that the modulation index (i.e., the derivative of the emitted optical power with respect to the pump current fluctuations) results: (5.11) where 0m is the modulation frequency. The presence of the natural laser resonance is always evident and in this case it limits the modulation bandwidth. If the expression of the coefficients is substituted in Equation 5.11 it is evident that, besides the presence of a resonance, gain saturation (represented by the factor E also con- tributes to shrink the bandwidth with respect to the theoretical limit, and that higher the gain saturation coefficient, the smaller is the modulation bandwidth. Similarly to the power modulation index, a frequency modulation index can be evalu- ated whose expression is Peak of the RIN spectrum (dB/Hz) Linewidth (MHz) FIGURE 5.9 Linewidth versus RIN spectrum peak relationship for a DFB laser. (After JDSU Application Note, Relative Intensity Noise, Phase Noise and Linewidth, JDSU Corporate, s.l., 2006, www.jdsu.com [accessed: May 25, 2010].) Telecommunication Networks (5.12) Equation 5.12 represents the theoretical frequency response of a semiconductor laser that is responsible for both the possibility of modulating the output field frequency by modu- lating the bias current (property exploited for example to implement the Brillouin dither) and the chirp that unavoidably is present when the laser is directly modulated. Equation 5.12, however, due to all the approximations that are the base to derive the rate equations, does not take into account several phenomena that cause the deviation of the fre- quency response of real lasers from the simple proportionality to the carrier density variations. Generally the frequency response is almost flat up to the resonance of the laser, but here it shows the resonance effects through a peak and then decreases rapidly. 5.2.1.3 Quantum Well Lasers A quantum well laser is a laser diode in which the active region of the device is formed by one or more regions SO narrow that quantum confinement occurs, alternated 