The concept of a "trapped rainbow" has generated considerable interest for optical data storage and processing. It aims to trap different frequency components of the wave packet at different positions permanently. However, all the previously proposed structures cannot truly achieve this effect, due to the difficulties in suppressing the reflection caused by strong intermodal coupling and distinguishing different frequency components simultaneously. In this article, we found a physical mechanism to achieve a truly "trapped rainbow" storage of electromagnetic wave. We utilize nonreciprocal waveguides under a tapered magnetic field to achieve this and such a trapping effect is stable even under fabrication disorders. We also observe hot spots and relatively long duration time of the trapped wave around critical positions through frequency domain and time domain simulations. The physical mechanism we found has a variety of potential applications ranging from wave harvesting and storage to nonlinearity enhancement.
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