The Independence Axiom and Asset Returns

This paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal asset-pricing framework. The resulting models are amenable to empirical analysis using market data and standard Euler equation methods. We are thereby able to provide the first non-laboratory-based evidence regarding the usefulness of several new theories of risk preference for addressing standard problems in dynamic economics. Using both stock and bond returns data, we find that a model incorporating risk preferences that exhibit firstorder risk aversion accounts for significantly more of the mean and autocorrelation properties of the data than models that exhibit only second-order risk aversion. Unlike the latter class of models which require parameter estimates that are outside of the admissible parameter space, e.g., negative rates of time preference, the model with first-order risk aversion generates point estimates that are economically meaningful. We also examine the relationship between first-order risk aversion and models that employ exogenous stochastic switching processes for consumption growth.

Topology optimization of freeform large-area metasurfaces

We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, with one degree of freedom per high-resolution "pixel," can be extended to large areas with the help of a locally periodic approximation that was previously only used for a few parameters per $\lambda^2$. In this way, we can computationally discover completely unexpected metasurface designs for challenging multi-frequency, multi-angle problems, including designs for fully coupled multi-layer structures with arbitrary per-layer patterns. Unlike typical metasurface designs based on subwavelength unit cells, our approach can discover both sub- and supra-wavelength patterns and can obtain both the near and far fields

The relation between solar cell flight performance data and materials and manufacturing data Final report

Flight performance data for solar cell power systems in satellites and correlation with manufacturing methods and material

High-efficiency degenerate four wave-mixing in triply resonant nanobeam cavities

We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr $\chi^(3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of resonant four-wave mixing processes and demonstrate the possibility of observing high-efficiency limit cycles and steady-state conversion corresponding to $\approx 100$% depletion of the pump light at low powers, even including effects due to losses, self- and cross-phase modulation, and imperfect frequency matching. Assuming operation in the telecom range, we predict close to perfect quantum efficiencies at reasonably low $\sim$ 50 mW input powers in silicon micrometer-scale cavities

Overlapping domains for topology optimization of large-area metasurfaces

We introduce an overlapping-domain approach to large-area metasurface design, in which each simulated domain consists of a unit cell and overlapping regions from the neighboring cells plus PML absorbers. We show that our approach generates greatly improved metalens quality compared to designs produced using a locally periodic approximation, thanks to $\sim 10\times$ better accuracy with similar computational cost. We use the new approach with topology optimization to design large-area ($200\lambda$) high-NA (0.71) multichrome and broadband achromatic lenses with high focusing efficiency ($\sim 50\%$), greatly improving upon previously reported works

Optimal economie dispatch for the nigerian grid system considering voltage and line flow constraints

The electric power industries worldwide have undergone considerable changes especially from vertical structure to full deregulated entities. These changes are now introducing new problems in terms of operations, controls and planning of the entire grid systems. This calls for a more reliable analytical tool ever than before. One feasible solution is to perform the Optimal Economic Dispatch (OED) paradigm on this restructured power system so as to provide fairness to all operators. In this paper, the economic dispatch problem with voltage and line flow constraints has been formulated for the hydro-thermal generating units feeding the Nigerian power system. In order to solve the arising power flow problem a MATLAB based simulation package, MATPOWER version 3.0 has been suitably modified to obtain feasible solutions for different loading system scenarios. The results obtained showed that the OED offered a better optimal power schedules, power loss minimization and reduced total fuel cost than earlier work based on Micro-Genetic Algorithm, (MGA) and Conventional Genetic Algorithm (CGA)

Inverse design of large-area metasurfaces

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize surfaces that can be thousands of wavelengths in diameter, with thousands (or millions) of parameters, the key is a fast approximate solver for the scattered field. We employ a "locally periodic" approximation in which the scattering problem is approximated by a composition of periodic scattering problems from each unit cell of the surface, and validate it against brute-force Maxwell solutions. This is an extension of ideas in previous metasurface designs, but with greatly increased flexibility, e.g. to automatically balance tradeoffs between multiple frequencies, or to optimize a photonic device given only partial information about the desired field. Our approach even extends beyond the metasurface regime to non-subwavelength structures where additional diffracted orders must be included (but the period is not large enough to apply scalar diffraction theory).Comment: 18 pages, 8 figure

End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e. the object can be described by a small number of non-zero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material: in both situations, our end-to-end framework computationally discovers optimal metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing