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Physical Review A

Dipole-dipole interaction in photonic-band-gap materials doped with nanoparticles

Mahi R. Singh

Published Apr 12, 2007• 37 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.75.043809

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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.
The phenomenon of spontaneous emission cancellation has been investigated in photonic-band-gap materials in the presence of dipole-dipole interaction. The material is densely doped with an ensemble of five-level nanoparticles. The mean field theory is used to calculate the effect of the dipole-dipole interaction whereas the linear response theory is used to calculate the expressions for the real and imaginary susceptibilities. Numerical simulations are performed for an isotropic photonic-band-gap material. Interesting results are predicted such as the control of the spontaneous emission cancellation by moving the resonance energies between the energy band and energy gap. It is also found that the photonic-band-gap material can be switched between absorptive and nonabsorptive states by changing the strength of the dipole-dipole interaction and the resonance energies in the energy band.
A theory of nonlinear phenomena has been developed for a photonic crystal in the presence of a pump and a coupling laser field. The crystal is doped with an ensemble of four-level nanoparticle impurities. It is considered that the impurity particles are not only interacting with the photonic crystal but also with each other via dipole-dipole interaction. An expression for the susceptibility has been obtained using the density matrix method. The nonlinear effects due to the coupling and the pump fields have been included in the formulation. The absorption spectrum has been calculated in the presence of the strong coupling and pump fields for an isotropic photonic crystal made from dielectric spheres. The photonic crystal has a gap to midgap ratio of about 21%. It is predicted that the absorption spectrum in the photonic crystal can have zero, one, two or three absorptionless states by tuning one of the transition energies within the bands. This is an interesting phenomenon which can be used to make photonic switching devices. We have also calculated the absorption spectrum in the presence of the dipole-dipole interaction. It is found that a symmetric absorption spectrum changes to an asymmetric one due to this interaction. It is also found that there is a large enhancement in the absorption and the dispersion simultaneously for certain values of the detuning and concentration.
The susceptibility has been calculated for a photonic crystal in the presence of spontaneous cancellation and dipole–dipole interaction. The crystal is densely doped with an ensemble of four-level nano-particles in Y-type configuration. Probe and a pump laser fields are applied to manipulate the absorption coefficient of the system. The expression of the susceptibility has been calculated in the linear response regime of the probe field but nonlinear terms are included for the pump field. It is found that in the presence of spontaneous emission cancellation there is an increase in the height of the two absorption peaks however the phenomenon of electromagnetically induced transparency (EIT) is not affected. On the other hand, there is a change in the height and location of the two peaks in the presence of dipole–dipole interactions. For certain values the particle density of the system can be switched from the EIT state to the non-EIT state. It is also found that when the resonance energies for two spontaneous emission channels lie close to the band edge, the EIT phenomenon disappears.
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 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.