hen Q > 3 to BER = by taking the first term in the series expansion (Gallion, 2002). Figure 6.15 shows how the BER depends on Q, from which it is obvious that the varia- tion becomes very rapid as Q increases. Two useful values to remember are BER = 10-9 when Q = 6 and BER = 10-12 when Q = 7. However, these and other values in Figure 6.15 apply only SO long as the assumption of Gaussian noise statistics is valid. The Laser Extinction Ratio The quality factor, Q (and hence BER), depends on the photocurrents of the 0 and 1 bits, I and I, and their corresponding variances, of and o2. Many approximations result from assuming that the transmitter laser plus the external modulator provide full extinction and therefore I = 0. In that case, Bit Error Rate Fig. 6.15 Variation of BER with the Q value, showing two useful values: Q = 6 and Q = 7. Q Value Fig. 6.16 Variation of the optical power penalty with respect to the extinction ratio. Marked an extinction ratio of 9.4 dB corresponds to a 1-dB power penalty. Extinction Ratio (dB) where R is the responsivity, as previously defined. Alternatively, we can define an extinction ratio of the 1 and 0 bits, rex = Pinc-1/Pinc-0, together with an average optical power arriving at the receiver, Pav = R(I1 + I2)/2 (see the earlier section on optical transmitters). Total extinc- tion gives an infinite value of rex. By substituting into the expression for Q, we have S = 10log10 (6.23) 8, called the "power penalty," tells us by how much (in decibels) we must increase the power arriving at the detector in order to obtain the same Q value (i.e., the same BER). To put it another way, when all else is equal, a given receiver requires an increased average incident optical power in order to provide the same BER when the transmitter cannot provide full extinction. The power penalty is a quantification of that additional power. The power penalty is of interest to optical transmission designers, who need to set an upper limit on the performance degradation they are willing to tolerate. Equation