Photonic band gap materials, commonly referred to as photonic crystals (PCs), have been a topic of great interest for almost two decades due to their promise of unprecedented control over the propagation and generation of light. We report investigations of the optical properties of a new PC structure based upon a triangular lattice in which adjacent [i, j] rows of holes possess different properties, creating a superlattice (SL) periodicity. Symmetry arguments predicted and quot;band folding and quot; and band splitting behaviors, both of which are direct consequences of the new basis that converts the Brillouin zone from hexagonal (six-fold) to rectangular (two-fold). Plane wave expansion and finite-difference time-domain (FDTD) numerical calculations were used to explore the effects of the new structure on the photonic dispersion relationship of the SL PC. Electron beam lithography and inductively coupled plasma dry etching were used to fabricate 1 mm2 PC areas (lattice constant, a =358 nm and 480 nm) with hole radius ratios ranging from 1.0 (triangular) to 0.585 (r2/r1 = 73.26 nm/125.26 nm) on Silicon-on-insulator wafers. The effects of modifying structural parameters (such as hole size, lattice constant, and SL strength) were measured using the coupled resonant band technique, confirming the SL symmetry arguments and corroborating the band structure calculations. Analysis of the dispersion contours of the static SL (SSL) PC predicted both giant refraction (change in beam propagation angle of 110 for an 8 change in incident angle) and superprism behavior (change in beam propagation angle of 108 for a 12% change in normalized frequency) in these structures. Dynamic control of these refraction effects was also investigated by incorporating electro-optic and nonlinear materials into the SSL PC structure. Wave vector analyses on these structures predicted a change in beam propagation angle and gt;96 when the refractive index inside of the holes of the structure changed from n=1.5 to 1.7. Through this investigation, the first successful measurement of the band folding effect in multidimensional PCs as well as the first explicit measurement of the dielectric band of a 2D PC were reported. In addition, the SL PCs impact on new opto-electronic devices was explored.

Background. Hyperplane folding was introduced by Lars Lundberg et al. in Hyperplane folding increased the margin while suffering from a flaw, referred to asover-rotation in this thesis. The aim of this thesis is to introduce a new different technique thatwould not over-rotate data points. This novel technique is referred to as RubberBand folding in the thesis. The following research questions are addressed: 1) DoesRubber Band folding increases classification accuracy? 2) Does Rubber Band fold-ing increase the Margin? 3) How does Rubber Band folding effect execution time? Rubber Band folding was implemented and its result was compared toHyperplane folding and the Support-vector machine. This comparison was done byapplying Stratified ten-fold cross-validation on four data sets for research question1 & 2. Four folds were applied for both Hyperplane folding and Rubber Band fold-ing, as more folds can lead to over-fitting. While research question 3 used 15 folds,in order to see trends and is not affected by over-fitting. One BMI data set, wasartificially made for the initial Hyperplane folding paper. Another data set labeled patients with, or without a liver disorder. Another data set predicted if patients havebenign- or malign cancer cells. Finally, a data set predicted if a hepatitis patient isalive within five years.Results.Rubber Band folding achieved a higher classification accuracy when com-pared to Hyperplane folding in all data sets. Rubber Band folding increased theclassification in the BMI data set and cancer data set while the accuracy for Rub-ber Band folding decreased in liver and hepatitis data sets. Hyperplane folding’saccuracy decreased in all data sets.Both Rubber Band folding and Hyperplane folding increases the margin for alldata sets tested. Rubber Band folding achieved a margin higher than Hyperplanefolding’s in the BMI and Liver data sets. Execution time for both the classification ofdata points and the training time for the classifier increases linearly per fold. RubberBand folding has slower growth in classification time when compared to Hyperplanefolding. Rubber Band folding can increase the classification accuracy, in whichexact cases are unknown. It is howevered believed to be when the data is none-linearly seperable.Rubber Band folding increases the margin. When compared to Hyperplane fold-ing, Rubber Band folding can in some cases, achieve a higher increase in marginwhile in some cases Hyperplane folding achieves a higher margin.Both Hyperplane folding and Rubber Band folding increases training time andclassification time linearly. The difference between Hyperplane folding and RubberBand folding in training time was negligible while Rubber bands increase in classifi-cation time was lower. This was attributed to Rubber Band folding rotating fewerpoints after 15 folds.

Les nanocavités à cristal photonique ont été largement étudiées au cours de la dernière décennie du fait de leur aptitude à fortement confiner la lumière (faible volume modal) et de leurs faibles pertes optiques (grand facteur de qualité). Parmi le grand nombre de géométries proposées, nous nous intéressons ici au cas de la cavité L3 étudiée par Noda et al. (trois trous manquants dans la direction K du réseau triangulaire sous-jacent) utilisée dans plusieurs applications et notamment pour la réalisation de nano-lasers et d’interrupteurs optiques. Cependant, l’injection ou l’extraction de lumière dans de telles nanocavités s’avère extrêmement difficile du fait de la diffraction importante dont souffrent ces structures. Différentes approches en champ proche ont été récemment développées et notamment le couplage évanescent utilisant des guides d’onde nanostructurés ou des fibres optiques étirées. Dans le but de pallier à la faible efficacité de couplage à l’espace libre, nous développons une conception récemment proposée par De Rossi et al. afin de changer radicalement le profil du diagramme de rayonnement. Cette approche utilise la méthode de repliement des bandes qui consiste à introduire au sein d’un réseau triangulaire de période (a), un sous-réseau de trous de période (2a) qui améliore considérablement l’efficacité de couplage dans la direction verticale. Bien que certaines mesures de l’efficacité de collection et du coefficient de qualité aient déjà été mentionnées dans la littérature, aucune mesure directe des diagrammes de rayonnement de ces nanocavités n’a été réalisée jusqu’alors. Nous étudions dans ce travail différents types de nanocavités et de molécules L3 à cristaux photoniques présentant des profils de champ lointain optimisés. Les diagrammes de rayonnement de cavités non-repliées et repliées incorporées dans des membranes actives suspendues en InP sont systématiquement mesurés et comparés. Un bon accord entre les simulations numériques et les diagrammes de champ lointain mesurés expérimentalement est obtenu, montrant des lobes d’émission très directionnels le long de la normale à l’échantillon. En outre, des expériences de couplage à l’espace libre ont été réalisées montrant des efficacités de couplage d’environ 15% pour des coefficients de qualité supérieurs à 10 000. Ces résultats valident ainsi la technique de repliement des bandes dans les cavités L3 qui, une fois repliées, conservent un faible volume modal et un coefficient de qualité élevé ainsi qu’une grande efficacité de couplage à l’espace libre, à la fois dans les configurations nanocavité unique et nanocavités couplés. Nous montrons aussi expérimentalement que l’écart spectral inter-modal dans deux cavités L3 couplées de manière évanescente peut être contrôlé grâce à l’ingénierie de la barrière photonique. La « barrière de potentiel » est formée par les trous d’air séparant les deux cavités. L’écart en fréquence entre les modes peut être fortement réduit et augmentée via une diminution ou une augmentation du rayon des trous de la rangée centrale de la barrière jusqu’à ∼ −30% ou ∼ 30% de sa valeur initiale. En outre, le signe de la l’écart spectral entre les modes peut être inversé de telle sorte que le mode fondamental peut être soit symétrique ou anti-symétrique et ce, sans modifier ni la géométrie de la cavité, ni la distance inter-cavité. / Photonic crystal (PhC) nanocavities have been intensively investigated during the last decade due to their capabilities of achieving tight light confinement and low optical losses simultaneously. Among the different geometries, the cavity proposed by Noda et al., namely a L3 cavity (three holes missing in the K direction of the underlying triangular lattice) with shifted end-holes has been widely used in several applications including laser emission and switching devices. However, input/output free space light coupling of such nanocavities is quite challenging. In this regard, near field coupling schemes have been recently developed, such as evanescent coupling using tapered optical fibers. In order to overcome the poor free space coupling, a new cavity design has been recently proposed by De Rossi et al. that totally changes the radiation pattern. This is based on a band folding approach introducing a modulation of the holes size at twice the period of the underlying PhC, which considerably increases the coupling efficiency in the vertical direction. While some measurements of the Q-factor and coupling efficiency were performed, no direct characterization of the far-field of such cavities has been performed so far. In this work we have studied different types of L3 photonic crystal cavities and L3 photonic molecules with optimized far-field profiles. Radiation patterns from « folded » and « unfolded » cavities incorporated in suspended InP active membranes were systematically measured and compared. Good agreement between simulations and experimental far-field patterns has been found, demonstrating highly directional emission lobes along the sample normal. Furthermore, free space input coupling experiments have been performed showing coupling efficiency of about 15% of contrast with quality factors exceeding 10 000. These results validate the « folded » L3 cavities as good candidates for small volume and high Q cavities with efficient free space coupling, either in single or coupled cavity configurations. We also experimentally show that the mode splitting in two-evanescently coupled Photonic Crystal L3 cavities can be controlled through photonic barrier engineering. The « potential barrier » is formed by the air-holes in between the two cavities. By changing the hole radius of the central row in the barrier up to ∼ 30% or down to ∼ −30% , the frequency splitting can be strongly increased or reduced. Moreover, the sign of the splitting can be reversed in such a way that the fundamental mode can be either the symmetric or the anti-symmetric one without altering neither the cavity geometry nor the inter-cavity distance.