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A novel broadband all-fiber LP02 mode converter is proposed and numerically analyzed. The converter is based on multimode interference in a multimode fiber (MMF) that interconnects a single-mode fiber (SMF) with a few-mode fiber, considered the transmission medium in future mode division multiplexing (MDM) systems. The proposed LP02 converter is reciprocal and polarization independent, and supports a very broad optical bandwidth of 150 nm with an over 20 dB extinction ratio, as well as an efficient coupling and easy connectivity as an all-fiber device. In a reciprocal operation, it performs mode filtering as well, therefore supporting mode demultiplexing. The dependence of the performance of the converter on the MMF length and core diameter is further investigated. The very broad bandwidth of the device renders it suitable for future transmission systems that need to combine MDM with wavelength division multiplexing targeting to achieve record transmission rates that cannot be reached with SMF transmission systems.