Characteristics Of Atomic Spontaneous Emission In Photonic Crystal Waveguide

Spontaneous emission is considered as one of the most severe limiting factor for many novel techniques in modern quantum optics,such as high frequency lasers,high precision measurement,and quantum information processing.An important interest of modern quantum optics is to find ways to modify and control the spontaneous emission,and the study of spontaneous emission in metallic cavity and photonic crystal is an important part of it.Principally,these two structures have different functions to modify the spontaneous emission,which can be accelerated or inhibited by the resonant mechanism in metallic cavity as well as the photonic band gap structure in photonic crystal.With combining both metallic cavity and photonic crystal,we present a type of photonic crystal waveguide that is composed of one dimensional photonic crystal with perfectly conducting boundary conditions in the two lateral directions at the periphery of the photonic crystal resulting square cross-section.We deducted the dispersion relations of the photonic crystal waveguide and calculated the photonic density of states and local photonic density of states by using the electrodynamical method.The characteristics of spontaneous emission in it is reveal through the study of lifetime distribution function.It is found that the combined action of the quantization of wave number in vertical-periodic directions and the dispersion relations of the photonic crystal can give rise to complete photonic band gaps and sharp peaks in photonic density of states when the confined width is compare to the lattice constant in the periodical direction, which leads to a wide lifetime distribution with the coexistence of accelerated and suppressed decay process of the atomic spontaneous emission.Moreover, the investigation of the local photonic density of states discloses the variation of spontaneous emission versus spatial coordinates.