  We present a systematic entanglement concentration protocol (ECP) for an
arbitrary unknown less-entangled three-photon W state, resorting to the optical
property of the quantum-dot spins inside one-sided optical microcavities. In
our ECP, the parties obtain not only some three-photon systems in the partially
entangled with two unknown parameters when one of the parties picks up the
robust odd-parity instance with the parity-check gate (PCG) on his two photons,
but also some entangled two-photon systems by keeping the even-parity instance
in the first step. By exploiting the above three-photon and two-photon systems
with the same parameters as the resource for the second step of our ECP, the
parties can obtain a standard three-photon W state by keeping the robust
odd-parity instance. Meanwhile, the systems in the even-parity instance can be
used as the resource in the next round of our ECP. The success probability of
our ECP is largely increased by iteration of the ECP process. As it does
require that all the coefficients are unknown for the parties, our ECP maybe
have good applications in quantum communication network in future.
