Page 300 - Fiber Optic Communications Fund

Optical Amplifiers 281

can be expressed as the superposition of the guided mode and radiation modes of the erbium-doped fiber.
The radiation modes escape to the cladding and do not degrade the system performance. Similarly, the ASE
propagating as a guided mode in the backward direction does not a effect the system performance. However,
backward-propagating ASE and radiation modes lead to degradation of the amplifier performance since the
ASE reduces the gain of the amplifier.

6.7.4 Comparison of EDFA and SOA

One of the disadvantages of SOAs is their polarization sensitivity. The amplifier gain G depends on whether
the mode in the waveguide is transverse electric (TE) or transverse magnetic (TM). Therefore, the incident
optical field with arbitrary polarization experiences different amounts of gain for its x- and y- polarization
components. This is known as polarization-dependent gain (PDG), which is undesirable for light-wave sys-
tems since it alters the polarization state of the light wave. Fiber amplifiers such as EDFA provide a uniform
gain for x- and y- polarization components because of the circular symmetry of the fiber.
Another drawback of the SOA is the presence of interchannel cross-talk for WDM systems (see Chapter 9).
Consider the signal corresponding to two channels of a WDM system,

q(t, z)= s (t, z) exp(i t)+ s (t, z) exp(i t), (6.196)
1 1 2 2
where and s (t, z) are the optical carrier frequency and field envelope of the jth channel. The total signal
j
j
power is
2
2
2
P = |q| = |s | + |s | + 2|s ||s | cos (Δt + − ), (6.197)
1
2
1
2
2
1
where Δ = | − | is the channel separation and = Arg[s ]. Substituting Eqs. (6.197) in Eqs. (3.117)
1
j
j
2
and (3.120), we obtain
dN N G (N − N )
e I e 0 e 0 2 2
= − − [|s | + |s | + 2|s ||s | cos (Δt + − )]. (6.198)
2
1
1
2
1
2
dt qV e ℏ
On the right-hand side of Eq. (6.198), we have a term oscillating at the beat frequency Δ. This leads to the
carrier population density N oscillating at the beat frequency Δ. Since the gain coefficient is related to N e
e
by Eq. (6.142), the gain is also modulated at frequency Δ and from Eq. (3.32), we have
P
= g(z, t)P. (6.199)
z
2
2
Since the gain coefficient g(z, t) depends on the instantaneous channel powers |s (t, z)| and |s (t, z)| ,the
1
2
amplifier gain changes with time depending on the bit patterns in channels 1 and 2. Owing to the randomly
changing bit patterns, the noise in the system is enhanced, leading to performance degradations. This is known
as interchannel cross-talk. This cross-talk can be avoided if the SOA operates in the unsaturated regime.
However, in the WDM system, saturation occurs quickly because there are many channels and the signal
saturation power is the sum of the powers of each channel.
The carrier lifetime ( ∼ 0.5 ns) of the SOA is much shorter than the lifetime ( ∼ 10 ms) associated
e e 21 21
with the excited state of erbium ions. When the bit interval T is much shorter than the lifetime ,erbium
b 21
ions do not follow the fast variations of the signal, but they respond only to the average power of the signal.
Therefore, in this case, all pulses experience the same gain in the case of an EDFA. For example, when the
bit rate is 2.5Gb/s, T = 0.4ns ≪ and the EDFA gain does not change from bit to bit. However, for SOA,
b 21
T and are comparable and the gain experienced by the current bit depends on the signal power of the
b e
previous bits.