  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.
