This paper proposes a double fiber taper-based mode converter that converts LP(01) to LP(02) and vice versa. The first taper is used to convert LP(01) to some higher order LP(0m) (m>1) modes while the second taper suppresses the undesired higher order modes (m>2) and results in LP(02) overwhelmingly dominated. A simulation shows that conversion efficiency of almost 100% at the central wavelength of O-, S-, and C-Band, and above 98% over the S- and C-Band was achieved. Moreover, suppression of undesired higher order modes is more than 10 dB over the whole O-, S-, and C-Band. In particular, the suppression is more than 19 dB for the whole C-Band. The analysis also shows that the performance of the mode converter is not sensitive to slight variations of the converter's parameters. The same converter also can be used to convert LP(02) back to LP(01). It is shown that conversion efficiency higher than 99% and suppression of undesired higher order modes higher than 30 dB can be obtained. Further, a (de)multiplexer for an LP(02) and an LP(01) mode was designed using the mode converter combined with a symmetric directional coupler. The multiplexer is broadband and has an insertion loss less than 0.5 dB in the C-Band.