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A few-cycle ultrashort laser field propagating through strongly coupled quantum wells (CQW) is numerically investigated. The results show that the harmonic signal can be tuned by the structure-control of CQW or enhanced due to propagation effects. If the structure of the CQW is spatial inversion symmetric, a disguised harmonic at the second-order harmonic position is disclosed within the normal odd-order harmonic sequence. However, if the structure of the CQW is adjusted to break the inversion symmetry, the odd-order and even-order harmonics both occur, whose intensities are also influenced by propagation effects. (a) Electric fields, (b) population differences, and (c) harmonic distributions for different well heights of barrier U1 at propagation distance of z = 120 µm. [ABSTRACT FROM AUTHOR]