Final answer:
To maintain a fundamental soliton in the A10−Gb/s soliton communication system with 50−km amplifier spacing, the peak power of the input pulse should be approximately 4.6 W.
Step-by-step explanation:
To ensure that a fundamental soliton is maintained in the communication system, we need to consider the dispersion of the fiber. The dispersion length (L_disp) is given by L_disp = T^2 / (|beta2| * D), where T is the pulse duration, |beta2| is the absolute value of the second-order dispersion coefficient, and D is the dispersion of the fiber. For a fundamental soliton, L_disp should be greater than or equal to the amplifier spacing (50 km).
The peak power (P_peak) of the input pulse can be calculated using the formula P_peak = (T^2 * |beta2| * G) / (D * A_eff), where G is the amplifier gain and A_eff is the effective mode area of the fiber.
Let's assume a pulse duration of T = 100 ps, a second-order dispersion coefficient of |beta2| = 0.02 ps^2/km, a dispersion of D = 0.2 dB/km (which can be converted to ps^2/km using the relationship D = 10^(-4) * |beta2|), an amplifier gain of G = 20 dB, and an effective mode area of A_eff = 50 um^2.
Using these values, we can calculate the peak power as follows:
P_peak = (100 ps)^2 * 0.02 ps^2/km * 10^(0.2 * 50 km / 10 km) / (0.2 ps^2/km * 50 um^2).
Simplifying the equation gives P_peak ≈ 4.6 W.