The characterization of short optical pulses has been a field of intense research and innovation closely following any new development in the generation of these pulses. A general framework describing some minimal requirements that must be fulfilled in order to measure the electric field of an isolated ultrashort optical pulse has been published [2,3]. It was shown that a time-non-stationary filter, i.e. an element with a response time of the order of the duration of the pulse under test, must be present. Such an element is in practice implemented using a fast detector, a fast modulator or a nonlinear interaction with one or several optical pulses (that can include the pulse under test itself). In the latter case, the non-stationarity (and not the nonlinearity) is the key element. More generally, a time-non-stationary filter is required to get any kind of temporal information on a short optical pulse. The inability of a setup constructed from time-stationary elements and time-integrating detectors to get any information on the spectral phase of an optical pulse can be demonstrated easily. Let’s call Ẽ(ω) the electric field of the pulse under test and R̃(ω) the transfer function of a time-stationary setup (i.e. a setup built only with time-stationary elements), which can be a function of several parameters (for example, a delay, a frequency or a spatial variable), in which case the experimental trace is the quantity measured by the integrating detector as a function of these parameters. Such dependence is removed for clarity. The output electric field is:

When the output pulse is incident on a time-integrating detector, the measured signal is:

Using the Parseval theorem, the signal can be expressed as:

Therefore, the measured signals only depend on the spectral density of the source. They would be identical for a short optical pulse, independently of its spectral phase, and for an incoherent white light with the same spectral density. Such a setup is thus unable of getting any temporal information. Typical examples are a monochromator (in which case the transfer function is a narrow pass-band function), or a Fourier-transform spectrometer (in which case the transfer function is the sum of two exponentials) [4].

The method proposed in [1] is based on a grating followed by an integrating detector (note that such a setup strongly resembles a grating-spectrometer). It does not contain any time-non-stationary element. It can be concluded that such a technique is only sensitive to the spectral density of the light under test. Equations 6, 7 and 8 of reference [1] are exactly of the same functional form as equation 3 of this comment.

The specific flaw in the derivation presented in [1] lies in the description of the pulse under test as a gaussian function of time without a phase. For such a pulse, it is obvious that the measurement of the spectrum allows the determination of the only parameter present in the model, which is the width of that gaussian function. However, propagating such a pulse in a material with second order dispersion would give the same experimental trace (since the spectrum is not modified), but would be represented with a gaussian temporal intensity and a quadratic temporal phase, a function that is not taken into account by the proposed derivation. Errors of this kind can be avoided by using a full, assumption-free, description of the pulse under test using the analytic signal as a function of time or frequency.

Temporal information on a short optical pulse can be obtained with a linear setup, either using a fast detector or a more elaborate device including a time-non-stationary element [5, 6, 7, 8, 9]. Note that if a known reference pulse is available, the pulse under test can be characterized completely with a linear technique without any time-non-stationary elements provided that the spectral support of the reference pulse encompasses the spectral support of the pulse under test [4]. These interferometric approaches are either spectral interferometry [10,11] or Fourier-transform dispersive spectrometry [12].

In conclusion, I have argued that the setup presented in [1] would be unable to gather any kind of temporal information on the light source under test because of the absence of a time-non-stationary filter. The proposed setup was shown to be only sensitive to the spectral density of the source under test.