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Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set…
Optical skyrmions have attracted significant attention across diverse physical systems for their promising scenarios in ultra-precise metrology, optical information processing, and quantum technologies. However, the lack of effective method…
The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal…
The ability of metallic nanostructures to confine light at the sub-wavelength scale enables new perspectives and opportunities in the field of nanotechnology. Making use of this unique advantage, nano-optical trapping techniques have been…
Topological properties of energy flow of light are fundamentally interesting and have rich practical applications in optical manipulations. Here, skyrmion-like structures formed by Poynting vectors are unveiled in the focal region of a pair…
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case,…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…
We generalize the geometrical model of transformation optics to Rieman-Cartan space with torsion by introducing topological defects in physical space. By relaxing the integrable condition, we show explicitly that the generalized equivalent…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically-thin material, where the light polarization can be used to control the spin and valley degrees-of-freedom for the development of…
The scattering of light impacts sensing and communication technologies throughout the electromagnetic spectrum. Overcoming the effects of time-varying scattering media is particularly challenging. In this article we introduce a new way to…
Optical skyrmions, the optical analogue of topological configurations formed by three-dimensional vector fields covering the whole 4{\pi} solid angle but confined in a two-dimensional (2D) domain, have recently attracted growing interest…
A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a…
Topological phases of matter give rise to exotic physics that can be leveraged for next generation quantum computation and spintronic devices. Thus, the search for topological phases and the quantum states that they exhibit have become the…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
We investigate the optical conductivity, along with longitudinal and transverse conductivities, in buckled hexagonal lattice such as silicene subjected to both an in-plane magnetic field and a perpendicular electric field. In this model, we…
Monolayers of transition metal dichalcogenides (TMdC) are promising candidates for realization of a new generation of optoelectronic devices. The optical properties of these two-dimensional materials, however, vary from flake to flake, or…