Dynamically encircling exceptional points in a three-mode waveguide system

Abstract

Dynamically encircling exceptional points (EPs) in non-Hermitian systems has attracted considerable attention recently, but all previous studies focused on two-state systems, and the dynamics in more complex multi-state systems is yet to be investigated. Here we consider a three-mode non-Hermitian waveguide system possessing two EPs, and study the dynamical encircling of each single EP and both EPs, the latter of which is equivalent to the dynamical encircling of a third-order EP that has a cube-root behavior of eigenvalue perturbations. We find that the dynamics depends on the location of the starting point of the loop, instead of the order of the EP encircled. Compared with two-state systems, the dynamical processes in multi-state systems exhibit more non-adiabatic transitions owing to the more complex topological structures of energy surfaces. Our findings enrich the understanding of the physics of multi-state non-Hermitian systems and may lead to the design of new wave manipulation schemes.

Multimode parity-time and loss-compensation symmetries in coupled waveguides with loss and gain

“…Another exciting direction is the observation and utilization of the higher-order EPs, where more than two eigenmodes coalesce. Such EPs can be realized either in the systems containing three or more resonant elements [21,32,33] or by hybridizing several usual (second-order) EPs [34,35]. It should be noted that the most considerations of non-Hermitian effects are limited to the single-mode case with the use of the coupled-mode theory (CMT) [36].…”

Third-order exceptional point and successive switching among three states in an optical microcavity

“…The integration of an EP3 in any real system and realization of successive conversions among three states due to parametric encirclement require a complicated system topology that have been shown using individually pumped coupled-cavity [32] * somiit@rediffmail.com and waveguide [33,34] systems. Recently, the nonadiabatic state-dynamics due to dynamical encirclement around an EP3 has also been explored in coupled [35] and planar [36] waveguide systems. However, there is still a technological demand to locate an EP3 with associated successive state conversion in a simple, fabrication feasible system having minimum number of control parameters.…”

“…Here, the effect of an EP3 has been realized with simultaneous presence of these two EP2s inside a closed gain-loss parameter space. Beyond the reported systems with more complex topology [32][33][34][35], we present a robust successive topological conversion between three consecutive states around an EP3, for the first time, using only two tunable parameters associated with the imposed gain-loss profile. Proposed design hosting an EP3 having rich physics and unique features will certainly be suitable for state-of-the-art device implementation.…”

Exotic light dynamics around a fourth order exceptional point

“…The effect of dynamical parametric encirclement process around a single EP [9,10,14,26,40]. or two connecting EPs (or an analogous EP3) [13,43] have widely been investigated using various planar or coupled guide-wave systems.…”

“…It should be quite interesting, if one can manipulate the simultaneous interaction among the four states in the vicinity of an EP4. In general, dynamical encirclements of second-or third-order EPs have attracted enormous attention to develop mode-conversion devices [9,10,13,14,26,40,43]. Thus, a general question comes out in the context of EP4, i.e., what is the outcome of dynamical encirclement around an EP4?…”