Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum

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We construct several examples of distinct asymmetric-symmetric pulse pairs with identical or essentially identical intensity autocorrelations and power spectra. From these examples, we infer that pulse retrieval methods based on these two data sets alone produce ambiguous solutions. Furthermore, we used the constructed pulse pairs as test cases to assess the degree of difference in the corresponding interferometric autocorrelations. In several cases, we found that the differences in the interferometric autocorrelations are sufficiently small that they might be quite challenging to distinguish in a practical experimental context.