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Theoretical and experimental investigation of radiative decay rates in active slot waveguides

Celestino Creatore, Lucio Claudio Andreani, Galli, M, M. Miritello, Roberto Lo Savio, Francesco Priolo, ,, ,

Published Nov 1, 2009• 0 citations
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Abstract

We present a quantum-electrodynamical formalism to study the spontaneous emission from dipoles embedded in a non-absorbing and lossless multilayer dielectric structure. In this model the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical modes and the analytical expressions for the emission rates are obtained within the framework of perturbation theory. We apply our model to investigate the 1.54 μm transition of Er 3+ -doped SiO 2 thin layers acting as active material in planar slot waveguides in polycrystalline silicon. The theoretical results show that a strong reduction of the radiative lifetime does occur in the slot waveguide. Furthermore, by using the theoretical analysis together with photoluminescence measurements, we estimate also the radiative efficiency which is found to be only slightly reduced with respect to the value for Er 3+ in a bulk of SiO 2 . These results are important for future realization of silicon-compatible active optical devices and show the relevance of our model to study the spontaneous emission processes in multilayer structures.

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We present a quantum-electrodynamical formalism to study the spontaneous emission from dipoles embedded in a non-absorbing and lossless multilayer dielectric structure. In this model the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical modes and the analytical expressions for the emission rates are obtained within the framework of perturbation theory. We apply our model to investigate the 1.54 μm transition of Er 3+ -doped SiO 2 thin layers acting as active material in planar slot waveguides in polycrystalline silicon. The theoretical results show that a strong reduction of the radiative lifetime does occur in the slot waveguide. Furthermore, by using the theoretical analysis together with photoluminescence measurements, we estimate also the radiative efficiency which is found to be only slightly reduced with respect to the value for Er 3+ in a bulk of SiO 2 . These results are important for future realization of silicon-compatible active optical devices and show the relevance of our model to study the spontaneous emission processes in multilayer structures.
We present a quantum-electrodynamical formalism to study the spontaneous emission from dipoles embedded in a non-absorbing and lossless multilayer dielectric structure. In this model the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical modes and the analytical expressions for the emission rates are obtained within the framework of perturbation theory. We apply our model to investigate the 1.54??m transition of Er3+-doped SiO2 thin layers acting as active material in planar slot waveguides in polycrystalline silicon. The theoretical results show that a strong reduction of the radiative lifetime does occur in the slot waveguide. Furthermore, by using the theoretical analysis together with photoluminescence measurements, we estimate also the radiative efficiency which is found to be only slightly reduced with respect to the value for Er3+ in a bulk of SiO2. These results are important for future realization of silicon-compatible active optical devices and show the relevance of our model to study the spontaneous emission processes in multilayer structures.
A complete set of cavity modes in planar dielectric multilayer structures is presented which naturally includes the guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incident on the stack from the air and from the substrate. Using this set of cavity modes, we present a quantization scheme in idealized lossless stratified dielectric structures. This enables us to discuss the vacuum quantum fluctuations of the fields within the multilayer stack. The spontaneous emission of photons by a two-level atom located at any position inside the stratified planar structure is derived using the quantum approach and standard perturbation theory. The spontaneous emission rate as well as the radiation pattern in the air, in the substrate and in the guided mode are presented. Finally, a numerical analysis of the radiative properties of an erbium atom located in an asymmetrical Fabry - Perot multilayer structure is investigated. We show that a large part of the emitted power is directed in one half-space although a significant amount of light remains trapped in the guided modes of the structure.
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
A general analysis of spontaneous emission in the vicinity of a symmetric slab dielectric waveguide is presented using explicit energy-normalized functions for the complete set of bound and radiating TE and TM modes. Expressions for the spontaneous emission rates are derived for each mode type, and calculated results are presented illustrating the emission behavior as a function of the position of the radiating atom, for various slab waveguides. The model is used to analyze the spontaneous emission coupling efficiency to guided modes in planar erbium-doped amplifier structures. Spontaneous emission factors for the TE and TM modes are calculated for the cases of erbium doping of the core and of the cladding.>
A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-P\'erot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-P\'erot resonance, which increases the spontaneous emission rate in a normal direction. \textcopyright{} 1996 The American Physical Society.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.