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We design and experimentally demonstrate a broadband 1310/1550 nm wavelength demultiplexer based on a multimode interference coupler with a tapered internal photonic crystal (PC) structure for the silicon-on-insulator platform. The tapered internal PC structure is engineered to reflect the C-band light while transmitting the O-band light. Novel PC nanotapers are introduced for the internal PC structure that effectively suppress the sidelobe of the photonic bandgap and enable our device to be operable over the O-band. The device was fabricated using electron beam lithography, and its performance has been experimentally characterized. The measured extinction ratios are higher than 15 dB over a 74 nm bandwidth from 1286 to 1360 nm at the O-band, and over a 103 nm bandwidth from 1527 to 1630 nm that covers the C-band and the L-band.