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Journal of Physics Condensed Matter

A study of the ac Stark effect in doped photonic crystals

I. Haque, Mahi R. Singh

Published Mar 27, 2007• 29 citations
Publisher

Abstract

In this paper we present calculations of level populations and susceptibility for an ensemble of five-level atoms doped in a photonic crystal, using the master equation method. The atoms in the ensemble interact with the crystal which acts as a reservoir and are coupled with two strong pump fields and a weak probe field. It is found that, by manipulating the resonance energy associated with one of the decay channels of the atom, the system can be switched between an inverted and a non-inverted state. We have also observed the ac Stark effect in these atoms and have shown that due to the role played by the band structure of the photonic crystal, it is possible to switch between an absorption state and a non-absorption state of the atomic system. This is a very important finding as techniques of rendering material systems transparent to resonant laser radiation are very desirable in the fabrication of novel optical and photonic devices.

DOI
10.1088/0953-8984/19/15/156229

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Nanoscale Research Letters•Jan 6, 2010•7 citations
In this paper we present calculations of level populations and susceptibility for an ensemble of five-level atoms doped in a photonic crystal, using the master equation method. The atoms in the ensemble interact with the crystal which acts as a reservoir and are coupled with two strong pump fields and a weak probe field. It is found that, by manipulating the resonance energy associated with one of the decay channels of the atom, the system can be switched between an inverted and a non-inverted state. We have also observed the ac Stark effect in these atoms and have shown that due to the role played by the band structure of the photonic crystal, it is possible to switch between an absorption state and a non-absorption state of the atomic system. This is a very important finding as techniques of rendering material systems transparent to resonant laser radiation are very desirable in the fabrication of novel optical and photonic devices.
In this thesis, we study light-matter interaction in the contexts of coherent population trapping (CPT) and the ac Stark effect in nanoparticles embedded (doped) in two important classes of reservoirs -- photonic crystals and dispersive materials. These materials have gaps in their energy spectra and are studied widely due to their unusual optical properties and potential for novel applications. We consider that the reservoirs are doped with an ensemble of five-level nanoparticles, each with a single Λ core (consisting of a lower doublet and an upper energy level), which interact with both the host reservoir and external radiation fields. We have also included studies of cases where the nanoparticles interact with each other as well via dipole-dipole interaction (DDI), which is included in the mean field approximation. This only happens when the doping concentration is high (~ 1018 per cubic meter).\nIn studying CPT, we have developed a novel technique of optical switching by devising a system whereby the doped nanoparticles become stable against absorption from the radiation field(s) i.e. they switch to their ground states. We have confirmed the occurrence of CPT in both types of reservoir and have also identified a number of important contrasting features which have markedly different utilities. Most significantly, we have found that the strength of the DDI between the nanoparticles plays a very important role in determining the conditions required for CPT in both materials. In studying the ac Stark effect in photonic crystals, we have used an ensemble of five-level nanoparticles, each with a single cascade core [ladder configuration], both with and without DDI. We found that, in the ac Stark regime, resonance tuning of the transitions within the nanoparticles, in relation to the band structure of these crystals, offers a new mechanism for switching the nanoparticle system from an inverted to a non-inverted state. Specifically, a doped nanoparticle can effectively become transparent to any radiation field tuned to the probed transition. Under DDI, we found that the absorption in the system decreases with increasing DDI strength. These findings have very exciting potential for applications in optical switching.
A possible switching mechanism has been investigated for nonlinear photonic crystals doped with an ensemble of non-interacting three-level nanoparticles. In this scheme, an intense pump laser field is used to change the refractive index of the nonlinear photonic crystal while a weaker probe field monitors an absorption transition in the nanoparticles. In the absence of the strong laser field the system transmits the probe field when the resonance energy of the nanoparticles lies near the edge of the photonic band gap due to strong coupling between the photonic crystal and the nanoparticles. However, upon application of an intense pump laser field the system becomes absorbing due to a band edge frequency shift that arises due to a nonlinear Kerr effect which changes the refractive index of the crystal. It is anticipated that the optical switching mechanism described in this work can be used to make new types of photonic devices.
In this thesis we demonstrate that the photonic band edge facilitates fundamental switching effects for resonant two-level atomic systems. In a photonic crystal, a coherent laser beam can drive a two-level atom to inverted atomic states, a phenomenon forbidden in ordinary vacuum. In this process, the atomic system switches from a passive medium to a gain medium as a function of the driving field intensity. We show that the large differential gain exhibited by the atomic medium is robust against non-radiative relaxation and dephasing mechanisms. This switching effect exhibits collective enhancement for a large number of two-level atoms within a cubic wavelength. In this case, the ensemble of atoms sharply switches to a highly inverted state at a very well defined threshold value of the laser field intensity. We next demonstrate that a probe laser field of prescribed wavelength experiences a substantial differential gain by slight modulations in the control laser field. We suggest that a doped photonic band gap material may, in this sense, be used as an all-optical micro-transistor. We analyze the effects of inhomogeneous line broadening on the probe beam spectrum and demonstrate that further electromagnetic density of states engineering combined with photo-bleaching techniques can be used to both offset the deleterious effects of inhomogeneous broadening and to enlarge the switching bandwidth. We investigate the prospects and challenges in designing microstructures with characteristics required by our proposal. We further show that the switching power and the response time of an all-optical transistor can be dramatically reduced by including collective effects, which also provide a natural mechanism of broadening of the gain spectrum. Finally, we develop an exact multi-photon scattering theory of resonance fluorescence in frequency-dependent photonic reservoirs. We show that, in the limit of weak driving field, the scattering cross section becomes strongly non-Lorentzian, reflecting the non exponential character of the atomic decay. As the driving field intensity increases, the scattered field acquires new features, consistent with predictions of a dynamical decoupling of the atomic system from the photonic reservoir.
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 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.
In this work, the absorption coefficient of a metallic photonic crystal doped with nanoparticles has been obtained using numerical simulation techniques. The effects of quantum interference and the concentration of doped particles on the absorption coefficient of the system have been investigated. The nanoparticles have been considered as semiconductor quantum dots which behave as a four-level quantum system and are driven by a single coherent laser field. The results show that changing the position of the photonic band gap about the resonant energy of the two lower levels directly affects the decay rate, and the system can be switched between transparent and opaque states if the probe laser field is tuned to the resonance frequency. These results provide an application for metallic nanostructures in the fabrication of new optical switches and photonic devices.