Anomalous electromagnetically induced transparency in photonic-band-gap materials Mahi R. Singh Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada N6A 3K7 (Received 3 July 2003; revised manuscript received 3 May 2004; published 28 September 2004) The phenomenon of electromagnetically induced transparency has been studied when a four-level atom is located in a photonic band gap material. Quantum interference is introduced by driving the two upper levels of the atom with a strong pump laser field. The top level and one of the ground levels are coupled by a weak probe laser field and absorption takes place between these two states. The susceptibility due to the absorption for this transition has been calculated by using the master equation method in linear response theory. Numerical simulations are performed for the real and imaginary parts of the susceptibility for a photonic band gap material whose gap-midgap ratio is 21%. It is found that when resonance frequencies lie within the band, the medium becomes transparent under the action of the strong pump laser field. More interesting results are found when one of the resonance frequencies lies at the band edge and within the band gap. When the resonance frequency lies at the band edge, the medium becomes nontransparent even under a strong pump laser field. On the other hand, when the resonance frequency lies within the band gap, the medium becomes transparent even under a weak pump laser field. In summary, we found that the medium can be transformed from the transparent state to the nontransparent state just by changing the location of the resonance frequency. We call these two effects anomalous electromagnetically induced transparency. DOI: 10.1103/PhysRevA.70.033813 PACS number(s): 42.50.Gy, 42.70.-a, 78.20.Ci, 78.20.Bh I. INTRODUCTION Recently, there has been considerable interest in studying the phenomenon of quantum interference in atomic systems [1–9]. The interest stems from the early work of Agarwal [2] who showed that the ordinary spontaneous decay of an ex- cited degenerate V-type three-level atom can be modified due to the interference between the two atomic transitions. Since then, many interesting results have been found such as elec- tromagnetically induced transparency (EIT) [3], high- contrast resonance [4], lasing without inversion [5], amplifi- cation without population inversion [5,6], enhancement of the index of refraction without absorption [7], ultraslow ve- locities of light [8], and coherent population trapping [9]. The aim of the present paper is to study EIT in photonic band gap (PBG) and dispersive polaritonic band gap (DPBG) materials due to their unusual optical properties and potential applications [10–18]. There exists an energy gap in their photon (polariton) dispersion relations. In PBG materials, the existence of the energy gap is due to the multiple photon scattering with spatially correlated scatterers [10], while in DPBG materials such as semiconductors and dielectrics, the energy gap is caused by photons coupling with elementary excitations (excitons, optical phonons, etc.) of the media [17]. Recently, Paspalakis et al. and Angelakis et al. have stud- ied EIT in -type three-level atoms placed in a modified vacuum interacting with a laser probe field and a reservoir [14]. They assumed that the reservoir has an inverse square- root singularity in its density of states and can be a PBG material. They found that transparency can occur in steady state absorption when one of the atomic transitions is coupled to the reservoir. Here, the transparency occurs due to the singularity in the density of states. Generally, EIT occurs through the application of a pair of strong and weak laser fields [1]. John and Quang [15] have studied the self-induced trans- parency and the dielectric response of the impurity two-level atoms placed within an imperfect linear dielectric PBG ma- terial interacting with a probe laser field. They considered that the response dipole-dipole interaction (RDDI) is medi- ated by the exchange of high-energy virtual photons between the atoms. The atoms are randomly distributed and their atomic positions are modeled by means of a Gaussian distri- bution of the RDDI’s. When the Rabi frequency associated with the probe laser field exceeds the RDDI energy, the imaginary part of the susceptibility saturates, whereas the real part of the nonlinear susceptibility remains large. Thus PBG materials may act as nearly lossless, but highly nonlin- ear dielectrics. For a broad range of parameters, the glassy behavior of the atomic system is dominant. They suggested that the resonant, lossless, nonlinearity associated with the glass state may lead to self-induced transparency in a PBG material. Rostovtsev et al. [16] have investigated the EIT effect due to the nonlinear propagation of light waves in the forbidden region of nonlinear PBG materials. Their model PBG mate- rial consists of one-dimensional hetrostructures formed by a spatially modulated density of optically active -type three- level atoms. An intense probe laser field interacts with atoms. This produces a periodic nonlinear dielectric structure which produces an energy gap in the system. The gap depends on the spatial modulation of the density of atoms and the non- linear dielectric constant produced by these atoms. These structures are called nonlinear PBG materials. They calcu- lated the dispersion relation of this model structure and found the EIT effect for waves with frequency lying in the forbidden range. Here EIT occurs due to the periodic nonlin- ear dielectric constant produced by the doped atoms. In this paper, we study the EIT effect when noninteracting four-level atoms are located in linear dielectric PBG and DPBG materials. Quantum interference is introduced by PHYSICAL REVIEW A 70, 033813 (2004) 1050-2947/2004/70(3)/033813(7)/$22.50 ©2004 The American Physical Society 70 033813-1