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AIP conference proceedings

Radiation dynamics of a spin system in a photonic band gap material

Christian Wolff, U. Hoeppe, H. Benner, Kurt Busch

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.4750107

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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.
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.
In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.
In the first part of this introductory review we outline the developments in photonic band gap materials from the physics of photonic band gap formation to the fabrication and potential applications of photonic crystals. We briefly describe the analogies between electron and photon localization, present a simple model of a band structure calculation and describe some of the techniques used for fabricating photonic crystals. Also some applications in the field of photonics and optical circuitry are briefly presented. In the second part, we discuss the consequences for the interaction between an atom and the light field when the former is embedded in photonic crystals of a specific type, exhibiting a specific form of a gap in the density of states. We first briefly review the standard treatment (Weisskopf – Wigner theory) in describing the dynamics of spontaneous emission in free space from first principles, and then proceed by explaining the alterations needed to properly treat the case of a two-level atom embedded in a photonic band gap material.
We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit. In that situation, the atomic emission occurs in the form of evanescent waves which are detected with less efficiency the farther we place the detector. The methodology presented in this paper may be useful to study the non-Markovian dynamics of any quantum open system in linear interaction with a harmonic oscillator reservoir and within the weak-coupling approximation.
Photonic crystals are optical materials that have an intricate structure with length scales of the order of the wavelength of light. The flow of photons is controlled in a manner analogous to how electrons propagate through semiconductor crystals, i.e., by Bragg diffraction and the formation of band structures. If the interaction between light and matter is made strong, multiple diffraction and multiple scattering effects dominate. A main research goal is the realization of a "photonic band gap", that is, a frequency range for which no light can propagate in a crystal in any direction, which causes radical modifications of the density of radiative states. Important consequences of photonic band gaps are the complete control over spontaneous and stimulated emission of light, as well as over the propagation of light, in particular photon localization. This opens up the possibility to achieve a "cage for light": trap photons and do with them whatever one chooses. In this talk we will also review means for making such structures, and recent experimental advances in optical experiments.