Investigation On Negative Refractive Index Based On Incoherent Pump

In physics, the dielectric constant and magnetic permeability are described in the media even the most basic properties of electromagnetic fields two physical quantities. As known in the material world, for the dielectric, the permittivity and permeability are positive, and the electric field, magnetic field and wave vector relationship between the three constitute a right-handed helix, so that the material is known as right-handed materials. This right-hand rule has always been the material world be considered conventional, but in the last century 60's subversive challenges encountered.In 1967, the former Soviet physicist Veselago in the former Soviet Union on an academic journal published a paper and the first time reported the theoretical study of electromagnetic material properties of the new study and found that: when and are negative check, the electric field , between the magnetic field and wave vector relations constitute a left-handed spiral. He said the material for such a hypothetical left-handed materials (negative refractive index characteristics). However, left-handed materials with negative refractive index (with negative permittivity and negative permeability, the electric field, magnetic field and wave vector rule comply with the special left-handed materials) of the development is not smooth sailing. In this subversive concept after a period of several decades, although it has a lot of novelty in nature, such as negative group velocity, inverse Doppler frequency shift, anomalous Cerenkov radiation and imaging lens perfect, but because only at the theoretical level and should not found in nature, the true left-handed materials, the assumption that the academic does not immediately accept, but in a situation where almost no one pay attention to. On this situation until the end of the century, before the beginning of this century a turnaround.Pendry British scientists in 1999, at the same time achieve a negative dielectric permittivity and negative permeability ingenious design, for implementation in the experiment on the foundation left-handed materials.Pendry first designed a micro-structure unit, metallic split ring resonators (SRRS), which can produce strong magnetic response. One SRRS is composed of two concentric ring resonators with small openings. When a magnetic field vertical to the SRRS is applied, according to the Faraday's law of electromagnetic induction, we know that the current and then the inductance will be induced. In addition, due to the space between the inner and outer rings, the capacitance will also exist. Then one can achieve LC resonance related to the geometry size and shape of SRRS, and the magnetic permeability of an array of periodic SRRS can be expressed asPendry also presented a method of realizing negative dielectric permittivity. He found that an array of periodic conductive wires is similar to the plasma as far as its electromagnetic response is concerned. Plasma is a neutral system composed of a large number of charged particles moving almost freely, and its permittivity is given where is the eigen-frequency of a plasma. Clearly, whenω<ω_p, it will have negative values. Usually the eigen-frequency of metallic plasma is in the UV band, so one can achieve negative permittivity in the visible optical band. To facilitate the macroscopic management, one need to realize negative permittivity in the microwave band. This requires much lower eigen-frequency of plasma. An array of periodic metallic wires has very low effective electron density n e and very high effective electron quality m_eff, thus has very low eigen- frequency of plasma, This allows us to achieve negative permittivity with reasonable values in the microwave band.Based on this scheme, several groups in the world have observed the special electromagnetic properties belonged to only left-handed materials, which provides important experimental support for the relevant theories.In 2003, a group in Turkey's Bilkent University realized in experiment the two-dimensional photonic crystal based negative refraction phenomenon using a square lattice structure composed of the sapphire coshes. As a comparison, they repeated their experiment with the plate composed of ordinary polystyrene ball to replace the photonic crystal. Once again, the experimental results agreed well with numerical simulations by showing the negative refraction phenomenon.In the above, we have briefly introduced two different methods for realizing left-handed materials in the microwave band with the classical electromagnetism. In the following, we will introduce a third method for realizing left-handed materials in the optical band, which is based on the electromagnetically induced transparency theory in quantum optics. The basic idea is to utilize quantum coherence effect and local field effect in dense atomic gases to control the permittivity and magnetic permeability of two different transitions so that the two quantities simultaneously have negative values in the same frequency region.This method was first separately proposed by Oktel et al. and Shen et al. where they consider a simple three-levelΛsystem. The energy space between the lowest and the middle levels is the same as that between the middle and the highest levels, and the lowest and middle levels have the same parity while the highest one is different from them in parity. Thus, theΛsystem has one magnetic-dipole transition and one electric-dipole transition at an optical frequency. It is well known that the coupling coefficient for the electric field is 1 /α(α=137 is the fine structure constant) times larger than that for the magnetic field when an optical wave interacts with an atomic system, so one must find a proper way to make the density matrix element on the magnetic -dipole transition much larger than that on the electric-dipole transition so that the permittivity and the magnetic permeability on the two transitions are of the same order. It has been verified that the technique of quantum coherence based on electromagnetically induced transparency can well fulfill this task. To ensure the magnetic permeability and the permittivity negative simultaneously, the atomic density must be large enough so that the local field effect arising from dipole-dipole interaction has to be taken into account.In this thesis, we have further developed a pump-based non-coherent left-handed materials with negative refractive index of the study, namely, at the same time the use of non-coherent pumping and strong coherent coupling field to achieve left-handed materials. Incoherent pump field in the original ground state of the particles on the pump to a higher level, because of the rapid relaxation of the non-radiation, the majority of particles and transition to the metastable energy level up, so that the lowest energy level and the metastable level particles between the number of the population inversion. Coherent coupling field as part of particles will not only pumped up to the highest level and the metastable-level split into two sub-level dressed states. Over the last decade, against left-handed materials with negative refractive index properties, it has carried out many studies and found that the use of non-coherent pumping and strong coherent coupling field coherent control of media can be easily radiation, absorption and dispersion, such as optical properties. We consider a four level atomic system as shown in fig. 1, where levels |1> , |3> and |4> have same parity; and the parity of level 2 is opposite with theirs. Transition between level |2> and |4> is driven by a strong coherent field whose Rabi frequency is . Incoherent pump field drives the populations in ground level |1> into level |3> and its pumping rate denotes asΛ.First of all, in the dipole approximation and rotating wave approximation under the conditions of our interaction from the Hamiltonian of the system, the use of density operator master equation, one group has been all about the density matrix elements of the equations. Then, under the weak field approximation theory and numerical simulation, a detailed study of our non-coherent and incoherent pumping rate of coupling field Rabi frequency, such as parameters on the dielectric constant and magnetic permeability of the impact. The results showed that, when the atomic gas density is large enough, they can at a certain frequency range so that the dielectric constant and magnetic permeability at the same time the real part is negative, that is, left-handed materials achieve negative refraction, as shown in Figure 2.The property of negative refraction of the system is dependent with the pump rateΛand Rabi frequency of the coherent fieldΩc. With the incoherent pump rateΛ=0 the system can be treated as a three-level ladder-type EIT system composed of levels 1 , 2 and 4 . There is no coherence between level pair andα_m=0. As in fig.3, It has no sense for the left-handedness.In order to prove the effect of quantum coherent electromagnetically induced left-handedness, we show that the real and imaginary parts of the relative electric permittivityεr and magnetic permeabilityμr verus probe frequency in figure 4 under the condition that Rabi frequency of the coherent fieldΩc=0. It turns to be a traditional optical amplification system composed of levels |1> , |2> and |3> . From figure 4, we find that simultaneous negative permittivity and permeability can either not happen in some range or occur in other frequency range but the magnetic part of the probe field will endure strong absorption in the medium. So it is necessary for our system to get electromagnetically induced left-handedness by using both coherent field and incoherent pump simultaneously.Our research work to further develop a left-handed materials can achieve coherent atom gas method, and for the first time non-coherent pumping of quantum coherence effects taken into account, thus increasing the control of left-handed materials with negative refractive index and other optical properties of the neo-liberal degrees, and some new conclusions.