Time-reversal of μs-long radiofrequency signals based on approximate temporal imaging

We propose a purely analog way to time reverse optically-carried radiofrequency signals. Taking advantage of the time-space duality, we implement an approximate temporal imaging device that combines a time-lens and a single dispersive line. For military applications, this dispersive element must offer a group delay dispersion high enough to time-reverse μs-long signals. We propose to use spectral hole burning to tailor the absorption profile of erbium ions embedded in a crystalline lattice of yttrium orthosilicate. This way, we achieve a group delay dispersion 10⁵ larger than reached with km-long dispersive fibers, allowing us to extend the time-reversal process from the ns-range to the μs-range.