The Spontaneous Emission Of An Atom In A Semi-Infinite Rectangular Waveguide

Spontaneous emission is a process of a atom transition from the high level states to the low level states spontaneously in the absence of external effect, and emit a photon simultaneously, it is the most basic interact performance between light field and substances. Usually, we studies the spontaneous radiation of atoms interact with the vacuum (i.e.,free space). The spontaneous emission in vacuum is the result of the interaction between atoms and the vacuum electromagnetic field, and the spontaneous emission rate is exponential decay with time. When the environment surrounding atom changes, the spontaneous emission phenomenon will change also.We consider a two-level atom which interact with a semi-infinite long rectan-gular waveguide (i.e., existing a single-end) in this paper, and study the atom’s spontaneous emission characteristics. Semi-infinite long rectangular waveguide’s dispersion relation is the function of wave vector, and the wave vector is continu-ous variation quantity, this is the common point with free space. The different is, semi-infinite long rectangular waveguide’s dispersion relationship is nonlinear, there is a cutoff frequency, and have transverse mode, an unlimited number of transverse mode, each transverse mode has a cut-off frequency. According to these characteris-tics, we consider it with the atomic transition frequency ω0 increase gradually from low to high.When the atomic transition frequency ω0 is lower than the first mode cutoff frequency Ω1, using Weisskopf-Wigner approximation, we found that the spontaneous radiation are suppressed. When ω0 is very close to Ω1, the atom jump to the ground state quickly. When ω0 add to the between the first and second trans-verse mode cutoff frequency Ω1,Ω2, but not close to the two cut-off frequency value, We got the atomic excited amplitudes’delay differential equation, by the dispersion relation of linear approximation, we see the atomic excited amplitudes deviate from the exponential decay, show us the oscillation, there will be one or more peaks, and the size of the peak decreases with time. When ω0 continue to increase to more than Ω2, and very close to Ω2, at this point, there are two modes interact with atoms, use Weisskopf-Wigner approximation again, we found that the second wave mode can make the atoms decay to the ground state quickly. When Q2<ω0<Ω3, and be away from the two cut-off frequency, by linear approximation,we found that the atomic excited amplitudes also deviates from the exponential decay, show us oscil-lation. Different from single mode, the two mode’s decay more faster, the size of its peak decreases faster too. In addition, we also consider the influence of the atomic position. Keep the atoms’cross-section position unchanged, change the distances in the direction of propagation in the waveguide, we found that, when atom in the waveguide border, it back to the exponential decay with time. When ω0 is located in the frequency band between Ω1 and Ω2, the T M11 guiding mode contribute to the spontaneous rate. There is an enhancement or inhibition of spontaneous decay depending on the factor cos(kz0).In a node of the wave cos(kzo), spontaneous decay is inhibited while in an antinode it is enhanced.Q2<ω0<Ω3, the atom interacts with the continua of two guiding modes TM11 and TM31. The spontaneous rate increases although it still depends on z0. As ω0 increases, more and more guiding modes are included to increase the spontaneous rate.