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Non-Markovian Radiation Dynamics in Photonic Band Gap Materials

Christian Wolff, Kurt Busch

Published Jan 1, 2013• 0 citations
Publisher

Abstract

The theoretical analysis of a recent experiment on the modified radiation dynamics of a magnetic dipole emitter embedded in a three-dimensional Photonic Band Gap material is presented. This analysis allows the first-time demonstration of non-Markovian dynamics.
DOI
10.1364/cleo_qels.2013.jm3a.4

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It is our aim to study the dynamics of a two-level atom immersed in the modified radiation field of a photonic band-gap material using non-Markovian stochastic Schr\"odinger equations. Up to now, such methodology has only been applied to toy models and not to physically realistic systems as the one presented here. In order to check its validity, we shall study several of the physical phenomena already described in the literature within non-Markovian master equations, such as the long-time-limit residual population in the excited level of the atom and the population inversion which occurs in the atomic system when applying an external laser field. In addition to the stochastic equation, we propose a non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity. We propose a correlation function for the radiation field (environment) that captures many of the physically relevant aspects of the problem and describes the short-time behavior in a more accurate way than previously proposed ones. This characteristic permits a correct description of the fluctuations of the electromagnetic field, which in the stochastic formalism are represented by the noise, and a better description of the non-Markovian effects in the atomic dynamics. The methodology presented in this paper to apply stochastic Schr\"odinger equations can be followed to study more complex systems, like many-level atoms embedded in more complicated photonic band-gap structures.
The radiation dynamics of a magnetic dipole located inside a photonic crystal has been considered as an analogue for optical emission of a point-like emitter in such a crystal. We have experimentally realized this situation by fixing a single crystal yttrium iron garnet (YIG) sphere of 1.7 mm diameter inside a photonic crystal consisting of dielectric alumina rods. These rods form a woodpile structure of size 16 × 6 × 6 cm3 . The photonic crystal shows a band gap at microwave frequencies between 12.9 and 14.3 GHz as calculated and verified from the transmission characteristics of the crystal. The radiation feedback of the YIG sphere was probed by ferromagnetic resonance experiments covering a large frequency range from 8 to 17 GHz. Whereas outside the band gap the radiation-induced linewidth amounts up to 30 Oe, it is almost completely suppressed inside the gap. From the full analysis of linewidth and resonance shift, we could clearly prove the non-Markovian character of the radiation dynamics at the edges of the gap as expected from theory. The experimental control of spontaneous emission, as realized in our experiment, is a very promising step towards future optical applications in low threshold lasers, highly efficient light emitting diodes or photovoltaic solar modules.
The attempt to control spontaneous emission via modifications of the photonic environment using dielectric or plasmonic nanostructures has been a very active field of research for several decades. In particular the prospect of inhibiting fluorescence altogether by means of a photonic band gap has attracted great interest. In a recent paper, we have fully characterized the full non-Markovian radiation dynamics of a microwave spin system in a woodpile photonic crystal with a complete band gap near 14 GHz and found excellent agreement with ab-initio numerics. Here, we report on numerical details of this work.