A Review of designing freeform optical surfaces by the Monge–Ampère equations

Background: The equations of Monge–Ampère type which arise in geometric optics is used to design illumination lenses and mirrors. The optical design problem can be formulated as an inverse problem: determine an optical system consisting of reflector and/or refractor that converts a given light distribution of the source into a desired target light distribution. For two decades, the development of fast and reliable numerical design algorithms for the calculation of freeform surfaces for irradiance control in the geometrical optics limit is of great interest in current research. Objective: The objective of this paper is to summarize the types, algorithms and applications of Monge–Ampère equations. It helps scholars to grasp the research status of Monge–Ampère equations better and to explore the theory of Monge–Ampère equations further. Methods: This paper reviews the theory and applications of Monge–Ampère equations from four aspects. We first discuss the concept and development of Monge–Ampère equations. Then we derive two different cases of Monge–Ampère equations. We also list the numerical methods of Monge–Ampère equation in actual scenes. Finally, the paper gives a brief summary and an expectation. Results: The paper gives a brief introduction to the relevant papers and patents of the numerical solution of Monge–Ampère equations. There are quite a lot of literatures on the theoretical proofs and numerical calculations of Monge–Ampère equations. Conclusion: Monge–Ampère equation has been widely applied in geometric optics field since the predetermined energy distribution and the boundary condition creation can be well satisfied. Although the freeform surfaces designing by the Monge–Ampère equations is developing rapidly, there are still plenty of rooms for development in the design of the algorithms.

An Ultra-Compact Design of Plasmonic Memristor with Low Loss and High Extinction Efficiency Based on Enhanced Interaction between Filament and Concentrated Plasmon

We present a numerical design of the plasmonic memristive switching device operated at the telecommunication wavelength of 1.55 μm, which consists of a triangle-shaped metal taper mounted on top of a Si waveguide, with rational doping in the area below the apex of the taper. This device can achieve optimal vertical coupling of light energy from the Si waveguide to the plasmonic region and, at the same time, focus the plasmon into the apex of the metal taper. Moreover, the area with concentrated plasmon is overlapped with that where the memristive switching occurs, due to the formation/removal of the metallic nano-filament. As a result, the highly distinct transmission induced by the switching of the plasmonic memristor can be produced because of the maximized interactions between the filament and the plasmon. Our numerical simulation shows that the device hasa compact size (610 nm), low insertion loss (~1 dB), and high extinction efficiency (4.6 dB/μm). Additionally, we point out that stabilizing the size of the filament is critical to improve the operation repeatability of the plasmonic memristive switching device.

Numerical design studies of meander structures for self-expanding absorbable stents

Absorbable stents made of poly-L-lactic acid (PLLA) exhibit inferior mechanical properties compared with metal based devices. Therefore, design optimization by means of finite element analysis (FEA) plays an important role in development of high performance absorbable stents. In the present study, three different meander structures made of PLLA material were compared in terms of their radial resistive force (RRF) using FEA. Material tests were performed to obtain input parameters of PLLA for the simulation. FEA was carried out to simulate the RRF and the length change of the meander structures as a function of the diameter. In addition, the numerical results were compared to the experimental outcome using corresponding meander based stents performing radial testing with a segmented head mechanism. Comparable high stresses occurred in the Ubends of the examined stent designs. In designs with a large radius of curvature less stress was observed while crimping. One meander structure developed comparatively higher structural resistance against radially acting forces, due to its curved strut design. In general, FEA revealed consistent results compared to the experimental investigations.

Negative imaginariness and positive realness analysis of state-space symmetric systems with interval uncertainty

In this article, the state-space symmetric systems with symmetrical interval uncertainty that have positive real and negative imaginary properties are studied. First, a necessary and sufficient test in view of a state matrix is derived for a state-space symmetric system to be negative imaginary, which allows having poles at the origin. Second, bounds on symmetrical interval uncertainty that guarantee the positive realness and negative imaginariness of state-space symmetric systems are provided. Finally, the main results are illustrated by a resistor–capacitor network and a numerical design example.