Wideband Gaussian Noise Model of Nonlinear Distortions From Semiconductor Optical Amplifiers

Abstract

A wideband Gaussian Noise Model of the nonlinear noise power spectral density is developed for a single semiconductor optical amplifier as described by the Agrawal model. A simple, interpretable closed-form expression is obtained for the nonlinear noise-to-signal ratio of broadband wavelength-division multiplexed signals as a function of the Agrawal model parameters, the amplifier output power and the transmission bandwidth. The accuracy of the closed-form expression and its region of validity are assessed in numerical simulations. The error is smaller than 0.1 dB when the product of bandwidth and gain recovery time $B\timesτ_c$ exceeds 100. A complete treatment of gain compression is shown to enhance nonlinear noise by a factor $1+P_\text{out}/P_\text{sat}$ compared to the first-order perturbation theory result.

Figures (12)

• Figure 1: Absolute square of the low-pass filter $H_c(f)=1/(1+if/f_c)$. The cutoff frequency is defined as $f_c=1/(2\pi\tau_c)$.
• Figure 2: Schematic representation of the input power spectral density $G_\text{in}(f)$ and the spectral origin of the dominant contributions to the nonlinear interference noise power spectral density $G_\text{NLI}(f)$. a) Cross-channel interference (XCI). b) Self-channel interference (SCI).
• Figure 3: Schematic representation of the idealized WDM signal with flat input power spectral density $G_\text{in}(f)$ used for the calculation of the nonlinear interference noise, with the channel of interest indicated by the shaded region.
• Figure 4: Schematic representation of the integration region where the product $g_\text{in}(f_1)g_\text{in}(f_2)g_\text{in}(f_1+f_2)$ is non-zero (gray shaded area) and the extended integration region (dashed square) used in computation of the two-dimensional integral \ref{['eq:gnlifinal']} for the first contribution to the closed-form approximation proportional to $|H_c(f_2)|^2$ ($\tau_c=100$ ps and $B\tau_c=20$). Contour lines of the relative magnitude of this function are overlaid. Because of the rapid decay of this function, the extension of the integral domain essentially does not change the value of integral. For larger product $B\tau_c$ the decay is even faster.
• Figure 5: Schematic representation of the integration region where the product $g_\text{in}(f_1)g_\text{in}(f_2)g_\text{in}(f_1+f_2)$ is non-zero (gray shaded area) and the extended integration region (dashed square) used in computation of the two-dimensional integral \ref{['eq:gnlifinal']} for the second contribution to the closed-form approximation proportional to $H_c(f_2)H_c^*(f_1)$. The magnitude of the functions $|H_c(f_2)|$ and $|H_c^*(f_1)|$ is shown as well as contour lines indicating the relative magnitude of their product ($\tau_c=100$ ps and $B\tau_c=20$).