Mesoscale optics provides a framework for understanding a wide range of phenomena occurring in a variety of fields ranging from biological tissues to composite materials and from colloidal physics to fabricated nanostructures. When light interacts with a complex system, the outcome depends significantly on the length and time scales of interaction. Mesoscale optics offers the apparatus necessary for describing specific manifestations of wave phenomena such as interference and phase memory in complex media. In-depth understanding of mesoscale phenomena provides the required quantitative explanations that neither microscopic nor macroscopic models of light-matter interaction can afford. Modeling mesoscopic systems is challenging because the outcome properties can be efficiently modified by controlling the extent and the duration of interactions. In this dissertation, we will first present a brief survey of fundamental concepts, approaches, and techniques specific to fundamental light-matter interaction at mesoscopic scales. Then, we will discuss different regimes of light propagation through randomly inhomogenous media. In particular, a novel description will be introduced to analyze specific aspects of light propagation in dense composites. Moreover, we will present evidence that the wave nature of light can be critical for understanding its propagation in unbounded highly scattering materials. We will show that the perceived diffusion of light is subjected to competing mechanisms of interaction that lead to qualitatively different phases for the light evolution through complex media. In particular, we will discuss implications on the ever elusive localization of light in three-dimensional random media. In addition to fundamental aspects of light-matter interaction at mesoscopic scales, this dissertation will also address the process of designing material structures that provide unique scattering properties. We will demonstrate that multi-material dielectric particles with controlled radial and azimuthal structure can be engineered to modify the extinction cross-section, to control the scattering directivity, and to provide polarization-dependent scattering. We will show that dielectric core-shell structures with similar macroscopic sizes can have both high scattering cross-sections and radically different scattering phase functions. In addition, specific structural design, which breaks the azimuthal symmetry of the spherical particle, can be implemented to control the polarization properties of scattered radiation. Moreover, we will also demonstrate that the power flow around mesoscopic scattering particles can be controlled by modifying their internal heterogeneous structures. Lastly, we will show how the statistical properties of the radiation emerging from mesoscopic systems can be utilized for surface and subsurface diagnostics. In this dissertation, we will demonstrate that the intensity distributions measured in the near-field of composite materials are direct signatures of the scale-dependent morphology, which is determined by variations of the local dielectric function. We will also prove that measuring the extent of spatial coherence in the proximity of two-dimensional interfaces constitutes a rather general method for characterizing the defect density in crystalline materials. Finally, we will show that adjusting the spatial coherence properties of radiation can provide a simple solution for a significant deficiency of near-field microscopy. We will demonstrate experimentally that spurious interference effects can be efficiently eliminated in passive near-field imaging by implementing a random illumination.
Mesoscale optics provides a framework for understanding a wide range of phenomena occurring in a variety of fields ranging from biological tissues to composite materials and from colloidal physics to fabricated nanostructures. When light interacts with a complex system, the outcome depends significantly on the length and time scales of interaction. Mesoscale optics offers the apparatus necessary for describing specific manifestations of wave phenomena such as interference and phase memory in complex media. In-depth understanding of mesoscale phenomena provides the required quantitative explanations that neither microscopic nor macroscopic models of light-matter interaction can afford. Modeling mesoscopic systems is challenging because the outcome properties can be efficiently modified by controlling the extent and the duration of interactions. In this dissertation, we will first present a brief survey of fundamental concepts, approaches, and techniques specific to fundamental light-matter interaction at mesoscopic scales. Then, we will discuss different regimes of light propagation through randomly inhomogenous media. In particular, a novel description will be introduced to analyze specific aspects of light propagation in dense composites. Moreover, we will present evidence that the wave nature of light can be critical for understanding its propagation in unbounded highly scattering materials. We will show that the perceived diffusion of light is subjected to competing mechanisms of interaction that lead to qualitatively different phases for the light evolution through complex media. In particular, we will discuss implications on the ever elusive localization of light in three-dimensional random media. In addition to fundamental aspects of light-matter interaction at mesoscopic scales, this dissertation will also address the process of designing material structures that provide unique scattering properties. We will demonstrate that multi-material dielectric particles with controlled radial and azimuthal structure can be engineered to modify the extinction cross-section, to control the scattering directivity, and to provide polarization-dependent scattering. We will show that dielectric core-shell structures with similar macroscopic sizes can have both high scattering cross-sections and radically different scattering phase functions. In addition, specific structural design, which breaks the azimuthal symmetry of the spherical particle, can be implemented to control the polarization properties of scattered radiation. Moreover, we will also demonstrate that the power flow around mesoscopic scattering particles can be controlled by modifying their internal heterogeneous structures. Lastly, we will show how the statistical properties of the radiation emerging from mesoscopic systems can be utilized for surface and subsurface diagnostics. In this dissertation, we will demonstrate that the intensity distributions measured in the near-field of composite materials are direct signatures of the scale-dependent morphology, which is determined by variations of the local dielectric function. We will also prove that measuring the extent of spatial coherence in the proximity of two-dimensional interfaces constitutes a rather general method for characterizing the defect density in crystalline materials. Finally, we will show that adjusting the spatial coherence properties of radiation can provide a simple solution for a significant deficiency of near-field microscopy. We will demonstrate experimentally that spurious interference effects can be efficiently eliminated in passive near-field imaging by implementing a random illumination.
General overview In many areas in the physical sciences, the propagation of waves in complex mediaplays a central role. Acoustics, applied mathematics, elastics, environmental sciences, mechanics, marine sciences, medical sciences, microwaves, and seismology are just a few examples, and of course nanophotonics [6, 429, 448, 449]. Here, complex media are understood to exhibit a strongly inhomogeneous spatial structure, which determines to a large extent their linear and nonlinear properties. Examples of complex media are random, heterogeneous, porous, and fractal media. The challenges that researchers in these areas must surmount to describe, understand, and ultimately predict wave propagation are formidable. Right from the start of this field – in the early 1900s – it was clear that new concepts and major approximations had to be introduced. Famous examples of such concepts are the effective medium theory [55, 60, 321] and the radiative transport theory [81, 491]. These concepts are very much alive, even today. The fundamental challenge with these approximate concepts is that often the length scales of the inhomogeneities in the complex medium are comparable with the wavelength, whereas the range of validity of these approximations is restricted to situations where these length scales are much larger than the wavelength. Consequently, many relevant situations arise where either the effective medium theory, or radiative transport theory, or both, fail dramatically. Examples of such situations are given in this introduction and throughout this book. The complexity of the medium that supports wave propagation can be classified in a number of ways. Many different types of spatial inhomogeneities in a host matrix can be envisioned, varying from completely random, via aperiodic and waveguide structures, to quasi-crystalline and even structures with long-range periodic order. The in homogeneities could be of a self-organized form, or the fruit of precise engineering. An additional classification is whether or not the complexity is confined to the surface (in two dimensions (2D)) or is present throughout the volume of the medium (in three dimensions (3D)), as in porous media.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
Interactions between light and molecular matter featuring photon absorption are commonly associated with excitation of individual chromophores. Subsequent relaxation is achieved through numerous mechanisms, such as scattering and energy transfer to neighbouring chromophores. The efficiency of such processes depends on many factors, including the intensity and wavelength of the optical input, the absorption cross-section of the molecule and the relative orientation of molecular components. New photonic materials are developed on the principle that such factors are controllable, duly tailoring the system to suit new technological applications. The parameters that determine the linear response in multicomponent materials are typically assessed within the theoretical framework of classical optics. However, with improved interest and capability in fabricating nanoscale structures (especially those that exhibit quantum effects), it is becoming increasingly relevant to develop theory that more faithfully represents how individual photons engage with matter. In such constructs, the interaction of materials with optical waves and photons is highly dependent on local molecular environment, therefore surrounding structures and ancillary species exert forms of influence on the photophysical processes inherent within dielectric media. At optical wavelengths where the secondary structure displays little intrinsic optical absorption, the role of such components is often interpreted as modifying the input through a corrective local index of refraction. Although expedient in the discussion of bulk properties of a macroscopic medium, it is reasonably supposed at a local chromophore-photon level that optical mechanisms operate in a different fashion. Using a fully quantized approach to the representation of local molecular electronic structure and electrodynamics, this research develops rigorous theory and a corresponding physical interpretation of how photon absorption, scattering and energy transfer are modified by vicinal, non-absorbing chromophores. The results provide insight into the mechanisms achieved within multi-chromophore systems, highlighting factors that assist in the optimization of optical characteristics in designer materials.
Light propagation in matter is described by vibration eigenstates, called modes, which characterize the light-matter interaction. In the specific case of random media, according to the strength of the disorder, the modes can be either extended over the whole system or spatially localized. This disorder-based confinement is called Anderson’s localization.In the first part, we introduce basic notions used along this manuscript. In particular the light-matter interaction requires a semiclassical approach: The electromagnetic field is described by Maxwell’s equations while the quantum nature of matter must be considered. In this thesis open media are studied. In such systems the modal description requires a specific analytic treatment different from closed problems. In the second part, we focus on Anderson-localized modes in open passive random media. Any change of the disorder induces modifications of modes. Therefore, it enables the control over the light properties. Moreover, when inserting an emitter inside an Anderson-localized mode, strong light-matter interaction regimes can be reached. In the third part, active random media, commonly called random lasers, are introduced. Using our experimental achievements, characteristics of random lasers are presented. The notion of mode enables us to describe complex mechanisms involved in the lasing emission. Last, we demonstrate both experimentally and numerically that a non-uniform excitation of random lasers can lead to a control of the properties of the emission. In particular a multimode spectrum for a uniform pumping can be turned into single-mode using an adapted pumping.
The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.