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Direct frequency modulation characteristics in semiconductor lasers are described theoretically in a physics-based multidimensional framework. A microscopic formulation of a phase equation without the need of linewidth enhancement factors is derived directly from Maxwell's equations. This novel model uses a local material phase coefficient instead of the linewidth enhancement factor. Hence, the impact of local phase changes on the optical mode can be described via a spatial integration in analogy to mode gain. The model is applied to the modulation-induced fine structure of the laser power spectrum. It is found that the asymmetry in the modulation-induced fine structure observed in measurements can be explained by the proposed model taking temperature, carrier, and photon effects on the material phase coefficient into account. Furthermore, the implementation of the photon phase into a multidimensional device simulator is described.