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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

Numerical simulations of photon trapping in doped photonic crystals doped with multi‐level atoms

Mahi R. Singh, I. Haque

Published May 1, 2005• 7 citations
Publisher

Abstract

A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200460747

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A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
We have studied the nonlinear susceptibility in dispersive polaritonic band-gap (DPBG) materials in the presence of five-level impurity atoms. Initially, the atom is prepared in a coherent superposition of two levels |b〉 and |c〉. The levels |b〉 and |c〉 are coupled to the upper level |a〉 with a coherent laser field. The nonlinear susceptibility has been calculated corresponding to transitions |a〉 → |c〉 and |a〉 → |b〉 using the equation of motion for the density matrix. The atomic system is interacting with the polariton reservoir. The effect of atom-polariton reservoir coupling on the imaginary part of the nonlinear susceptibility has been studied when the resonance energy lies in lower band of the polariton spectrum. It is found that by shifting the resonance energy away from the band edge, the system goes to the probe gain state. It is also found that by changing the intensity of the coherent laser field, the system switches from gain to loss state and vice-versa. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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 linear susceptibility has been developed in the presence of dipole-dipole interaction for photonic-band-gap (PBG) materials doped with an ensemble of five-level nanoparticles. An external probe laser induces dipole moments in nanoparticles. When the concentration of the particles is high, the induced dipoles interact with one another through dipole-dipole interaction. Mean-field theory is used to include the effect of dipole-dipole interaction in the calculation of susceptibility. Numerical simulations are performed for the real and imaginary susceptibilities and it is found that the system switches between inversionless and noninversionless states. In addition the system switches between absorptionless and nonabsorptionless states. These occur when the resonance energy lies near the valence-band edge of the photonic-band-gap material. The theory also predicts a polarization catastrophe in PBG materials doped with nanoparticles.
A theory of nonlinear two-photon absorption has been developed for a polaritonic band-gap material doped with an ensemble of three-level nanoparticles. We have considered that the nanoparticles are interacting with the polaritonic material. An expression of two-photon absorption has been obtained by using the density-matrix method. The effect of the dipole-dipole interaction (DDI) has also been included in the formulation, which leads to interesting phenomena. For example, it has been found that the two-photon absorption can be turned on and off when the decay resonance energy of the three-level nanoparticles is moved within the lower-energy band. It has also been found that the inhibition effect can also be achieved by controlling the strength of the DDI.
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.