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We vary the time-frequency mode structure of ultrafast pulse-pumpedmodulational instability (MI) twin beams in an argon-filled hollow-corekagom\'e-style PCF by adjusting the pressure, pump pulse chirp, fiber lengthand parametric gain. Compared to solid-core systems, the pressure dependentdispersion landscape brings increased flexibility to the tailoring of frequencycorrelations and we demonstrate that the pump pulse chirp can be used to tunethe joint spectrum of femtosecond-pumped sources. We also characterize theresulting mode content, not only by measuring the multimode second-ordercorrelation function g(2) but also by directly reconstructing the shapes andweights of time-frequency Schmidt (TFS) modes. We show that the number of modesdirectly influences the shot-to-shot pulse-energy and spectral-shapefluctuations in MI. Using this approach we control and monitor the number ofTFS modes within the range from 1.3 to 4 using only a single fiber.

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