Gain bandwidth optimization in two-pump fiber optical parametric amplifiers under bounded zero-dispersion wavelength fluctuations

We study gain bandwidth optimization in a two-pump fiber optical parametric amplifier (2P-OPA) with bounded zero-dispersion wavelength (ZDW) uncertainty. Maximum-bandwidth 2P-OPAs are designed ensuring positive parametric gain, tunable gain spectrum, and robustness against ZDW fluctuations. By recognizing the polynomial nature of the phase mismatch, the design task is formulated as a nonconvex multivariate polynomial optimization problem, which is then solved through the latest convex programming techniques based on linear matrix inequality relaxations. The proposed framework exhibits superior computational efficiency and guarantees, up to modeling accuracy, globally optimal wavelength assignment. It provides an analytical ground to assist experimental tunings in practice, and allows visualization of tradeoff between gain bandwidth and spectrum quality against ZDW uncertainty.