Polariton Theory Research Articles

A non-perturbative approach for the theory of excitonic polaritons in disordered microcavities

We apply a closed-path time Green's function approach as an alternative to the replica technique to formulate a non-perturbative description of cavity polaritons in the presence of a symmetry-breaking disorder. Our calculations show that the theory of Zittartz cannot be applied to the cavity polaritons with only minor modifications.

Quantum theory of a resonant photonic crystal

We present a quantum model of two-level atoms localized in a three-dimensional lattice based on the Hopfield polariton theory. In addition to a polaritonic gap at the excitation energy, a photonic band gap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the excitation energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of $25\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, up to ${10}^{5}$ times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing probability density of atomic excitations.

Theory of trapped polaritons in patterned microcavities

AbstractWe consider the system of a quantum well embedded in a planar semiconductor microcavity with a shallow circular mesa patterned on top of the cavity spacer. For this system we develop the linear coupling theory of polaritons. We then compute polariton eigenstates and the corresponding optical spectrum. The theory predicts the existence of laterally confined polariton states with a discrete energy spectrum, as well as continuum states above the finite mesa potential barrier. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Stimulated polariton scattering in intersubband lasers: Role of motional narrowing

We have developed a theory of polariton scattering in the inhomogeneously broadened intersubband transitions and have shown that motional narrowing plays important role. This explains abnormally high gain of the experimentally observed parametric process.

Optical coherent manipulation of polariton modes and of their radiative decay

The coherent optical control of polariton modes is studied in time-resolved pulse-transmission experiments on a $\mathrm{ZnSe}∕\mathrm{ZnSSe}$ heterostructure. Using a phase-locked pulse pair at low excitation intensity it is shown that the polariton modes, their quantum beat structure, and the radiative decay can be coherently manipulated. Calculations based on a microscopic polariton theory can explain the measured findings without the use of fit parameters. Additionally, the decay times of the coherent polarization, which depend on the involved polariton modes and their radiative decay, are extracted on the basis of a phenomenological model.

Localization theory of surface exciton polaritons on a rough semiconductor surface

We develop a numerical model to investigate the localization of surface exciton polaritonsin the presence of random roughness and spatial dispersion. The localization criteria areexamined. The localization effects are embodied in the large enhancement and rapid decayof the field intensity on the surface. The calculation shows that there is a transition fromthe localized state to the extended state. It has been found that the localization occurs ina limited frequency range above the resonant frequency of transverse excitons.

Theory of dark-state polariton collapses and revivals

We investigate the dynamics of dark-state polaritons in an atomic ensemble with ground-state degeneracy. A signal light pulse may be stored and retrieved from the atomic sample by adiabatic variation of the amplitude of a control field. During the storage process, a magnetic field causes rotation of the atomic hyperfine coherences, leading to collapses and revivals of the dark-state polariton number. These collapses and revivals should be observable in measurements of the retrieved signal field, as a function of storage time and magnetic field orientation.

Dispersion polaritons on metallized surfaces of optically uniaxial crystals

We have constructed a theory of dispersion polaritons (localized electromagnetic waves) on arbitrarily oriented metallized surfaces of optically uniaxial crystals. The domain of existence of polaritons is defined by the following inequalities for permittivities eo and ee of the crystal and the angle θ between the optical axis and the surface: −eetan2θ 0. The frequency boundaries of this region are specified for the case when the eo(ω) dependence corresponds to the model of a single polar excitation. The azimuthal orientation φ of the optical axis projection onto the surface does not appear in the criterion for polariton existence, but affects (together with angle θ) its main dispersion characteristics, such as the refractive index and partial wave localization parameters. This effect is analytically described in detail. Anomalies in the behavior of polariton parameters are studied in the vicinity of the boundaries of the domain of its existence, where the wave fields are especially sensitive to variations in the angles θ and φ. It is shown that a polariton in the plane of propagation (sagittal plane) passing through the optical axis is transformed into a one-partial bulk wave satisfying the boundary conditions. Accordingly, the wave branch under investigation for close orientations (when the optical axis forms a small angle with the sagittal plane) describes deeply penetrating (quasi-bulk) polaritons.

Light Scattering from Polaritons in GaP Crystals

The theory of polariton scattering on stimulated Raman scattering and of coherent anti-Stokes scattering of light in dispersing and dissipative media has been developed in the approximation of a constant intensity which takes into account the reverse influence of excited waves on exciting ones and makes it possible to simultaneously consider the phase difference and decay of all interacting waves. It has been established that, unlike a constant-field approximation, the complex amplitude of the Stokes wave depends on the intensity of the polariton one and vice versa. A comparison of the behavior of the polariton-wave intensity for a GaP crystal in both approximations has been carried out.

Theory of polaritons in bounded spatially dispersive media

In crystal optics with spatial dispersion there are two alternative approaches to the polariton problems starting from either mechanical excitons ~ME’s ! or Coulomb excitons ~CE’s !, respectively. The difference between them arises from the different treatment of that part of the polarized crystal unit interaction which is associated with the long-range curl-free proper crystal field, generated by fictitious charges of macroscopic dielectric polarization. In the case of the CE scheme the unperturbed ~by electromagnetic field! energy operator contains that part, while in the case of the ME scheme it does not. This is the peculiarity that makes their dispersion laws and all other characteristics, including the boundary conditions, essentially different. Both primary conceptions are equally used in theoretical research and have their own advantages and shortcomings. The agreement between those for infinite space has been proven by a lot of investigations, but solving the same problem for finite media has not been done. Moreover, the majority of papers in the field use the same boundary conditions for excitonic polarizations in both schemes. This makes them all true only for some particular cases but, certainly, the contradictions appearing should be eliminated. The aim of this paper is the critical analysis of the existing inconsistencies and the fitting of the solutions to the boundary-value problems for polaritons formed from those two different types of exciton states. Partially we fill the arised recess by making both approaches in line with the case of the N-exponential Frenkel exciton model, when describing the polarization of some bounded spatially dispersive dielectrics in the excitonic spectrum region. The light reflection coefficient is taken as the main quantity to be fitted in both of the above calculation schemes. This is possible only by including several exciton transport mechanisms at once ~that is, for N>2) and by using the concept of Pekar’s ‘‘missing’’ electromagnetic wave. With success in this particular case, we hope to induce further investigations in the area for other exitonic models and in a general enough case, such as the case for infinite media.

Nonlinear surface polaritons in semimagnetic semiconductor

The paper develops the theory of s-polarized nonlinear surface polaritons in the semimagnetic semiconductor placed in the external static magnetic field. A model of a uniaxial nonlinear medium for the semimagnetic semiconductor is considered. Rigorous criteria of existence of different new types of nonlinear surface polaritons are formulated. It is shown that the new polaritons may exhibit monotonic and nonmonotonic fall of the field in a nonlinear medium. We suggest the method of estimation of the antiferromagnetic resonance frequency in the semimagnetic semiconductors due to the nonlinear surface polariton excitation by the attenuated total reflection method.

Systematic formulation of slow polaritons in atomic gases

We formulate a theory of slow polaritons in atomic gases and apply it to the slowing down, storing, and redirecting of laser pulses in an electromagnetically induced transparency (EIT) medium. The normal modes of the coupled matter and radiation are determined through a full diagonalization of the dissipationless Hamiltonian. Away from the EIT resonance, where the polaritons acquire an excited-state contribution, lifetimes are introduced as a secondary step. With detuning included various four-wave mixing possibilities are analyzed. We investigate specifically the possibility of reverting a stopped polariton by reversing the control beam.

Quantum theory of exciton polaritons in cylindrical semiconductor microcavities

A quantum-mechanical formalism is developed in order to study the interaction between a quantum-well exciton and the electromagnetic (e.m.) field inside a cylindrical microcavity. The cavity modes are evaluated as a function of the radius according to a self-consistent procedure, and are found to be in good agreement with the experiment [J.M. G\'erard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, Appl. Phys. Lett. 69, 449 (1996)]. The cavity polaritons are then evaluated by diagonalizing the total Hamiltonian, which is written in second quantized form and includes also the self-interaction term. The mixed radiation-matter states manifest themselves with the characteristic anticrossing behavior. The Rabi splitting is found to depend on the quantum numbers of the mode and on its polarization: for a large radius of the cavity it approaches the planar cavity limit, and it decreases for decreasing radius. This effect is interpreted in terms of the leakage of the cavity modes in the outside region, which decreases the overlap between the exciton wave function and the e.m. field. Although the interaction between material and radiation excitations with the same quantum numbers still remains the dominant one, different boundary conditions applying to the exciton and to cavity mode wave functions lead to interactions between states with different radial quantum numbers. Removal of the exciton degeneracy is predicted: the large energy separation between radiation modes with different quantum numbers produces an energy splitting of the otherwise degenerate exciton states inside a cylindrical microcavity.

Polaritons in highly ordered cyanine dye films

The interaction of dye crystals with light lead to an excitation (excitons) and polarization of the material. The coupling of the excitons with the polarization is described by polaritons. In anisotropic materials, they cause a strong dependence of absorption energy on the crystal direction. A possible shift of absorption wavelength from 635 to 336 nm was calculated from the reflection spectra of single crystals of 1.7-bis(dimethylamino)heptamethine hexafluorophosphate. The use of this effect in transmission requires highly ordered dye layers of 50–100 nm thickness. We have prepared such layers by a spherulitic crystallization process (Thin Layer Aggregation, TLA). Three different crystal faces in millimeter size but only 80 nm thick were obtained, which showed quite different dichroic colors although the material, the crystal structure, and the layer thickness did not change. The spectra were described by the polariton theory.

Polariton Motional Narrowing in Semiconductor Multiple Quantum Wells

We demonstrate a new fast-scan ultrafast coherent reflectivity technique that tracks the amplitude and phase of excitons in GaAs heterostructures at densities down to $4\ifmmode\times\else\texttimes\fi{}{10}^{6}{\mathrm{cm}}^{\ensuremath{-}2}$. Observed growth in the exciton coherence over the first 1.5 ps is direct evidence for the presence of interfering polariton modes. Polariton theory provides a good account of the data as the number of quantum wells is increased. Polariton motional narrowing of spectral lines from multiple quantum wells is demonstrated both experimentally and theoretically, annealing out the inhomogeneous broadening of the exciton energies.

Lateral motion of confined excitonic polaritons

Transient-grating measurements on high-quality ${\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ heterostructures reveal a strong increase of the lateral polariton-transport coefficient with the ZnSe thickness $L$ in a range from 5 to 30 excitonic Bohr radii. In this weak-confinement regime a strict quantization of the polariton--wave-vector component ${k}_{z}$ normal to the layer occurs, as is experimentally verified for our samples. On this basis, it is shown by use of polariton theory that the observed increase of the lateral transport coefficient can be explained by an intrinsic drastic increase of the lateral polariton group velocity. This is caused by a transition from quasiexcitonic to polaritonic transport when the first quantized mode with ${k}_{z}^{1}=\ensuremath{\pi}/L$ passes through the bottleneck region of the lower polariton branch for increasing $L$.

Nonlinear Polariton Propagation

The nonlinear optical response of excitonic polaritons to the presence of a background of incoherent polaritons in quasi-equilibrium is investigated for thin ZnSe layers in the temporal and spectral domain. At low densities the transmission spectra are dominated by strain-split heavy-hole and light-hole resonances the former being further split into several Fabry-Pérot modes caused by polariton interference inside the layers. In the temporal domain this corresponds to complex structured transients of transmitted pulses exhibiting pronounced propagation beats. Under resonant pumping of the heavy-hole polariton the nonlinear spectra exhibit a strongly asymmetric shape of the quantized polariton modes. The transients show induced transmission around t = 50 fs which is followed by a complex-structured induced absorption at t > 200 fs. Almost quantitative agreement is found between the experimental data and calculations based on polariton theory clearly demonstrating the strong influence of spatial dispersion also on nonlinear polariton propagation. This allows to determine the density dependence of the oscillator strength, damping, and energy shift of the heavy-hole polariton.

Nonlinear Polaritons in Anisotropic Superlattices

In this paper, we present a dielectric theory for polaritons in semiconductor superlattices. The coherent optical field is classical, satisfying Maxwell's equations, while the carriers are treated fully quantum-mechanically. The dielectric function is obtained through the solutions of modified semiconductor Bloch equations for superlattices, described as an anisotropic medium. The equations combine the most relevant many-body and effective dimensionality effects. Numerical results are presented for GaAs/AlGaAs superlattices.

Continuum treatment of phonon polaritons in semiconductor heterogeneous structures

A phenomenological approach is applied to the theory of phonon polaritons in semiconductor heterogeneous structures, with special emphasis on semiconductor nanostructures. Applying the macroscopic approach to continuous media, seven coupled partial differential equations are derived for the fundamental quantities involved: the three components of the displacement field u, those of the magnetic potential A, and the electric potential \ensuremath{\varphi} in the Lorentz gauge. Our treatment is rather general in its conception: no assumptions on the system geometry and composition are made. We develop a general method allowing us to obtain the exact analytical solutions of the equations when the constituent materials can be assumed to be isotropic. The matching boundary conditions at the structure interfaces are derived from the differential equations and interpreted in physical terms. This theory leads to a phenomenological description of phonon polaritons valid in the long-wavelength limit. We apply it to the case of the double heterostructure, and calculate both the mechanical displacements u and the potentials A, \ensuremath{\varphi} of normal modes in the GaAs/AlAs prototype system. We also discuss the dispersion relations for these modes which are of transverse-electric and transverse-magnetic character. A comparison is made with some limiting cases: the unretarded case $(c\ensuremath{\rightarrow}\ensuremath{\infty})$ reproducing our previous results for polar-optical phonons, and the nondispersive case $({\ensuremath{\beta}}_{T}\ensuremath{\rightarrow}0),$ which leads to the Fuchs-Kliewer slab modes.

Propagation of confined excitonic polaritons at high densities

The propagation of excitonic polaritons is investigated in the nonlinear optical regime by real-time-resolved pump-and-probe measurements on a femtosecond time scale. High-quality ${\mathrm{ZnS}}_{\mathrm{x}}$${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$/ZnSe/${\mathrm{ZnS}}_{\mathrm{x}}$${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ heterostructures are used which, in linear absorption, show clearly resolved Fabry-P\'erot resonances of polaritons confined in the ZnSe layer. Without pumping, the transmitted probe pulses exhibit a complex temporal beating behavior caused by quantum beating between heavy-hole and light-hole polaritons as well as by propagation beats. For increasing flux of a preceding pump pulse the transmitted power is temporally redistributed from later times toward the leading maximum of the pulse. Additionally, the amplitude of the beats continuously decreases. Almost quantitative agreement is found between the experimental data and calculations based on semiclassical polariton theory, clearly demonstrating the strong influence of spatial dispersion also on nonlinear polariton propagation. This allows determination of the density dependence of the oscillator strength, damping, and energy shift of the heavy-hole polariton.