230 CHAPTER 6. OPTICAL AMPLIFIERS
Here,Pouts is smaller thanPsby about 30%. Indeed, by noting thatG 0 2 in practice
(G 0 =1000 for 30-dB amplifier gain),Pouts ≈(ln 2)Ps≈ 0. 69 Ps. As seen in Fig. 6.2,
Pouts becomes nearly independent ofG 0 forG 0 >20 dB.
6.1.3 Amplifier Noise.........................
All amplifiers degrade the signal-to-noise ratio (SNR) of the amplified signal because
of spontaneous emission that adds noise to the signal during its amplification. The
SNR degradation is quantified through a parameterFn, called theamplifier noise figure
in analogy with the electronic amplifiers (see Section 4.4.1) and defined as [2]
Fn=(SNR)in
(SNR)out, (6.1.12)
where SNR refers to the electric power generated when the optical signal is converted
into an electric current. In general,Fndepends on several detector parameters that gov-
ern thermal noise associated with the detector (see Section 4.4.1). A simple expression
forFncan be obtained by considering an ideal detector whose performance is limited
by shot noise only [2].
Consider an amplifier with the gainGsuch that the output and input powers are
related byPout=GPin. The SNR of the input signal is given by
(SNR)in=〈I〉^2
σs^2=
(RPin)^2
2 q(RPin)∆f=
Pin
2 hν∆f, (6.1.13)
where〈I〉=RPinis the average photocurrent,R=q/hνis the responsivity of an ideal
photodetector with unit quantum efficiency (see Section 4.1), and
σs^2 = 2 q(RPin)∆f (6.1.14)is obtained from Eq. (4.4.5) for the shot noise by setting the dark currentId=0. Here
∆fis the detector bandwidth. To evaluate the SNR of the amplified signal, one should
add the contribution of spontaneous emission to the receiver noise.
The spectral density of spontaneous-emission-induced noise is nearly constant (white
noise) and can be written as [2]
Ssp(ν)=(G− 1 )nsphν, (6.1.15)whereνis the optical frequency. The parameternspis called thespontaneous-emission
factor(or the population-inversion factor) and is given by
nsp=N 2 /(N 2 −N 1 ), (6.1.16)whereN 1 andN 2 are the atomic populations for the ground and excited states, respec-
tively. The effect of spontaneous emission is to add fluctuations to the amplified signal;
these are converted to current fluctuations during the photodetection process.
It turns out that the dominant contribution to the receiver noise comes from the beat-
ing of spontaneous emission with the signal [2]. The spontaneously emitted radiation