Tapered photonic switching

The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use temporal inhomogeneities to achieve forms wave control, amidst greater vision engineering metamaterials across both space and time. When properties an unbounded medium are abruptly switched time, propagating waves efficiently converted different frequencies, partially coupled their back-propagating phase-conjugate partners, through a process called time-reversal. However, realistic switching time is necessarily finite, playing central role resulting scattering features. By identifying leveraging crucial electromagnetic momentum conservation time-reversal processes, here we develop very general analytical formalism quantify due arbitrary profile. Finally, deploy our analytic theory formalism, analogous spatial tapering theory, that enables tailoring desired spectral response, demonstrating its for realization broadband frequency converters filters.