Perfect Dispersive Medium for Real-Time Signal Processing

Dispersion lies at the heart of real-time signal processing systems across the entire electromagnetic spectrum from radio to optics. However, the performance and applicability of such systems have been severely plagued by distortions due to the frequency-dependent nature of the amplitude response of the dispersive media. This frequency dependence is a fundamental consequence of causality, incarnated by Kramers-Kronig relations or, equivalently, by the Bode relations. In order to resolve this issue, we introduce here the concept of a perfect dispersive medium, which is a loss-gain medium characterized by a perfectly flat magnitude response along with a quasi-arbitrary phase response. This property results from equalized electric and magnetic dipole dispersions, whence the amplitude and phase of the transmission functions of the isolated loss and gain contributions become the inverse and remain the same, respectively, under sign reversal of the imaginary part of the equalized magnetodielectric polarizability. Such a perfect dispersive medium may be realized in the form of a metamaterial, and this paper demonstrates a corresponding stacked loss-gain metasurface structure for illustration. From a practical standpoint, perfect dispersive media may propel real-time signal processing technology to a new dimension, with a myriad of novel ultrafast communication, sensing, imaging, and instrumentation applications.