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(Chen et al., 2017; Hodaei et al., 2017; Miri and Alù, 2019). The degeneracy at EPs emerges in physical sys- tems characterized by underlying symmetries; breaking these symmetries as a result of external perturbations produces shifting and splitting of the coincident reso- nant frequencies of a cavity where EPs are formed. The shifts and splits of these resonances can be exploited for the detection and possibly for the quantification of such perturbations (Figure 1b). Many conventional sen- sors rely on the detection of shifts in resonances that
are typically linearly proportional with respect to the perturbations that cause them.
In contrast, the separation of resonances around EPs is superlinear and, therefore significantly more sensitive to changes. A new class of sensing concepts may emerge by not solely relying on these pronounced shifts but also exploiting the underlying nontrivial topological features. These concepts may find applications in temperature, flow, and pressure sensing, among others (Xiao et al., 2019; Kononchuk and Kottos, 2020). The generation of EPs can occur in systems obeying parity-time (PT) sym- metry, which feature balanced distributions of gain and loss (Bender and Boettcher, 1998).
In the context of active sensing, gain and loss can be introduced in acoustic platforms in the form of arrays acting as transmitters and receivers, which are properly placed within a medium to be monitored (Fleury et al., 2015). The medium may be subjected to property changes due to material degradations, the onset of damage or environmental changes (e.g., temperature, pressure).
Figure 5. a: Permafrost monitoring using geometric phase: difference in geometric phase for a model forest of uniformly dispersed trees, and the local slope versus ground stiffness (β1; corresponding temperature range from 0 to −12°C) (Lata et al., 2020). b: Schematic for crack detection through EP evaluation. Top: elastic domain with microscopic crack monitoring. Bottom: variation of Δf in terms of crack depth for EP perturbation (red) and traditional single mode shift (blue) showing the different orders (Rosa et al., 2021).
Recently, the ultrasonic detection of a crack developing in a metallic structural component (Figure 5b) has been observed through transducer arrays that both actively monitors the propagation of an ultrasonic wave and implements gain and loss along the wave path to induce an EP (Rosa et al., 2021). The crack perturbs the EP symmetry, inducing two resonant peaks separated by a
1⁄2
frequency interval (Δf ∝ 𝜖 ). Here, 𝜖 is a small pertur-
bation quantifying the crack depth (Figure 5c, red line). The spectral shifts that would be observed in a conven- tional sensor not involving an EP only vary linearly with (Figure 5c, blue line). Given a specific Δf , for example,
that defines the resolution of a detection device translates into the ability of the EP sensor to detect smaller cracks. For Δf = 2 Hz as the available resolution, for example, this translates into the ability to detect cracks that are 85% smaller than those detectable through conventional sen- sors. It should be mentioned here that there is an ongoing debate regarding the actual superiority of EP sensors compared with other sensing techniques because a super- linear frequency splitting does not necessarily translate into enhanced sensor precision in the presence of realis- tic noise (Langbein, 2018; Wiersig, 2020). This debate is driving additional explorations devoted to reducing the
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