International Journal of Modern Physics B

Band structure of one-dimensional doped photonic crystal with three level atoms using the Fresnel coefficients method

Akbar Jafari, A. Rahmat, S. Bakkeshizadeh

Published Aug 11, 2017• 0 citations

Abstract

We consider a one-dimensional photonic crystal (1DPC) composed of double-layered dielectrics. Electric permittivity and magnetic permeability of this crystal depends on the incident electromagnetic wave frequency. We suppose that three level atoms have been added to the second layer of each dielectric and this photonic crystal (PC) has been doped. These atoms can be added to the layer with different rates. In this paper, we have calculated and compared the band structure of the mentioned PC considering the effect of added atoms to the second layer with different rates through the Fresnel coefficients method. We find out that according to the effective medium theory, the electric permittivity of the second layer changes. Also the band structure of PC for both TE and TM polarizations changes, too. The width of bandgaps related to “zero averaged refractive index” and “Bragg” increases. Moreover, new gap branches appear in new frequencies at both TE and TM polarizations. In specific state, two branches of “zero permittivity” gap appear in the PC band structure related to TM polarization. With increasing the amount of the filling rate of total volume with three level atoms, we observe a lot of changes in the PC band structure.

DOI: 10.1142/s0217979217502770

Related papers

Modification of the Electromagnetic Field in the Photonic Crystal Medium and New Ways of Applying the Photonic Band Gap Materials

R. Kh. Gainutdinov, Хамадеев Марат Актасович, A A Akhmadeev +1 more

Photonic crystals (PCs) are periodic systems that consist of dielectrics with different refractive indices. Photonic crystals have many potential technological applications. These applications are mainly based on the photonic bang gap effect. However the band gap is not only effect that follows from the periodic changing of the refractive index in the photonic crystal. The periodic change of the photon-matter interaction in photonic crystal medium gives rise to the fact that the mass of an electron in the photonic crystal must differ from its mass in vacuum. Anisotropy of a photonic crystal results in the dependence of the electromagnetic mass correction on the orientation of the electron momentum in a photonic crystal. This orientation dependence in turn gives rise to the significant correction to the transition frequencies in an atom placed in air voids of a photonic crystal. These corrections are shown to be comparable to the atomic optical frequencies. This effect allows one to control the structure of the atomic energy levels and hence to control resonance processes. It can serve as the basis for new line spectrum sources. The effect provides new ways of realization of quantum interference between decay channels that can be important for quantum information science.

InTech eBooksApr 4, 20181 citation

Controlling the One-Dimensional Photonic Crystal Bandgap Structures Via Manipulation of Electromagnetically Induced Transparency Atomic Vapor

Xu Sen

Using the Transfer matrix method to reserch the one-dimensional photonic crystal bandgap structure which is made of electromagnetically induced transparency atomic vapor.The results show that the photonic crystal bandgap can be manipulated by varying the refractive index of electromagnetically induced transparency atomic vapor.The EIT atomic vapor relative refractive index gradually increasing with the Rabi frequency.With the Rabi frequency gradually increasing,the band gap of the photonic crystal becomes more and more narrow,but the change is becoming slower.

Chinese Journal of Spectroscopy LaboratoryJan 1, 20130 citations

Effect of photonic band gap on the propagation of reflected pulse from a slab doped with two-level and three-level atoms

Samad Roshan Entezar, Maryam Nikkhou

In this paper the effect of photonic band gap on the group velocity of reflected pulse from a dielectric slab doped with two-level or three-level atoms has been investigated. It is assumed that the slab is sandwiched between a uniform medium (like vacuum) and a one-dimensional photonic crystal. It is shown that the reflected pulse from the slab doped with two-level (three-level) atoms will be superluminal (subluminal) if the carrier frequency of the incident Gaussian pulse is in the photonic band gap. In contrast, for the incident pulse with the carrier frequency at the edge of photonic band gap, the reflected pulse from the slab doped with two-level (three-level) atoms is subluminal (superluminal).

Iranian Journal of Physics ResearchSep 15, 20130 citations

Cavity quantum electrodynamics with three-dimensional photonic band gap crystals

Willem L. Vos, Léon A. Woldering

Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.

Cambridge University Press eBooksNov 30, 201412 citations

Spontaneous emission in one-dimensional photonic crystals

Adán S. Sánchez, P. Halevi

We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.

Physical Review ENov 16, 200527 citations

Study on optical gain of one-dimensional photonic crystals with active impurity

Zhenghua Li, Tinggen Shen, Xuehua Song +3 more

Localized fields in the defect mode of one-dimensional photonic crystals with active impurity are studied with the help of the theory of spontaneous emission from two-level atoms embedded in photonic crystals. Numerical simulations demonstrate that the enhancement of stimulated radiation, as well as the phenomena of transmissivity larger than unity and the abnormality of group velocity close to the edges of photonic band gap, are related to the negative imaginary part of the complex effective refractive index of doped layers. This means that the complex effective refractive index has a negative imaginary part, and that the impurity state with very high quality factor and great state density will occur in the photonic forbidden band if active impurity is introduced into the defect layer properly. Therefore, the spontaneous emission can be enhanced, the amplitude of stimulated emission will be very large and it occurs most probably close to the edges of photonic band gap with the fundamental reason, the group velocity close to the edges of band gap is very small or abnormal. OCIS codes: 130.3120, 120.7000, 160.4670, 120.4570, 160.5690, 230.4170. More and more importance has been attached to the unique behaviors of electromagnetic wave propagating in photonic crystals, a novel and artificial photonic mate-

Jan 1, 20071 citation