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An analytical theory is presented for the study of injection locking in multisection semiconductor lasers. The Helmoltz equation for the electric field is solved using the Green's function method and the injected fields are included via the boundary conditions. Two cases are distinguished, injection through the front facet of the laser and injection through the rear facet. In both cases, an equation of evolution for the envelope of the electric field is established, taking into account the longitudinal distribution of the carrier and photon densities and the nonlinear gain. The expressions of the intensity, phase and carrier density noise spectra are derived using a matrix formulation. Comparison to classical equations used for Fabry-Perot lasers is discussed. The locking properties of a distributed feedback laser with an antireflection coated front facet are studied in detail. Results demonstrate the strong sensitivity of the locking properties on the phase grating and rear facet reflectivity.