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Physical Review A

Giant refractive-index enhancement in dispersive polaritonic band-gap and photonic band-gap materials

Mahi R. Singh

Published Feb 17, 2004• 16 citations
Publisher

Abstract

A theory for the refractive-index enhancement due to quantum coherence and interference has been developed in dispersive polaritonic and photonic band-gap materials doped with an ensemble of noninteracting three-level atoms. Quantum coherence is introduced by driving the atoms with a coherent monochromatic laser field. The real and the imaginary parts of the susceptibility have been calculated by using the master equation and the Laplace transform methods. It is found that the energy gap in these materials plays an important role in the refractive-index enhancement. Numerical simulations for the real and the imaginary parts of susceptibility are performed for SiC as a function of the probe laser frequency. It is found that there is a giant refractive-index enhancement with vanishing absorption when the resonance frequencies lie near the lower band edge.

DOI
10.1103/physreva.69.023807

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A theory for the refractive-index enhancement due to quantum coherence and interference has been developed in dispersive polaritonic and photonic band-gap materials doped with an ensemble of noninteracting three-level atoms. Quantum coherence is introduced by driving the atoms with a coherent monochromatic laser field. The real and the imaginary parts of the susceptibility have been calculated by using the master equation and the Laplace transform methods. It is found that the energy gap in these materials plays an important role in the refractive-index enhancement. Numerical simulations for the real and the imaginary parts of susceptibility are performed for SiC as a function of the probe laser frequency. It is found that there is a giant refractive-index enhancement with vanishing absorption when the resonance frequencies lie near the lower band edge.
Numerical simulations are performed on the narrowing of transient linewidths of the absorption peaks of an ensemble of four-level atoms doped in a dispersive band-gap material. The atoms do not interact with each other. They are, however, interacting with a reservoir, due to which, the top two levels of the atoms decay to a pair of lower levels. A probe laser field is applied to study the absorption characteristics of the system. The density matrix method is used to calculate the photon yield for the absorption peak in order to observe linewidth narrowing. Numerical simulations are performed for SiC which is a dispersive polaritonic band-gap material. We have observed the occurrence of linewidth narrowing in SiC when the resonance energies lie within the bands. But when the resonance energy lies near the lower band edge of the polaritonic crystal, the narrowing disappears. On the other hand, when the resonance energy lies near the upper band edge, the narrowing of the linewidth remains as pronounced as before. Moreover, we have found that the photon yield is very sensitive to the locations of the resonance energies within the band. These unusual properties can be used to make new types of photonic devices such as switches, gates, etc. Similar results are also found in photonic band-gap materials.
A theory of coherent population trapping (CPT) has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials when doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra leading to unusual optical properties. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. The transition between the two lower states of an atom is dipole forbidden. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations are performed for both PBG and DPBG materials with the phase factor between the coherent states chosen such that the number density of the upper state becomes zero when the photon fields have the same intensity. It is found that when the resonance energies lie away from the band edges and within the lower band, the CPT effect is observed in both materials when the fields have identical intensities. Similar results are also found when the resonance energies lie away from the band edges and within the upper band. When one of the resonance energies lies near the lower band edge, the number density vanishes at all intensities of the fields for both materials. This is an effect of the band structure of the materials and is not due to the CPT effect. A similar result is seen when one of the resonance energies lies near the upper band edge of a PBG material. However, for a DPBG material, the number density does not become zero when one of the resonance energies lies near the upper band edge, except due to the CPT effect brought on by the identical intensities of the photon fields. This is a very interesting phenomenon.
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.
We study the electromagnetically induced transparency in dispersive band gap materials when an ensemble of non-interacting four-level atoms is doped. The system is interacting with a pump field, a probe field and a reservoir. The method of master equation and Lap lace transform has been used in calculating the expression for the susceptibility. Numerical simulations are performed on the susceptibility in dispersive band gap material (i.e. SiC). The phenomenon of electromagnetically induced transparency has been predicted in SiC. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Quantum electrodynamics of two identical two-level atoms placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied within the framework of the dipole resonance (rotating-wave) approximation. For finite interatomic distances a polariton-atom bound state lying within the polaritonic gap is shown to be split into a doublet due to an effective atom-atom interaction. Evaluating the splitting as a function of the interatomic separation, we estimate a width of a polariton-impurity band when a system of spatially correlated atoms is present. The results obtained for the case of two atoms are then generalized to the case of an atomic chain (a one-dimensional atomic lattice). The equations describing a propagation of a band polariton are derived and the expressions for the band polariton spectrum and its effective mass are obtained. The model under consideration has quite a general structure and is applied to the case of photonic-band-gap materials as well. Numerical calculations are presented for SiC semiconductors.
We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.