116 CHAPTER 3. OPTICAL TRANSMITTERS
acts as a bandpass filter of bandwidthΩRto spontaneous-emission fluctuations. At
a given frequency, RIN decreases with an increase in the laser power asP−^3 at low
powers, but this behavior changes toP−^1 dependence at high powers.
The autocorrelation functionCpp(τ)is calculated using Eqs. (3.5.31) and (3.5.32).
The calculation shows thatCpp(τ)follows relaxation oscillations and approaches zero
forτ>Γ−R^1 [83]. This behavior indicates that intensity fluctuations do not remain cor-
related for times longer than the damping time of relaxation oscillations. The quantity
of practical interest is the SNR defined asP ̄/σp, whereσpis the root-mean-square
(RMS) noise. From Eq. (3.5.30), SNR=[Cpp( 0 )]−^1 /^2. At power levels above a few
milliwatts, the SNR exceeds 20 dB and improves linearly with the power as
SNR=
(
εNL
Rspτp) 1 / 2
P ̄. (3.5.33)
The presence ofεNLindicates that the nonlinear form of the gain in Eq. (3.5.15) plays
a crucial role. This form needs to be modified at high powers. Indeed, a more accu-
rate treatment shows that the SNR eventually saturates at a value of about 30 dB and
becomes power independent [83].
So far, the laser has been assumed to oscillate in a single longitudinal mode. In
practice, even DFB lasers are accompanied by one or more side modes. Even though
side modes remain suppressed by more than 20 dB on the basis of the average power,
their presence can affect the RIN significantly. In particular, the main and side modes
can fluctuate in such a way that individual modes exhibit large intensity fluctuations,
but the total intensity remains relatively constant. This phenomenon is calledmode-
partition noise(MPN) and occurs due to an anticorrelation between the main and side
modes [2]. It manifests through the enhancement of RIN for the main mode by 20 dB
or more in the low-frequency range 0–1 GHz; the exact value of the enhancement factor
depends on the MSR [84]. In the case of a VCSEL, the MPN involves two transverse
modes. [85]. In the absence of fiber dispersion, MPN would be harmless for optical
communication systems, as all modes would remain synchronized during transmis-
sion and detection. However, in practice all modes do not arrive simultaneously at the
receiver because they travel at slightly different speeds. Such a desynchronization not
only degrades the SNR of the received signal but also leads to intersymbol interference.
The effect of MPN on the system performance is discussed in Section 7.4.3.
3.5.5 Spectral Linewidth
The spectrum of emitted light is related to the field-autocorrelation functionΓEE(τ)
through a Fourier-transform relation similar to Eq. (3.5.31), i.e.,
S(ω)=∫∞−∞ΓEE(t)exp[−i(ω−ω 0 )τ]dτ, (3.5.34)whereΓEE(t)=〈E∗(t)E(t+τ)〉andE(t)=
√
Pexp(iφ)is the optical field. If intensity
fluctuations are neglected,ΓEE(t)is given by
ΓEE(t)=〈exp[i∆φ(t)]〉=exp[−〈∆φ^2 (τ)〉/ 2 ], (3.5.35)