Topology optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The optimization problem is efficiently solved using mathematical programming-based optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind topology optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

Phononic band-gap materials prevent elastic waves in certain frequency ranges from propagating, and they may therefore be used to generate frequency filters, as beam splitters, as sound or vibration protection devices, or as waveguides. In this work we show how topology optimization can be used to design and optimize periodic materials and structures exhibiting phononic band gaps. Firstly, we optimize infinitely periodic band-gap materials by maximizing the relative size of the band gaps. Then, finite structures subjected to periodic loading are optimized in order to either minimize the structural response along boundaries (wave damping) or maximize the response at certain boundary locations (waveguiding).

Structural materials are used in myriad applications, including aerospace, automotive, biomedical, and acoustics. Most materials have positive or zero Poisson's ratio, with cork serving as a well-known example of the latter type of behavior. The Poisson's ratio describes the relative amount a given material contracts transversally when stretched axially. Recently, artificial materials that exhibit a negative Poisson's ratio have been introduced. [1][2][3] These auxetic materials expand transversally when axially stretched, seemingly defying the fundamental laws of nature. [1][2][3] They exhibit enhanced mechanical properties, such as shear resistance, [4,5] indentation resistance [6][7][8][9] and extraordinary damping properties, [10] making them well suited for targeted applications. To date, several types of auxetic materials have been introduced [2,3,[11][12][13][14][15][16][17][18][19][20] . However, current embodiments suffer from two primary limitations: 2(1) they only exhibit the desired response over a narrow range of strains (less than a few %) and (2) they are difficult to manufacture in a scalable manner. [17,[21][22][23][24][25] While recent structures (e.g. chiral honeycombs, [14] tilting square structures [24] or Bucklicrystals [19] ), for specific values of Poisson's ratio, exhibit near constant values over large strains, they are either not generalizable to other Poisson's ratio values or they exhibit low effective stiffness and/or must be pre-stressed to yield the desired performance.Here, we combine topology optimization to programmably design their architecture with 3D printing to digitally fabricate the designs and validate against the numerically predicted behavior. Specifically, we create a new class of architected materials with programmable Poisson's ratios between -0.8 and 0.8 that display a nearly constant Poisson's ratio over large deformations of up to 20% or more. Figure 1 shows two representative examples of microstructures designed using topology optimization. [26] The linear model that is applied by existing design methods ( Figure 1a) assumes small deformations. By contrast, an emerging approach (Figure1b), described in detail in a recent study [26] by Sigmund and coworkers, uses a geometrically nonlinear model and includes a requirement of a constant prescribed Poisson's ratio when straining the material. While both examples are designed to have a Poisson's ratio of -0.8, the performance of the linearly designed material rapidly deteriorates when the material is strained more than a few percent ( Figure 1c).Mathematically, the optimization goal is defined as minimizing the error between the actual and the pre-defined value of Poisson's ratio over a range of discrete, nominal strain values up to 20%. [26] To ensure scalable fabrication of these architectures, several geometric constraints are imposed on the topology optimization design problem. A requirement of uniform structural features is implemented as a combination of imposing a minimum [27,28] and a maximum length scale. Th...

Biocatalytic transamination is being established as key tool for the production of chiral amine pharmaceuticals and precursors due to its excellent enantioselectivity as well as green credentials. Recent examples demonstrate the potential for developing economically competitive processes using a combination of modern biotechnological tools for improving the biocatalyst alongside using process engineering and integrated separation techniques for improving productivities. However, many challenges remain in order for the technology to be more widely applicable, such as technologies for obtaining high yields and productivities when the equilibrium of the desired reaction is unfavorable. This review summarizes both the process challenges and the strategies used to overcome them, and endeavors to describe these and explain their applicability based on physiochemical principles. This article also points to the interaction between the solutions and the need for a process development strategy based on fundamental principles.

Topology optimization is a promising method for systematic design of optical devices. As an example, we demonstrate how the method can be used to design a 90° bend in a two-dimensional photonic crystal waveguide with a transmission loss of less than 0.3% in almost the entire frequency range of the guided mode. The method can directly be applied to the design of other optical devices, e.g., multiplexers and wave splitters, with optimized performance.

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Topology optimization is used to design a planar photonic crystal waveguide component resulting in significantly enhanced functionality. Exceptional transmission through a photonic crystal waveguide Z-bend is obtained using this inverse design strategy. The design has been realized in a silicon-on-insulator based photonic crystal waveguide. A large low loss bandwidth of more than 200 nm for the bandgap polarization is experimentally confirmed.