Finding and manipulating multiple exceptional points in wave-chaotic microwave cavities with tunable metasurfaces*

Exceptional points (EP’s) have historically been found by using highly engineered and carefully designed systems to create the conditions needed for making eigenvalues and eigenfunctions of a matrix operator degenerate. Additionally, in these systems usually only a single exceptional point can be observed. In contrast, using generic microwave cavities having no special symmetries, but endowed with tunable metasurfaces, we are able to observe and electronically manipulate numerous scattering matrix EP’s. This has enabled us to explore new phenomena of exceptional points, such as encircling multiple EP’s by purely electronic means and seeing how the eigenvalue topology changes as different numbers of EP’s are enclosed in the loop. We also find that by using two metasurfaces we can collide and annihilate pairs of exceptional points, as well as bring pairs of new EP’s into existence. This gives us the opportunity to explore “EP dynamics” and to develop new insights into the topological properties of the parameter spaces that host EP’s.