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The European Physical Journal D

Dynamics of atomic decay in a special one dimensional photonic crystal

Jing Xu, Yaping Yang

Published Jul 16, 2008• 0 citations
Publisher
DOI
10.1140/epjd/e2008-00139-6

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The dynamic evolution of atomic spontaneous emission in one-dimensional photonic crystals (1DPC) is investigated by using mode functions for the 1DPC. Our attention is focused on the non-Markovian processes in the first several optical cycles of the spontaneous emission decay. The integral-differential dynamic equation is directly solved by numerical calculation without using the Markovian approximation. The interference of the multireflected fields plays an important role in the non-Markovian processes. Due to the interference of the fields successive arrived at the atom due to the reflection at the interfaces, the decay rate shows a series of pulselike peaks. If the interference is constructive, the spontaneous decay is enhanced, while if the interference is destructive, the spontaneous decay is suppressed. The steady decay rate is approximately equal to the vacuum decay rate, when the atomic transition frequency corresponds to an allowed normal mode of the 1DPC. The spontaneous emission decay is suppressed if the atomic transition frequency is within the forbidden gap of the 1DPC.
The dynamical characteristics of the spontaneous decay of a single excited atom or molecule depend strongly on its position within a photonic crystal (PC) and the relative orientation of its dipole and the electric field there. Measuring its dynamical characteristics of the spontaneous decay in a PC can only obtain the local density of states (DOS) in the PC, but cannot reflect the total DOS in the PC. It is found, theoretically, that using different number density distributions of luminescent molecules within the PC, one can probe the partial information or even all of the total DOS in the PC. In this paper, we separate, for the first time to our knowledge, the total DOS into two parts, DOS in the scatterer and DOS in the matrix of the Wigner-Seitz unit cell, according to their origin, and demonstrate that a special number density distribution of fluorescent molecules can reflect the total scatterers DOS or total matrix DOS or even both of them, i.e. the total DOS in the PC. This is meaningful in explaining and designing the experiments of prohibiting and enhancing the spontaneous emission of excited molecules.