DESCRIPCION MOTIVOS MODIFICACION DE CANTIDADES

As shown in Subsection 1.1.4, spatio-temporal distortions are very important optical effects in terms of laser pulse propagation and often cannot be ignored. In the ultrashort regime, this question should be considered with more care, as the large bandwidth of pulses in the femtosecond timescale can lead to a significant complexity of their structure in space and time if the spatio-temporal couplings are not corrected properly. Therefore, techniques that can detect STCs are essential in ultrafast and attosecond optics. Such optical approaches are often related to the spatio-temporal field reconstruction. Here, a few relevant methods for measuring the STCs and the electric field in space-time are described.

Perhaps the most straightforward technique for the detection of common STCs like pulse-front tilt and spatial chirp is GRENOUILLE [80], which is almost identical to SHG FROG, described in the previous subsection. In the standard FROG setup, a partial re- flector is employed to split the beam into two identical pulses. In contrast, GRENOUILLE utilizes a Fresnel biprism to obtain two pulses through spatial splitting. In this case, an input pulse containing spatial chirp with separated frequencies in the cross-section results in the output beams carrying different frequency components. Therefore, the signal in a χ(2) crystal will have a variation of wavelength over the time delay, yielding a shift in the trace proportional to the magnitude of the spatial chirp [81]. Likewise, an input beam with a pulse-front tilt is split into two constituents, consequently introducing a measurable shift of the intersection area in the crystal [82]. Although this technique does not provide the spatio-temporal electric field, it is still useful for the simple detection of one-dimensional spatio-temporal distortions.

A basic concept of metrology techniques for extracting the spatio-temporal field relies on a measurement of spatially-resolved spectral interference of a test field with a refer- ence beam. One such interferometric approach is called Spatially Encoded Arrangement Temporal Analysis by Dispersing a Pair of Light Electric-fields (SEA TADPOLE) [83]. The pulse retrieval mechanism of SEA TADPOLE is based on the individual coupling of the test and reference pulses into short single-mode optical fibers, the output of which is collimated and crossed horizontally causing spatial fringes on a camera. Additionally, a grating is placed to map the wavelength to a spatial position. As a result, SEA TADPOLE measures a relative difference in the spectral phase between the reference and test pulses. The field E(ω) for one position (x0, y0) can be obtained by Fourier filtering the interfero-

gram, similar to standard spectral interferometry. If the fiber entrance is sufficiently small compared with the test pulse dimensions, the scan of the fiber in x, y, z directions with a mechanical stage yields the spatio-spectral field E(x, y, z, ω). However, the technique requires an additional temporal measurement of the reference pulse: the pulse waveform Er(t) must be known to extract the test field E(x, y, z, t) from the interferogram through

the inverse Fourier transform of E(x, y, z, ω). The reader may also be interested in other detection schemes related to SEA TADPOLE [84, 85].

An alternative technique relying on combined principles of spectral interferometry and holography [86] often referred to as spatially-resolved Fourier transform spectrometry [87] has been recently presented. This approach does not require an additional reference beam

1.2 Ultrafast Characterization Techniques 23

Δt

Test pulse

CCD

Figure 1.8: Operational principles of spatially resolved Fourier transform spectrometry. but utilizes a spatially homogeneous portion of the original beam as a reference. In other words, this method is self-referenced, exploiting a special Mach–Zehnder interferometer as shown in Fig. 1.8. The reference arm with homogeneous structure can be generated by focusing the pulse and placing a pinhole at the focus [87] or by direct defocusing using a small convex mirror [88]. A small spatially filtered portion of the spreading beam represents a relatively unperturbed region without any potential spatio-temporal distortions that can be present in the original pulse. The interference pattern on a CCD can be recorded as a function of the time delay between the two arms. As a result, the linear cross-correlation function between the beams is measured at each pixel, allowing the application of an iterative algorithm for the extraction of the spectral phase of the test field. In analogy to the previous interferometric approach, the retrieval of the full spatio-temporal electric field requires temporal field characterization at a single point in space [87, 88].

Similarly, a recently developed interferometric scheme called INSIGHT allows for the characterization of focused pulses [89]. The conceptual model incorporates a test pulse and its time-delayed replica, enabling the measurement of spatially-resolved linear auto- correlation using a CCD. The procedure of calculating the corresponding spatio-spectral amplitude at the focus is repeated for two other positions along the propagation axis near the focus. With this set of data, an iterative algorithm can be applied to retrieve the spectral phase of the test field. However, a spatially-homogeneous spectral phase needs still to be measured using, for example, FROG to reconstruct the test field in space-time. It has to be noted that none of the above-mentioned and other techniques like [90–93] for spatio-spectral/temporal field reconstruction have become popular in the community, as the level of complexity is still high, with a need for the application of phase retrieval algorithms. Besides, these methods primarily yield a spatio-spectral field, which is typically difficult to treat and analyze, with a requirement of an extra measurement to convert it into the spatio-temporal dimension. Accordingly, to determine the CEP of the test field, a CEP sensitive measurement must be performed to the reference pulse, making the exploitation of interferometric approaches even less attractive. For this reason, a simple and direct method for spatio-temporal metrology is in great demand at the moment.