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In recent years, the topic of negative frequencies has resurfaced in opticsmotivated by the optical analogue of Hawking radiation. We discuss the physicalmeaning of negative frequencies and the conditions under which they arerelevant. We review how negative frequencies are treated in current pulsepropagation models based on the electric field and the analytic signal. Wefocus on experimentally measured signals predicted by the conservation ofnegative comoving frequency in the nonlinear polarization terms to advancethese concepts. We propose a new formalism called the double analytic signalwhich clearly separates negative frequencies from positive ones. Additionally,we reduce this new formalism to the analytic signal to prove their equivalence.Throughout the paper, we present numerical solutions of the unidirectionalpulse propagation equation to illustrate the electric field, analytic signal,and double analytic signal formalisms and to highlight their differences.

Negative frequencies in pulse propagation equations and the double analytic signal