The complexity properties of polarization-resolved chaotic signals generated in a ring network of vertical-cavity surface-emitting lasers (VCSELs) mutually coupled with multiple delays are investigated quantitatively by using the proposed mean permutation entropy (MPE). For direct comparison, the complexity of polarization-resolved chaos in a ring network of VCSELs coupled with single delay is also considered. The effects of injection current, coupling strength, and frequency detuning on the chaotic complexity for both a single-delay ring network (SDRN) and a multiple-delay ring network (MDRN) are evaluated quantitatively and compared by the MPE. The effects of internal parameters of VCSELs on the complexity are also discussed, and the correlation properties between different polarization-resolved modes are also analyzed. It is shown that the complexity of chaos in two polarization-resolved modes of VCSELs in MDRN is much higher than those in SDRN in a much wider parameter region. Besides, wider range of injection current, coupling strength, and frequency detuning can be tuned to achieve the enhancement of chaotic complexity in MDRN. These results provide an effective quantifier, the proposed MPE, to evaluate quantitatively the complexity of chaos generated in systems with multiple delays, and the multichannel complexity-enhanced polarization-resolved chaos generated in MDRN of mutually coupled VCSELs is extremely meaningful for the chaos-based random number generators.
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