We investigate the threshold-crossing of a single-mode semiconductor laser, with special emphasis on its transfer function. Spontaneous emission, looked upon as the driving source of the radiation, is described in a semi-classical way in the spectral domain. The internal and emitted fields are filtered into the resonance modes of the whole structure: their spectral density are described by the generalized Airy-like transfer function, well approximated by a Lorentzian, which contains all essential mechanisms at work in a laser oscillator: Gain, losses and sources. The active zone is saturated through Amplified Spontaneous Emission, integrated over its whole spectral range. Continuously valid across threshold, the method enables one to derive in a simple way the main steady-state properties of the laser oscillation. Most specifically, we obtain analytical expressions, in normalized units, for emitted power, linewidth sharpening, carrier clamping and frequency shift, with the pumping rate as the only external parameter. In this approach, the optical properties of the active medium (the gain, the source and the refractive index) are supposed to be uniquely determined by the steady-state values of the carrier and photon density, obtained within the framework of the rate equation formalism and assumed uniform along the active zone.