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Journal of the Optical Society of America B

Emission power of an electric dipole in the photonic band structure of the fcc lattice

Toshio Suzuki, Paul K. L. Yu

Published Apr 1, 1995• 111 citations
Publisher

Abstract

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.

DOI
10.1364/josab.12.000570

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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.
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.
The lifetime distribution functions of the spontaneous emission (SE) of the excited atoms embedded in two-dimensional (2D) photonic crystals (PCs) with square lattice, consisting of square air rods in dielectric medium with different filling factors, are calculated by using the plane wave expansion method. The numerical results show that the SE in the 2D PCs cannot be prohibited completely but it can be inhibited intensively by the pseudo-PBG of the PCs. In the pseudoband edges, the SE is accelerated obviously. The reduced average lifetime of the excited atoms and the extension of the reduced lifetime distribution in the 2D PCs both are the same as those in the 3D PCs in the order of magnitude. Our results provide an available way to control the behavior of the SE by changing the structures of the 2D PCs.
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.
Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.
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.