"Chirpons": one-dimensional phase singularities as atypical local oscillations

In this work, phase singularities embedded in a wavepacket are shown to act as sources of atypical localized oscillations when the packet interacts with a linear system. We refer to these oscillations as $\mathit{\text{chirpons}}$, since they arise as strong variations of the instantaneous frequency (chirp). A mathematical expression is then provided to describe $\mathit{\text{chirpons}}$, and their behavior is explored through the interaction of a super-bandwidth wavepacket – containing two singularities – with a damped harmonic oscillator, a fundamental model for many physical systems. This interaction is analyzed theoretically, and the predictions are verified experimentally using a resonant electrical circuit as a realization of the oscillator. The results show that $\mathit{\text{chirpons}}$ evolve in a manner fundamentally different from standard Fourier oscillations, revealing features of linear systems that are otherwise inaccessible. This introduces a new approach to analyze and characterize system responses, with potential applications in high-resolution spectroscopy and signal sensing.