Quantum theory of photonic crystal polaritons

We formulate a full quantum mechanical theory of the interaction between electromagnetic modes in photonic crystal slabs and quantum well excitons embedded in the photonic structure. We apply the formalism to a high index dielectric layer with a periodic patterning suspended in air. The strong coupling between electromagnetic modes lying above the cladding light line and exciton center of mass eigenfunctions manifests itself with the typical anticrossing behavior. The resulting band dispersion corresponds to the quasi-particles coming from the mixing of electromagnetic and material excitations, which we call photonic crystal polaritons. We compare the results obtained by using the quantum theory to variable angle reflectance spectra coming from a scattering matrix approach, and we find very good quantitative agreement.Comment: Proceedings of the "8th Conference on Optics of Excitons in Confined Systems" (OECS-8), 15-17 September 2003, Lecce (Italy

Profile alterations of a symmetrical light pulse coming through a quantum well

The theory of a response of a two-energy-level system, irradiated by symmetrical light pulses, has been developed.(Suchlike electronic system approximates under the definite conditions a single ideal quantum well (QW) in a strong magnetic field {\bf H}, directed perpendicularly to the QW's plane, or in magnetic field absence.) The general formulae for the time-dependence of non-dimensional reflection {\cal R}(t), absorption {\cal A}(t) and transmission {\cal T}(t) of a symmetrical light pulse have been obtained. It has been shown that the singularities of three types exist on the dependencies {\cal R}(t), {\cal A}(t), {\cal T}(t). The oscillating time dependence of {\cal R}(t), {\cal A}(t), {\cal T}(t) on the detuning frequency \Delta\omega=\omega_l-\omega_0 takes place. The oscillations are more easily observable when \Delta\omega\simeq\gamma_l. The positions of the total absorption, reflection and transparency singularities are examined when the frequency \omega_l is detuned.Comment: 9 pages, 13 figures with caption

Self-tuned quantum dot gain in photonic crystal lasers

We demonstrate that very few (1 to 3) quantum dots as a gain medium are sufficient to realize a photonic crystal laser based on a high-quality nanocavity. Photon correlation measurements show a transition from a thermal to a coherent light state proving that lasing action occurs at ultra-low thresholds. Observation of lasing is unexpected since the cavity mode is in general not resonant with the discrete quantum dot states and emission at those frequencies is suppressed. In this situation, the quasi-continuous quantum dot states become crucial since they provide an energy-transfer channel into the lasing mode, effectively leading to a self-tuned resonance for the gain medium.Comment: 4 pages, 4 figures, submitted to Phys. Re

Band structure and optical properties of opal photonic crystals

A theoretical approach for the interpretation of reflectance spectra of opal photonic crystals with fcc structure and (111) surface orientation is presented. It is based on the calculation of photonic bands and density of states corresponding to a specified angle of incidence in air. The results yield a clear distinction between diffraction in the direction of light propagation by (111) family planes (leading to the formation of a stop band) and diffraction in other directions by higher-order planes (corresponding to the excitation of photonic modes in the crystal). Reflectance measurements on artificial opals made of self-assembled polystyrene spheres are analyzed according to the theoretical scheme and give evidence of diffraction by higher-order crystalline planes in the photonic structure.Comment: to appear in PR

Exciton polaritons in two-dimensional photonic crystals

Experimental evidence of strong coupling between excitons confined in a quantum well and the photonic modes of a two-dimensional dielectric lattice is reported. Both resonant scattering and photoluminescence spectra at low temperature show the anticrossing of the polariton branches, fingerprint of strong coupling regime. The experiments are successfully interpreted in terms of a quantum theory of exciton-photon coupling in the investigated structure. These results show that the polariton dispersion can be tailored by properly varying the photonic crystal lattice parameter, which opens the possibility to obtain the generation of entangled photon pairs through polariton stimulated scattering.Comment: 5 pages, 4 figure

Polariton Dispersion Law in Periodic Bragg and Near-Bragg Multiple Quantum Well Structures

The structure of polariton spectrum is analyzed for periodic multiple quantum well structures with periods at or close to Bragg resonance condition at the wavelength of the exciton resonance. The results obtained used to discuss recent reflection and luminescent experiments by M. H\"{u}bner et al [Phys. Rev. Lett. {\bf 83}, 2841 (1999)] carried out with long multiple quantum well structures. It is argued that the discussion of quantum well structures with large number of wells is more appropriate in terms of normal modes of infinite periodic structures rather then in terms of super- and sub- radiant modes.Comment: replaced with a new version, an error in one of the equations is correcte

Elastic Light Scattering by Semiconductor Quantum Dots

Elastic light scattering by low-dimensional semiconductor objects is investigated theoretically. The differential cross section of resonant light scattering on excitons in quantum dots is calculated. The polarization and angular distribution of scattered light do not depend on the quantum-dot form, sizes and potential configuration if light wave lengths exceed considerably the quantum-dot size. In this case the magnitude of the total light scattering cross section does not depend on quantum-dot sizes. The resonant total light scattering cross section is about a square of light wave length if the exciton radiative broadening exceeds the nonradiative broadening. Radiative broadenings are calculated

CO excitation in the Seyfert galaxy NGC7130

We present a coherent multi-band modelling of the CO Spectral Energy Distribution of the local Seyfert Galaxy NGC7130 to assess the impact of the AGN activity on the molecular gas. We take advantage of all the available data from X-ray to the sub-mm, including ALMA data. The high-resolution (~0.2") ALMA CO(6-5) data constrain the spatial extension of the CO emission down to ~70 pc scale. From the analysis of the archival CHANDRA and NuSTAR data, we infer the presence of a buried, Compton-thick AGN of moderate luminosity, L_2-10keV ~ 1.6x10^{43} ergs-1. We explore photodissociation and X-ray-dominated regions (PDRs and XDRs) models to reproduce the CO emission. We find that PDRs can reproduce the CO lines up to J~6, however, the higher rotational ladder requires the presence of a separate source of excitation. We consider X-ray heating by the AGN as a source of excitation, and find that it can reproduce the observed CO Spectral Energy Distribution. By adopting a composite PDR+XDR model, we derive molecular cloud properties. Our study clearly indicates the capabilities offered by current-generation of instruments to shed light on the properties of nearby galaxies adopting state-of-the art physical modelling.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

Effect of the Spatial Dispersion on the Shape of a Light Pulse in a Quantum Well

Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed discrete, and two closely located excited levels are taken into account. A wide quantum well (the width of which is comparable to the length of the light wave, corresponding to the pulse carrying frequency) is considered, and the dependance of the interband matrix element of the momentum operator on the light wave vector is taken into account. Refractive indices of barriers and quantum well are assumed equal each other. The problem is solved for an arbitrary ratio of radiative and nonradiative lifetimes of electronic excitations. It is shown that the spatial dispersion essentially affects the shapes of reflected and transmitted pulses. The largest changes occur when the radiative broadening is close to the difference of frequencies of interband transitions taken into account.Comment: 7 pages, 5 figure