Topological Insulators by Topology Optimization

An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo spin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive; consisting of acoustically hard members placed in an air background and has an operational bandwidth of $\approx$12.5\% showing high transmission. Further analysis demonstrates confinement of more than 99\% of the total field intensity in the TI within at most six lattice constants from the TI interface. The proposed design hereby outperforms a reference from recent literature regarding energy transmission, field confinement and operational bandwidth.Comment: 6 pages, 5 figure

Designing Photonic Topological Insulators with Quantum-Spin-Hall Edge States using Topology Optimization

Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a photonic topological insulator reminiscent of the shrink-and-grow approach to quantum-spin-Hall photonic topological insulators but with notable differences in the topology of the crystal as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50 \% larger than previous designs. Furthermore, we find a directional beta factor exceeding 99 \%, and very low losses for sharp bends. Our approach allows for the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto unexplored symmetry constraints.Comment: 7 pages, 5 figure

Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities

Small manufacturing-tolerant photonic crystal cavities are systematically designed using topology optimization to enhance the ratio between quality factor and mode volume, Q/V. For relaxed manufacturing tolerance, a cavity with bow-tie shape is obtained which confines light beyond the diffraction limit into a deep-subwavelength volume. Imposition of a small manufacturing tolerance still results in efficient designs, however, with diffraction-limited confinement. Inspired by numerical results, an elliptic ring grating cavity concept is extracted via geometric fitting. Numerical evaluations demonstrate that for small sizes, topology-optimized cavities enhance the Q/V-ratio by up to two orders of magnitude relative to standard L1 cavities and more than one order of magnitude relative to shape-optimized L1 cavities. An increase in cavity size can enhance the Q/V-ratio by an increase of the Q-factor without significant increase of V. Comparison between optimized and reference cavities illustrates that significant reduction of V requires big topological changes in the cavity

Inverse design in photonics by topology optimization: tutorial

Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions and satisfaction of manufacturing constraints. We here provide a tutorial for the systematic and efficient design of nano-photonic structures by Topology Optimization (TopOpt). The implementation is based on the advanced and systematic approaches developed in TopOpt for structural optimization during the last three decades. The tutorial presents a step-by-step guide for deriving the continuous constrained optimization problem forming the foundation of the Topology Optimization method, using a cylindrical metalens design problem as an example. It demonstrates the effect and necessity of applying a number of auxiliary tools in the design process in order to ensure good numerical modelling practice and to achieve physically realisable designs. Application examples also include an optical demultiplexer.Comment: 8 figures, 19 page

A Century of Psychology as Science

This reissued edition (originally published by McGraw-Hill in 1985) of A Century of Psychology as Science comprehensively assesses the accomplishments, status, and prospects of psychology at the end of its first century as a science, while offering a new postscript. The forty-three contributors are among psychology\u27s foremost authorities. Among the fields addressed are sensory processes and perception, learning, motivation, emotion, cognition, development, personality, and social psychology.https://scholarship.richmond.edu/bookshelf/1168/thumbnail.jp

The Stokes-Einstein Relation in Supercooled Aqueous Solutions of Glycerol

The diffusion of glycerol molecules decreases with decreasing temperature as its viscosity increases in a manner simply described by the Stokes-Einstein(SE) relation. Approaching the glass transition, this relation breaks down as it does with a number of other pure liquid glass formers. We have measured the diffusion coefficient for binary mixtures of glycerol and water and find that the Stokes-Einstein relation is restored with increasing water concentration. Our comparison with theory suggests that addition of water postpones the formation of frustration domainsComment: 4 Pages and 3 Figure

Observable Optimal State Points of Sub-additive Potentials

For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system. This paper generalizes Dai's result to the non-ergodic case, and proves that under some mild additional hypothesis, one can choose points with negative growth rates from a positive Lebesgue measure set, even if the system does not preserve any measure that is absolutely continuous with respect to Lebesgue measure.Comment: 16 pages. This work was reported in the summer school in Nanjing University. In this second version we have included some changes suggested by the referee. The final version will appear in Discrete and Continuous Dynamical Systems- Series A - A.I.M. Sciences and will be available at http://aimsciences.org/journals/homeAllIssue.jsp?journalID=

A Fluid Dynamics Calculation of Sputtering from a Cylindrical Thermal Spike

The sputtering yield, Y, from a cylindrical thermal spike is calculated using a two dimensional fluid dynamics model which includes the transport of energy, momentum and mass. The results show that the high pressure built-up within the spike causes the hot core to perform a rapid expansion both laterally and upwards. This expansion appears to play a significant role in the sputtering process. It is responsible for the ejection of mass from the surface and causes fast cooling of the cascade. The competition between these effects accounts for the nearly linear dependence of $Y$ with the deposited energy per unit depth that was observed in recent Molecular Dynamics simulations. Based on this we describe the conditions for attaining a linear yield at high excitation densities and give a simple model for this yield.Comment: 10 pages, 9 pages (including 9 figures), submitted to PR