Universal transient radiation dynamics by abrupt and soft temporal transitions in optical waveguides

When an excited electromagnetically open optical waveguide goes through a temporal transition of its material properties, it radiates to the ambient surroundings. In this paper, we explore this radiation and reveal, using asymptotic evaluation of path integral in the complex frequency (Laplace) plane, a peculiar space-Time dependence of its frequency. Specifically, we derive an asymptotically exact formula (Eq. (11)) for the instantaneous radiation frequency, which exhibits a chirp behavior with respect to time. This simple formula depends on the ambient properties and on the longitudinal wavenumber β of the guided mode before the temporal transition but not on the specific waveguide structure or materials. In addition, we derive a t-3/2 decay rate of the radiative field amplitude on time. We verify our analytic results using full-wave simulations of a dispersive and lossy indium tin oxide waveguide that undergoes smooth temporal long transitions over up to ∼200 cycles at the initially guided mode frequency. Thus, these theoretical findings offer valuable insights into the behavior of general optical waveguides experiencing temporal transitions and provide a powerful tool for analyzing and designing such THz and optical setups, with potential use in sensing and imaging.