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Journal of Physics B Atomic Molecular and Optical Physics

The study of nonlinear two-photon phenomenon in photonic crystals doped with nanoparticles

Mahi R. Singh

Published Jan 25, 2007• 11 citations
Publisher

Abstract

A theory of the nonlinear two-photon absorption has been developed in a photonic crystal doped with an ensemble of four-level nanoparticles. We have considered that the nanoparticles are interacting with the photonic crystal. An expression of two-photon absorption has been obtained by using the density matrix method. The effect of the dipole–dipole interaction has also been included in the formulation. Interesting new phenomena have been predicted. For example, it is found that the inhibition of two-photon absorption can be turned on and off when the decay resonance energies of the four-level nanoparticles are moved within the energy band.

DOI
10.1088/0953-4075/40/4/003

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A theory of the nonlinear two-photon absorption has been developed in a photonic crystal doped with an ensemble of four-level nanoparticles. We have considered that the nanoparticles are interacting with the photonic crystal. An expression of two-photon absorption has been obtained by using the density matrix method. The effect of the dipole–dipole interaction has also been included in the formulation. Interesting new phenomena have been predicted. For example, it is found that the inhibition of two-photon absorption can be turned on and off when the decay resonance energies of the four-level nanoparticles are moved within 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.
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 have investigated the nonlinear switching mechanism in nanostructures doped in photonic crystals. The nonlinear phenomenon studied in this paper is the two-photon absorption process. A probe laser field is applied between the ground state and the next excited state of the nanoparticles to measure the two-photon absorption spectrum. A coupling field is applied between the two excited states of nanoparticles to control the two-photon process. It is found that when the decay resonance energy lies away from the photonic band edge the inhibition of two-photon absorption is observed. However, when the probe field is not resonance, the inhibition of two photons absorption is not observed. An interesting result is observed when the decay resonance energy lies near the band edge. It is found that the inhibition of the two-photon absorption disappears. It means that the phenomenon of two-photon absorption can be switched on and off by tuning the resonance energy within the lower band of the crystal. This mechanism can be used to make a new type of photonic switching devices using photonic crystals.
We have studied the phenomenon of two-photon absorption in photonic nanowires doped with an ensemble of four-level nanoparticles. The photonic nanowire is made from two photonic crystals, A and B, where A is embedded in B. Photons are confined in the nanowire due to the band structure engineering of photonic crystals. It is considered that one of the resonance levels of nanoparticles lies near a photon-bound state of the nanowire. The two-photon absorption coefficient has been calculated using the time-dependent Schrödinger equation. It is found that there is an inhibition of two-photon absorption in the system. This is due to the strong coupling between nanoparticles and the nanowire.
We have studied the quantum information processing phenomenon in photonic crystals doped with four-level nanoparticles. This phenomenon occurs due to the switching mechanism in the system. We consider that one of the transition energies of nanoparticles is coupled near resonantly with a photonic band gap edge. The dipole-dipole interaction between the nanoparticles has also been included. It is found that the system switches between the transparent and nontransparent states due to the dipole-dipole interaction and the band edge coupling. This is an interesting finding and can be used to produce logical photon switches in the quantum information processing.
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.