12.4 Stimulated Brillouin Scattering
485
there are normally optical isolators to prevent backscattered signals from entering
the amplifier. Consequently, the impairment due to SBS is limited to the degradation
occurring in a single amplifier-to-amplifier span.
One criterion for determining at what point SBS becomes a problem is to consider
the SBS threshold power P th . This is defined to be the signal power at which the
backscattered light equals the fiber-input power. The calculation of this expression
is rather complicated, but an approximation is given by [8]
P th ≈ 21
A e f f b
g B L e f f
1 +
ν source
ν B
(12.5)
Here, A eff is the effective cross-sectional area of the propagating wave, ν source is
the source linewidth, and the polarization factor b lies between 1 and 2 depending
on the relative polarizations of the pump and Stokes waves. The effective length L eff
is given in Eq. (12.1) and g B is the Brillouin gain coefficient, which is approximately
4 × 10
−11 m/W, independent of the wavelength. Equation (12.5) shows that the SBS
threshold power increases as the source linewidth becomes larger.
Example 12.2 Consider an optical source with a 40-MHz linewidth. Using the values
ν B = 20 MHz at 1550 nm, A eff = 55 × 10
−12 m
2 (for a typical dispersion-shifted
single-mode fiber), L eff = 20 km, and assuming a value of b = 2, then from Eq. (12.5)
it follows that P th = 8.6 mW = 9.3 dBm.
Drill Problem 12.3 Consider an optical source with a 60-MHz linewidth. Using
the values ν B = 20 MHz at 1550 nm, A eff = 55 × 10
−12 m
2 (for a typical
dispersion-shifted single-mode fiber), L eff = 20 km, assuming a value of b =
1, and letting g B = 3.5 × 10
−11 m/W, show from Eq. (12.5) that P th = 5.0 mW
(or 7.0 dBm).
Figure 12.7 illustrates the effect of SBS on unmodulated signal power once the
threshold is reached. The plots give the relative Brillouin scattered power and the
signal power transmitted through a fiber as a function of the input power. Below a
certain signal level called the SBS threshold, the transmitted power increases linearly
with the input level. The effect of SBS is negligible for these low power levels but
becomes greater as the optical power level increases.
At the SBS threshold, the SBS process becomes nonlinear and the launched
signal loses an increasingly greater percentage of its power as the signal strength
becomes larger. Beyond the SBS threshold, the percentage increase in signal depletion continues to grow with signal strength until the SBS limit is reached. Any additional optical power launched into the fiber after this point merely is scattered backward along the fiber due to the SBS effect. Thus above the SBS limit the transmitted
power remains constant for higher inputs, because all the added power is extracted
from the signal to feed the scattered wave.
485
there are normally optical isolators to prevent backscattered signals from entering
the amplifier. Consequently, the impairment due to SBS is limited to the degradation
occurring in a single amplifier-to-amplifier span.
One criterion for determining at what point SBS becomes a problem is to consider
the SBS threshold power P th . This is defined to be the signal power at which the
backscattered light equals the fiber-input power. The calculation of this expression
is rather complicated, but an approximation is given by [8]
P th ≈ 21
A e f f b
g B L e f f
1 +
ν source
ν B
(12.5)
Here, A eff is the effective cross-sectional area of the propagating wave, ν source is
the source linewidth, and the polarization factor b lies between 1 and 2 depending
on the relative polarizations of the pump and Stokes waves. The effective length L eff
is given in Eq. (12.1) and g B is the Brillouin gain coefficient, which is approximately
4 × 10
−11 m/W, independent of the wavelength. Equation (12.5) shows that the SBS
threshold power increases as the source linewidth becomes larger.
Example 12.2 Consider an optical source with a 40-MHz linewidth. Using the values
ν B = 20 MHz at 1550 nm, A eff = 55 × 10
−12 m
2 (for a typical dispersion-shifted
single-mode fiber), L eff = 20 km, and assuming a value of b = 2, then from Eq. (12.5)
it follows that P th = 8.6 mW = 9.3 dBm.
Drill Problem 12.3 Consider an optical source with a 60-MHz linewidth. Using
the values ν B = 20 MHz at 1550 nm, A eff = 55 × 10
−12 m
2 (for a typical
dispersion-shifted single-mode fiber), L eff = 20 km, assuming a value of b =
1, and letting g B = 3.5 × 10
−11 m/W, show from Eq. (12.5) that P th = 5.0 mW
(or 7.0 dBm).
Figure 12.7 illustrates the effect of SBS on unmodulated signal power once the
threshold is reached. The plots give the relative Brillouin scattered power and the
signal power transmitted through a fiber as a function of the input power. Below a
certain signal level called the SBS threshold, the transmitted power increases linearly
with the input level. The effect of SBS is negligible for these low power levels but
becomes greater as the optical power level increases.
At the SBS threshold, the SBS process becomes nonlinear and the launched
signal loses an increasingly greater percentage of its power as the signal strength
becomes larger. Beyond the SBS threshold, the percentage increase in signal depletion continues to grow with signal strength until the SBS limit is reached. Any additional optical power launched into the fiber after this point merely is scattered backward along the fiber due to the SBS effect. Thus above the SBS limit the transmitted
power remains constant for higher inputs, because all the added power is extracted
from the signal to feed the scattered wave.