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Exciton–Polariton Light–Semiconductor Coupling Effects H REVIEW ARTICLE PUBLISHED ONLINE: 6 MARCH 2011 | DOI: 10.1038/NPHOTON.2011.15 Exciton–polariton light–semiconductor coupling effects H. M. Gibbs1*, G. Khitrova1 and S. W. Koch2 The integrated absorption of an excitonic resonance is a measure of a semiconductor’s coupling to an optical field. The concept of an exciton–polariton expresses the non-perturbative coupling between the electromagnetic field and the optically induced mat- ter polarization. Ways to alter this coupling include confining the light in optical cavities and localizing the excitonic wavefunc- tion in quantum wells and dots, which is illustrated by quantum strong coupling between a single dot and an optical nanocavity. Positioning quantum wells in periodic or quasiperiodic lattices with spacing close to a half wavelength results in pronounced modifications to the light transmission. Light–matter coupling can also be used to generate and interrogate an exciton popula- tion, for example by the recently developed technique of absorbing terahertz radiation. emiconductors and their nanostructures exhibit many fas- material. The boundary conditions were introduced in an ad hoc cinating features that are attributable to their intricate light– fashion that allowed for different choices, making this explanation Smatter coupling properties. The response of a material to highly controversial4–7 until a proper solution was obtained8 through a weak field, known as its linear optical response, is governed by a fully self-consistent space–time-dependent calculation of the prop- the transition amplitude of an electron from the valence band to agating fields coupled to the inhomogeneous excitonic polarization. the conduction band. The missing valence-band electron — the Polaritons are intrinsically a concept of a linear system, and it was hole — is a quasiparticle with positive charge that experiences an noted9,10 quite early on that a polariton-based analysis of excitonic attractive Coulomb interaction with the negatively charged con- laser processes in bulk semiconductors allows for a simplified mod- duction-band electron. The resulting pair state, commonly referred elling of experimentally observed features. Owing to the severely to as the (Wannier) exciton, has a binding energy ranging from a limited numerical resources of the 1970s, these treatments often few millielectronvolts to a hundred millielectronvolts, giving rise to had to resort to poorly controlled approximations, such as the treat- resonances in the optical spectrum that are energetically well below ment of excitons as interacting Bosons by ignoring the fundamen- the fundamental absorption edge (that is, below the bandgap of the tal Fermionic features of the constituent electrons and holes. Such unexcited material). Hence, the linear optical semiconductor prop- simplified models are sometimes used even today and may allow for erties are inherently governed by Coulombic interaction effects. interesting insights, although often at the expense of full theoreti- From Maxwell’s equations, we know that an electromagnetic cal consistency. A systematic treatment of light–matter interaction field interacts with a charge-neutral dielectric medium, such as a effects can be achieved by microscopically describing electron–hole semiconductor, through the optically induced dipoles commonly pair excitations, their many-body interactions and how they couple described by the material’s polarization. Because the electromag- to the light field11–14. In such an analysis, polariton features appear netic field and polarization are both characterized by amplitude and automatically through the self-consistent treatment of the light– phase, we refer to them as coherent fields, in contrast with optically matter interaction. incoherent quantities such as light intensity or carrier populations, Although Hopfield originally introduced the polariton concept which have no phase information. The imaginary part of the polari- for bulk semiconductors, it is by no means limited to these structures. zation determines the optical absorption spectrum, which exhibits Exciton polaritons are also important for describing the light–matter strong excitonic resonances, whereas the real part determines the coupling in quantum well (QW) lattices and in planar microcavities optically induced refractive index changes. containing QWs, as we will discuss in the following sections. In 1958, John Hopfield noted in his groundbreaking paper1 that the fundamental optical absorption process is not a conversion of Tailoring the light–matter coupling photons into excitons but rather a two-stage process with excitons Owing to their mixed-mode nature, polariton features can be (we refer to this state as the excitonic polarization) as an interme- manipulated by changing either the excitonic properties or the opti- diate step; that is, the electromagnetic field induces an excitonic cal eigenmodes of the system; ideally one wants to optimize both polarization that can then be converted into a population by the simultaneously. High-quality low-dimensional semiconductor sys- interaction processes. Hopfield introduced the term ‘polariton’ to tems are often introduced into dielectrically structured environ- denote the coupled light and polarization fields that form a mixed- ments for this purpose. mode excitation in a semiconductor system. One of the main reasons for choosing low-dimensional semi- Because the original analysis by Hopfield focused on bulk semi- conductors rather than bulk material is because the excitonic conductor systems, the inclusion of spatial dispersion made it nec- binding energy — and thus the oscillator strength of the resonance — essary to introduce ‘additional boundary conditions’2,3 to match increases with decreasing system dimensionality. Whereas an ideal the single incoming electromagnetic field at the semiconductor– two-dimensional (2D) exciton is four times as strongly bound as air interface with the two propagating polariton modes inside the its 3D counterpart15, the exciton binding in a strictly 1D system is 1College of Optical Sciences, The University of Arizona, 1630 E. University Blvd., Tucson, Arizona 85721-0094, USA. 2Department of Physics and Material Sciences Center, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany. *e-mail: [email protected] NATURE PHOTONICS | VOL 5 | MAY 2011 | www.nature.com/naturephotonics 275 © 2011 Macmillan Publishers Limited. All rights reserved. REVIEW ARTICLE NAtURE pHOtOnICS DOI: 10.1038/NPHOTON.2011.15 30 a b ) –1 m µ 20 10 Absorption coecient ( 0 1.4881.490 1.4921.494 1.4961.498 1.500 Energy (eV) c 3.0 ~10 nm (meV) 2.5 γ 2.0 ~117 nm 1.5 1.0 0.5 HWHM total linewidth 0.0 0102030405060708090100 100 nm Number of quantum wells Figure 1 | MBE and narrow-linewidth excitonic transitions. Using MBE to grow semiconductor layers with almost monolayer precision has resulted in narrow-linewidth excitonic transitions that enhance the light–matter coupling needed for creating pronounced exciton–polariton effects.a , Transmission electron microscopy image of four In0.04Ga0.96As QWs separated by GaAs barriers. b, Absorption coefficient per QW for 30 0.04In Ga0.96As/GaAs QWs with a 0.56 meV FWHM heavy-hole exciton linewidth. c, Reflectivity linewidth as a function of number of QWs, with the Bragg separation λ( /2) between QWs and with the top and bottom of the sample coated in an antireflective layer. The points are experimental linewidths with error bars depicting 10% uncertainty. The slope of the straight line yields 27 ± 2 μeV for the radiative damping rate of a single QW. infinitely strong16. Because real structures are never truly 1D, no have an optical path length (refractive index n times the physical such divergence exists in nature. Although truly 2D systems also do length) a quarter of the vacuum wavelength λv. Each partial reflec- not exist, high-quality QW structures based on GaAs-type materials tion is in phase, resulting in a total reflectivity that approaches show quasi-2D behaviour with strongly enhanced exciton effects. In unity as the number of interfaces becomes very large. Two such quasi-0D quantum dot (QD) systems, the full motional quantization DBRs, separated by a spacer whose thickness is an integer multiple of electrons and holes leads to intrinsically discrete exciton states. of half-wavelengths, forms a planar microcavity — a Fabry–Pérot In addition to the enhancement of excitonic effects, low- interferometer with an extension of a few optical wavelengths dimensional semiconductor nanostructures have the significant (Fig. 2a). The quality factor Q of the cavity is very high because advantage that they can be grown with very high quality using cur- the reflectivity of a DBR mirror is close to unity, which leads to rent state-of-the-art molecular beam epitaxy (MBE) techniques strongly enhanced intracavity light fields (Fig. 2b). (Fig. 1a). Besides the controlled growth of individual structures, the The optical periodicity of the DBR allows it to be visualized as a introduction of passive separation (barrier or buffer) layers allows 1D photonic crystal. Both 2D and 3D photonic crystal structures have for a desired spatial arrangement and/or deposition onto prestruc- also been demonstrated17,18 and studied extensively. Etching periodic tured material, such as high-quality mirrors (see below). arrays of air holes into a planar semiconductor structure forms a 2D As always, problems may arise from the presence of undesira- photonic crystal if the optical path length between the
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