168 CHAPTER 4. OPTICAL RECEIVERS
as a measure of receiver sensitivity is quite common. In the quantum limitN ̄p=10.
The power can be calculated from Eq. (4.5.25). For example, for a 1.55-μm receiver
(hν= 0 .8eV),P ̄rec=13 nW or− 48 .9dBmatB=10 Gb/s. Most receivers operate
away from the quantum limit by 20 dB or more. This is equivalent to saying thatN ̄p
typically exceeds 1000 photons in practical receivers.
4.6 Sensitivity Degradation.........................
The sensitivity analysis in Section 4.5 is based on the consideration of receiver noise
only. In particular, the analysis assumes that the optical signal incident on the receiver
consists of an ideal bit stream such that 1 bits consist of an optical pulse of constant
energy while no energy is contained in 0 bits. In practice, the optical signal emitted by
a transmitter deviates from this ideal situation. Moreover, it can be degraded during its
transmission through the fiber link. An example of such degradation is provided by the
noise added at optical amplifiers. The minimum average optical power required by the
receiver increases because of such nonideal conditions. This increase in the average
received power is referred to as thepower penalty. In this section we focus on the
sources of power penalties that can lead to sensitivity degradation even without signal
transmission through the fiber. The transmission-related power-penalty mechanisms
are discussed in Chapter 7.
4.6.1 Extinction Ratio
A simple source of a power penalty is related to the energy carried by 0 bits. Some
power is emitted by most transmitters even in the off state. In the case of semiconductor
lasers, the off-state powerP 0 depends on the bias currentIband the threshold current
Ith.IfIb<Ith, the power emitted during 0 bits is due to spontaneous emission, and
generallyP 0 P 1 , whereP 1 is the on-state power. By contrast,P 0 can be a significant
fraction ofP 1 if the laser is biased close to but above threshold. Theextinction ratiois
defined as
rex=P 0 /P 1. (4.6.1)
The power penalty can be obtained by using Eq. (4.5.11). For ap–i–nreceiver
I 1 =RP 1 andI 0 =RP 0 , whereRis the responsivity (the APD gain can be included
by replacingRwithMR). By using the definitionP ̄rec=(P 1 +P 0 )/2 for the receiver
sensitivity, the parameterQis given by
Q=
(
1 −rex
1 +rex)
2 RP ̄rec
σ 1 +σ 0. (4.6.2)
In general,σ 1 andσ 0 depend onP ̄recbecause of the dependence of the shot-noise
contribution on the received optical signal. However, both of them can be approximated
by the thermal noiseσTwhen receiver performance is dominated by thermal noise. By
usingσ 1 ≈σ 0 ≈σTin Eq. (4.6.2),P ̄recis given by
P ̄rec(rex)=(
1 +rex
1 −rex)
σTQ
R