5.4. SOURCES OF POWER PENALTY 211
Figure 5.11: Chirp-induced power penalty as a function of|β 2 |B^2 Lfor several values of the
chirp parameterC. The Gaussian optical pulse is assumed to be linearly chirped over its entire
width.
parameters and must be determined for each laser through experimental measurements
of the frequency chirp. In practice,∆λcitself depends on the bit rateBand increases
with it.
For lightwave systems operating at high bit rates (B>2 Gb/s), the bit duration is
generally shorter than the total duration 2tcover which chirping is assumed to occur in
the foregoing model. The frequency chirp in that case increases almost linearly over
the entire pulse width (or bit slot). A similar situation occurs even at low bit rates if the
optical pulses do not contain sharp leading and trailing edges but have long rise and fall
times (Gaussian-like shape rather than a rectangular shape). If we assume a Gaussian
pulse shape and a linear chirp, the analysis of Section 2.4.2 can be used to estimate the
chirp-induced power penalty. Equation (2.4.16) shows that the chirped Gaussian pulse
remains Gaussian but its peak power decreases because of dispersion-induced pulse
broadening. Defining the power penalty as the increase (in dB) in the received power
that would compensate the peak-power reduction,δcis given by
δc=10 log 10 fb, (5.4.13)wherefbis the broadening factor given by Eq. (2.4.22) withβ 3 =0. The RMS widthσ 0
of the input pulse should be such that 4σ 0 ≤ 1 /B. Choosing the worst-case condition
σ 0 = 1 / 4 B, the power penalty is given by
δc=5 log 10 [( 1 + 8 Cβ 2 B^2 L)^2 +( 8 β 2 B^2 L)^2 ]. (5.4.14)Figure 5.11 shows the chirp-induced power penalty as a function of|β 2 |B^2 Lfor
several values of the chirp parameterC. The parameterβ 2 is taken to be negative,