464
11 Basics of Optical Amplifiers
preamplifier is dominated by signal–ASE beat noise. Under what conditions does
Eq. (11.46) hold?
Solution: For sufficiently high gain G, Eq. (11.46) becomes
G
2
− 1 ≈ G
2
>
N
N
≈
σ
2
s−AS E
σ
2
th
Substituting Eq. (6.17) and Eq. (11.28) into this expression, using Eq. (11.24) for
S ASE , and solving for P s,in yields
P s,in <
k B T hν
Rn sp η 2 q 2
If T = 300 K, R = 50 , λ = 1550 nm, n sp = 2, and η = 0.65, then P s,in < 490 μW. This
level is much higher than any expected received signal, so the condition in Eq. (11.46)
is always satisfied. However, note that this only specifies the upper bound on P s,in .
It does not mean that by making G sufficiently high, the improvement in sensitivity
can be made arbitrarily large, because there is a minimum received optical power
level that is needed to achieve a specific BER.
11.7 Raman Optical Amplifiers
11.7.1 Principle of Raman Gain
A Raman optical amplifier is based on a nonlinear effect called stimulated Raman
scattering (SRS), which occurs in fibers at high optical powers [20–23]. Chapter 12
describes this characteristic in more detail. The SRS effect is due to an interaction
between an optical energy field and the vibrational modes of the lattice structure
in a material. Basically what happens is that an atom first absorbs a photon at a
particular energy and then releases another photon at a lower energy, that is, at a longer
wavelength than that of the absorbed photon. The energy difference between the
absorbed and the released photons is transformed into a phonon, which is a vibrational
mode of the material. The power transfer to higher wavelengths occurs over a broad
spectral range of 80–100 nm. The shift to a particular longer wavelength is referred to
as the Stokes shift for that wavelength. Figure 11.10 shows the Raman gain spectrum
for a pump laser operating at 1445 nm and illustrates the SRS-induced power transfer
to a signal at 1535 nm, which is 90 nm away from the pump wavelength. Depending
on the link architecture, the SRS-generated signal can act as either an intentional
amplification of a particular data wavelength or it could be an unwanted interference
signal at that wavelength (see Chap. 12). The gain curve is given in terms of the
Raman gain coefficient g R units of 10
−14 m/W.
11 Basics of Optical Amplifiers
preamplifier is dominated by signal–ASE beat noise. Under what conditions does
Eq. (11.46) hold?
Solution: For sufficiently high gain G, Eq. (11.46) becomes
G
2
− 1 ≈ G
2
>
N
N
≈
σ
2
s−AS E
σ
2
th
Substituting Eq. (6.17) and Eq. (11.28) into this expression, using Eq. (11.24) for
S ASE , and solving for P s,in yields
P s,in <
k B T hν
Rn sp η 2 q 2
If T = 300 K, R = 50 , λ = 1550 nm, n sp = 2, and η = 0.65, then P s,in < 490 μW. This
level is much higher than any expected received signal, so the condition in Eq. (11.46)
is always satisfied. However, note that this only specifies the upper bound on P s,in .
It does not mean that by making G sufficiently high, the improvement in sensitivity
can be made arbitrarily large, because there is a minimum received optical power
level that is needed to achieve a specific BER.
11.7 Raman Optical Amplifiers
11.7.1 Principle of Raman Gain
A Raman optical amplifier is based on a nonlinear effect called stimulated Raman
scattering (SRS), which occurs in fibers at high optical powers [20–23]. Chapter 12
describes this characteristic in more detail. The SRS effect is due to an interaction
between an optical energy field and the vibrational modes of the lattice structure
in a material. Basically what happens is that an atom first absorbs a photon at a
particular energy and then releases another photon at a lower energy, that is, at a longer
wavelength than that of the absorbed photon. The energy difference between the
absorbed and the released photons is transformed into a phonon, which is a vibrational
mode of the material. The power transfer to higher wavelengths occurs over a broad
spectral range of 80–100 nm. The shift to a particular longer wavelength is referred to
as the Stokes shift for that wavelength. Figure 11.10 shows the Raman gain spectrum
for a pump laser operating at 1445 nm and illustrates the SRS-induced power transfer
to a signal at 1535 nm, which is 90 nm away from the pump wavelength. Depending
on the link architecture, the SRS-generated signal can act as either an intentional
amplification of a particular data wavelength or it could be an unwanted interference
signal at that wavelength (see Chap. 12). The gain curve is given in terms of the
Raman gain coefficient g R units of 10
−14 m/W.