Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift (original) (raw)
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Spontaneous emission rate and level shift of an atom inside a dielectric microsphere
Journal of Modern Optics
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.
Dielectric microspheres as optical cavities: thermal spectrum and density of states
Journal of The Optical Society of America B-optical Physics, 1987
Many recently observed optical properties of dielectric microspheres arise from the fact that they behave as optical cavities with little leakage. The thermal spectrum and the density of states are evaluated for such cavitites as a first step toward quantizing the electromagnetic field. The density of states is shown to obey an asymptotic sum rule.
Physical Review A, 1999
The interaction of a two-level atom with modified modes of free space (MMFS) is studied in the presence of a dielectric microsphere. The frequency range corresponds to the existence of the whispering gallery modes (WGM) in the microsphere. Under minimum assumptions from the first principles the simple equations were obtained describing the spectral properties of one-photon continuum and relaxation processes in it. If initially an atom is excited, when the interaction is strong enough the doublet structure in spectrum of emitted photons is formed. If initially a microsphere is excited, the spectrum of excited photons is essentially dependent on the way of excitation. Resonant excitation of MMFS results in the effective excitation of an atom with subsequent formation of Rabi-doublet in fluorescence spectrum. When deviating from the condition of resonance the spectrum becomes triplet. Under strong mismatching between excitation source and MMFS an atom is not excited practically with fluorescence being of the singlet type. Significant part of the obtained results is of general importance and may be easily applied to the other cases of strong interaction of an atom with resonators.
Optical coupling between spherical dielectric atoms
2005 Quantum Electronics and Laser Science Conference, 2005
It is shown that dielectric microspheres with strongly detuned whispering gallery modes can be effectively coupled. The transition from strong to weak coupling is demonstrated as a function of separation between nonidentical microspheres.
Journal of Modern Optics
The frequency shift and linewidth variation of an oscillator placed next to a dielectric microsphere are found within the framework of the classical approach. Both the frequency shift and the linewidth are shown to be substantially dependent on the location of the atom and the size of the microsphere and are capable of reaching very high values near the surface of the microsphere under resonance conditions. Near microsphere resonance, a blue frequency shift is predicted, leading to repulsive forces between the atom and the dielectric microsphere.
Decay of an excited atom near an absorbing microsphere
Physical Review A, 2001
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essentially determine the feasible enhancement of spontaneous decay. In particular, strong enhancement can be observed for transition frequencies within the interval in which the surface-guided field resonances strongly overlap. When material absorption becomes significant, then the highly structured emission pattern that can be observed when radiative losses dominate reduces to that of a strongly absorbing mirror. Accordingly, nonradiative decay becomes dominant. In particular, if the distance between the atom and the surface of the microsphere is small enough, the decay becomes purely nonradiative.
Quadrupole radiation of an atom in the vicinity of a dielectric microsphere
Physical Review A, 1996
The process of quadrupole radiation of an atom in the vicinity of a dielectric sphere is considered within the framework of both quantum-mechanical and classical approaches. It is shown that spontaneous transition probabilities can be calculated correctly within the framework of the classical approach. The quadrupole transition probability is shown to be capable of increasing by several orders of magnitude in the neighborhood of the microsphere, to become comparable with the intensity of dipole transitions, the frequency shifts calculated in the classical approximation being much greater than in the case of dipole transitions. ͓S1050-2947͑96͒06410-4͔
Spontaneous Emission of Europium Ions Embedded in Dielectric Nanospheres
Physical Review Letters, 2002
We measure fluorescence lifetimes of emitters embedded in isolated single dielectric nanospheres. By varying the diameters of the spheres from 100 nm to 2 m and by modifying their dielectric surrounding, we demonstrate a systematic change of paradigm in the spontaneous emission rate, as we cross the border from the superwavelength regime of Mie resonances to the nanoscopic realm of Rayleigh scattering. Our data show inhibition of the spontaneous emission up to 3 times and are in excellent agreement with the results of analytical calculations. Spontaneous emission can be described by the interaction of an atomic dipole with the electromagnetic vacuum field [1]. It is therefore possible to modify the decay rate of an atomic excited state by placing it in a confined geometry where the vacuum fluctuations are altered due to reflections from boundaries . Drexhage demonstrated this in 1970 by examining a flat mirror very close to a thin fluorescent layer [3] while many other groups have modified the radiative decay rate of emitters by putting them between two flat reflectors [4], between mirrors of high-finesse optical cavities , and in whispering gallery mode resonators . In addition to superwavelength geometries, one might also expect that the presence of nanometer scale material could lead to the scattering of the vacuum field and therefore modification of the spontaneous emission rate. Indeed, several theoretical reports have predicted this phenomenon for an atom in the near field of nanoscopic spheroids, sharp tips, and substrates with lateral nanostructures [7], as well as for atoms inside subwavelength spheres . Experimentally, a few reports have indicated that the fluorescence lifetime of chromium ions in ruby microcrystals [10], of color centers in diamond nanocrystals , and of emitters in ensembles of colloidal particles [12,13] differ from their bulk values. However, quantitative and conclusive investigations have been lacking. In this Letter we present a systematic demonstration that the spontaneous emission rate of ions placed in dielectric spheres is substantially reduced as one crosses the border from the superwavelength regime of Mie resonances to the nanoscopic realm of Rayleigh scattering.
Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets
Physical Review Letters, 1991
Cavity-QED-enhanced stimulated visible emission was observed in 14-pm-diam rhodamine-66-ethanol droplets pumped by cw 514.5-nm radiation. Use of droplets provides an excellent test of cavity QED theory for spherical geometries. The mode number and order of the spherical-cavity resonances responsible for the observed emission peaks were identified and their Q values calculated from Lorenz-Mie theory. By equating stimulated gain to calculated/measured cavity losses, it was determined that spherical-cavity g's of only 10 -10 lead to cavity QED enhancements in excess of 120 in the emission cross section of rhodamine 66, consistent with theory.