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The demonstration of a three‐dimensional tapered mode‐selective coupler in a photonic chip is reported. This waveguide‐based, ultra‐broadband mode multiplexer was fabricated using the femtosecond laser direct‐write technique in a boro‐aluminosilicate glass chip. A three‐core coupler has been shown to enable the multiplexing of the LP₀₁, LP and LP spatial modes of a multimode waveguide, across an extremely wide bandwidth exceeding 400 nm, with low loss, high mode extinction ratios and negligible mode crosstalk. Linear cascades of such devices on a single photonic chip have the potential to become a definitive technology in the realization of broadband mode‐division multiplexing for increasing optical fiber capacity.