presented. It is shown that values of SER form in the space a three- axial ellipsoid. Differences in the values of SER for the electric dipole transition in the same host crystal are up to 34%.

DOI: 10.1117/12.639052

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Abstract The influence of the anisotropy of the host crystal on the spontaneous emission rate of the single‐impurity molecule and thus also on the radiative line width has taken into account. The anisotropy reveals itself in the dependence of the spontaneous emission rate on the orientation of the radiative transition dipole moment in the crystal. In this paper calculations of the relative spontaneous emission rate (the spontaneous emission rate divided by the spontaneous emission rate in the case when the transition dipole moment is parallel to the optical axis) of the quadrupole transition in a uniaxial host crystal are presented in the form which is convenient for experimenters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A reduced equation of motion that describes the excited-state dynamics of interacting two-level impurity molecules in a dielectric host crystal is derived starting from a microscopic model for the total system. Our theory generalizes the derivation of the conventional superradiance master equation for molecules in vacuum; the role of photons in the conventional theory is played by polaritons (mixed crystal-radiation excitations) in our approach. Our final equation thus contains dispersive and superradiant polariton-mediated intermolecular interactions. The effect of the dielectric host is completely contained within a rescaling of these interactions with the transverse dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) of the crystal taken at the impurity's transition frequency. Our theory yields all local field and screening factors for both the dispersive and the dissipative couplings from a single, unified starting point. Known scaling laws for the spontaneous-emission rate and the instantaneous dipole-dipole interaction are extended to the frequency region where the dispersion of \ensuremath{\epsilon}(\ensuremath{\omega}) is important.

We study theoretically the spontaneous emission rate of a two-level quantum emitter in any nanophotonic system. We derive a general representation of the rate on the orientation of the transition dipole by only invoking symmetry of the Green function. The rate depends quadratically on orientation and is determined by rates along three principal axes, which greatly simplifies visualization: emission rate surfaces provide insight on how preferred orientations for enhancement (or inhibition) depend on emission frequency and location, as shown for a mirror, a plasmonic sphere, and a photonic band-gap crystal. Moreover, insight is provided on means to ``switch'' the emission rates by actively controlling the orientation of the emitters' transition dipole.