Electromagnetically Induced Single And Multiple Photonic Bandgaps Structure And Phase Grating

In this thesis, based on electromagnetically induced transparency, we study the double and multiple photonic band gaps and phase grating induced by the standing-wave field, which consists of four parts.I. All-optical routing using dynamically induced transparency windows and photonic band gapsIn this part, we investigate the optical response of a Tripod system coupled by a travelling-wave (TW) and a perfect standing-wave (SW) field. First, we calculate the Bloch vector and corresponding reflection and transmission spectra in the case of the same detunings of two coupling fields (Δc=Ag). We find that if the Rabi frequency of TW equals to zero, i.e., this four level Tripod-type system degenerates into a three levelΔ-type one, the photonic bandgap (PBG) cannot be well formed due to the absorption at nodes of perfect SW. However, if the Rabi frequency of TW is not zero, a nearly perfect photonic bandgap appears with reflectivity exceeding 95%.Second, we consider the case that the SW grating and the TW coupling may be assigned to have different detunings (Δc≠Δg). From the reflection and transmission spectra, we find a high-transmission region with comparable width appear besides a high-reflection band gap. This is because the TW coupling and the SW grating effectively interact with the weak probe at different probe detuningsΔp via two-photon transitions whenΔc is different with Ag, and the two effectively interaction atΔc andΔg correspond to an electromagnetically induced transparency window (high-transmission region) and a photonic bandgap (high-reflection region). Moreover, the positions of transmission region and reflection region are mainly determined byΔc andΔg, respectively. Thus, the high-reflection and the high-transmission region may exchange their positions as we modulate the TW and SW detunings as well as the misaligned angle of the forward and backward components of SW.We devise an efficient scheme for the all-optical routing of weak light signals using the high-transmission region and the high-reflection band gap with controllable positions and widths. The schematic is showed in Fig.1, where A, B and C are the nodes in information network. In particular, node B is the Tripod-type system dressed by a TW coupling and a perfect SW grating. The two signals labeled by 1 and 2 overlap in space and time. If the frequency of signal 1 falls in the high-transmission region while that of signal 2 falls in the high-reflection region, signal 1 will be routed (transmitted) into the t channel toward node C while signal 2 will be routed (reflected) into the r channel toward node A. If we make the two regions exchange their positions by modulating the parameters of two couplings, the routing process is totally inversed to allow signal 1 (signal 2) going into the r channel (the t channel). II. Dynamically induced double photonic bandgaps in the presence of spontaneously generated coherenceIn this part, we develop a double-PBG structure induced by a SW field in the presence of spontaneously generated coherence (SGC). The system we investigate is a double-A system consisting of two closely lying upper doublets coupled to a low level by a strong SW field and another low populated level by a weak probe field. There are coherences generated by spontaneous emission from doublets to two ground states, the intensities of which are represented by p1 and p2, respectively. By calculating the PBG structure and the reflection spectra, we find that no matter in symmetric or dissymmetric system, two symmetric PBGs with high reflectivities are generated at left and right wings of the probe resonance in the presence of p1=p2=1 and both PBGs become poorly developed and hardly defined with reduced probe reflectivities when either p1 or p2 is decreased to weaken the SGC effect. However, to obtain the good double-PBG structure, in symmetric system both p1 and p2 should be maximal, while in dissymmetric system only p1 need to be maximal. Through the reflection spectra in different SGC intensities, we explain the formation of two well developed PBGs. The underlying physics is that the SW coupling splits the transparent background into two space-dependent EIT windows, and SGC can suppress the absorption at SW nodes further which provided a high transparent background. At last we discuss the impacts of Rabi frequency of SW field and the interval of the doublets on the two PBGs. When Rabi frequency of SW gradually increases, the width of two PBGs get wider and wider accompanying with the reduction of their reflectivities. As the interval of the doublets increase gradually, the reflection rates of the two bandgaps, firstly, increase gradually, and then begin to decline.III. Triple photonic band gap structure and expansion. So far all investigations on dynamically induced PBGs are restricted in the controlled generation and potential application of one or two band-gaps. In this part, we extend our research on single and double PBGs and demonstrate a feasible scheme for generation of multiple PBGs. We first study a triple-A system interacting with a weak probe field and a strong driving field as well as exhibiting the SGC effects on both probe transitions and driving transitions. By analyzing the optical response of this system with transfer-matrix method, we can see that in the presence of maximal SGC on both probe and driving transitions, a triple-PBG structure manifests with probe reflectivities up to 92% in three different spectral regions. However, when the intensity of SGC on either probe or driving transition decreases, the probe absorption arising from nodes of SW within three EIT windows gets larger so that the reflectivities inside all the three bandgaps become smaller, which means the three PBGs are destroyed. Considering the difficulty of finding an atom or molecule existing SGC effect, we obtain the triple-PBG structure in a five-level chain-A system without SGC which in the dressed state representation of two additional TW coupling fields is equivalent to a five-level triple-A system with SGC. Then we study the impact of Rabi frequency of coupling fields on three bandgaps in order to determine the conditions for perfect bandgaps. Analyzing the results from the preceding investigations of double- and triple-PBG structures, we believe that more PBGs may be simultaneously generated in multiple-A system and chain-A system.IV. Electromagnetically induced phase gratingWe first introduce a method from a paper for achieving giant Kerr nonlinearities between two weak laser beams, which is based on Raman resonance with far detuning from the excited state to eliminate the two-photon absorption. The key advantage of our scheme over EIT is that the coupling laser beam can be arbitrary small even at the several photons level. The key disadvantage is that the single-photon linear absorption of beams is not eliminated. However the single-photon linear absorption can be suppressed by enlarging the detuning between the Raman transition and the excited state. On these bases, we introduce a SW control field instead of TW control field in this Raman transition and then propose an electromagnetically induced phase grating (EIG). For the case in which the incident probe laser is a plane wave, we show the Fraunhofer diffraction by the Fourier transform and find that the first-order diffraction efficiency of the grating exceeds 30%. From the analysis expression of the transmission and phase shift, we find a large phase modulation of the transmission function is observed reaching a peak phase shift value ofπ, and the transmissivity is not relevant to the intensity of control field, i.e., transmissivity is space-independent. Thus this phase grating is very close to an ideal sinusoidal phase grating. In order to find the experimentally achievable parameters, we show how the parameters such as detuning, the dephasing rate of Raman transition and interval of separation of the two Raman resonances affect the diffraction efficiency. Compared with the phase grating based on the Kerr nonlinearity of an atomic medium under electromagnetically induced transparency, the diffraction efficiency of this grating proposed here is high with a lower absorption length of sample and the intensity of the control field may be extremely weak.