Parameters
Wavelength = 1550 nm
1550 nm
Fiber Loss (dB/km)
0.6 dB/km
Laser Linewidth (MHz)
1 MHz
Mode Field Diameter (um)
10.4 um
Brillouin Bandwidth (MHz)
40 MHz
Brillouin Gain (xE-11 m/W)
2.0 xE-11 m/W
Plot 2: Constant Parameter To Calculate Phonon Lifetime
1
π
2π
4π
Plot 3: Pulse Delay (ns)
45 ns
Plot 4: Pulse Duration (ns)
20 ns
Plot 3 + 4: Fiber Length (m)
2520 m
Plots 3 + 4: Chosen Length for Calculations
Fiber Length
Effective Fiber Length
Plot 1: SBS Threshold vs Fiber Length (CW Operation)
Plot 2: SBS Threshold vs Pulse Duration (L >> Pulse)
Plot 3: SBS Threshold vs Pulse Duration (with Pulse Delay = 1000 ns)
Plot 4: SBS Threshold vs Pulse Delay (20ns Pulse, L >> Pulse)
SBS Threshold Formulas
Basic Parameters
Effective Area: \[A_{eff} = \pi(\frac{MFD}{2})^2\]
Fiber Loss Coefficient: \[\alpha = \frac{\alpha_{dB} \cdot \ln(10)}{10}\]
Effective Length: \[L_{eff} = \frac{1-e^{-\alpha L}}{\alpha}\]
Brillouin Parameters
Brillouin Phonon Lifetime: \[T_B = \frac{1}{\Delta\nu_B \cdot Q}\] where Q = 1, π, 2π, or 4π
Effective Brillouin Gain: \[g_{B_{eff}} = g_B\frac{\Delta\nu_B}{\Delta\nu_B + \Delta\nu_p}\]
Plot 1: CW SBS Threshold
Base Threshold Power at 1% reflection: \[P_{th} = \frac{17A_{eff}}{g_{B_{eff}}L_{eff}}\]
Plot 2: Pulsed Operation
Pulse Length: \[L_{pulse} = v_g\tau_p= \frac{c}{n}\tau_p\]
Pulsed Threshold (Fiber length >> Pulse roadtrip): \[P_{th,pulse} = \frac{2\Theta}{g_{B_{eff}}\cdot v_g\cdot \tau_p}(\frac{T_B\Theta}{\tau_p} + 1)A_{eff}\] where \[Θ ≈ 22\]
Plot 3+4: Delay between Pulses Effects
SBS Threshold with Duty Cycle at 1% reflection: \[P_{th} = \frac{17A_{eff}}{g_{B_{eff}}L_{overlap}}\]
Pulse Period: \[T_{period} = \tau_p + \tau_{delay}\] where \(\tau_p\) is pulse duration and \(\tau_{delay}\) is pulse delay
\[\]
Effective Interaction Length: \[\] IF : \(L_{chosen} ≤ \frac{T_{period} \cdot v_g}{2} :\) \[L_{overlap} = \min(L_{chosen}, \frac{v_g \cdot \tau_p}{2})\]
IF : \( L_{chosen} > \frac{T_{period} \cdot v_g}{2} : \) \[L_{overlap} = L_{overlap_1} + L_{overlap_2}\] where \[L_{overlap_1} = (N-1) \cdot \frac{v_g \cdot \tau_p}{2}\] \[L_{overlap_2} = \min(\frac{v_g \cdot \tau_p}{2}, L_{chosen} - 0.5(N-1)T_{period} \cdot v_g)\] where \[N = <\frac{2*L_{chosen}}{v_g*T_{period}}>\]