Photonic crystals (PhCs) are periodically structured electromagnetic media, generally characterised by not permitting light of defined ranges of frequency to propagate through the structure. These disallowed ranges of frequency are known as photonic band gaps. The intentional introduction of defects into the crystal gives rise to localized electromagnetic states that provide a mechanism for the control of the propagation of photons through PhCs. In the case of one dimensional (1-D) PhCs, the introduction of a single defect into a finite PhC results in the formation of a resonant cavity structure, a so-called microcavity. The ease of fabrication and scope for integration make 1-D PhCs good candidates for the future applications of PhCs in light transmission systems and, as such, these structures are the focus of the research reported here. The aim of this thesis is to report a practical study of passive 1-D PhC devices and thereby extend the base of measurements that support and extend the results of theory and simulation. Various types of 1-D PhC structures have been fabricated using electron beam lithography and inductively coupled plasma technologies in a clean-room environment. The fabricated structures in effect demonstrate a first or primitive level of integration of 1-D PhCs with another optical device, namely a ridge waveguide. Measurements were performed by butt-coupling from a single mode fibre taper of the transmission characteristics of the resulting integrated waveguides, whilst a Side-band measurement method for very high resolution (0.2pm) microcavity characterisation was invented during the measurement process. A multiple wavelength transmission optical filter transmitting at the telecommunication wavelengths of 1310nm and 1550nm, and which could be used in a WDM system was demonstrated. The effect of introducing mode matching structures to minimize II the scattering loss and boost the quality factor value was investigated. Optimum positioning of the tapers produced a significant enhancement of Q. Finally, a narrow pass band filter constructed from coupled cavities was fabricated and characterised. A quasi-flat transmission peak with a pass band width of just 4nm was observed.

In this research photonic crystal fibres were developed for the purpose of generating coherent supercontinua. Two photonic crystal fibres were fabricated with all-normal group velocity dispersion profiles, with low dispersion at pump wavelengths 800 nm and 1064 nm. Supercontinua generated using these fibres were shown to have superior stability and coherence compared with supercontinua generated in fibres with anomalous dispersion at the pump wavelength. Using a short piece of photonic crystal fibre with all-normal group velocity dispersion, pumped at 1064 nm, a self phase modulation spectrum spanning 200 nm was generated. The supercontinuum was re-compressed using linear chirp compensation to 26 fs, which was within a factor of two of the theoretical transform limit. This demonstrates the high spectral coherence, stability, and almost-linear chirp of the supercontinuum. Simulations showed that pulse compression using a supercontinuum generated in a photonic crystal fibre with anomalous dispersion at the pump wavelength would be limited by shot-to-shot fluctuations in the spectral intensity and phase, and the nonlinear chirp. Using a longer piece of all-normal dispersion photonic crystal fibre, supercontinuum is generated by self phase modulation, and optical wave breaking. A broad flat supercontinuum spanning 700 nm, centred at 1064 nm was generated. This supercontinuum was spectrally filtered, and the pulses obtained analysed in the temporal domain. Clean, stable sub-picosecond pulses were achieved, demonstrating the applicability of such a supercontinuum as part of a compact, tunable laser source. The same experiment was carried out using a photonic crystal fibre with anomalous dispersion at the pump wavelength, resulting in pulses with a large portion of energy contained in broad shoulders, and higher order modes. Interferometric coherence measurements were carried out at 800 nm using a Ti:Sapphire laser. A supercontinuum was generated in all-normal dispersion photonic crystal fibre with low dispersion at 800 nm, spanning 400 nm. Supercontinuum pulses generated by consecutive laser pulses were brought together in time using an interferometer. The interference between consecutive pulses was viewed spectrally, and the interference fringes had high visibility across the whole supercontinuum bandwidth. This demonstrates high spectral coherence. A supercontinuum generated in photonic crystal fibre with anomalous dispersion at 800 nm was tested in the same way, and the interference fringes obtained had lower visibility, indicating low spectral coherence. The research presented demonstrates that photonic crystal fibres with all-normal dispersion profiles can be used to generate supercontinua with high coherence and intensity stability. This type of supercontinuum is applicable to ultra-short pulse compression, and can be spectrally filtered to create a broadband tunable ultra-short laser source.

Les réseaux de neurones artificiels constituent des systèmes alternatifs pour effectuer des calculs complexes, ainsi que pour contribuer à l'étude des systèmes neuronaux biologiques. Ils sont capables de résoudre des problèmes complexes, tel que la prédiction de signaux chaotiques, avec des performances à l'état de l'art. Cependant, la compréhension du fonctionnement des réseaux de neurones dans la résolution de problèmes comme la prédiction reste vague ; l'analogie avec une boîte-noire est souvent employée. En combinant la théorie des systèmes dynamiques non linéaires avec celle de l'apprentissage automatique (Machine Learning), nous avons développé un nouveau concept décrivant à la fois le fonctionnement des réseaux neuronaux ainsi que les mécanismes à l'œuvre dans leurs capacités de prédiction. Grâce à ce concept, nous avons pu imaginer un processeur neuronal hybride composé d'un réseaux de neurones et d'une mémoire externe. Nous avons également identifié les mécanismes basés sur la synchronisation spatio-temporelle avec lesquels des réseaux neuronaux aléatoires récurrents peuvent effectivement fonctionner, au-delà de leurs états de point fixe habituellement utilisés. Cette synchronisation a entre autre pour effet de réduire l'impact de la dynamique régulière spontanée sur la performance du système. Enfin, nous avons construit physiquement un réseau récurrent à retard dans un montage électro-optique basé sur le système dynamique d'Ikeda. Celui-ci a dans un premier temps été étudié dans le contexte de la dynamique non-linéaire afin d'en explorer certaines propriétés, puis nous l'avons utilisé pour implémenter un processeur neuromorphique dédié à la prédiction de signaux chaotiques. / Artificial neural networks are systems prominently used in computation and investigations of biological neural systems. They provide state-of-the-art performance in challenging problems like the prediction of chaotic signals. Yet, the understanding of how neural networks actually solve problems like prediction remains vague; the black-box analogy is often employed. Merging nonlinear dynamical systems theory with machine learning, we develop a new concept which describes neural networks and prediction within the same framework. Taking profit of the obtained insight, we a-priori design a hybrid computer, which extends a neural network by an external memory. Furthermore, we identify mechanisms based on spatio-temporal synchronization with which random recurrent neural networks operated beyond their fixed point could reduce the negative impact of regular spontaneous dynamics on their computational performance. Finally, we build a recurrent delay network in an electro-optical setup inspired by the Ikeda system, which at first is investigated in a nonlinear dynamics framework. We then implement a neuromorphic processor dedicated to a prediction task.

One of the daunting challenges in wave physics is to accurately control the flow of light at the subwavelength scale. By patterning the optical medium one can design anisotropic artificial medium, this engineering method is commonly known as photonic crystals or metamaterials. Negative or zero index of refraction, slow-light propagation, cloaking with transformation optics material, and beam collimation are only a few such unique functionalities that can be achieved in engineered media at the subwavelength scale. Another interesting phenomenon in wave physics, Anderson localization, which suggests electron localization inside a semiconductor, has been intensely investigated over the past years, including transverse localization in bulk and waveguide arrays periodic in one and two dimensions. Here we report the photon transport and collimation enhanced by transverse Anderson localization in chip-scale anisotropic artificial medium, a similar physical model to doping the impurity in insulator and turning it into a semiconductor. First, by engineering the photonic crystal, we demonstrate a new type of anisotropic artificial medium for diffraction-free transport through cascaded tunneling of guided resonances. High-resolution near-field measurements demonstrate the coupling of transverse guided resonances, supported by large-scale numerical modeling. Second, with the disordered scattering sites in this superlattices, we uncover the mechanism of disorder-induced transverse localization in chip-scale. Arrested spatial divergence is captured in the power-law scaling, along with the exponential asymmetric mode profiles and enhanced collimation bandwidth for increasing disorder, over 4,000 scattering sites. With increasing disorder, we observe the crossover from cascaded guided resonances into transverse localization regimes, beyond the ballistic and diffusive transport of photons. As disorder is ubiquitous in natural and artificial materials, the transport through random media is of great importance. It also leads to various interesting optical phenomena, of which the most surprising one is Anderson localization of light. However, not all the states in disordered system are localized. Nonlocalized modes that extend over the whole sample via coupling between multiple local cavities with similar resonance frequencies are also present in disordered systems. These extended modes are called necklace states. Here, we also show that long-distance beam collimation can be witnessed in millimeter-scale photonic crystals that were fabricated lithographically with ultrahigh resolutions. By precisely controlling the disorder level of three million scattering sites in photonic crystals, we uncovered the transformation of light flows from the propagation of regular Bloch modes to necklace states.

Master of Science / Department of Physics / Kristan L. Corwin / We have developed short acetylene-filled photonic microcells (PMCs’) as optical frequency references in the near infrared region for applications in telecommunication, gas sensing, and metrology. The PMC is a 5-10 cm long hollow-core photonic crystal fiber (HC-PCF) in which the high pressure acetylene gas is confined by sealing the ends of HC-PCF. Acetylene provides 50 strong v vrotational-vibrational combination bands within 1510-1540 nm which covers the telecommunication window at 1550 nm. PMC’s are a possible replacement for optical frequency references based on gas-filled vapor cells, like the SRM2517a produced by the National Institute of Standards and Technology (NIST). While such cells made practical and accurate frequency calibration readily available, and have been built into measurement equipment and lasers, they are relatively bulky compared to the small footprint now achieved by commercially available lasers. Short PMC’s in particular are compact and robust. In fact, a PMC of similar length would occupy a smaller volume because it has a simple design and it is all-fiber based. Here we demonstrate a novel fabrication technique that is appropriate for making short high pressure optical frequency references using photonic bandgap fibers. Consequently, the aforementioned short PMC has some application of NIST SRM 2517a and can be used for moderate accuracy frequency measurements with fractional accuracy of 7.7×10-8. By using a tapering technique to seal the microcells, we were able to achieve high transmission efficiency of 80% and moderate accuracy of 10 MHz (1) in finding the line center. This approaches that of the NIST SRM 2517a 10 MHz (2) accuracy. Using an earlier Q-tipping technique, 37% off-resonant transmission and 5 MHz accuracy were achieved in finding the line center, but a larger etalon-like effect which is approximately 13%, appears on the wings of the optical depth. By using a tapering technique, we were able to decrease the etalon-like effect to less than 1%. In both cases, the microcells could be connectorized, albeit with reduction in off-resonant transmission efficiency, for integration into multi-mode fibers or free-space optical systems. Although contamination is introduced during both fabrication techniques, the P13 PMC line center shift with respect to sub-Doppler center is small according to experimental data. Data show that the PMC line center shift from the sub-Doppler feature for PMC no. 53 with 83% contamination was -15.4 ± 3.3 MHz which is a fractional value of 7.7×10-8 with respect to the value of the P13 line center of 195 THz. Finally, repeatable measurements show that PMCs are stable in terms of total pressure over approximately one year.

Porous silicon (PSi) photonic crystals have aroused research interest as label-free chemical and biological sensing transducers owing to the ease of fabrication, high quality optics and a sensitive optical response to changes in efractive index. A major impediment to using PSi materials as sensors is the relative instability of the silicon surface to oxidation in ambient air and aqueous environments. This thesis reports methods for derivatising PSi towards realisation of 1-D silicon-based photonic materials for applications in biology and medicine. Narrow-linewidth rugate filters, a class of photonic crystal, are fabricated on silicon to display a high reflectivity resonant line in the reflectance spectrum. The position of the resonance is sensitive to changes in refractive index, thus allowing quantification of infiltrating biological species. The efficacy of rugate filters as biosensing transducers requires 1) protection from aqueous degradation, 2) resistance to non-specific adsorption and 3) distal reactivity for coupling of biorecognition molecules. Two chemical strategies based on hydrosilylation of functional alkenes are compared for stabilising the PSi structure against oxidation whilst resisting non-specific adsorption of biomolecules. Immobilisation of peptides to the organic layers is demonstrated for optical detection of protease enzymes. Introduction of protease results in cleavage of the immobilised peptides within the rugate filters, detected by an optical blue-shift to shorter wavelengths. To increase the sensitivity to proteolysis, covalent mmobilisation of biopolymers is evaluated using gelatin as a model substrate. Digestion of gelatin is detected down to 37 attomoles of protease. Furthermore, the surface chemistry allows specific capture of live cells and incubation with stimulated macrophages in tissue culture results in optical detection of released gelatinase enzymes. The generality of the surface chemistry allows for a range of other biological applications to be investigated. An alternative biorecognition interface, hybrid lipid bilayer membranes, containing specific recognition elements for cholera toxin allows optical detection of affinity capture and concentration within the PSi. In addition, the suitability of chemically modified photonic crystals as reservoirs for mass spectrometry is evaluated towards biomolecule quantification after optical detection. A robust and flexible surface chemistry on PSi photonic crystals is critical to performance in a range of biological assays and a necessary requirement for wide-scale employment.

Light manipulation is an important method to enhance the light-matter interactions in micro and nano photonic materials and structures by generating usefulelectric field components and increasing time and pathways of light propagationthrough the micro and nano materials and structures. For example, quantum wellinfrared photodetector (QWIP) cannot absorb normal incident radiation so thatthe generation of an electric field component which is parallel to the original incident direction is a necessity for the function of QWIP. Furthermore, the increaseof time and pathways of light propagation in the light-absorbing quantum wellregion will increase the chance of absorbing the photons.The thesis presents the theoretical studies of light manipulation and light-matter interaction in micro and nano photonic materials and structures, aiming atimproving the performance of optical communication devices, photonic integrateddevices and photovoltaic devices.To design efficient micro and nano photonic devices, it is essential to knowthe time evolution of the electromagnetic (EM) field. Two-dimensional and three-dimensional finite-difference time-domain (FDTD) methods have been adopted inthe thesis to numerically solve the Maxwell equations in micro and nano photonicmaterials and structures.Light manipulation in micro and nano material and structures studied in thisthesis includes: (1) light transport in the photonic crystal (PhC) waveguide, (2)light diffraction by the micro-scale dielectric PhC and metallic PhC structures(gratings); and (3) exciton-polaritons of semiconductor quantum dots, (4) surfaceplasmon polaritons at semiconductor-metallic material interface for subwavelengthlight control. All these aspects are found to be useful in optical devices of multiplebeam splitter, quantum well/dot infrared photodetectors, and solar cells. / QC 20120507

The AAO membrane with nanopore arrays were fabricated by anodizing highly pure aluminum foils (99.9995%) in electrolyte. Ordered array have been obtained under optimized anodizing condition, and pore diameter can be controlled by different anodic voltage and electrolyte. After we got such an ordered arrangement porous alumina array, the following analysis of the material optical properties were characterized. Photoluminescence measurements showed a strong PL peak in blue. The PL peak was 420nm excited by He-Cd laser. From the transmittance spectra, the results showed that material was transparent above 400nm. The XRD spectra of AAO without and with annealing, both showed the diffraction peaks of (311)¡B(400)¡B(440), corresponding to the £^-Al2O3 phase appear. High ordered anodic porous alumina with holes interval 65nm was prepared in mixture solution of H3PO4 and H2SO4 under high temperature and high concentration. Through the use of porous anodic alumina masks, nanopore arrays were fabricated on Si¡BGaAs substrates by reactive ion etching. Also, metal nanodot arrays were formed through the AAO mask by evaporation. Thin AAO slabs also enhance the light extraction from the QDs, and control the PL emission wavelength.

We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. It involves smoothing the singular Green's functions in the integrands and finding correction terms to the resulting smooth integrals. The analytical method is based on the singular integral methods of J. Thomas Beale, while the scattering problem is motivated by the 2D work of Stephanos Venakides, Mansoor Haider, and Stephen Shipman. The 3D problem was done with boundary element methods by Andrew Barnes. We present a method that is both more straightforward and more accurate. In solving these problems, we have used the M\"{u}ller integral equation formulation of Maxwell's equations, since it is a Fredholm integral equation of the second kind and is well-posed. M\"{u}ller derived his equations for the case of a compact scatterer. We outline the derivation and adapt it to a periodic scatterer. The periodic Green's functions found in the integral equation contain singularities which make it difficult to evaluate them numerically with accuracy. These functions are also very time consuming to evaluate numerically. We use Ewald splitting to represent these functions in a way that can be computed rapidly.We present a method of smoothing the singularity of the Green's function while maintaining its periodicity. We do local analysis of the singularity in order to identify and eliminate the largest sources of error introduced by this smoothing. We prove that with our derived correction terms, we can replace the singular integrals with smooth integrals and only introduce a error that is third order in the grid spacing size. The derivation of the correction terms involves transforming to principal directions using concepts from differential geometry. The correction terms are necessarily invariant under this transformation and depend on geometric properties of the scatterer such as the mean curvature and the differential of the Gauss map. Able to evaluate the integrals to a higher order, we implement a \mbox{GMRES} algorithm to approximate solutions of the integral equation. From these solutions, M\"{u}ller's equations allow us to compute the scattered fields and transmission coefficients. We have also developed acceleration techniques that allow for more efficient computation.We provide results for various scatterers, including a test case for which exact solutions are known. The implemented method does indeed converge with third order accuracy. We present results for which the method successfully resolves Wood's anomaly resonances in transmission. / Dissertation

The past decade and a half has seen the rapid emergence of a new material class known as photonic crystals (PCs), structures that exhibit 1, 2, or 3, dimensional periodicity of their dielectric constant, resulting in a modification of the dispersion characteristics from the normal w = vk relationship found in isotropic materials. Several remarkable electromagnetic phenomenon result, including the formation of photonic band gaps (PBGs), which are specific energy ranges where electromagnetic wave propagation is forbidden, and the existence of energies where the photon group velocity is slowed drastically from its normal value. The resulting modification of a materials photonic band structure allows unprecedented control of light, resulting in phenomena such as self-collimation, and spontaneous emission modification or lasing threshold reduction through either band edge effects (low group velocity) or microcavity defect incorporation. PCs for operation at visible wavelengths are difficult to form due to the need for nanoscale fabrication techniques. The research described focused on the fabrication of photonic crystal phosphors by using the infiltration and subsequent removal of self-assembled opal templates to make inverted opal-based photonic crystals. This thesis shows the advantages that atomic layer deposition (ALD) has as an important method for use in photonic crystal fabrication, and highlights the exciting results of use of ALD to fabricate luminescent ZnS:Mn and optically inactive titania inverse opals, as well as ZnS:Mntitania luminescent composite inverse opals.