Unidirectionally propagating wave (UPW) such as surface magnetoplasmon (SMP) has been a research hotspot in the last decades. In the study of the UPW, metals are usually treated as perfect electric conductors (PECs). However, it was reported that the transverse resonance condition induced by the PEC wall(s) may significantly narrow up the complete one-way propagation (COWP) band. In this paper, ultra-broadband one-way waveguides are built by utilizing the epsilon-negative (ENG) metamaterial (MM) and/or the perfect magnetic conductor (PMC) boundary. In both cases, the total bandwidth of the COWP bands are efficiently enlarged by more than three times than the one in the original metal-dielectric-semiconductor-metal structure. Moreover, the one-way waveguides consisting of gradient-index metamaterial are proposed to achieve broadband truly rainbow trapping (TRT). In the full-wave simulations, clear broadband TRT without back reflection is observed in terahertz regime. Besides, giant electric field enhancement is achieved in a PMC-based one-way structure, and the amplitude of the electric field is enormously enhanced by five orders of magnitude. Our findings are beneficial for researches on broadband terahertz communication, energy harvesting and strong-field devices.