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Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability, or bring forward a bifurcation to enable rapid switching between states.…

Structured light fields, featuring unique topological properties and high tunability, have opened new frontiers in light-matter interactions with magnetic systems. However, the ultrafast and reconfigurable optical encoding of various types…

Structured optical fields embedded with polarization singularities (PSs) have attracted extensive attention due to their capability to retain topological invariance during propagation. Many advances in PSs research have been made over the…

Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating…

There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of…

A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…

Topological quasiparticles such as skyrmions and merons have recently attracted enormous attentions in the form of diverse optical degrees of freedom. However, these structures have not been explored in the fundamental momentum vectors of…

Optical singularities play a major role in modern optics and are frequently deployed in structured light, super-resolution microscopy, and holography. While phase singularities are uniquely defined as locations of undefined phase,…

Optical design and fabrication techniques are crucial for making optical elements. From conventional lenses to diffractive optical elements, and to recent metasurfaces, various types of optical elements have been proposed to manipulate…

The interaction of optical vortices (or phase singularities, screw dislocations) with ordinary matter is treated with simple approach. Using total internal reflection phenomenon and superposition of four plane waves incident on a material…

Defects play an important role in a number of fields dealing with ordered structures. They are often described in terms of their topology, mutual interaction and their statistical characteristics. We demonstrate theoretically and…

The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…

Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…

The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…

In addition to a plethora of emergent phenomena, the spatial topology of optical vortices enables an array of applications spanning communications to quantum photonics. Nonlinear optics is essential in this context, providing access to an…

Precise spatial manipulation of particles via optical forces is essential in many research areas, ranging from biophysics to atomic physics. Central to this effort is the challenge of designing optical systems that are optimized for…

Trapping and manipulation of small particles underlies many scientific and technological applications. Recently, the precise manipulation of multiple small particles was demonstrated using a Stokes trap that relies only on fluid flow…

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible…

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous…