Stationary Light Pulse And Tunable Photonic Stop Bands In Solids And Direct Generation Of Stationary Light Pulse In Gas

In this thesis for doctorate we study the several phenomena based on the standing wave coupled electromagnetically induced transparency (EIT). The experimental and theoretical studies based on EIT can be roughly divided into two categories. As shown in the Fig 1, the first one is the travelling wave coupled EIT, and the second on is the standing wave coupled EIT. 1 The SLP in solids with long-lived coherenceWe consider the four-level doubleΛsystem with two excited levels 3 and 4 and two lower levels 1 and 2 . The inhomogeneous broadenings are need to be considered in the solid materials. Fig. 3. show the main idea of the algorithm on the calculating such broadenings.The level 4 of those ions are distributed over a small range because of the inhomogeneous broadening of the transition 4 - 3 which could be regarded as the same as that of the spin transition 2 - 1. So, after we treat the broadening of 3 - 1 as the optical broadening ( F opt), the broadening of 4 - 1 should be We obtain three necessary conditions for realize the SLP in solid by solving the density equations and the Maxwell equations.1) The decoherence rate of the optical transitions are equal.2) The inhomogeneous broadenings of the coherence transition is much smaller as compared with that of the optical transitions.3) The coupling fields are so stronger than probe pulse that makes most of the ions are on the ground state. We obtain the analytical solution of Maxwell equations which clearly indicate that the SLP in solids undergoes the decay and diffusion process. inhomogeneous broadening of the spin (optical) transition. As we can see from the above equations, the decay (diffuse) process is associated with the broadenings of the spin (optical) transitions. According to our calculations, the life-time of the stationary light pulse is depended on Gs?p1 in2 The direct conversion of slow light to stationary light pulse We consider an ensemble of double-Λ-type four-level atoms comprising two excited state 3 , 4 and two lower states 1 , 2 which represent the hyperfine states of 87 Rb , as shown in Fig. 3. We focus on anther form of stationary light pulse here. As shown Fig. 4. The forward coupling field is always on to make sure the probe pulse travelling as slow light. Then, the backward coupling field is switched on to transform the slow light pulse By solving the density matrix element equations and the Maxwell equations, we obtain the mathematical expression of the DSLP. We can obtain the characteristic length of the medium: L0 =Γβ. Whereβis the constant in Maxwell equations. For the medium we choose here,β= 9.27×10⁹ (IU). Largerβvalues means that the differential of the electric fields change more severely to make the DSLP generated more quickly.Γis the population decay rate of the optical transition. HereΓequals In order to describe such system, the inhomogeneous broadening of the transitions must be taken into account. We need to integrate the steady-state solution of the density element equations over the entire range of the inhomogeneous broadenings. The refractive index experienced by the probe can be described by a dressed dielectric function: The larger coupling Rabi frequency makes more atoms to participate in the interaction. But it also affect the depth and the width of the EIT window to smooth the spatial variation of the refractive index. Fig. 8 shows the reflectivity and absorption of the optical crystals under different coupling Rabi frequencies. We assume that R₂ = R₃ = R. The smaller R can enhance the coupling strength at wave nodes to force more atom participate into the interaction, but it will also smooth the spatial variation of the refractive index. Fig 9 shows the spatial variation of the the refractive index depends on the parameterα= x- x'λ. Fig 11 shows the relation between the band-gap andα divided into two parts. Using the theory of dressed state, this phenomenon can be perfectly explained. When there is only a standing waveΩ2, the level 4 is split into two dressed states + and ? . Then considering the other standing waveΩ3 is introduced into the system, and two band-gap is form byΩ3. Fig 12 shows the split of the band-gap under different coupling frequencies.In Summary, We investigate the three kinds of physical phenomena which all based on the standing wave coupled EIT: 1, the stationary light pulse in solids with long-lived coherences. 2, the direct stationary light pulse. 3, the photonic stop bands in Pr:YSO. We expect that our general analysis my prompt a more exhaustive understanding of the standing wave coupled EIT.