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AIP conference proceedings

Classical and Quantum Light Propagation in One-dimensional Finite Photonic Crystals

А. С. Малоштан, Dmitry N. Chigrin

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We present theoretical approach for description of a classical light propagation and an atom‐field interaction for a system of two level atoms in one dimensional finite photonic crystal (PC). Classical light propagation description based on Green’s functions technique. Atoms are interacting with a quantized light field mode propagating thought the photonic crystal. By using this model it is possible to consider time‐spatial excitation distribution and the single photon shape transformation by finite one‐dimensional PC.

DOI
10.1063/1.3253887

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We present theoretical approach for description of a classical light propagation and an atom‐field interaction for a system of two level atoms in one dimensional finite photonic crystal (PC). Classical light propagation description based on Green’s functions technique. Atoms are interacting with a quantized light field mode propagating thought the photonic crystal. By using this model it is possible to consider time‐spatial excitation distribution and the single photon shape transformation by finite one‐dimensional PC.
A model of the propagation of a quantized electromagnetic field in a one-dimensional photonic crystal that contains two-level atoms that interact with the field is proposed. The model separately considers the interaction of the quantized radiation with the quantum system and with the photonic crystal. The use of the model is exemplified by its application to the study of the decay of excited states of one- and two-level atoms placed in the photonic crystal. The possibility of the transformation of the front of a single photon by a finite dielectric is demonstrated.
Based on a formalism that describes atom-light interactions in terms of the classical electromagnetic Green's function, we study the optical response of atoms and other quantum emitters coupled to one-dimensional photonic structures, such as cavities, waveguides, and photonic crystals. We demonstrate a clear mapping between the transmission spectra and the local Green's function, identifying signatures of dispersive and dissipative interactions between atoms. We also demonstrate the applicability of our analysis to problems involving three-level atoms, such as electromagnetically induced transparency. Finally we examine recent experiments, and anticipate future observations of atom-atom interactions in photonic band gaps.
We investigate spontaneous emission from a two-level atom embedded in a photonic crystals with three-dimensional dispersion relation, where the dependence of wave vectors on direction is taken into account. Due to the difference of the density of states of electromagnetic modes between a three-dimensional and a one-dimensional photonic crystal (lack of singularity), the dynamics of the population in the excited state and the emitted field are quite different from those of a one-dimensional photonic crystal. There is no quasi-oscillation for the population evolution. The localized field and the propagating field cannot coexist. When the upper level moves from the gap to the band, the emitted field changes from a localized field to a diffusion field and then to a propagating field. The energy of the diffusion and propagating fields propagates out incoherently and coherently, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is smaller than that in an ordinary vacuum or in one-dimensional photonic crystals.
We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses.
We investigate the spontaneous emission (SpE) of a two-level atom embedded in one-dimensional photonic crystals composed of left-hand material (LHM) and right-hand material. A complete set of mode functions is constructed for quantizing the radiation field. The radiated field distribution under the condition of impedance matching is calculated. The radiated field is focused in each layer and propagates along the direction normal to each layer due to the LHM. With such a structure we can control the propagation of the SpE field without changing the SpE rate.