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Summary form only given. Here we demonstrate a mechanism for converting complex order parameter systems, such as lasers, into real valued ones. The idea is to use a periodic injection (of zero, or very small, dc contribution) whose carrier frequency is close to the free-running laser frequency. As an example, in the simpler case of positive detuning, it can be shown that the laser field amplitude is the sum of two contributions. One of them follows the injection and the other one is governed by a Ginzburg-Landau equation with phase sensitive gain.