Chaotic fiber ring lasers (CFRLs) can be regarded as a type of complex multi-longitudinal-mode (MLM) lasers in optical frequency domain. However, most experimental investigations on laser chaos generation are only restricted to measurements of total intensity dynamics, with frequency-domain longitudinal mode information neglected. In this work, we experimentally study the longitudinal mode dynamics of a CFRL with pump modulation by utilizing a heterodyne detection scheme, in which a beat signal between the chaotic laser and a reference laser is generated. High-resolution instantaneous emission spectra reflecting the fine longitudinal-mode structure of the CFRL in overall are measured through heterodyne detection. Besides, longitudinal mode frequency and intensity dynamics of the CFRL are monitored simultaneously via time-frequency analysis and discussed in detail. Experimental results show that the CFRL exhibits dense and irregular MLM oscillation all the time when operating at intensity chaos state. Meanwhile, each oscillating longitudinal mode in the CFRL is broadened in spectral line due to pump modulation, and can perform chaotic or random-like behaviors in mode intensity. This work will play a significant role in the further analysis, understanding and application of chaotic fiber ring lasers.
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