This thesis proposes and tests an individually customizable model of the human crystalline lens. This model will be crucial in developing both research on the human eye and driving diagnostic tools to help plan and treat optical issues, such as those requiring refractive surgery. This thesis attempts to meet two goals: first, it will determine whether this new lens model can reproduce the major aberrations of real human eyes using a computational framework. Second, it will use clinical information to measure how well this model is able to predict post-operation results in refractive surgery, attempting to meet clinical standards of error. The model of the crystalline lens proposed within this thesis is shown to be valid, as it is able to both reproduce individual patient's optical information, and correctly predicts the optical results of a refractive surgery of an individual human eye within clinical standards of error.

Ce travail de thèse s’intéresse à l’amélioration de la compacité des antennes destinées en priorité aux systèmes embarqués tout en respectant les exigences de performance et de compétitivité. L’approche explorée consiste à utiliser des matériaux artificiels fonctionnant en transmission et conçus en structurant la matière diélectrique à une échelle plus petite que la longueur d’onde (sub-longueur d’onde). Cette structuration permet en pratique d’opérer une variation de l’indice de réfraction effectif afin de réaliser des éléments diffractifs aptes à remplir une fonction hyperfréquence. Cependant, la particularité de ce type d’élément structuré est de mêler plusieurs échelles physiques engendrant une complexité dans leur étude. La plus grande dimension d’un composant structuré peut atteindre plusieurs dizaines de longueur d’onde, par exemple 20λ, alors que la taille minimale des structures sub-longueur d’onde peut être inférieure à une fraction de la longueur d’onde, tel que λ/20. Cet aspect multi-échelle allonge les temps de simulation des dispositifs antennaires intégrant ces éléments structurés, empêchant ainsi toute possibilité d’optimisation multi-paramètres dans des temps raisonnables. Afin de pouvoir exploiter pleinement le potentiel de ces matériaux structurés, un modèle numérique de calcul a été développé sur la base des chemins optiques. Ce modèle restitue des résultats sur le maximum de gain des antennes lentilles diffractives structurées avec une précision de 0,5 dB. Le temps de calcul du modèle est de l’ordre de la minute comparée à plus de 6 heures pour une simulation complète avec le logiciel de calcul électromagnétique CST. La rapidité et la précision de ce modèle ont été mises à profit pour optimiser la conception d’une lentille diffractive structurée. Pour illustrer la pertinence de cette approche structurée, ses performances ont été comparées à celles des antennes lentilles de Fresnel et à profil hyperbolique. Cette comparaison s’est faite dans des conditions d’encombrement identiques avec un rapport longueur sur diamètre L/D de 0,5. Le gain de la lentille structurée se révèle être plus élevé de 1,6 dB par rapport à celui de la lentille de Fresnel et de 2,7 dB par rapport à celui de la lentille hyperbolique. / This work focuses on the improvement of the antennas compactness used primarily for embedded systems while respecting the performance and competitiveness requirements. The approach explored consists in using artificial materials operating in transmission and designed by structuring the dielectric material on a scale smaller than the wavelength (sub-wavelength). This structuring makes it possible in practice to achieve a variation in the effective refractive index in order to produce diffractive elements capable of performing a microwave function. However, the particularity of this type of structured element is to mix several physical scales generating complexity in their study. The largest dimension of a structured component can reach several tens of wavelength, for example 20λ, while the minimum size of the sub-wavelength structures may be less than a fraction of the wavelength, as than λ / 20. This multi-scale aspect increases the simulation times of antenna devices integrating these structured elements, thus preventing any possibility of multi-parameter optimization in reasonable times. In order to exploit fully the potential of these structured materials, a numerical model of computation has been developed on the basis of optical paths. This model gives results on the maximum gain of structured diffractive lens antennas with an accuracy of 0.5 dB. The computation time of the model is of the order of the minute compared to more than 6 hours for a complete simulation with the electromagnetic calculation software CST Microwave Studio. The speed and precision of this model have been used to optimize the design of a structured diffractive lens. To illustrate the relevance of this structured approach, its performances were compared with those of Fresnel lens antenna and hyperbolic lens antenna. This comparison was carried out under identical footprint conditions with a length to diameter ratio L / D of 0.5. The gain of the structured lens was found to be 1.6 dB higher than the Fresnel lens and 2.7 dB higher than the hyperbolic lens.

Cette thèse a pour but de mettre en avant les récentes avancées dans le domaine des métasurfaces. Ces structures ont été utilisées dans le but d’améliorer les performances des antennes classiques ou de concevoir de nouveaux concepts d’antenne. Les travaux menés s’inscrivent dans le cadre d’une collaboration avec des partenaires industriels qui sont Airbus Safran Lunchers, Airbus Group Innovations et le CNES. La thèse est organisée en deux parties. La première partie est consacrée aux métasurfaces utilisées comme des surfaces partiellement réfléchissantes (SPR) pour concevoir des antennes à cavité Fabry-Perot. Un modèle analytique permettant de prédire le dépointage du faisceau d’antenne par une modulation de la phase sur la SPR a été développé. Ensuite, un nouveau concept de métasurface permettant de réaliser du dépointage de faisceau est proposé. Il consiste à appliquer un gradient de phase en faisant varier l’indice effectif le long du substrat diélectrique de la SPR. La deuxième partie de cette thèse est quant à elle consacrée à la conception d’une métasurface active permettant d’émuler plusieurs fonctions. Dans un premier temps, la métasurface est utilisée comme un réflecteur présentant une reconfigurabilité fréquentielle et angulaire. Ensuite cette métasurface est utilisée comme polariseur reconfigurable où une polarisation linéaire de l'onde incidente est convertie en polarisation circulaire. Enfin, la dernière étude concerne l’utilisation de la métasurface active pour la réalisation d’une antenne à réflecteur cylindro-parabolique et à réflecteur dièdre reconfigurables. / This thesis aims at highlighting recent advances in the field of metasurfaces. These structures have been used to improve the performances of conventional antennas or to design new antenna concepts. The work has been carried in the framework of a collaboration with industrial partners, namely Airbus Safran Launchers, Airbus Group Innovations and CNES. The manuscript is organized into two parts. The first part is devoted to metasurfaces used as partially reflecting surfaces (PRS) to design Fabry-Perot cavity antennas. In this part, an analytical model allowing to predict the beam steering angle by a phase modulation along the PRS is developed. Then, a new concept of metasurface allowing to steer the main antenna beam is proposed. It consists in applying a phase gradient by varying the effective index of the substrate that constitutes the PRS. The second part of this thesis is devoted to the design of an active metasurface that allows emulating different functionalities. First, the metasurface is utilized as a reflector with frequency and steering reconfigurability characteristics. Then, this metasurface is used as a reconfigurable polarizer where linearly polarized incident waves are converted into circularly polarized ones. Finally, the last study concerns the use of the active metasurface for the design of reconfigurablecylindro-parabolic and corner reflector antennas.

Femtosecond laser direct writing in transparent materials such as glass and optical fibers has been used as a versatile tool in order to fabricate various 3-D photonic structures such as active and passive waveguides, couplers, gratings and diffractive optical elements (DOEs). This capability of patterning and refractive index modification in the bulk of transparent materials depends on the nonlinear absorption phenomenon. This practical technique has the potential to be used for cost effective and simplified manufacturing in various applications. This thesis examines three advanced manufacturing techniques that use ultrashort pulse filamentary propagation induced by nonlinear absorption in the transparent materials. First, a new gradient index lens fabrication method using femtosecond laser direct writing is introduced. Light that passes through the lens with refractive index change resulting from localized energy deposition is focused using a beam profiler. Second, wide welding area of glass samples are used to fabricate microfluidic devices with long channels by adopting customized fixture. The fixture making artificial pressure helps the two glass samples have wide optical contact area and the highly intensive pulse filamentation strongly joins glass slides. As an example of a more specific application, microfluidic samples with long grooves sealed by femtosecond laser welding were successfully fabricated as part of this project. Finally, a screw-shaped, long period grating sensor was fabricated by rotating the optical fiber. This technique enables the fiber core to have asymmetric refractive index change, resulting in higher sensitivity compared to conventional long period grating sensors. Also, a new long-period grating sensor with reverse bending effect has been demonstrated by producing complex pitches of refractive index change. / Graduate

Ce travail de thèse concerne la focalisation des ondes élastiques se propageant dans une plaque mince ou à la surface d’un milieu semi-infini, au travers de lentilles acoustiques planes. Les dispositifs que nous avons étudiés sont basés sur des cristaux phononiques 2D, constitués d'inclusions d'air dans une matrice solide. Ces hétérostructures présentent un gradient de leurs propriétés élastiques le long d'une direction de la lentille. Le gradient d'indice est obtenu en modulant soit la taille des inclusions d'air, soit la distance entre deux inclusions consécutives. L’approche que nous avons adoptée est basée principalement sur la simulation numérique par éléments finis. Cependant une partie significative du travail concerne le calcul analytique de la trajectoire des rayons acoustiques ainsi que la vérification expérimentale des résultats théoriques.L’approche analytique a consisté à calculer la trajectoire des rayons acoustique dans la lentille, en tenant compte de l'anisotropie le long de chaque ligne d'inclusions. L'analyse analytique, appliquée à une onde de Lamb antisymétrique (A0), ainsi que les résultats numériques et les données expérimentales, expliquent parfaitement les caractéristiques du champ de déplacement dans la zone focale, y compris la position, la forme et les dimensions latérales de la tâche focale. Le formalisme s’applique quelle que soit la symétrie du cristal phononique et peut être étendu à des ondes élastiques présentant une autre polarisation. Nous montrons dans ce travail qu’une largeur à mi-hauteur aussi petite que 0.64 peut être obtenue lorsque la focalisation intervient au sein de la lentille.Le formalisme s’applique également à la focalisation derrière la lentille. Dans ce cas, la résolution au point focal est déterminée par le "nombre d'onde transversal maximal" à la sortie de la lentille, en bon accord avec les résultats numériques et expérimentaux. Ensuite, nous avons conçu une lentille à gradient d’indice avec des piliers résonnants érigés entre les inclusions d'air. L'analyse numérique prévoit une résolution légèrement au-delà de la limite de diffraction. Expérimentalement, nous mesurons une largeur à mi-hauteur de la tâche focale juste au-dessus de la limite de diffraction.Enfin, nous avons étudié la focalisation d’une onde de Rayleigh par une lentille à gradient d’indice. Nous avons trouvé un bon accord entre le calcul des trajectoires des rayons, les simulations numériques et les expériences. En outre, nous avons analysé la transmission de l’énergie élastique lorsque la focalisation intervient derrière la lentille. / This manuscript is about the focusing of elastic beams propagating in a plate or on the free surface of a semi-infinite medium, using flat acoustical lenses. The devices we have studied are based onto 2D phononic crystals that are made of air inclusions in a solid matrix and featuring a gradient of their elastic properties along one direction of the lens. The gradient index (GRIN) is obtained by modulating either the size of the air inclusions or the distance between two consecutive inclusions.We primarily adopted a computational approach but a significant part of the work concerns the analytical calculation of the ray trajectories as well as the experimental check of the theoretical findings. The analytical approach consists to calculate the ray trajectories of an elastic waves within the lens while accounting for the anisotropy along each lines of inclusions. The analysis applied to the lowest-order flexural Lamb wave (A0), together with both the numerical results and the experimental data, well explains the features of the displacements field in the focus area, including the location, shape and lateral width. The formalism applies whatever the symmetry of the phononic crystal is and can be extended to other polarization of the elastic wave. We show in this work that FWHM as small as 0.64 may be obtained when focusing inside the lens.The formalism applies also to the focusing behind the lens. In that case, the resolution at the focus is determined by the “maximum transverse wavenumber” at the exit of lens, in good agreement with the numerical and experimental results. Then we designed a GRIN phononic lens featuring resonant pillars in addition to the constitutive air inclusions. The numerical analysis foresees the resolution at the focus beyond the diffraction limit, while experimentally we measured the resolution to be just above the diffraction limit. Lastly, we turned to the subwavelength focusing of Rayleigh waves through GRIN lenses. We found a good agreement between the ray trajectories calculation, the numerical simulations and the experiments. We further analysed the influence of energy transmission when the focus is located behind the lens.

The human eye is a complex optical system comprised of many components. The crystalline lens, an optical component with a gradient index (GRIN), is perhaps the least understood as it is situated inside the eye and as a result is difficult to characterize. Its complex nonlinear structure is not easily measured and consequently not easily modeled. Presently several models of the GRIN structure exist describing the average performance of crystalline lenses. These models, however, do not accurately describe the performance of crystalline lenses on an individual basis and a more accurate individual eye model based on anatomical parameters is needed. This thesis proposes an anatomically correct, individually customizable crystalline lens model. This is an important tool and is needed both for research on the optical properties of human eyes and to diagnose and plan the treatment of optically based visual problems, such as refractive surgery planning. The lens model consisted of an interior GRIN with a constant refractive index core. The anterior and posterior surface was described by conic sections. To realize this eye model, the optical and biometric properties of mammalian lenses were measured and the correlation relationships between these measurements were used to simplify the model down to one fitting parameter which controls the shape of the GRIN. Using this data, an anatomically correct individualizable model of the lens was successfully realized with varying parameters unique to each lens. Using this customizable lens model, customizable human eye models based on measurements of the entire human eye can be realized.

The human eye is a complex optical system comprised of many components. The crystalline lens, an optical component with a gradient index (GRIN), is perhaps the least understood as it is situated inside the eye and as a result is difficult to characterize. Its complex nonlinear structure is not easily measured and consequently not easily modeled. Presently several models of the GRIN structure exist describing the average performance of crystalline lenses. These models, however, do not accurately describe the performance of crystalline lenses on an individual basis and a more accurate individual eye model based on anatomical parameters is needed. This thesis proposes an anatomically correct, individually customizable crystalline lens model. This is an important tool and is needed both for research on the optical properties of human eyes and to diagnose and plan the treatment of optically based visual problems, such as refractive surgery planning. The lens model consisted of an interior GRIN with a constant refractive index core. The anterior and posterior surface was described by conic sections. To realize this eye model, the optical and biometric properties of mammalian lenses were measured and the correlation relationships between these measurements were used to simplify the model down to one fitting parameter which controls the shape of the GRIN. Using this data, an anatomically correct individualizable model of the lens was successfully realized with varying parameters unique to each lens. Using this customizable lens model, customizable human eye models based on measurements of the entire human eye can be realized.

The human eye is a complex optical system comprised of many components. The crystalline lens, an optical component with a gradient index (GRIN), is perhaps the least understood as it is situated inside the eye and as a result is difficult to characterize. Its complex nonlinear structure is not easily measured and consequently not easily modeled. Presently several models of the GRIN structure exist describing the average performance of crystalline lenses. These models, however, do not accurately describe the performance of crystalline lenses on an individual basis and a more accurate individual eye model based on anatomical parameters is needed. This thesis proposes an anatomically correct, individually customizable crystalline lens model. This is an important tool and is needed both for research on the optical properties of human eyes and to diagnose and plan the treatment of optically based visual problems, such as refractive surgery planning. The lens model consisted of an interior GRIN with a constant refractive index core. The anterior and posterior surface was described by conic sections. To realize this eye model, the optical and biometric properties of mammalian lenses were measured and the correlation relationships between these measurements were used to simplify the model down to one fitting parameter which controls the shape of the GRIN. Using this data, an anatomically correct individualizable model of the lens was successfully realized with varying parameters unique to each lens. Using this customizable lens model, customizable human eye models based on measurements of the entire human eye can be realized.

The eye lens grows continuously throughout life and changes its shape as the eye changes focus from a distant to a near object (the process of accommodation). These changes are complex because they may affect not only the shape of the lens, but also its refractive index distribution. To date there has been no satisfactory technique for directly and non-invasively measuring these changes. In this study the refractive index distribution through the isolated lens was measured non-invasively using a novel MRI technique. The dependence of the refractive index value of lens tissue on its transverse relaxation rate (R2) was determined empirically from measurements on lens homogenate samples. Using a multi-spin-echo imaging sequence, data were acquired for constructing R2 maps of a central slice through the isolated lens. These R2 maps were transformed to refractive index maps using the empirically determined dependence of refractive index on R2. Using a standard algorithm for ray tracing through gradient index media, the propagation of light rays through the index map were simulated. The optical properties of the lens, such as focal length, were then measured. The technique was validated by also directly measuring the focal length of each lens using laser ray tracing. The subtle changes in refractive index distribution that are responsible for the dramatic change in the optical properties of the isolated lens with age, were observed for the first time. The decrease in surface power of the isolated lens with age accounted only partially for the decrease in total lens power with age, the remainder resulting from a reduction in the gradient of refractive index (GRIN) power. It is likely that this reduction in GFUN power is the mechanism by which the eye maintains emmetropia (good distant vision) with age despite the increasing curvature of its surfaces. The reduction in the GRIN power of the lens was found to be mainly due to a flattening of the refractive index profile in the central region of the lens, accompanied by steepening of the profile near the edge of the lens. In agreement with a previous MRI study of the isolated human eye lens, this study found a decrease in the refractive index of the nucleus with age. However the age related change in this study was not as large and not found to be statistically significant. The results demonstrate that existing simple models for the optics of the eye lens are inadequate to accurately describe its properties. Several more sophisticated models were considered in an attempt to describe better the age-dependent changes that occur in both the power of the lens and its longitudinal aberration. Mathematical modelling was also used to simulate the accommodative process and investigate possible changes in the index distribution of the lens that may occur with accommodation. A preliminary in vivo study was performed aimed at observing the change in the refractive index distribution of the eye lens with age and accommodation. These results demonstrated the feasibility of the technique for in vivo applications and showed that within experimental error there is little change in the central refractive index of the lens with age. However the resolution achievable with standard clinical imaging sequences and signal detection hardware was not optimal for in vivo refractive index mapping of changes in the human eye lens with accommodation. Finally therefore, methods for refining the technique for in vivo applications are discussed which may make it possible to directly and simultaneously measure both the shape and refractive index distribution of the lens with age and accommodation.

The human eye is a complex optical system comprised of many components. The crystalline lens, an optical component with a gradient index (GRIN), is perhaps the least understood as it is situated inside the eye and as a result is difficult to characterize. Its complex nonlinear structure is not easily measured and consequently not easily modeled. Presently several models of the GRIN structure exist describing the average performance of crystalline lenses. These models, however, do not accurately describe the performance of crystalline lenses on an individual basis and a more accurate individual eye model based on anatomical parameters is needed. This thesis proposes an anatomically correct, individually customizable crystalline lens model. This is an important tool and is needed both for research on the optical properties of human eyes and to diagnose and plan the treatment of optically based visual problems, such as refractive surgery planning. The lens model consisted of an interior GRIN with a constant refractive index core. The anterior and posterior surface was described by conic sections. To realize this eye model, the optical and biometric properties of mammalian lenses were measured and the correlation relationships between these measurements were used to simplify the model down to one fitting parameter which controls the shape of the GRIN. Using this data, an anatomically correct individualizable model of the lens was successfully realized with varying parameters unique to each lens. Using this customizable lens model, customizable human eye models based on measurements of the entire human eye can be realized.