This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

The core advantage of metalenses over traditional bulky lenses lies in their thin volume and lightweight. Nevertheless, as the application scenarios of metalenses extend to the macro-scale optical imaging field, a contradiction arises between the increasing demand for large-aperture metalenses and the synchronous rise in design and processing costs. In response to the application requirements of metalens with diameter reaching the order of 10⁴λ or even 10⁵λ, this paper proposes a novel design method for fixed-height concentric-ring metalenses, wherein, under the constraints of the processing technology, a subwavelength 2D building unit library is constructed based on different topological structures, and the overall cross-section of the metalens is assembled. Compared to global structural optimization, this approach reduces computational resources and time consumption by several orders of magnitude while maintaining nearly identical focusing efficiency. As a result, a concentric-ring metalens with a designed wavelength of 632.8 nm and a diameter of 46.8 mm was developed, and a quasi-telecentric telescope system composed of aperture stop and metalens was constructed, achieving high-resolution detection within a 20° field of view. In the subsequent experiments, the unique weak polarization dependence and narrowband adaptability of the meta-camera are quantitatively analyzed and tested, and excellent imaging results were finally obtained. Our work not only ensures the narrowband optical performance but also promotes the simplicity and light weight of the metalens based telescopic system, which further advances the deep application of large-diameter metalenses in the field of astronomical observation.

Topology Optimization of Capillary, Two-Phase Flow Problems - Volume 22 Issue 5 - Yongbo Deng, Zhenyu Liu, Yihui Wu