Steady-State Exceptional Point Degeneracy and Sensitivity of Nonlinear Saturable Coupled Oscillators
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| Format: | Preprint |
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2026
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| _version_ | 1866908801581449216 |
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| author | Bradshaw, Benjamin Hakimi, Amin Capolino, Filippo |
| author_facet | Bradshaw, Benjamin Hakimi, Amin Capolino, Filippo |
| contents | A coupled oscillator system displays enhanced sensitivity of its saturated steady-state (SS) oscillation frequency to small parameter perturbations near an exceptional point degeneracy (EPD), a property that can be used to realize EPD-based sensors. Linear $\mathcal{PT}$-symmetric systems, consisting of two coupled resonators, exhibit EPDs around which square-root sensitivity is observed. However, linear models are insufficient for realistic systems that rely on nonlinear, saturable gain elements, particularly when $\mathcal{PT}$-symmetry is broken. Thus, we study the SS of a general system of two coupled oscillators featuring EPDs and saturable nonlinear gain, using coupled-mode theory. We do this by synthesizing and extending prior SS analyses of the system's stability, and its square-root and cubic-root oscillation frequency sensitivity at a unique third-order SS-EPD. We include an SS analysis of the saturated gain values, energy, and the oscillation frequency's sensitivity in the vicinity of the third-order SS-EPD, providing a comprehensive analysis of the system's various SS regimes. We determine that the stable and bistable regions in parameter space directly depend on the saturated gain values; that the dynamic range of high sensitivity around degenerate conditions is extended by increasing losses, consequently reducing the system's stored energy; and that, to exploit the cubic-root-like sensitivity associated to the third-order SS-EPD, the suggested working regime is best confined to operation within the weakly coupled regime and not exactly at the third order SS-EPD. Finally, we apply the model to two electronic circuits that exhibit cubic-root sensitivity, demonstrating the application and limitations of this analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Steady-State Exceptional Point Degeneracy and Sensitivity of Nonlinear Saturable Coupled Oscillators Bradshaw, Benjamin Hakimi, Amin Capolino, Filippo Applied Physics A coupled oscillator system displays enhanced sensitivity of its saturated steady-state (SS) oscillation frequency to small parameter perturbations near an exceptional point degeneracy (EPD), a property that can be used to realize EPD-based sensors. Linear $\mathcal{PT}$-symmetric systems, consisting of two coupled resonators, exhibit EPDs around which square-root sensitivity is observed. However, linear models are insufficient for realistic systems that rely on nonlinear, saturable gain elements, particularly when $\mathcal{PT}$-symmetry is broken. Thus, we study the SS of a general system of two coupled oscillators featuring EPDs and saturable nonlinear gain, using coupled-mode theory. We do this by synthesizing and extending prior SS analyses of the system's stability, and its square-root and cubic-root oscillation frequency sensitivity at a unique third-order SS-EPD. We include an SS analysis of the saturated gain values, energy, and the oscillation frequency's sensitivity in the vicinity of the third-order SS-EPD, providing a comprehensive analysis of the system's various SS regimes. We determine that the stable and bistable regions in parameter space directly depend on the saturated gain values; that the dynamic range of high sensitivity around degenerate conditions is extended by increasing losses, consequently reducing the system's stored energy; and that, to exploit the cubic-root-like sensitivity associated to the third-order SS-EPD, the suggested working regime is best confined to operation within the weakly coupled regime and not exactly at the third order SS-EPD. Finally, we apply the model to two electronic circuits that exhibit cubic-root sensitivity, demonstrating the application and limitations of this analysis. |
| title | Steady-State Exceptional Point Degeneracy and Sensitivity of Nonlinear Saturable Coupled Oscillators |
| topic | Applied Physics |
| url | https://arxiv.org/abs/2601.13638 |