We theoretically show that the Goos-Hänchen (GH) shifts [F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947)] of the TE- and TM-polarized beams reflected from a slab of the weakly absorbing left-handed material can be large positive near the resonant transmission if the absorption of the slab is sufficiently weak. The GH shift of the TM-polarized reflected beam can be large negative or positive near the Brewster angle.
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