Nonlinear Threshold

The permissible launched probe power for the Brillouin based OTDR is governed by the onset of the nonlinear effects. The main influence of the nonlinear effects is to distort the spectral profile of the probe pulse travelling in the optical fibre. Such effects may be useful in applications related to the operation of nonlinear optical devices, but are generally undesirable in the Brillouin based OTDR sys- tem. It is vital to quantify the power at which these nonlinear effects occur in the optical fibre, such that these phenomena can be avoided by operating the probe power below the threshold power. Stimulated Raman scattering (SRS), stimu- lated Brillouin scattering (SBS) and self-phase modulation (SPM) are the three key nonlinear effects that can potentially degrade the performance of the direct detection system.

The SRS and SBS are detrimental as they result in the depletion of the power of the probe pulse. The threshold powers for both cases are defined as the input pump power for which the Stokes power is equivalent to the pump power at the output of the fibre [8]. The critical powers for the SBS and SRS can be expressed as [8] PSBS = 21Aef f K Lef f gB (2.9) PSRS = 16 Aef fK Lef f gR (2.10) where gB is the Brillouin gain coefficient, gR is the Raman gain coefficient, K

is the polarisation factor and Aef f is the effective core area. The effective area

for the conventional SMF is given by 80µm2 _{at 1550 nm [43]. The Brillouin and}

Raman gain coefficients were reported to be 5×10−11_{m/W [8] and 3×10}−14_m/W,

at a pump wavelength of 1550 nm[44] respectively. This Brillouin gain coefficient is based on the assumption that the linewidth of the pump is smaller than the Brillouin linewidth.

Its value is affected by the pump linewidth, ∆νP, and consequently the critical

power for the SBS may change according to the pump linewidth. The Brillouin gain coefficient as a function of pump linewidth [8], is given by

f

gB(∆νP)≈

∆νB

∆νB+ ∆νP

gB f or ∆νP >∆νB (2.11)

wheregfB(∆νP) is the new Brillouin gain coefficient,gB is the Brillouin gain coeffi-

cient when the pump linewidth is smaller than the Brillouin linewidth, ∆νB is the

Brillouin linewidth and ∆νP is the pump linewidth. The main difference in evalu-

ating the critical power for these two nonlinear effects, is the effective length. The effective length of the SBS in the pulse regime is half the pulsewidth, as a result of the counterpropagating nature of the pump and signal. Whereas, the effective length in the pulse regime for the forward SRS is governed by the walk-off length. The effective lengths in the pulse regime for both effects are given by [45, 46]

LSBS = W vg 2 (2.12) LSRS = W D∆λ (2.13)

where D is the dispersion parameter and ∆λ is the difference in wavelength be- tween the pump and signal. Typically, D is 17 ps/nm/km for SMF at 1550 nm [47] and ∆λis 100 nm. The walk-off length is defined as the interaction length be- tween the probe and pump pulse along the fibre. As a result of dispersion, the two pulses will cease to interact at a certain distance along the fibre. These two nonlin- ear processes provide an upper limit requirement to the maximum launched pulse power. Moreover further analysis indicates that SPM occurs at a lower power level. The critical powers versus different pulsewidths for the three nonlinear effects are analysed and discussed at the end of this section.

SPM is due to the change in the phase of the pulse resulting from the intensity dependence of the refractive index of the optical fibre. It induces spectral broad- ening of the pulse and is a function of the effective length and the power. Since the separation between the Rayleigh and Brillouin lines are relatively small ∼11 GHz at 1550 nm, spectral broadening of the pulse exceeding this value is undesirable. The critical power for the SPM can be expressed as [8]

PSP M = φmax γ Lef f (2.14) where γ = 2π n2 λ Aef f (2.15) Lef f = 1−exp(−αpL) αp (2.16)

where φmax is the maximum phase shift, Lef f is the effective length, αp is the

Rayleigh scattering coefficient, γ is the nonlinear-index coefficient, Aef f is the

effective area, n2 is the nonlinear refractive index and λ is the probe wavelength.

Taking the values of n2 = 2.2×10−20m2/W [48], Aef f = 80µm2 at 1550 nm and

λ = 1550 nm, result inγ = 1.1 W−1_km−1_{. The broadening factor of the linewidth}

is proportional to the maximum phase shift, φmax. The relationship between the

aforementioned parameters, assuming that the pulse is Fourier transform limited, can be expressed as [8]

δν = 0.86φmax

W (2.17)

whereδν is the broadening factor and W is the pulsewidth of the source. In order to estimate the threshold power for this effect, we defined it as the power which resulted in the spectrum broadened to 1 GHz. Equation 2.17 is substituted in equation 2.14 and the critical power for SPM, PSP M, is evaluated for different

The critical powers for the SBS, SRS and SPM evaluated as a function of pulsewidth in the range of 1 ns to 400 ns are illustrated in figure 2.6.

Figure 2.6: The plot of the critical power of SBS, SRS and SPM versus pulsewidth for a sensing length of 50 km. The critical power for SBS is in- dicated by a dashed line, SRS is indicated by a line and SPM is indicated by a

dashed double dot line.

For a pulsewidth of less than 35 ns, the nonlinear effects are dominated by SPM as it has a lower threshold compared to SBS and SRS. The threshold power for SPM is calculated to be 50 mW for a pulsewidth of 1 ns and this value increased to 1.9 W at a pulsewidth 35 ns. From a pulsewidth of 35 ns and up to 360 ns, the threshold power is governed by the SRS. The threshold power in this regime is calculated to be 1.9 W. Beyond 360 ns, the threshold power is determined by the SBS effect.