Shaping frequency correlations of ultrafast pulse-pumped modulational instability in gas-filled hollow-core PCF

We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagom\'e-style PCF by adjusting the pressure, pump pulse chirp, fiber length and parametric gain. Compared to solid-core systems, the pressure dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function g(2) but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.