Chiral behaviour of the wave functions for three wave guides in the vicinity of an exceptional point of third order

Abstract

A simple matrix model that has been used to describe essential features of a PT symmetric set-up of three coupled wave guides is investigated. The emphasis of the study lies on the occurrence of an exceptional point of third order. It is demonstrated that the eigenfunctions in close vicinity of the exceptional point have a distinctive chiral behaviour.Using data describing realistic situations it is argued that such chiral behaviour can be tested experimentally.

Exceptional points of third-order in a layered optical microdisk cavity

“…An additional characteristic of an EP3 is the circling behavior of Ω in the complex plane while the EP3 is encircled three times in parameter space [32,33,36]. As already shown in figure 5 (and more clearly in figure 7(d)) we observe this phenomenon via encircling the configuration (7)-(11) in the R 1 -R 2 plane along a very small radius r = -R 10 8 .…”

“…For larger radii of the parameter circles the morphology of the Ω-trajectories in the complex plane changes, see figures 7(a)-(c). Such twisted curves are a signature that the parameter loop encloses further EP2s [32,36]. Nevertheless, the characteristic behavior of the threefold encircling is still visible for the larger parameter loop radii.…”

“…In comparison to an EP2, however, the preparation of an EP3 is a challenging task but experimentally feasible [12,21]. In pioneering works usually simple models are considered, e.g., describing the behavior of individually pumped coupled waveguides [4,32,33] or cavities [21,34,35]. Only quite recently EP3s have been studied as the solutions of full Maxwell's equations for a setup with three coupled waveguides with gain and loss [36].…”

Dynamically encircling exceptional points in a three-mode waveguide system

“…The adiabatic trajectory of state evolution following loop-4 is shown in Supplementary Fig. 3b, where the sequence of eigenmode variations is indeed the same as that of encircling the first type of third-order EP mentioned above 17,18,31 . In fact, the position of EP-1 and EP-2 can be tuned by changing the system parameters.…”

“…In a two-state system, eigenmode exchange occurs when the EP is encircled stroboscopically (i.e., assuming the process is adiabatic) [14][15][16] . Stroboscopic encircling of a high-order EP can reveal the more complex topological structure of multi-state systems 17,18 . Unexpected physics and phenomena have also been revealed when EPs are encircled stroboscopically along non-homotopic loops in multistate systems 19 .…”