This article presents a 220-GHz wideband converter for terahertz (THz) applications, which facilitates the transition from the TE10 mode of the rectangular waveguide (RWG) to the TE20 mode of the substrate-integrated waveguide (SIW). This converter consists of waveguides, a dipole antenna, a grounded slotline, and a SIW. The dipole antenna effectively couples the TE10-mode guided wave from the RWG into the slotline. Due to the quasi-slotline mode and SIW TE20 mode being odd modes with similar electric field distributions, the longitudinal slotline effectively excites the TE20 mode within the SIW. This study elucidates the converter's principles and propagation properties through electric field analysis and electromagnetic (EM) simulations. Besides, a back-to-back converter prototype was fabricated and measured, exhibiting an insertion loss of 2.1-5.0 dB from 198 to 238 GHz (18.3% bandwidth) and a return loss better than 6.1 dB. The estimated loss for a single converter is 1.1-2.5 dB, including the loss of a 1.4-mm-long SIW. Furthermore, based on the proposed mode converter, an SIW bandpass filter and a balun were designed and demonstrated, providing further evidence of the existence of the TE20 mode in SIW. To the best of our knowledge, this article presents the first 220-GHz converter from the RWG TE10 mode to the SIW TE20 mode, demonstrating its potential applications in THz planar integration.