Here we study the noise correlations of a birefringent crystal based single-cavity dual-comb laser operating at 160 MHz repetition rate. We characterize the temporal fluctuations of one RF comb line, the repetition-rate difference Δf_rep, the f_CEO of the individual combs, and their difference Δf_CEO. This is achieved by coupling both combs into a single f-2f interferometer and simultaneously measuring heterodyne beat-notes with cw lasers. We find that the dual-comb Δf_CEO fluctuations are 20-dB lower than those of f_CEO, indicating highly correlated combs. Furthermore, we show that Δf_CEO and Δf_rep fluctuations are almost fully anti-correlated, enabling narrow linewidth in free-running operation.
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