Arpit Khandelwal

Abstract: A phase field model is used to study crack propagation in staggered structures that are commonly found in several biological and biomimetic composites. The composite is modelled by creating an elastic mismatch between the two phases, ‘mineral’ and ‘organic’ which form into a staggered brick and mortar type micro-structure. The huge disparity in the stiffness of the two constituent phases gives rise to a non-uniform stress field near crack tips in these materials. Depending on the arrangement of the mineral platelets, different mechanisms of crack propagation may be observed. We find that cracks propagate straight when the aspect ratio of the mineral platelets is higher than a critical value. For lower values of aspect ratio, the cracks tend to exhibit a tortuous crack path in which fracture predominantly occurs in the soft organic phase. This critical aspect ratio is found to be a function of the mineral volume fraction as well as the elastic modulus mismatch. For some configurations, micro cracking in regions close to the crack tips is also observed. A simple theory is presented to analyse the observed crack paths in staggered composites.

Abstract: We present a mathematical analysis and comparison of the performance of integrated on-chip semiconductor ring laser gyroscope (SRLG) fabricated using GaAs/AlGaAs and InP/InGaAsP technologies. The performance parameters of the gyro are modeled in terms of fundamental material, waveguide, and resonator parameters. In addition to this, influence of phenomena specific to semiconductor lasers such as nonlinear coupling, spatial hole burning, gain grating formation, and carrier induced index change on the gyro performance is also included. The analysis helps in identifying critical parameters, which must be optimized to improve the gyro performance.Best achievable performance of integrated SRLG is calculated, and design modifications are suggested to enhance it for high-performance military applications.

Abstract: The sensitivity of a monolithically integrated semiconductor ring laser gyro is severely limited by the high value of the lock-in threshold. In this work, we calculate the lock-in threshold using perturbation theory and coupled mode theory analysis. It is shown that gyro sensitivity is limited to an input rotation rate of 108 deg / h due to nonlinear coupling between the countertraveling modes. This coupling arises due to the backreflection of modes from moving index gratings, induced by rotation. Lock-in threshold is directly proportional to the strength of nonlinear coupling and spatial overlap of the modes’ energy densities with periodic index perturbations.

Abstract: Ring laser gyroscopes (RLG) are optical inertial rotation sensors used to measure the rate and direction of rotation. With the help of accelerometers, they provide accurate information about the position and orientation of an object. Their sensitivity depends upon the intended application: military navigation requires gyros with sensitivity of 0.01-0.1 deg/h while automobiles and handheld application need sensitivity of 1-10 deg/h. As the sensitivity of gyro is directly proportional to its size, the high performance military applications are dominated by the bulky He-Ne RLG. Over the past few decades, strong theoretical research backed up by advanced fabrication technologies have improved the performance of He-Ne RLG significantly. In the era of on-chip integrated optical devices, large size and high power requirement of He-Ne RLG limits its applications. This is where Semiconductor RLG (SRLG) provides a viable alternative. SRLG is a compact, low cost and low power inertial rotation sensor working on the principle of Sagnac effect. It offers the promise of fabricating the complete gyro system on a single Photonic Integrated Circuit (PIC). Many implementations of bulk-optic and integrated SRLG have been proposed, but their reported performance has been highly inferior to He-Ne RLG. While bulk-optic SRLG has shown sensitivity of 103 deg/h, the reported sensitivity of integrated SRLG has been 108 deg/h, which is unacceptable even for low performance applications like automobiles. While the poor performance of integrated SRLG has been attributed to phenomena like mode coupling and gain competition, a detailed performance analysis has not yet been reported. Hence, critical performance limiting parameters could not be identified and feasible practical solutions to enhance the performance could not be proposed. This has inhibited the development of SRLG technology towards high performance applications. In this thesis, SRLG has been mathematically modeled using rate equations of counter-traveling electric fields inside the gain medium and the resonant cavity. The Sagnac beat signal obtained by simulating the model is verified by rotating the experimental setup of the gyro. The sensitivity, which is found to be limited by locking of the counter-traveling fields, is enhanced by proposing few novel designs and biasing techniques. Although these techniques improve the sensitivity of SRLG, the overall performance is still very poor compared to the military navigation standards. In order to identify the critical performance limiting parameters and phenomena, every metric of SRLG such as quantum limit, angle random walk, scale factor stability, null shift and lock-in threshold have been thoroughly modeled in terms of material, geometry and environmental parameters. Moreover, effects of nonlinearities such as spatial hole burning, mode coupling, gain saturation etc. on the SRLG sensitivity have been evalu-

Abstract: The semiconductor gain medium has rich non-linear dynamics and several internal parameters influence the generation and propagation of light through it. With the gain medium being an integral part of semiconductor ring laser gyroscope (SRLG) cavity, its parameters affect the overall performance of the gyro. The effect is further elevated in integrated SRLG due to stronger confinement of charge carriers and photons leading to a more intense interaction between them. In this paper, we evaluate the influence of semiconductor gain medium parameters such as gain saturation coefficient, linewidth, internal quantum efficiency etc. on the sensitivity of bulk fiber-optic SRLG. Ways of controlling these parameters and optimizing their values to enhance the performance of SRLG are also discussed.

Abstract: One of the most intriguing protein materials found in nature is bone, a material composed of assemblies of tropocollagen molecules and tiny hydroxyapatite mineral crystals that form an extremely tough, yet lightweight, adaptive and multifunctional material. Bone has evolved to provide structural support to organisms, and therefore its mechanical properties are of great physiological relevance. In this article, we review the structure and properties of bone, focusing on mechanical deformation and fracture behavior from the perspective of the multidimensional hierarchical nature of its structure. In fact, bone derives its resistance to fracture with a multitude of deformation and toughening mechanisms at many size scales ranging from the nanoscale structure of its protein molecules to the macroscopic physiological scale.

Abstract: Low-cost chip-scale optoelectronic gyroscopes having a resolution ≤ 10 °/h and a good reliability also in harsh environments could have a strong impact on the medium/high performance gyro market, which is currently dominated by well-established bulk optical angular velocity sensors. The R&D activity aiming at the demonstration of those miniaturized sensors is crucial for aerospace/defense industry, and thus it is attracting an increasing research effort and notably funds. In this paper the recent technological advances on the compact optoelectronic gyroscopes with low weight and high energy saving are reviewed. Attention is paid to both the so-called gyroscope-on-a-chip, which is a novel sensor, at the infantile stage, whose optical components are monolithically integrated on a single indium phosphide chip, and to a new ultra-high Q ring resonator for gyro applications with a configuration including a 1D photonic crystal in the resonant path. The emerging field of the gyros based on passive ring cavities, which have already shown performance comparable with that of optical fiber gyros, is also discussed.

Abstract: We show that a certain fundamental limit applies to the accuracy of all optical rotation sensors which use laser light as a probe. We derive this fundamental rotation-rate uncertainty from the Heisenberg uncertainty relations and Glauber's minimum uncertainty states. The same relationship is obtained from a spontaneous-emission noise formulation. We present experimental data on a (nondithered) four-frequency ring laser gyroscope for which this limit is attained.

Abstract: Mechanical behavior of layered materials and structures greatly depends on the mechanical behavior of interfaces. In the past decades, the failure in such layered media has been studied by many researchers due to their critical role in the mechanics and physics of solids. This study aims at investigating crack-interface interaction in two-dimensional (2-D) and three-dimensional (3-D) layered media by a phase field model. Our objectives are fourfold: (a) to better understand fracture behavior in layered heterogeneous systems under quasi-static load; (b) to introduce a new methodology for better describing interfaces by a regularized interfacial transition zone in the context of variational phase field approach, exploring its important role; (c) to show the accuracy, performance and applicability of the present model in modeling material failure at the interfaces in both 2-D and 3-D bodies; and (d) to quantitatively validate computed crack path with respect to experimental data. Phase field models with both perfectly and cohesive bonded interfaces are thus derived. A regularized interfacial transition zone is introduced to capture characteristics of material mismatch at the interfaces. Numerical examples for 2-D and 3-D layered systems with experimental validation provide fundamentals of fracture behavior in layered structures. The obtained results shed light on the behavior of crack paths, which are drastically affected by the elastic modulus mismatch between two layers and interface types, and reveal the important role of the proposed interfacial transition zone in phase field modeling of crack-interface interactions.