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Annual Meeting Optical Society of America

Atomic emission rates in photonic band structures

Jonathan P. Dowling, Charles M. Bowden

Published Jan 1, 1992• 0 citations
Publisher

Abstract

There has been a great deal of interest lately in periodic dielectric materials that exhibit photonic band structures. One of the more interesting features of such a substance is its ability to alter the emission rate of probe atoms embedded in the periodic lattice. Large enhancements and complete inhibition of emission rates can be obtained. It has been known for some time that the influence of a cavity on atomic emission is essentially a classical effect. Hence, we develop a general classical treatment of radiation rates in an inhomogeneous medium. Our results agree with those of a fully quantum calculation, and are applied to a simple scalar model of a dipole in a one-dimensional periodic lattice of the Kronig-Penney type.

DOI
10.1364/oam.1992.fee6

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There has been a great deal of interest lately in periodic dielectric materials that exhibit photonic band structures. One of the more interesting features of such a substance is its ability to alter the emission rate of probe atoms embedded in the periodic lattice. Large enhancements and complete inhibition of emission rates can be obtained. It has been known for some time that the influence of a cavity on atomic emission is essentially a classical effect. Hence, we develop a general classical treatment of radiation rates in an inhomogeneous medium. Our results agree with those of a fully quantum calculation, and are applied to a simple scalar model of a dipole in a one-dimensional periodic lattice of the Kronig-Penney type.
There has been a great deal of interest in periodic dielectric materials that exhibit photonic band structures. One of the more interesting features of such a substance is its ability to alter the emission rate of probe atoms embedded in the periodic lattice. Large enhancements and complete inhibition of emission rates can be obtained. It has been known for some time that the influence of a cavity on atomic emission is essentially a classical effect. Hence, we develop a general classical treatment of radiation rates in an inhomogenous medium. Our results agree with those of a fully quantum calculation, and are applied to a simple scalar model of a dipole in a one-dimensional periodic lattice of the Kronig-Penney type.
A photonic crystal, defined as a periodic dielectric structure, can influence the radiation rate of an embedded dipolar emitter. A theory of this effect is developed and the efficiency of a dipolar photonic source is calculated for a realistic three-dimensional crystal. Taking as a starting point the photonic band structure and its associated eigenfields, it is shown that the emission rate is strongly correlated with the density of modes, but also that the density of modes alone cannot explain all features found in the emission spectrum. For an infinite crystal, the computation of the field propagator confirms that the emission rate falls to zero in the frequency range defined by the photonic band gap. The emitter lifetime changes with the dipole location and orientation, leading to a radiation rate enhancement or inhibition according to the direction of the emission. These results may open routes to photonic sources with very high quantum efficiency.
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.
It has been suggested that spontaneous emission can be inhibited if atomic transition frequencies fall inside photonic band gaps, that is, three-dimensional frequency stop bands of electromagnetic waves generated by three-dimensional periodic dielectric materials (photonic crystals). There has been a growing interest in how atomic emission spectra are changed quantitatively inside the photonic crystals. We develop a classical theory for the calculation of the emission power from the electric dipole located in three-dimensional photonic crystals by incorporating the plane-wave method, dyadic Green’s function, Poynting theorem, and tetrahedron k-space integration. With the method we perform numerical computations for the emission power of an electric dipole located in the photonic crystals of the fcc lattice structure with spherical atoms. The results show the total inhibition of emission in the photonic band gap as well as strong enhancement around the band edges. In addition, the data indicate the strong dependencies of the emission spectrum on the dipole position and the dipole moment in the photonic crystal.
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.
This paper considers an exact model of atomic spontaneous dipole emission and classical dipole radiation in a finite photonic bandgap (PBG) structure. The full three-dimensional (3-D) or two-dimensional (2-D) problem is reduced to a finite one-dimensional (1-D) model, which then is solved for analytically using algebraic matrix transfer techniques. The results give insight to the electromagnetic emission process in periodic dielectrics, quantitative predictions for emission in 1-D dielectric stacks, and qualitative formulas for the 2-D and 3-D problem.