  We study spin imbalance effects on the Larkin-Ovchinikov-Fulde-Ferrel (LOFF)
state relevant for superconductors under a strong magnetic field and spin
polarized ultracold Fermi gas. We obtain the exact solution for the condensates
with arbitrary spin imbalance and the fermion spectrum perturbatively in the
presence of small spin imbalance. We also obtain fermion zero mode exactly
without perturbation.
