Das Strahlungsfeld in einem absorbierenden, periodischen Dielektrikum ist kanonisch quantisiert worden. Dabei wurde ein eindimensionales Modell mit punktförmigen Streuern betrachtet, deren Polarisierbarkeit den Kramers-Kronig Relationen gehorcht. Es wurde ein Quantisierungsverfahren nach Knöll, Scheel und Welsch [1] verwendet, das als eine Ergänzung zum mikroskopischen Huttner-Barnett Schema [2] aufgefaßt werden kann und in dem auf der Basis der phänomenologischen Maxwell Gleichungen eine bosonische Rauschpolarisation als die Quelle des Feldes auftritt. Das Problem reduziert sich dabei auf die Bestimmung der klassischenGreens Funktion. Die Kramers-Kronig Relationen der komplexen Polarisierbarkeit der Punktstreuer sichert die korrekte Verknüpfung zwischen Dispersion und Absorption. Der Punktstreuer ist dabei ein idealisiertes Modell, um periodische Hintergrundmedien, denen das Strahlungsfeld ausgesetzt ist, zu beschreiben. Er bedarf jedoch eines Kompromisses, um die entsprechenden Rauschquellen zu konstruieren. Es konnte gezeigt werden, daß der Punktstreuer dasselbe Streuverhalten wie eine dünne Potentialschwelle besitzt und damit die technischen Schwierigkeiten für den Fall eines absorptiven Punktstreuers überwunden werden können. An Hand dieses Beispiels konnte das Quantisierungsschema nach Knöll, Scheel und Welsch auf periodische und absorbierende Strukturen angewendet werden. Es ist bekannt, daß die Bestimmung der Modenstruktur für den Fall der Modenzerlegung des Strahlungsfeldes ein rein klassisches Problem darstellt. Mit Ausnahme des Vakuums ist eine zweckmäßige Modenzerlegung nur dann durchführbar, wenn mit einer reellen Polarisierbarkeit die Absorption vernachlässigt werden kann. Aus den Kramers-Kronig Relationen wird klar, daß solch eine Annahme nur in bestimmten Intervallen des Frequenzspektrums gerechtfertigt werden kann. Es wurde gezeigt, daß auch das quantisierte Strahlungsfeld in Anwesenheit der Punktstreuer in eben solchen Intervallen in Quasimoden entwickelt werden kann, wenn man neue Quasioperatoren als Erzeuger und Vernichter einführt. Die bosonischen Vertauschungsrelationen dieser Operatoren konnten bestätigt werden. Die allgemeine Vertauschungsrelation kanonisch konjugierter Variablen im Sinne der kanonischen Quantisierung kann für das elektrische Feld und das Vektorpotential beibehalten werden. In der Greens Funktion sind sämtliche Informationen über die dispersiven und absorptiven Eigenschaften des Dielektrikums sowie über die räumliche Struktur enthalten. Die wesentlichen Merkmale werden dabei durch den Reflexionskoeffizienten nach Boedecker und Henkel [3] bestimmt, der das Reflexionsverhalten an einem unendlich ausgedehnten Halbraum aus periodisch angeordneten Punktstreuern beschreibt. Mit Hilfe des Transfermatrixformalismus war es möglich einen allgemeinen Zugang zum Reflexionsverhalten zunächst endlicher Strukturen zu erhalten. Die Ausdehnung auf den Halbraum mit Hilfe der Klassifizierung in Untergruppen der Transfermatrizen nach ermöglichte es, den Reflexionskoeffizienten nach Boedecker und Henkel [3] auch geometrisch plausibel zu machen. Ein wesentlicher Aspekt von periodischen Systemen ist die Translationssymmetrie, die im Fall unendlich ausgedehnter, verlustfreier Systeme auf eine ideale Bandstruktur führt. Mit Hilfe der Untergruppenklassifizierung kann im verlustfreien Fall die Geometrie der Anordnung indirekt mit der Bandstruktur verknüpft werden. Es konnte nachgewiesen werden, daß auch der einzelne Punktstreuer immer in einer dieser Untergruppen zu finden ist. Dabei besitzt die Bandstruktur der unendlich periodischen Anordnung dieser Streuer immer eine von der Polarisierbarkeit abhängige Bandkante und eine von der Polarisierbarkeit unabhängige Bandkante. Die Bandstruktur, die mit den verlustbehafteten Feldern einhergeht, ist eine doppelt komplexe. Alternativ zu dieser nur schwer zu interpretierenden Bandstruktur wurden die Feldfluktuationen selektiv nach reellen Frequenzen und Wellenzahlen sondiert. Es zeigt sich, daß Absorption besonders in der Nähe der Bandkanten die Bänder verbreitert. Die Ergebnisse, die mit Hilfe der lokalen Zustandsdichtefunktion gewonnen wurden, konnten dabei bestätigt werden. [1] S. Scheel, L. Knöll and D. G. Welsch, Phys.Rev. A 58, 700 (1998). [2] B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992). [3] G. Boedecker and C. Henkel, OPTICS EXPRESS 11, 1590 (2003). / A canonical scheme based on the phenomenological Maxwell equations in the presence of dielectric matter is used to quantize the electromagnetic field in a periodic and lossy linear dielectric. We focus on a one-dimensional model of point scatterers with given frequency-dependent complex permittivity, and construct an expansion of the field operators that is based on the Green function and preserves the canonical equal-time commutation relations. Translation symmetry is secured by working with an infinite lattice. The impact of absorption is examined using the local density of states and the decay rate of a phase-coherent dipole chain located inside the structure. Incidentally the model is used to bring about a geometrical interpretation of the reflection from multilayers

Virtual aperture culling of the eigenmodes of a resonator (VACER) is a technique to focus light within turbid media at arbitrary locations. A seed pulse of light is directed through a phase-conjugate mirror (PCM) into a turbid medium. Though much of the light may be lost, any light which reaches the second PCM is phase conjugated and thus returned to the first PCM where the light will be phase conjugated again. Amplification by the PCMs can prevent decay of the light cycling between the PCMs. Introducing a mechanism which filters light based on position enables attenuation of the modes not traveling through the center of the virtual aperture resulting in a focusing of light at the center of the virtual aperture. The seed pulse and the positioning of the PCMs on opposite sides of the virtual aperture ensure that modes cannot bypass the virtual aperture. Magnetic fields and ultrasound waves are potential means for implementation of a virtual aperture. Generally, only weak filtration mechanisms like magnetic fields and ultrasound waves are innocuous to turbid media. Fortunately, weak effects can strongly cull modes in VACER because the filtration mechanism affects the modes during each pass between PCMs and the modes compete. A combination of theory and computational modeling prove that sound physical principles underlie VACER. Moreover, computational modeling reveals how mode overlap, the seed pulse, and other variables impact VACER performance. Good experimental performance is predicted. / text

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (leaves 73-77).

Dans les milieux fortement hétérogènes, les ondes ne se propagent pas de façon balistique. Elles peuvent interagir de nombreuses fois avec les hétérogénéités du milieu et entrer ainsi dans le régime de diffusion multiple. Dans ce régime, les méthodes classiques d'imagerie basées sur les trajets des ondes directes ou simplement diffusées sont inefficaces. Les formes d'ondes multiplement diffusées (coda) sont trop complexes pour être modélisées exactement mais elles sont parfaitement reproductibles et très sensibles aux variations du milieu de propagation. Des travaux récents ont démontré la possibilité de mesurer de faibles changements de vitesse d'un milieu grâce aux ondes diffuses, à l'échelle de la croûte terrestre (coda sismique) comme à l'échelle des matériaux (coda ultrasonore). Ces travaux s'intéressent majoritairement à des changements globaux ou régionaux des différents milieux. La problématique de cette thèse concerne la possibilité d'utiliser la coda pour étudier des changements locaux du milieu. Deux études complémentaires sont développées : Le problème direct consiste à modéliser les variations de la coda engendrées par un changement local. Nous distinguons le cas d'un changement local de structure (fort contraste d'impédance) du cas d'un changement local de vitesse (faible contraste d'impédance). Le problème inverse consiste à utiliser les mesures de variations de la coda pour tenter de localiser et de caractériser les changements survenus. Les applications potentielles de ces travaux concernent entre autres le suivi temporel de structures géologiques ainsi que le contrôle non destructif de matériaux hétérogènes. Avec cet objectif, les différentes méthodes développées sont illustrées par des simulations numériques d'ondes acoustiques et sismiques ainsi que par des expériences en ultrasons dans des éléments en béton. / In highly heterogeneous media, waves don't propagate ballistically. They can interact several times with the heterogeneities of the medium and enter the multiple scattering regime. In this regime, classical imaging techniques, based on direct or singly scattered waves fail. Multiply scattered waveforms (coda) are too complex for being exactly modeled but are perfectly reproducible and very sensitive to small variations of the medium. Recent works demonstrated the possibility of measuring small velocity variations with diffuse waves, either at the geophysical scale (seismic coda) or at the material scale (ultrasonic coda). These works are mainly focused in monitoring global or regional changes of the medium. The present thesis deals with the possibility of using coda waves to study local changes of the medium. Two complementary studies are developed: The forward problem addresses the modeling of the coda variations generated by a local change. We distinguish the case of a structural change (strong impedance contrast) from the case of a velocity change (small impedance contrast). The inverse problem consists in using the coda variations measurements to locate and characterize the changes that occurred. Potential applications may concern, among others, monitoring of geological structures and non-destructive testing of heterogeneous materials. This in mind, we illustrate the different studies with numerical simulations of acoustic and seismic waves and with ultrasound experiments in concrete blocks.

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La discrétion acoustique est un enjeu majeur dans le domaine de la défense navale. Dans ce contexte, DCNS Research souhaite évaluer la capacité des métamatériaux acoustiques aléatoires localement résonnants à constituer une rupture technologique, comparativement aux matériaux anéchoïques actuels. Nous nous proposons de dimensionner, suite à une étude paramétrique conséquente, des structures contenant une répartition aléatoire d’inclusions sphériques. Des échantillons de matériaux localement résonnants ont été fabriqués. Leur réponse acoustique a été mesurée et confrontée aux prédictions issues de modèle. L’impact des résonances des inclusions et de l’angle d’incidence a été mis en évidence. Enfin, une méthode d’identification de leurs propriétés effectives a été développée à partir de mesures en réflexion et en transmission. Elle repose sur une configuration expérimentale originale. Des difficultés liées à l’extraction de la masse volumique dynamique sont mises en exergue. / Stealth is a major issue in naval defence. In this context, DCNS Research wants to know if locally-resonant acoustic metamaterials represent a technological breakthrough in comparison to current anechoic materials. We propose here a design of structures with randomly distributed spheres, based on a consequent parametric study. Samples of locally resonant materials were manufactured. Then, their acoustic response has been measured and compared to predictions based on multiple scattering theories. The presence of resonances and the impact of a non-null incidence angle have been highlighted. Finally, we developed a characterization method of the effective properties, from measurements of coefficients of reflection and transmission. Its design is based on an originally experimental setup. Difficulties coming from the retrieval of the dynamic mass density have been showed.

Les matériaux acoustiques super absorbants, sub-longueur d’ondes et large bande, ouvrent de nouvelles perspectives prometteuses pour l’isolation sonore. Dans ce contexte, nous avons conçu et synthétisé des structures hétérogènes comportant des microbilles sphériques de silicone poreux « ultra-lentes », distribuées dans des matrices aqueuses ou élastomériques. Dans un premier temps, nous avons démontré pourquoi la vitesse du son est aussi basse dans les silicones poreux (<100 m/s) comparativement à celle de milieux homogènes (~1000 m/s). Ce fort contraste de propriétés acoustiques entre phases étant susceptible d’induire des propriétés extrêmement diffusantes des microbilles, nous avons étudié l’impact de la nature de la matrice et de l’arrangement (aléatoire ou périodique) des microbilles sur les propriétés acoustiques d’échantillons se présentant sous forme de plaques sub-longueurs d’ondes à faces parallèles. Nous avons montré que la présence de minima prononcés dans le coefficient de transmission de ces métaplaques était pilotée par la résonance monopolaire des microbilles, et était fortement conditionnée par la nature de la matrice environnante. Enfin, toutes les mesures ultrasonores de l’étude ont été confrontées avec succès à des prédictions issues de modèles de diffusion multiple. / Acoustic metamaterials may behave like sub-wavelength and broadband sound-absorbers, opening thus new promising routes for sound insulation. In this context, we have designed and achieved heterogeneous structures composed of soft porous silicone rubber microbeads with ultra-low sound speeds, dispersed in various aqueous or elastomeric matrices. First, we show why the sound speed is so low in soft porous silicone rubber materials (<100m/s) in comparison with soft homogeneous materials (~1000m/s). Such a large sound-speed contrast resulting in strongly scattering properties of the microbeads, we have studied the influence of the matrix characteristics as well as the arrangement of microbeads (random or ordered) on the acoustic properties of the samples in form of sub-wavelength slabs. We have evidenced deep and wide minima of acoustic transmission due to the strong monopolar resonances of the microbeads, which strongly depend on the properties of the surrounding matrix. All our ultrasonic measurements have been compared with theoretical predictions based on various Multiple Scattering Theories, revealing an excellent quantitative agreement.

Understanding the phenomenon of wave scattering by random media is a ubiquitous problem that has instigated extensive research in the field. This thesis focuses on wave scattering by quasiperiodic media as an alternative approach to provide insight into the effects of structural aperiodicity on the propagation of the waves. Quasiperiodic structures are aperiodic yet ordered so have attributes that make them beneficial to explore. Quasiperiodic lattices are also used to model the atomic structures of quasicrystals; materials that have been found to have a multitude of applications due to their unusual characteristics. The research in this thesis is motivated by both the mathematical and physical benefits of quasiperiodic structures and aims to bring together the two important and distinct fields of research: waves in heterogeneous media and quasiperiodic lattices. A review of the past literature in the area has highlighted research that would be beneficial to the applied mathematics community. Thus, particular attention is paid towards developing rigorous mathematical algorithms for the construction of several quasiperiodic lattices of interest and further investigation is made into the development of periodic structures that can be used to model quasiperiodic media. By employing established methods in multiple scattering new techniques are developed to predict and approximate wave propagation through finite and infinite arrays of isotropic scatterers with quasiperiodic distributions. Recursive formulae are derived that can be used to calculate rapidly the propagation through one- and two-dimensional arrays with a one-dimensional Fibonacci chain distribution. These formulae are applied, in addition to existing tools for two-dimensional multiple scattering, to form comparisons between the propagation in one- and two-dimensional quasiperiodic structures and their periodic approximations. The quasiperiodic distributions under consideration are governed by the Fibonacci, the square Fibonacci and the Penrose lattices. Finally, novel formulae are derived that allow the calculation of Bloch-type waves, and their properties, in infinite periodic structures that can approximate the properties of waves in large, or infinite, quasiperiodic media.

The book presents my PhD thesis, which is about aerosol-cloud interactions by means of a dual-field-of-view polarization lidar. Aerosol-cloud interactions (ACI) are a big challenge to quantify the overall effect of human activities on the radiative, heat, and precipitation budgets of the atmosphere. New observational capabilities are demanded. To study the influence of aerosol particles on cloud microphysics an analysis scheme composed of newly-developed arrays is introduced. The retrieval of microphysical properties of liquid-water clouds and of the aerosol particles below the clouds from lidar observations, in a practical and replicable way, is the major challenge tackled in this work. A lidar-based approach to derive liquid-water cloud microphysical properties from dual-field-of-view (DFOV) depolarization measurements is introduced. In addition, a new method to accurately obtain the aerosol properties below cloud layers was developed and implemented into the analysis infrastructure. Comparisons with alternative observational and modeling approaches corroborate the accuracy of both methods. The number concentration of cloud condensation nuclei (CCN) is derived from the aerosol particle extinction coefficient below the cloud, and in combination with the cloud-microphysics retrieval, they provide an aerosol-cloud scene, which allow us to study ACI. Long-term observations at the pristine location of Punta Arenas (PA), Chile, and at the polluted site of Dushanbe (DB), Tajikistan, were analyzed for this purpose. On average, similar values of cloud droplet and below-cloud CCN number concentrations, in the range of 10--150~cm$^{-3}$, were observed at PA. At DB, larger cloud droplet number concentrations were observed, in the order of 200--400 cm-3 but much larger CCN concentrations of about 700--900 cm-3 were found. The so-called ACI index was assessed from the collected data sets. The most robust estimate of the index was obtained when calculating monthly averages over the whole measurement periods, fourteen months at PA and seven months at DB. Values of 0.83 +/- 0.20 and 0.57+/ 0.26 were derived at PA and DB, respectively, and they were used to estimate the radiative forcing due to the Twomey effect. A radiative cooling from -0.70 to -0.17 Wm-2 for PA and between -1.89 and -0.66 Wm-2 for DB is found. These results agree with global estimates of the cloud-mediated aerosol effect but are slightly larger than those values usually found at the specific locations considered. Furthermore, the results obtained at PA show the relevance of updraft movements to trigger ACI. When considering only updraft-dominated periods, the ACI index is up to 50% larger than when no wind information is considered. The new capabilities illuminated during this work may provide a big help for estimations of the cloud-mediated radiative effect and may provide a baseline to confront models dealing with cloud microphysics in future studies.:1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2 Aerosol, clouds and their interaction - State of the art and research questions. . 7 2.1 Aerosol and clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Aerosol effect on liquid-water clouds . . . . . . . . . . . . . . . . . . . . . . . . .8 2.1.2 Aerosol effect on ice-containing clouds . . . . . . . . . . . . . . . . . . . . . . .9 2.1.3 Cloud processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 2.1.4 Modeling droplet number concentration Nd . . . . . . . . . . . . . . . . . . 10 2.2 Aerosol radiative effect via ACI in liquid-water clouds . . . . . . . . . . . . . .11 2.2.1 Aerosol-cloud-interaction index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Observational approaches for the ACI index. . . . . . . . . . . . . . . . . . . .14 2.2.3 Strategies to evaluate the ACI index from observations . . . . . . . . . . .16 2.2.4 ACI studies based on lidar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Lidar measurements of aerosol-cloud interaction – Overview of applied methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 3.1 Multiple-scattering lidar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 3.2 DFOV-Raman technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3 Single-FOV polarization lidar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 3.3.1 Comparison between DFOV-Raman and SFOV-Depol methods . . . 27 3.4 Dual-FOV depolarization approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.1 Calibration of the lidar system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.2 DFOV-Depol measurement cases . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 Implementation of the DFOV-Depol approach into the standardized lidar sys- tem Polly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 4 Research results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 4.1 First publication: Polarization lidar: an extended three-signal calibration approach . . . . . . .39 4.2 Second publication: The dual-field-of-view polarization lidar technique: A new concept in monitoring aerosol effects in liquid-water clouds – Theoretical framework . . . . . . . . .59 4.3 Third publication: The dual-field-of-view polarization lidar technique: A new concept in monitoring aerosol effects in liquid-water clouds – Case studies . . . . . . . . . . . . . . . .79 5 Discussion and further applications – Long-term observations of aerosol- cloud interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101 5.1 Observations on cloud scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102 5.2 Long-term results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.1 Comparison of DFOV-Depol products with available estimations and observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 5.3 Assessment of the ACI index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.4 Relevance of the ACI index for the radiative effect . . . . . . . . . . . . 112 6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 Appendix A: Aerosol properties with lidar . . . . . . . . . . . . . . . . . . . .125 A.1 Lidar principles of elastic and Raman lidar . . . . . . . . . . . . . . . .125 A.2 Raman lidar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.2.1 Retrieval of extinction coefficient . . . . . . . . . . . . . . . . . . . . . 128 A.2.2 Retrieval of backscattering coefficient. . . . . . . . . . . . . . . . . . 128 A.2.3 Bottom-up approximation for Raman Signals . . . . .. . . . . . . 129 A.2.4 Evaluation of Raman methods. . . . . . . . . . . . . . . . . . . . . . . 130 A.3 Elastic Lidar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 A.3.1 Klett-Fernald Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 A.3.2 Quasi-backscattering for high resolved retrievals. . . . . . . . . 133 A.3.3 Bottom-up approximation for elastic signals . . . . . . . . . . . . 135 A.3.4 Evaluation of methods based on elastic lidar. . . . . . . . . . . . 137 A.3.5 Microphysical properties from optical properties. . . . . . . . . . 139 Appendix B Characterization of DFOV-Depol lidar . . . . . . . . . . . . 143 B.1 Transmission ratio based on long-term analysis . . . . . . . . . . . 144 Appendix C: Author’s contributions to the three publications . . . . 149 Appendix D Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151 D.1 List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151 D.2 List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 D.3 List of Symbols (excluding cumulative part) . . . . . . . . . . 156 D.4 List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158