  We propose two optimal entanglement concentration protocols (ECPs) for
arbitrary single-photon multi-mode W state and multi-photon polarization W
state, respectively. In both ECPs, we only require one pair of partially
entangled W state, and do not consume any auxiliary photon. Both ECPs are based
on the linear optics which can be easily realized. On the other hand, the
concentrated maximally entangled states can be remained, which are quite
different from the previous ECPs. Moreover, for the concentration of the
arbitrary single-photon N-mode W state or N-mode polarization W state, the
total success probability is equal to Nth the modulus square of the Schmidt
coefficient of the smallest magnitude. It makes both ECPs optimal than all the
previous ECPs. Our ECPs may be useful in current quantum communication fields.
