us derivation of the laser linewidth that is possible starting from (5.9) [8] would conclude that the laser linewidth is not Lorentian, but is composed by a Lorentian lobe plus two side peaks far from the central wavelength, exactly the frequency of relaxation oscillations. However, in high-quality lasers these lobes are SO reduced that a Lorentian approximation of the linewidth is more than accurate. Assuming a Lorentian linewidth, the expression of the full width at half maximum (FWHM) is given by Av = Rsp (1+a2) (4r) (5.10) where r is the cavity refraction index. Technology for Telecommunications: Integrated Optics and Microelectronics The curve relating the linewidth and the maximum of the RIN spectrum is shown in Figure 5.9 besides a set of experimental points from [11]. In particular the theoretical curve is obtained by best fitting the experimental data. Another important characteristic of the semiconductor lasers is that they can be directly modulated acting on the bias current. However, when the bias current fluctuates, a com- plex dynamical behavior is observed, mainly due to the coupling between field amplitude and phase and to the resonance at SR. This phenomenon causes the contemporary presence of intensity and phase modulation, which always creates a frequency chirp in the direct modulated pulse train. Besides this fundamental effect, a second phenomenon constraining the direct modula- tion bandwidth of semiconductor lasers is the presence of parasitic capacities in the struc- ture. Reducing them is a key issue to increase the direct modulation bandwidth. Considering again the rate equations with spatially constant variables and neglecting the noise terms, it is possible to study direct modulation by applying the substitutions in Equation 5.5 where now the fluctuations are due not to the noise but to the modulation. In this condition the equations can be linearized again around the laser bias point. In this case Equation 5.7 can be used to pass from the field into the cavity to the emitted field SO 