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Physical Review A

Radiation and lifetimes of atoms inside dielectric particles

Herman W. Chew

Published Oct 1, 1988• 237 citations
Publisher

Abstract

The transition rates of atoms inside spherical dielectric particles are computed and studied as functions of the transition frequency and of the physical properties of the host particle. The rates are found to range from about 0.2 to more than 1500 times the free-space value, depending on the location of the atom and other relevant physical parameters. The radiation from distributions of atoms inside liquid drops is also studied. Analytic and numerical results are given for the case of a uniform distribution of excited atoms. Large enhancements of the power output (some 100 times the value for the same distribution in bulk material) are found to occur under resonant conditions.

DOI
10.1103/physreva.38.3410

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The transition rates of atoms inside spherical dielectric particles are computed and studied as functions of the transition frequency and of the physical properties of the host particle. The rates are found to range from about 0.2 to more than 1500 times the free-space value, depending on the location of the atom and other relevant physical parameters. The radiation from distributions of atoms inside liquid drops is also studied. Analytic and numerical results are given for the case of a uniform distribution of excited atoms. Large enhancements of the power output (some 100 times the value for the same distribution in bulk material) are found to occur under resonant conditions.
The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.
The coherent radiation of N atoms that are excited by an external field is studied close to a resonant transition. The resonant atoms are uniformly distributed over a sphere and the external field is a pulse that propagates in a fixed direction. The linear classical continuum theory is used for the above configuration. Exact expressions are obtained for the polarization, for the fields everywhere in space, and for the energy radiated and absorbed by the resonant atoms. Two equivalent methods for the derivation of the exact expression of the polarization are given, i.e., either by solving Maxwell’s equations and boundary conditions, or by solving an integral equation inside the sample. The equivalence of the two methods, in the general case of an arbitrary external field, has been proved elsewhere. Approximate expressions are also obtained for the physical quantities mentioned above in the extreme cases of a dilute and a dense resonant sample with radius much smaller than the radiation wavelength. Inside the dense small sample the polarization depends on position, and this space dependence is expressed in terms of spherical Bessel functions and vector spherical harmonics. It is shown that outside the dense small sample, a broadening of the original resonant line and a shift of the resonance frequency occur in the radiation spectrum of the atoms.
We present calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.
Radiative lifetime of an atom is theoretically studied in the presence of neighboring dielectrics in terms of a microscopic semiclassical theory where the effect of dielectrics is renormalized into radiation Green's function. Some results are presented for the cases of planar (semi-infinite and slab) and spherical dielectrics. A QED calculation in the semi-infinite case confirms the semi-classical result. The interaction of atom resonance and a whispering gallery mode of a sphere leads to “vacuum Rabi” splitting and a cross-over behavior of their radiative widths.
The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantum-mechanical model. The medium is a collection of randomly distributed thermally excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.