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In-plane polarization anisotropy of optical gain in compressively strained GaInAsP-InP quantum wire (Q-wire) lasers including elastic strain relaxation induced band mixing is studied. The interaction between two-dimensional (2-D) quantum confinement and elastic strain relaxation effects is found to be complex depending qualitatively also on the wire width. Additional valence band mixing due to strain relaxation has a strong influence on the polarization dependence of optical gain. In the absence of elastic strain relaxation, gain is the maximum for tranverse electric (TE) polarization with the electric field parallel to the wire axis (TE/sub /spl par//), in agreement with the existing theory. On the other hand, when strain relaxation is strong, contrary to the existing theory, valence band mixing causes the gain to be the maximum in TE polarization with the electric field normal to the wire axis (TE/sub /spl perp//). Moreover, Q-wire lasers without suppression of strain relaxation are more likely to exhibit ground-state lasing for TE/sub /spl perp// polarization. These results suggest that in the presence of strong strain relaxation, a laser cavity parallel to the wire axis would provide higher gain. Therefore, the appropriate orientation of the laser cavity in strained GaInAsP-InP Q-wire lasers should be decided after carefully studying the polarization dependence of gain. Our calculation also shows that strong strain relaxation causes in-plane polarization anisotropy to show complex, nonmonotonic dependence on the wire width. Consequently, in such structures, in-plane polarization anisotropy may not be regarded as a direct measure of 2-D confinement effects.