Role of the phase in the identification of delay time in semiconductor lasers with optical feedback

We consider a semiconductor laser with external optical feedback operating at a regime for which the delay time signature is extremely difficult to identify from the analysis of the intensity time series, using standard techniques. We show that such a delay signature can be successfully retrieved by computing the same quantifiers from the phase, the real or the imaginary part of the field, even in the presence of noise. Therefore, the choice of the observable is the determinant for parameter identification.