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The multimode evolution, optical losses and wavelength response of non-adiabatic micro/nano-fiber (MNF) tapers are numerically simulated using a three-dimensional finite-difference beam propagation method. For a non-adiabatic MNF taper, it is illustrated that optical losses vary with the transition region length and the optical wavelength. We explain how the complicated multimode evolutions result in the complicated optical loss and wavelength response properties, especially when the waist diameters are large enough to allow much higher-order modes. These results may offer valuable references for trapping and guiding cold atoms in atom optics and practical application of micro/nano-devices.