Covariance spectroscopy of molecular gases using fs pulse bursts created by modulational instability in gas-filled hollow-core fiber

We present a technique that uses noisy broadband pulse bursts generated by modulational instability to probe nonlinear processes, including infrared-inactive Raman transitions, in molecular gases. These processes imprint correlations between different regions of the noisy spectrum, which can be detected by acquiring single shot spectra and calculating the Pearson correlation coefficient between the different frequency components. Numerical simulations verify the experimental measurements and are used to further understand the system and discuss methods to improve the signal strength and the spectral resolution of the technique.