Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback

Time-delay (TD) signatures of chaotic outputs generated by vertical-cavity surface-emitting lasers (VCSELs) are investigated quantitatively by using two proposed estimators, the peak signal to mean ratio (PSMR) calculated based on the auto-correlation function, and the valley signal to mean ratio (VSMR) calculated based on an information-theory-based estimator, the permutation entropy (PE) function. The VCSELs subject to variable-polarization optical feedback (VPOF) are considered, and the effects of polarizer angle, feedback strength, feedback delay and injection current are discussed. When the feedback strength is small, the TD signatures for the fully developed chaotic outputs of VCSELs can be well concealed for all polarizer angles. While for large feedback strength, the TD signatures cannot be concealed for any polarizer angle. However, for moderate feedback strength, the TD signatures of VCSELs with VPOF at intermediate polarizer angles can be better concealed than those of VCSELs with conventional polarization-selected optical feedback. Thus, the VCSELs with VPOF are extremely interesting for the security-enhanced chaotic optical communication systems.