Outgoing wave conditions in photonic crystals and transmission properties at interfaces

We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was not available for $x$-dependent coefficients. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a (weak) uniqueness result, formulated in terms of the Bloch measure of solutions. We use the new radiation condition to analyze the transmission problem where, at fixed frequency, a wave hits the interface between free space and a photonic crystal. We derive that the vertical wave number of the incident wave is a conserved quantity. Together with the frequency condition for the transmitted wave, this condition leads (for appropriate photonic crystals) to the effect of negative refraction at the interface

Bound states in the continuum

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work.National Science Foundation (U.S.) (Grants DMR-1307632)Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract W911NF-13-D- 0001)United States. Department of Energy. Office of Science. Solid-State Solar Thermal Energy Conversion Center (Grant DE-SC0001299)United States-Israel Binational Science Foundation (Award 2013508

One-dimensional reflection by a semi-infinite periodic row of scatterers

AbstractThree methods are described in order to solve the canonical problem of the one-dimensional reflection by a semi-infinite periodic row of identical scatterers. The exact reflection coefficient R is determined. The first method is associated with shifting the domain by a single period and subsequently considering two scatterers, one being a single scatterer and the second being the entire semi-infinite array. The second method determines the reflection coefficient RN associated with a finite array of N scatterers. The limit as N→∞ is then taken. In general RN does not converge to R in this limit, although we summarize various arguments that can be made to ensure the correct limit is achieved. The third method considers direct approaches. In particular, for point masses, the governing inhomogeneous ordinary differential equation is solved using the discrete Wiener–Hopf technique

On the Spectral Properties of Dispersive Photonic Crystals

This thesis is concerned with a parameter-nonlinear spectral problem which describes light propagation in certain two-dimensional, dispersive photonic crystals. A realization of the equation leads to the analysis of an operator pencil with a periodic coefficient depending on the spectral variable. It is shown that the corresponding spectrum is related to a family of eigenvalue equations posed on the underlying periodicity cell. Spectra and eigenfunctions of these problems are analyzed in detail

Design and Characterization of Silicon-on-Insulator Passive Polarization Converter with Finite-Element Analysis

As optical fiber systems evolve to higher data rates, the importance of polarization control and manipulation steadily increases. Polarization manipulating devices, such as polarization splitters and converters, can be realized by introducing material anisotropy or geometric asymmetry. Compared to active devices, passive polarization converters are more simply fabricated and controlled; therefore they have attracted increasing attention during the past two decades. However, materials employed in previous polarization rotating waveguides are mainly limited to low index-contrast III-V semiconductors such as InP and GaAs. Such III-V devices possess large radiation loss, large curvature loss, and low coupling efficiency to single-mode fibers; in addition, due to the weak optical confinement, the device spacing has to be large, which prevents high-density and large-scale integration in optoelectronic integrated circuits (OEIC) and planar lightwave circuits (PLC). In this dissertation, the silicon-on-insulator (SOI) technology is introduced to the design and fabrication of passive polarization rotators (PR). Efficient and accurate full-vectorial finite-element eigenmode solvers as well as propagation schemes for characterizing novel SOI PRs are developed because commercial software packages based on finite-difference techniques are inefficient in dealing with arbitrary waveguide geometries. A set of general design procedures are accordingly developed to design a series of slanted-angle polarization converters, regardless of the material system (SOI or III-V), outer-slab layer configuration (symmetric or asymmetric), and longitudinal loading (single- or multi-section). In particular, our normalized design charts and simple empirical formula for SOI polarization converters are applicable to a wide range of silicon-guiding-film thickness, e. g. , from 1 to 30 μm, enabling fast and accurate polarization rotator design on most commercial SOI wafers. With these procedures, in principle 100% polarization conversion efficiency can be achieved by optimizing waveguide geometric parameters. A novel configuration with asymmetric external waveguiding layers is proposed, which is advantageous for fabrication procedure, manufacturing tolerance, single-mode region, and conversion efficiency. By etching along the crystallographic plane, the angled-facet can be perfectly fabricated. Completely removing external waveguiding layer beside the sloped sidewall not only simplifies production procedures but also enhances fabrication tolerances. To accurately and efficiently characterize asymmetric slanted-angle SOI polarization converters, adaptive mesh generation procedures are incorporated into our finite-element method (FEM) analysis. In addition, anisotropic perfectly-matched-layer (PML) boundary condition (BC) is employed in the beam propagation method (BPM) in order to effectively suppress reflections from the edges of the computation window. For the BPM algorithm, the power conservation is strictly monitored, the non-unitarity is thoroughly analyzed, and the inherent numerical dissipation is reduced by adopting the quasi-Crank-Nicholson scheme and adaptive complex reference index. Advantages of SOI polarization rotators over III-V counterparts are studied through comprehensive research on power exchange, single-mode condition, fabrication tolerance, wavelength stability, bending characteristics, loss and coupling properties. The performance of SOI PRs is stable for wavelengths in the ITU-T C-band and L-band, making such devices quite suitable for DWDM applications. Due to the flexible cross-section of SOI polarization converters, the coupling loss to laser diodes and single mode fibers (SMF) can be designed to be very small and can be further reduced by a tapered waveguide with cross-sections always satisfying the single-mode criteria. Slanted-angle SOI polarization rotators display asymmetric bending characteristics and permit extremely small curvatures with negligible radiation loss when the angled-facet is located at the outer bend radius. Moreover, SOI polarization rotators can be manufactured with low-price processing techniques that are fully compatible with CMOS integrated circuits (IC) technology, and thus can be integrated on both photonic and electronic chips. Experimental verifications have shown good agreement with theoretical analysis and have confirmed the promising characteristics of our novel asymmetric SOI polarization converters. Similar asymmetric-outer-slab geometry has recently been employed by peer researchers to fabricate high performance III-V polarization rotators. We therefore believe that results in this dissertation will contribute much to related research fields

Integrated optical devices based on liquid crystals embedded in polydimethylsiloxane flexible substrates

The contribution of this thesis is to find possible solutions for the creation of interconnections and optical switches to be used in microoptofluidic systems in the frame of the research activities of the Optoelectronic laboratory of the Department of Information Engineering, Electronics and Telecommunications (DIET). The main goal is to explore a new technology for integrated optic based on a low cost technology to produce low driving power devices. Optofluidics is the science which links the field of photonics with microfluidics, for the creation of innovative and state-of-the-art devices. Liquid crystals (LC) can be used for optofluidic applications because they have the possibility to change without external mechanical actions, the average direction of the molecules through the application of electric fields, reorienting the crystal molecules in such a way as to alter their optical properties [1-2]. The research on LC is more than a century old, but only since the ‘80s of the past century these materials were employed in various fields, from flat panel displays used for televisions, tablets, and smartphones, to biomedical and telecommunication applications [3-5]. The results reported in this thesis include simulation, design and preliminary fabrication of optofluidic prototypes based on LC embedded in polydimethylsiloxane (PDMS) channels, defined as LC:PDMS, with co-planar electrodes to control LC molecular orientation and light propagation. Fabrication techniques which were used include microelectronic processes such as lithography, sputtering, evaporation, and electroplating. The simulations were performed through the combined use of COMSOL Multiphysics® and BeamPROP®. I used COMSOL Multiphysics® to determine the positioning of the molecules in a LC:PDMS waveguide. The LC are the core through which light propagates in a PDMS structure. In addition to these simulations, I used COMSOL Multiphysics® to determine the orientation of the LC under the effect of an electric field [6-7] to create low-power optofluidic devices [8], [11]. I used BeamPROP® to explore the optical propagation of various optical devices such as: optical couplers, the zero gap optical coupler, and a multimodal interferometer. All these devices have been simulated through various combinations of geometries which will be extensively explained in the following chapters. The fabrication of prototypes was made in the Microelectronic Technologies laboratory of DIET. The optofluidic prototypes that I designed could be used in interconnection systems on biosensing devices for chemical or biological applications [10-11], wearable [12], or lab on chips [13], which are increasingly being applied in many research fields [14]. Many of these devices need to interface with electronics for processing signals coming from the interaction between the device with molecules, liquids or other biological substances. Moreover it is necessary to create flexible and biocompatible interfaces, whose features are not guaranteed in classic metal tracks. As it will be clear in the first chapter, metal interconnections must be designed with spatial, energy and throughput restrictions. To develop the optofluidic prototypes, I chose to use a combination of two materials for their commercial availability and ease of use: E7 and 5CB LC produced by Merck® as the transmissive medium and PDMS Sylgard 184 produced by Dow Corning® for the cladding [15-16]. The molecules of the LC are anisotropic, whose shape is elongated like that of a cigar. Under appropriate temperature conditions these molecules retain a state of aggregation in which, while retaining some mechanical properties of the fluids, they have the characteristics of crystals such as birefringence or x-ray reflection. These properties are due to two factors that characterize the various phases of LC: the orientational and positional order that vary according to the temperature. E7 was used in its nematic mesophase. The material used for the cladding of my prototypes was PDMS, a thermosetting polymer, flexible, biocompatible, economical, easy to work, and suitable for the creation of optical and optofluidic devices due to its transparency. The thesis is organized in six chapters whose contents are briefly outlined below: • In the first chapter there is a brief description of optofluidics and the transport phenomena of the liquids in the microchannels. The essential parameters for a correct interpretation of the behavior of the materials in the devices will be defined. Some examples of microfluidic devices, Optofluidic Optical Components (OOC) will be mentioned. • In the second chapter, LC’s will be presented, along with their general characteristics and their behavior in the presence of electric fields. An overview of integrated optic devices based on LC will be reported. • In the third chapter the experimental results will be presented concerning the fabrications and the technologies used to obtain electro-optical LC:PDMS waveguides. • The fourth chapter will be dedicated to a brief description of COMSOL Multiphysics® and BeamPROP® simulators, and the implementation of the model of LC channels in PDMS both in 2D and 3D. Also a brief description of Monte Carlo simulations based on Lebwohl-Lasher potential will be mentioned. • In the fifth chapter an LC:PDMS optical directional coupler and the most significant results will be described. • The sixth chapter is dedicated to the multimodal interferometer and its field of application, the theory behind this device and the results obtained from the simulations using the BeamPROP® • In the conclusion, a brief recap of the results obtained in this thesis and future developments will be presented

Simulation Of Lightwave Propagation In Photonic Devices

Disertasi ini adalah tertumpu kepada simulasi rambatan gelombang cahaya dalam peranti fotonik leper, ianya termasuk penyiasatan keadaan satu mod dalam pandu gelombang rusuk, reka bentuk pemutar dan pembelah polarisasi, penyiasatan pantulan berganda dalam pengganding interferens-berganda hablur fotonik dan reka bentuk pembahagi panjang-gelombang hablur fotonik hibrid I-D dan 2-D dan antarasilih saluran. This dissertation focuses on the simulation of lightwave propagation in planar devices, which include investigation of single mode conditions in rib waveguide, designs of compact silica polarization rotator and splitters, investigation of multiple reflections in photonic crystal (PhC) multimode interference couplers and design of hybrid I-D and 2-D PhC wavelength division multiplexers and channels interleavers

Optimization of silicon photonic devices for polarization diversity applications

This thesis discusses two important designs, analysis and optimization of polarization-based devices such as polarization rotator and splitter. Many optical sub-systems integrate with guided wave photonic devices with two-dimensional confinement and high contrast between the core and cladding. The modes present in such waveguides are not purely of the TE or TM type. They are hybrid in nature, where all six components of the magnetic and electric fields are present. This causes the system fully to be polarization dependent. Currently, the polarization issue is a major topic to be dealt with during the design of high efficiency optoelectronic subsystems for further enhancement of their performances. To characterize the device polarization properties a vectrorial approach is needed. In this work, the numerical analysis has been carried out by using the powerful and versatile full vectorial H-field based finite element method (FEM). This method has been proved to be one of the most accurate numerical methods to date for calculating the modal hybridness, birefringence and consequently to calculate the device length, which is an important parameter when designing devices concerning the polarization issues. Polarization devices may be fabricated by combining several butt-coupled uniform waveguide sections. The Least Squares Boundary Residual (LSBR) method is used to obtain transmission and reflection coefficients of all the polarized modes by considering both the guided and the radiated modes. On the other hand, finite element method cannot calculate the power transfer efficiency directly, hence the LSBR method is used along with the FEM for this purpose. The LSBR method is rigorously convergent, satisfying the boundary conditions in the least square sense over the discontinuity interface. Using this method, the power transfer from the input to the coupler section and at the output ports can be evaluated. When designing polarization rotators, it is necessary to calculate the modal hybridness of a mode. In this research, it is identified that when the symmetric waveguides are broken, the modal hybridity is enhanced, and thereby a high polarization conversion is expected. This work is devoted to the study of design optimization of a compact silicon nanowire polarization device. An interesting and useful comparison is made on their operating properties such as the crosstalk, device length, polarization dependence, and fabrication tolerances of the polarization in directional coupler based devices. In this study initially the H-field modal field profile for a high index contrast silicon nanowire waveguide is shown. The effects of waveguide’s width on the effective indices, hybridness, power confinement in the core, and the cladding have been investigated. The modal birefringence of such silicon nanowire waveguides also is shown. It is presented here that for a silicon nanowire waveguide with height of 220 nm, fundamental and second modes exist in the region of the width being 150 – 300 nm, and 500 – 600 nm, respectively. A compact 52.8 μm long passive polarization rotator (PR) using simple silicon nanowire waveguides is designed with a power transfer of 99 % from input TE to output TM power mode, with cross-talk better than – 20 dB and loss value lower than 0.1 dB. Furthermore, an extensive study of fabrication tolerances of a compact (PR) is undertaken. The design of an ultra-compact polarization splitter (PS) based on silicon-on-insulator (SOI) platform is presented. It is shown here that a low loss, 17.90 μm long compact PS, and wide bandwidth over the entire C-band can be achieved