Time delay (TD) signatures are studied experimentally in orthogonal polarizations and in individual transverse modes respectively in a VCSEL operating with three transverse modes. Different types of concealment of the TD signatures are observed when the polarization of feedback is rotated through large angles. Effects of feedback strength and external cavity length on the TD signatures are investigated. Weak feedback leads to better concealment of the TD signatures in the dominant polarization. When the roundtrip time difference between the two external cavities is close to a half of the relaxation oscillation period, the TD signatures are minimized.

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