One of the most intriguing topological features of open systems is that they exhibit exceptional point (EP) singularities. Apart from the widely explored second-order EPs (EP2s), the exploration of higher-order EPs in any system requires more complex topology, which is still a challenge. Here, we encounter a third-order EP (EP3) with the simultaneous presence of multiple second-order EPs in a simple fabrication feasible gain-loss assisted trilayer optical microcavity. Using the scattering-matrix formalism, we study the simultaneous interactions between three successive coupled states via avoided-resonance-crossing (ARC) phenomena, and we identify two EP2s near two ARC regimes. Such an occurrence of two EP2s inside a closed two-dimensional parametric space associated with an unbalanced gain-loss profile leads to the functionality of a cube-root branch point, i.e., an EP3. Following an adiabatic variation of two control parameters around the embedded EP3 in the presence of two identified EP2s, we present a robust successive-state-conversion mechanism among three coupled states. The proposed scheme indeed opens up a unique platform to manipulate light in integrated photonic devices.

We report a specially configured open optical microcavity, imposing a spatially imbalanced gain–loss profile, to host an exclusively proposed next-nearest-neighbor resonance coupling scheme. Adopting the scattering matrix ($S$-matrix) formalism, the effect of interplay between such proposed resonance interactions and the incorporated non-Hermiticity in the microcavity is analyzed drawing a special attention to the existence of hidden singularities, namely exceptional points (EPs), where at least two coupled resonances coalesce. We establish adiabatic flip-of-state phenomenon of the coupled resonances in the complex frequency plane ($k$-plane), which is essentially an outcome of the fact that the respective EP is being encircled in the system parameter plane. Encountering such multiple EPs, the robustness of flip-of-states phenomena has been analyzed via continuous tuning of coupling parameters along a special hidden singular line which connects all the EPs in the cavity. Such a numerically devised cavity, incorporating the exclusive next neighbor coupling scheme, has been designed for the first time to study the unconventional optical phenomena in the vicinity of EPs.

Using scattering matrix formalism, we report the formation of a special hidden singular line connecting multiple second-order hidden singular points, in a non-uniformly pumped degenerate optical microcavity. Such singularities are known as exceptional points (EPs), and the line is proposed as an exceptional line. Exploring the unconventional behavior of cavity resonances created by a spatially imbalanced gain–loss profile, we have established the adiabatic state-flipping mechanism of coupled resonances encountering such EPs. Various interesting encircling situations, incorporating smooth as well as fluctuating variations of the control parameters, have been analyzed. We exploit the above scheme for the first time, to the best of our knowledge, to analyze the optical performance and stability of the cascaded flip-of-state phenomenon assisted by successive encirclement of either single or multiple singularities following the exceptional line in the context of optical mode converters.

The implementation of exceptional points (EPs), a special type of topological singularities, has emerged as a new paradigm for engineering the quantum-inspired or wave-based photonic systems. Even though there exists a range of investigations on EPs of order two and three (say, EP2s and EP3s, respectively), the hosting of fourth-order EPs (EP4s) in any real system and the exploration of associated topological features are lacking. Here we have designed a simple Fabry-Pérot type gain-loss-assisted open optical microcavity to host EPs up to order four. The scattering-matrix formalism has been used to analyze the microcavity numerically. With the appropriate modulation of the gain-loss profile in the same cavity geometry, we have encountered multiple different orders of EPs by investigating the simultaneous interactions among four coupled cavity states via level-repulsion phenomena. Besides affirming the second-order and third-order branch-point behaviors of the embedded EP2s and EP3s, the fourth-order branch-point functionality of an EP4 has been manifested by encircling three connecting EP2s simultaneously in the closed gain-loss parameter space. We have established a unique successive state-switching phenomenon among four coupled states by implementing such an EP4-encirclement scheme in the system's parameter space. The proposed scheme indeed offers potential applications in state-switching and control in quantum-inspired integrated photonic circuits, where the presence of an EP4 serves as a new light manipulation tool.