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This thesis addresses the subject of diffractive axicons inpartially coherent or oblique illumination. Design andcharacterization of the axicons are performed using asymptoticwave optics, employing the stationary-phase method to obtainapproximations of the diffraction integrals. A design method for axicons in partially coherentillumination is derived. The method can be applied to anyincident illumination on radially symmetric Schell-model form.It provides analytical solutions for some specific cases, butfor most incident intensity and coherence distributions it canbe solved numerically to yield the desired on-axis intensity.In addition, a method for estimating the width of the focalline is provided. For coherent light, the design method isidentical to the old one based on energy conservation in raybundles. Since the new method is derived entirely from waveoptics, it both clarifies the old method and extends it topartially coherent light. Oblique illumination of axicons, frequently encountered inapplications, causes degradation of the focal line. This changeis characterized, and from the asymptotic theory it is foundthat the focal line is described by an asteroid curve. Thewidth of the focal segment in oblique illumination isaccurately predicted, as confirmed by simulations andexperiments. It is also found that at a fixed angle, anelliptical axicon may be used to compensate for the adverseeffects of oblique illumination. Keywords:axicons, diffractive optics, coherence,asymptotic methods / NR 20140805

The inverse design of optical devices that exhibit desired functionalities as well as the solution of complex inverse problems are becoming essential research directions in modern optical engineering. Recent advancements in computation algorithms, machine learning architectures and optimization methods offer efficient means to deal with complex photonics problems with a large number of degrees of freedom. In this thesis, I present our work on developing an integrated framework for the inverse design of diffractive optical elements and nanophotonic media with tailored optical responses. In the first part of our work, we introduce the design of single-layer diffractive optical devices that extend conventional imaging functions to include dual-band multi-focal microlenses for multi-band imaging, modulated axilenses for ultracompact spectrometers, and hyperuniform phase plates for lensless imaging systems. We design these diffractive elements based on Rayleigh-Sommerfeld scalar diffraction simulations. We also fabricate them using scalable lithography and experimentally characterize their predicted diffraction and imaging performances. While we successfully validated our designs, we also identified the fundamental limitations and challenges of single-layer diffractive devices. In order to address these problems, in the second part of the work we introduce a novel and flexible approach for the inverse design of diffractive optical elements based on adaptive deep diffractive neural networks (a-D2NNs). In particular, we demonstrate two-layer dual-band multi-focal devices that exceed the efficiency limit of traditional single-layer devices and we leverage the powerful a-D2NN inverse design platform to engineer systems with targeted spectral lineshapes and focusing point-spread functions. Moreover, we apply a-D2NNs to the inverse design of ultracompact spectrometers and demonstrate nanometer-range spectral resolution for 100 micron-size devices that can be fabricated using conventional lithographic procedures. Finally, we apply the a-D2NNs approach to the design of hyperuniform scalar random fields that we have introduced as novel lensless imaging systems with modulated transfer functions that produce enhanced image quality compared to state-of-the-art phase plates based on the Perlin noise. We additionally show that a-D2NNs can be used to efficiently design different classes of hyperuniform random media that are currently being explored for a number of optical applications. In the third part of my thesis, we propose and develop a deep learning framework for solving inverse photonics problems by employing physics-informed neural networks (PINNs). We solve the non-local effective medium problem for finite-size metamaterials and address losses and radiation effects. Furthermore, we apply PINNs to solve the invisible cloaking inverse problem beyond the quasi-static limit. Finally, we develop a general PINN framework for inverse retrieval of optical parameters based on near-field data information. Based on our approach, we show the successful retrieval of the electric and magnetic optical parameters (i.e., non-local permittivity and permeability functions) of two-dimensional and three-dimensional scatterers in the presence of absorption losses. Additionally, we demonstrate the application of the inverse PINN design to the scanning near-field microscopy technique under localized excitation and in the presence of noise. In the last part of our work, we couple adjoint optimization methods with the rigorous multiple scattering theory of cylinder arrays (i.e., two-dimensional generalized Mie theory) for the inverse design of small-size, photonic structures, called “photonic patches”, that achieve different functionalities with optimal efficiencies. Specifically, we present the inverse design of photonic patches that angularly shape incoming radiation and that focus light intensity over Fresnel-zone distances (~ 10μm) with engineered spectral lineshapes, enhanced local density of states and resonance quality factors.

De nombreux travaux de recherche sont actuellement menés afin de rendre les caméras infrarouges plus compactes et moins chères. En infrarouge refroidi, le défi est de proposer un système cryogénique compact pouvant être intégré sur un système à faible capacité d’emport tel qu’un drone. Dans ce cadre, l’utilisation d’une lentille mince en remplacement du filtre froid du cryostat permettrait de limiter la masse supplémentaire à refroidir et de maintenir constant le temps de descente en froid. En infrarouge non refroidi, l’objectif est de concevoir un petit capteur infrarouge bas coût « grand public » que l’on pourra inviter dans nos maisons, nos voitures, voire nos smartphones. L’utilisation d’une lentille mince ouvrirait la voie à des imageurs infrarouges peu onéreux.Dans ce contexte, j’ai choisi d’étudier le comportement d’une lentille de Fresnel dite d’ordre élevé intégrée dans une configuration optique de type landscape lens. J’ai montré que cette architecture optique mince peut fonctionner sur une large bande spectrale et sur un grand champ de vue. Cependant, les lentilles de Fresnel d’ordre élevé étant mal modélisées dans la littérature, j’ai développé mes propres algorithmes de modélisation afin de prévoir les performances d’un tel système. Grâce à cette étude, j’ai ensuite proposé deux systèmes d’imagerie, l’un refroidi et l’autre non refroidi. Chacun des deux systèmes a fait l’objet d’un prototype et a été entièrement caractérisé expérimentalement. Les résultats expérimentaux obtenus m’ont permis de valider les performances anticipées théoriquement et de mettre en évidence un phénomène de chromatisme diffractif latéral. Ces systèmes ouvrent la voie à deux nouvelles générations de caméras infrarouges. J’ai montré que l’imageur infrarouge refroidi possède une qualité image satisfaisante pour des applications d’aide au pilotage. Le prototype non refroidi est lui entièrement compatible avec des applications domotiques. Il a suscité l’intérêt de différents acteurs industriels. / Miniaturizing infrared optical systems is a research area of great interest nowadays in order to make them lighter and cheaper. In the cooled infrared domain, the objective is to design a compact cryogenic camera that could be integrated in a small-capacity carrier like a drone. To that purpose, replacing the cold filter of the dewar by a thin lens would limit the cooled down mass and would stabilize the cool down time. In the uncooled infrared domain, the objective is to design a small general use camera at a low cost. Its use could be generalized in houses, cars or even smartphones. The use of a thin lens would also pave the way for low-cost infrared imagers. In this context, I chose to study the imagery properties of a high order Fresnel lens integrated in a landscape lens architecture. I have demonstrated that this architecture can be used within a wide spectral range and over a wide field of view. However, current optical design software perform poorly on high order Fresnel lenses. Therefore, I have developed my own algorithms to model the performances of such a system. With that study, I have been able to design two prototypes with their own objectives: the first one is cooled and the second one is uncooled. Both systems have been demonstrated and entirely characterized. The experiment results have validated the theoretical performances of the systems and they highlighted an original kind of lateral chromatic aberration.These two systems pave the way to two new generations of infrared cameras. Indeed, on one hand I have proved that the cooled infrared quality may be good enough to qualify for an aircraft piloting aid. On the other hand, the uncooled prototype is fully compatible with low cost surveillance applications and the system raised the interest of various companies.

Non-mechanical variable lenses are important for creating compact imaging devices. Various methods employing dielectrically actuated lenses, membrane lenses, and liquid crystal lenses were previously proposed [1-4]. In This dissertation the design, fabrication, and characterization of innovative flat tunable-focus liquid crystal diffractive lenses (LCDL) are presented. LCDL employ binary Fresnel zone electrodes fabricated on Indium-Tin-Oxide using conventional micro-photolithography. The light phase can be adjusted by varying the effective refractive index of a nematic liquid crystal sandwiched between the electrodes and a reference substrate. Using a proper voltage distribution across various electrodes the focal length can be changed between several discrete values. Electrodes are shunted such that the correct phase retardation step sequence is achieved. If the number of 2πzone boundaries is increased by a factor of m the focal length is changed from f to f/m based on the digitized Fresnel zone equation: f = rm²/2mλ, where r(m) is mth zone radius, and λ is the wavelength. The chromatic aberration of the diffractive lens is addressed and corrected by adding a variable fluidic lens. These LCDL operate at very low voltage levels (±2.5V ac input), exhibit fast switching times (20-150 ms), can have large apertures (>10 mm), and small form factor, and are robust and insensitive to vibrations, gravity, and capillary effects that limit membrane and dielectrically actuated lenses. Several tests were performed on the LCDL including diffraction efficiency measurement, switching dynamics, and hybrid imaging with a refractive lens. Negative focal lengths are achieved by adjusting the voltages across electrodes. Using these lenses in combination, magnification can be changed and zoom lenses can be formed. These characteristics make LCDL a good candidate for a variety of applications including auto-focus and zoom lenses in compact imaging devices such as camera phones. A business plan centered on this technology was developed as part of the requirements for the minor in entrepreneurship from the Eller College of Management. An industrial analysis is presented in this study that involves product development, marketing, and financial analyses (Appendix I).

The Point Spread Function (PSF) indirectly encodes the wavefront aberrations of an optical system and therefore is a metric of the system performance. Analysis of the PSF properties is useful in the case of diffractive optics where the wavefront emerging from the exit pupil is not necessarily continuous and consequently not well represented by traditional wavefront error descriptors such as Zernike polynomials. The discontinuities in the wavefront from diffractive optics occur in cases where step heights in the element are not multiples of the illumination wavelength. Examples include binary or N-step structures, multifocal elements where two or more foci are intentionally created or cases where other wavelengths besides the design wavelength are used. Here, a technique for expanding the electric field amplitude of the PSF into a series of orthogonal functions is explored. The expansion coefficients provide insight into the diffraction efficiency and aberration content of diffractive optical elements. Furthermore, this technique is more broadly applicable to elements with a finite number of diffractive zones, as well as decentered patterns.

This project is framed by a dilemma: representations of teaching practice are critical in teacher education, and yet the representations we rely on dangerously oversimplify teaching. My central questions emerge from this dilemma. In telling stories about teaching, how messy can the story be before it becomes unintelligible? Why does messiness matter and what does it produce for teachers-to-be? After examining both canonical accounts of teacher knowledge and emergent research that is productively disrupting the field, I draw on the work of Karen Barad to help me imagine both a new way of telling teaching stories, what I call diffractive storytelling, and a new way of thinking about their use in teacher education. In particular, I take up Barad’s concept of apparatus to consider what knowing is made possible by traditional teacher stories, what knowing is foreclosed, and what these possibilities and limitations mean for teacher education. Finally, I turn to other apparatuses at work in teacher education, especially standardized assessments such as edTPA, the new performance-based assessment of teacher readiness being implemented across the country. I argue that attending carefully to the apparatus-ness of the instruments used in teacher preparation allows us to contest the naturalization of narrow conceptions of teaching practice and sustains the paradox of holding to standards while resisting standardization.

Cette thèse a pour but de déterminer dans un certain nombre de cas l'importance de la prise en compte des effets transverses dans les modélisations des dispositifs lasers. Dans un premier temps, il est démontré la possibilité de mettre en forme le profil radial d'intensité d'un faisceau laser en utilisant des optiques diffractives de phase dites binaires. Trois applications concrètes seront développées : la « circularisation » d'un faisceau elliptique, la « rectangularisation » d'un faisceau circulaire et la génération d'un anneau de lumière polarisé radialement. Dans un second temps, nous montrons qu'une prise en compte rigoureuse des effets transverses est en mesure d'expliquer le comportement auto-déclenché d'un laser Cr:LiSAF, de justifier la présence d'une zone de bistabilité optique dans la caractéristique puissance de sortie en fonction de la puissance de pompe pour les lasers à base de verres phosphates codopés erbium et ytterbium fortement dopés. De plus, la prise en compte de la diffraction sur le profil de gain a permis d'expliquer l'apparition d'un mode fondamental annulaire dans un laser Nd:YVO4. La dernière partie de la thèse est consacrée à l'étude des lasers déclenchés passivement fonctionnant à 1,5µm. Une base de données expérimentales a été constituée avec un grand nombre d'absorbants saturables de nature différente testés. Cette base de données a permis de tester la fiabilité des modèles intégrant des degrés de complexité croissants dans la prise en compte des effets transverses.

Durante las últimas décadas, la construcción de anillos de almacenamiento de electrones exclusivamente dedicados a la producción de radiación sincrotrón ha sido la clave para justificar el gran desarrollo de los componentes ópticos para rayos X. Se requieren nuevos elementos ópticos para una explotación óptima de las propiedades de esta luz, que puede usarse para descubrir los secretos de la materia y para revelar el mundo microscópico. El uso de radiación sincrotrón como sonda ha hecho posible una gran cantidad de experimentos para expandir el conocimiento de muchas áreas científicas. Paulatinamente, la radiación sincrotrón se ha convertido en un instrumento indispensable para muchos científicos, que trabajan en disciplinas muy diferentes como la biología, la química, la ciencia de materiales o incluso la arqueología. La microscopía de rayos X ha emergido como técnica para observar estructuras que no son accesibles con microscopia óptica convencional, y que tiene ventajas respeto a la microscopía electrónica debido a la mayor longitud de penetración y a la sensibilidad química de la radiación X. La óptica de los microscopios de rayos X incluye componentes como las lentes zonales de Fresnel que se producen con técnicas de microfabricación. En este trabajo, se han fabricado lentes zonales de Fresnel utilizando distintas técnicas y se han testado en diversas Fuentes de Luz Sincrotrón. Describiremos en detalle las técnicas de micro- y nanofabricación que son necesarias para la producción de estos elementes, des de la litografía por haz de electrones a la transferencia del patrón a distintos materiales. En particular, presentamos lentes para rayos X blandos hechas de silicio. Mostraremos que éstas funcionan bien en las fuentes de luz existentes y que debido a su robustez serán también apropiadas para las fuentes de rayos X de 4a generación. También preparamos un elemento óptico difractivo que produce una mancha iluminación cuadrada y llana, y que puede usarse como lente condensadora en microscopía de rayos X de transmisión. Finalmente, también demostramos un nuevo método de fabricación que puede mejorar la resolución espacial última de las lentes difractivas para rayos X. Se fabricaron lentes zonales de Fresnel con una última zona de 20 nm y líneas de 15 nm han sido claramente resueltas en microscopía de rayos X de rastreo. Este trabajo se ha realizado en el Laboratorio de Luz Sincrotrón en Barcelona, con la participación del Centro Nacional de Microelectrónica de Barcelona (CSIC-CNM) y del Grupo de Óptica del Departamento de Física de la Universidad Autónoma de Barcelona. Al mismo tiempo, partes esenciales de este trabajo se han realizado con la colaboración del Dr. C. David y el Dr. K. Jefimovs del Labor fur Mikro- und Nanotechnologie al Paul Scherrer Institut en Villigen (Suiza). / During the last decades, the construction of electron storage rings exclusively dedicated to the production of synchrotron radiation has been a key reason to explain the large development of x-ray optics. New optical elements are required for an optimal exploitation of the properties of this light, which can be used to find out the secrets of matter and to reveal the microscopic world. The use of synchrotron light as a probe has made possible a large quantity of experiments to expand the knowledge in many scientific areas. Little by little, synchrotron radiation sources have become an indispensable tool for the research of lots of scientists, who work in very different disciplines such as biology, chemistry, physics, material science or even archaeology. X-ray microscopy has emerged as a technique to observe structures which are not accessible with conventional optical microscopy, and that has advantages in respect to electron microscopy due to the longer penetration depth and chemical sensitivity of the x-ray radiation. The optics of the x-ray microscopes includes components such as the Fresnel zone plate lenses which are made by means of microfabrication techniques. Within this work, Fresnel zone plate lenses were produced using different approaches and they have been tested in several Synchrotron Light Sources. We will describe in detail the micro- and nanofabrication techniques that are necessary for the production of such elements, from the electron beam lithography to the pattern transfer into different materials. In particular, we will present lenses for soft x-rays made of silicon. We show that they perform well at the current light sources and we think that due to their robustness they will also be suitable for the 4th generation x-ray sources. We also prepared a diffractive optical element which produces a square flat top illumination spot, and that can be used as a condenser lens in full-field transmission x-ray microscopy. Finally, we will also demonstrate a novel fabrication method which can push the ultimate spatial resolution of x-ray diffractive lenses. Fresnel zone plates with an outermost zone width of 20 nm have been fabricated and 15 nm lines have been clearly resolved in scanning transmission x-ray microscopy. This work has been carried out in the Laboratori de Llum Sincrotró in Barcelona, with the participation of the Centro Nacional de Microelectrònica de Barcelona (CSIC - CNM) and the Grup d'Òptica del Departament de Física de la Universitat Autònoma de Barcelona. At the same time, essential parts of this work have been done in close collaboration with Dr. C. David and Dr. K. Jefimovs from the Labor für Mikro- und Nanotechnologie at the Paul Scherrer Institut in Villigen (Switzerland).

A technique using diffractive elements for finding the absolute shape of a large-scale object is proposed. An accurate projected fringe profilometry can be built by applying the holographic technique in this system. The advantages of using the presented technique for projected fringe profilemetry are : (1) a large depth of field ; (2) very low fringe distortion ; (3) a compact design for the measurement system ; (4) high accuracy ; (5) fast measurement speed.