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For a generic semi-classical laser dynamics in the complex Ginzburg-Landauform, we develop a Bogoliubov approach for the computation of the laseremission linewidth. Our method provides a unifying perspective of thetreatments by Henry and Petermann: both broadening mechanisms are ascribed tothe non-orthogonality of the Bogoliubov modes, which live in a space withdoubled degrees of freedom. As an example of application, the method allows tostudy the interplay of driven-dissipation, interactions and spatialinhomogeneity typical of polariton condensates. The traditional theory of theHenry and Petermann factors is found to fail dramatically in the presence ofsizable polariton-polariton interactions. In particular, also in a strongconfining potential, the intrinsically  multi-mode nature of the density fluctuations has to be considered in orderto describe quantitatively phase diffusion {\em \`a la} Henry.

Bogoliubov theory of the laser linewidth and application to polariton condensates