Physical Layer Modeling and Optimization of Silicon Photonic Interconnection Networks

The progressive blooming of silicon photonics technology (SiP) has indicated that optical interconnects may substitute the electrical wires for data movement over short distances in the future. Silicon Photonics platform has been the subject of intensive research for more than a decade now and its prospects continue to emerge as it enjoys the maturity of CMOS manufacturing industry. SiP foundries all over the world and particularly in the US (AIM Photonics) have been developing reliable photonic design kits (PDKs) that include fundamental SiP building blocks such as wavelength selective modulators and tunable filters. Microring resonators (MRR) are hailed as the most compact devices that can perform both modulation and demodulation in a wavelength division multiplexed (WDM) transceiver design. Although the use of WDM can reduce the number of fibers carrying data, it also makes the design of transceivers challenging. It is probably acceptable to achieve compactness at the expense of somewhat higher transceiver cost and power consumption. Nevertheless, these two metrics should remain close to their roadmap values for Datacom applications. An increase of an order of magnitude is clearly not acceptable. For example costs relative to bandwidth for an optical link in a data center interconnect will have to decrease from the current $5/Gbps down to <$1/Gbps. Additionally, the transceiver itself must remain compact. The optical properties of SiP devices are subject to various design considerations, operation conditions, and optimization procedures. In this thesis, the general goal is to develop mathematical models that can accurately describe the thermo-optical and electro-optical behavior of individual SiP devices and then use these models to perform optimization on the parameters of such devices to maximize the capabilities of photonic links or photonic switch fabrics for datacom applications. In Chapter 1, Introduction, we first provide an overview of the current state of the optical transceivers for data centers and datacom applications. Four main categories for optical interfaces (Pluggable transceivers, On-board optics, Co-packaged optics, monolithic integration) are briefly discussed. The structure of a silicon photonic link is also briefly introduced. Then the direction is shifted towards optical switching technologies where various technologies such as free space MEMS, liquid crystal on silicon (LCOS), SOA-based switches, and silicon-based switches are explored. In Chapter 2, Silicon Photonic Waveguides, we present an extensive study of the silicon-on-insulator (SOI) waveguides that are the basic building blocks of all of the SiP devices. The dispersion of Si and SiO2 is modeled with Sellmiere equation for the wavelength range 1500–1600 nm and then is used to calculate the TE and TM modes of a 2D slab waveguide. There are two reasons that 2D waveguides are studied: first, the modes of these waveguides have closed form solutions and the modes of 3D waveguides can be approximated from 2D waveguides based on the effective index method. Second, when the coupling of waveguides is studied and the concept of curvature function of coupling is developed, the coupled modes of 2D waveguides are used to show that this approach has some inherent small error due to the discretization of the nonuniform coupling. This chapter finishes by describing the coefficients of the sensitivity of optical modes of the waveguides to the geometrical and material parameters. Perturbation theory is briefly presented as a way to analytically examine the impact of small perturbations on the effective index of the modes. In Chapter 3, Compact Modeling Approach, the concept of scattering matrix of a multi-port silicon photonic device is presented. The elements of the S-matrix are complex numbers that relate the amplitude and phase relationships of the optical models in the input and output ports. Based on the scattering matrix modeling of silicon photonics devices, two methods of solving photonic circuits are developed: the first one is based on the iteration for linear circuits. The second approach is based on the construction of an equivalent signal flow graph (SFG) for the circuit. We show that the SFG approach is very efficient for circuits involving microring resonator structures. Not only SFG can provide the solution for the transmission, it also provides the signal paths and the closed-form solution based on the Mason’s graph formula. We also show how the SFG method can be utilized to formulate the backscattering effects inside a ring resonator. In Chapter 4, Scalability of Silicon Photonic Switch Fabrics, we develop the models for electro-optic Mach-Zehnder switch elements (2×2). For the electro-optic properties, the empirical Soref’s equations are used to characterize how the loss and index of silicon changes when the charge carrier density is changed. We then use our photonic circuit solver based on the iteration method to find accurate result of light propagation in large-scale switch topologies (e.g. 4×4, and 8×8). The concept of advanced path mapping based on physical layer evaluation of the switch fabric is introduced and used to develop the optimum routing tables for 4×4 and 8×8 Benes switch topologies. In Chapter 5, Design space of Microring Resonators, we introduce the concept of curvature function of coupling to mathematically characterize the coupling coefficient of a ring resonator to a waveguide as a function of the geometrical parameters (ring radius, coupling gap, width and height of waveguides) and the wavelength. Extensive 2D and 3D FDTD simulations are carried out to validate our modeling approach. Experimental demonstrations are also used to not only further validate our modeling of coupling, but also to extract an empirical power-law model for the bending loss of the ring resonators as a function the radius. By combining these models, we for the first time present a full characterization of the design space of microring resonators. Moreover, the value of this discussion will be further apparent when the scalability of a silicon photonic link is studied. We will show that the FSR of the rings determines the optical bandwidth but it also impacts the properties of the ring resonators. In Chapter 6, Thermo-optic Efficiency of Microheaters, we develop analytical models for the thermo-optic properties of SiP waveguides. For the thermo-optic properties, the concept of thermal impulse response is mathematically developed for integrated micro-heaters. The thermal impulse response is a key function that determines the tradeoff between heating efficiency and heating speed (thermal bandwidth), as well as allows us to predict the pulse-width-modulation (PWM) optical response of the heater-waveguide system. One of the motivations behind this study was to find the highest possible efficiency for thermal tuning of microring resonators to use it in the evaluation of the energy consumption of a photonic link. The results indicate 2 nm/mW which is in agreement with the trends that we see in the literature. In Chapter 7, Crosstalk Penalty, we theoretically and experimentally investigate the optical crosstalk effects in microring-based silicon photonic interconnects. Both inter-channel crosstalk and intra-channel crosstalk are investigated and approximate equations are developed for their corresponding power penalties. Inclusion of the inter-channel crosstalk is an important part of our final analysis of a silicon photonic link. In Chapter 8, Scalability of Silicon Photonic Links, we present the analysis of a WDM silicon photonics point-to-point link based on microring modulators and microring wavelength filters. Our approach is based on the power penalty analysis of non-return-to-zero (NRZ) signals and Gaussian noise statistics. All the necessary equations for the optical power penalty calculations are presented for microring modulators and filters. The first part of the analysis is based on various ideal assumptions which lead to a maximum capacity of 2.1 Tb/s for the link. The second part of the analysis is carried out with more realistic assumptions on the photonic elements in the link, culminating in a maximum throughput of 800 Gb/s. We also provide estimations of the energy/bit metric of such links based on the optimized models of electronic circuits in 65 nm CMOS technology

Silicon photonic switching: from building block design to intelligent control

The rapid growth in data communication technologies is at the heart of enriching the digital experiences for people around the world. Encoding high bandwidth data to the optical domain has drastically changed the bandwidth-distance trade-off imposed by electrical media. Silicon photonics, sharing the technological maturity of the semiconductor industry, is a platform poised to make optical interconnect components more robust, manufacturable, and ubiquitous. One of the most prominent device classes enabled by the silicon photonics platform is photonic switching, which describes the direct routing of optical signal carriers without the optical-electrical-optical conversions. While theoretical designs and prototypes of monolithic silicon photonic switch devices have been studied, realizing high-performance and feasible switch systems requires explorations of all design aspects from basic building blocks to control systems. This thesis provides a holistic collection of studies on silicon photonic switching in topics of novel switching element designs, multi-stage switch architectures, device calibration, topology scalability, smart routing strategies, and performance-aware control plane. First, component designs for assembling a silicon photonic switch device are presented. Structures that perform 2×2 optical switching functions are introduced. To realize switching granularities in both spatial and spectral domains, a resonator-assisted Mach-Zehnder interferometer design is demonstrated with high performance and design robustness. Next, multi-stage monolithic switching devices with microring resonator-based switching elements are investigated. An 8×8 switch device with dual-microring switching elements is presented with a well-balanced set of performance metrics in extinction ratio, crosstalk suppression, and optical bandwidth. Continued scaling in the switch port count requires both an economic increase in the number of switching elements integrated in a device and the preservation of signal quality through the switch fabric. A highly scalable switch architecture based on Clos network with microring switch-and-select sub-switches is presented as a solution to reach high switch radices while addressing key factors of insertion loss, crosstalk, and optical passband to ensure end-to-end switching performance. The thesis then explores calibration techniques to acquire and optimize system-wide control points for integrated silicon switch devices. Applicable to common rearrangeably non-blocking switch topologies, automated procedures are developed to calibrate entire switch devices without the need for built-in power monitors. Using Mach-Zehnder interferometer-based switching elements as a demonstration, calibration techniques for optimal control points are introduced to achieve balanced push-pull drive scheme and reduced crosstalk in switching operations. Furthermore, smart routing strategies are developed based on optical penalty estimations enabled by expedited lightpath characterization procedures. Leveraging configuration redundancies in the switch fabric, the routing strategies are capable of avoiding the worst penalty optical paths and effectively elevate the bottom-line performance of the switch device. Additional works are also presented on enhancing optical system control planes with machine learning techniques to accurately characterize complex systems and identify critical control parameters. Using flexgrid networks as a case study, light-weight machine learning workflows are tailored to devise control strategies for improving spectral power stability during wavelength assignment and defragmentation. This work affirms the efficacy of intelligent control planes to predict system dynamics and drive performance optimizations for optical interconnect systems

Multidimensional quantum entanglement with large-scale integrated optics

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.Comment: Science, (2018

Reconfigurable Reflective Arrayed Waveguide Grating on Silicon Nitride

[ES] La presente tesis se ha centrado en el modelado, diseño y demonstración experimental por primera vez del dispositivo Reconfigurable Reflective Arrayed Waveguide Grating (R-RAWG). Para la consecución de este dispositivo que tiene posibilidades de uso en la espectrometría, una plataforma de nitruro de silicio llamada CNM-VLC se ha usado, ya que este material permite operar en un gran ancho de banda. Esta plataforma posee ciertas limitaciones y los elementos necesarios para el funcionamiento de este dispositivo tenían un performance bajo. Por ello, se ha desarrollado y validado una metodología que ha permitido obtener mejores divisores. Además, se ha diseñado un inverted taper que ha mejorado considerablemente el acoplo de luz al chip. Esto ha sido gracias a un exhaustivo análisis de opciones existentes en la literatura que también ha permitido escoger la mejor opción para realizar un espejo reconfigurable en la plataforma sin cambiar ni añadir ningún proceso de fabricación. Se han demostrado espejos reconfigurables gracias a utilizar divisores ópticos realimentados y también se ha desarrollado códigos que predicen el comportamiento del dispositivo experimentalmente. Con todo el trabajo realizado, se ha diseñado un R-RAWG para que pudiera operar en un gran ancho de banda y que los actuadores de fase no tuvieran peligro de estropearse. También se ha desarrollado un código para el modelado del R-RAWG que permite imitar la fabricación de estos dispositivos y que, gracias a esto, se ha desarrollado un método o algoritmo llamado DPASTOR, que usa algoritmos usados en machine learning, para optimizar la respuesta con tan sólo la potencia óptica de salida. Finalmente, se ha diseñado una PCB para poder conectar eléctricamente el chip fotónico y se ha desarrollado un método de medida que ha permitido tener una respuesta estable consiguiendo demostrar multitud de respuestas de filtros ópticos con el mismo dispositivo.[CAT] La present tesi s'ha centrat en el modelatge, disseny i demonstració experimental per primera vegada del dispositiu Reconfigurable Reflective Arrayed Waveguide Grating (R-RAWG). Per a la consecució d'aquest dispositiu que té possibilitats d'ús en l'espectrometria, una plataforma de nitrur de silici anomenada CNM-VLC s'ha usat ja que aquest material permet operar en una gran amplada de banda. Aquesta plataforma posseeix certes limitacions i els elements necessaris per al funcionament d'aquest dispositiu tenien un performance baix. Per això, s'ha desenvolupat i validat una metodologia que ha permés obtindre millors divisors i també, gràcies als processos de fabricació, s'ha dissenyat un acoplador que ha millorat considerablement l'acoble de llum al xip. Això ha sigut gràcies a un exhaustiu analisis d'opcions existents en la literatura que també ha permés triar la millor opció per a realitzar un espill reconfigurable en la plataforma sense canviar ni afegir cap procés de fabricació. S'han demonstrat espills reconfigurables gràcies a utilitzar divisors realimentats i també s'ha desenvolupat codis que prediuen el comportament del dispostiu experimentalment. Amb tot el treball realitzat, s'ha dissenyat un R-RAWG fent ús de determinades consideracions perquè poguera operar en una gran amplada de banda i que els actuadors de fase no tingueren perill de desbaratar-se. També s'ha desenvolupat un codi per al modelatge del R-RAWG que permet imitar la fabricació d'aquests dispositius i que, gràcies a això, s'ha desenvolupat un mètode o algorisme anomenat DPASTOR, que usa algorismes usats en machine learning, per a optimitzar la resposta amb tan sols la potència òptica d'eixida. Finalment, s'ha dissenyat una PCB per a poder connectar elèctricament el xip fotònic i s'ha desenvolupat un mètode de mesura que ha permés tindre una resposta estable aconseguint demostrar multitud de respostes de filtres òptics amb el mateix dispositiu.[EN] This thesis is focused on the modelling, design and experimental demonstration for the first time of Reconfigurable Reflective Arrayed Waveguide Grating (R-RAWG) device. In order to build this device, that can be employed in spectrometry, a silicon nitride platform termed CNM-VLC has been chosen since this material allows to operate in broad range of wavelengths. This platform has the necessary elements, but some limitations because the operation of this device had a low performance. Therefore, a methodology has been developed and validated, which has allowed to obtain better splitters. Also an inverted taper has been designed, which has considerably improved the coupling of light to the chip. This has been possible thanks to an exhaustive analysis of existing options in the literature, that has allowed choosing the best option to make a reconfigurable mirror on the platform without changing or adding new manufacturing steps. Reconfigurable mirrors have been demonstrated by using feedback splitters. Furthermore, codes have been developed to predict the behaviour of the actual device. With all the work done, a R-RAWG has been designed by using certain considerations so that it can operate over a broad wavelength range and the phase actuators are not in danger of being damaged. A code has also been developed for the modelling of the R-RAWG, which allows manufacturing imperfections to be considered, thanks to this, a method or algorithm called DPASTOR has been developed. DPASTOR resembles machine learning to optimise the response by just using the optical output power. Finally, a PCB and an assembly with the chip interconnected to it have been made and designed. Moreover, a measurement method has been developed, which has made it possible to have a stable response and to demonstrate a multitude of optical filter responses with the same device.Fernández Vicente, J. (2021). Reconfigurable Reflective Arrayed Waveguide Grating on Silicon Nitride [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/165783TESI