In the current subsection, an example of the synthesized transients will be demonstrated. Undoubtedly, the main interest is concentrated on the shortest synthesized pulses, which will be analyzed and spatiotemporally visualized. As described earlier, such short oscil- lating electric fields can be generated by a proper coherent combination of the individual components, which have been presented in the previous subsection. This is feasible with sufficient interferometric stability and precise control over the delay between the two arms. The electric field evolution of one of the shortest sub-cycle synthesized pulses, achieved in the experiment, is shown in Fig. 3.7a. The field is retrieved using the time-domain EOS, with a measured pulse duration of 4.5 fs. The interference between the two channels leads to single-peak light confinement, which is in great demand in ultrafast science [151]. The spectral intensity in Fig. 3.7b, obtained by the Fourier transform of the electric field, illustrates the multi-octave bandwidth of the synthesized waveform, which consists of two independent spectral regions with frequencies of 120-200 THz and 210-450 THz.
Experiments with a waveform synthesizer are not new in the community as many scientific groups have developed similar laser sources, sometimes with even shorter pulse durations [151–154]. However, the characterization of synthesized transients using the EOS metrology is indeed an exciting achievement, especially taking into account a potential extension of the time-domain field reconstruction to an imaging geometry and thereby the spatial domain. Thus, the EOI modality has the capacity to make synthesized pulses the most characterized ever, providing absolute spatio-temporal field information in a compact, simple setup in ambient conditions.
The band-pass filtered light with the 290-350 nm spectral region, which contains LO components of the UV-VIS channel and SFG components, generated by the same chan- nel and the synthesized field in the BBO, is redirected to the 4f UV imaging system for EOI measurements. The interference on the CCD camera and subtraction of the crossed- polarized images yield the electric field images as a function of the time delay. It is worth noting that the BBO is placed in the relative focus of both CH1 and CH2.
Three individual field frames for 0 fs, 0.8 fs, and 1.6 fs are depicted in Fig. 3.8a-c, respectively. The electric field image at 0 fs shows the spatial distribution at the dominant field strength and appears to be relatively round, without any obvious distortions. The field images with zero crossing and negative extremum complement the previous image and provide an opportunity to look inside the pulse’s structure.
The image of the field dynamics in the plane E(x = 0, y, t), shown in Fig. 3.8d, reveals interesting properties of the wavefront at the imaged position. Since the BBO is placed in the mean focal plane of both channels, which have a small difference in the focus position, the image discloses a different spatio-temporal behavior of the two components. According to the investigation of the individual arms in the previous subsection, the NIR channel (CH2) has the focal plane slightly further from the focusing element than the VIS-NIR channel (CH1). Thus, the physical shift of the EOS crystal towards the focusing element makes the detected CH2’s wavefront negative, i.e. the beam is converging. It is clearly seen in the image that the right-hand side oscillations with respect to the major peak represent the negatively curved lower frequencies. At the same time, the CH1’s wavefront is still positive and the beam is diverging (positively curved higher frequencies on the left-hand side). However, at the peak position of the electric field, the individual channels start to compensate each other, allowing the shaped wavefront to be relatively flat. In this particular context, EOI provides new, deeper insight into the process of the formation of synthesized fields. The 3D electric field visualization in Fig. 3.8e emphasizes the spatiotemporal sub-cycle structure of the synthesized pulse.
Interesting spatio-spectral effects can be also extracted by performing the Fourier trans- form of every single waveform of each pixel. This operation yields a hyperspectral image of the pulse, which provides the position of each frequency component in the cross-section. The false-color image is presented in Fig. 3.9a, where red, green and blue colors corre- spond to the spectral regions around 190 THz, 285 THz and 380 THz, respectively, with the channel bandwidth of 30 THz (see also Fig. 3.9e-g). The image reveals the spatial misalignment of the CH1 and CH2: the right-hand side of the synthesized beam tends to contain more low-frequency components rather than the high-frequency ones. This effect
3.2 Ultra-Broadband Synthesized Waveforms 57
Figure 3.8: Absolute spatio-temporal characterization of a synthesized pulse with visible- near-infrared spectrum. Electric field at the time of (a) highest field strength, (b) zero crossing and (c) negative maximum. (d) Spatio-temporal electric field distribution in the plane E(x = 0, y, t). (e) 3D image of the electric field, where semitransparent and opaque contours represent 12% and 60% of the maximum, respectively.
Figure 3.9: Fourier analysis of the synthesized pulse. (a) False-color image of the beam, where red, green, and blue are mapped to 190 THz, 285 THz, and 380 THz. (b)-(d) Time-domain waveforms at the left edge (x = −30 µm, y = 0), center (x = 0, y = 0) and right edge (x = 30 µm, y = 0) of the beam. (e)-(g) Corresponding spectra obtained by Fourier transform of the temporal waves.
may be an indication of unequal beam waists or different focus positions on the propaga- tion axis. In any case, this leads to the reduction of local bandwidth and, consequently, longer pulse durations in such areas.
In addition, three waveforms from the false-color image are analyzed in more detail — at a pixel at the left edge (x = −30 µm, y = 0), center (x = 0, y = 0), and right edge (x = 30 µm, y = 0) of the beam. Corresponding time-varying oscillations and their Fourier transform are presented in Fig. 3.9b-d and Fig. 3.9e-g, respectively. The pulse duration of the central pixel at the peak intensity is measured to be 5.1 fs, while the calculated spectrum spans almost the entire incident bandwidth. The pixel on the left side of the beam (x = −30 µm, y = 0) contains significantly reduced local bandwidth, missing the
3.3 Outlook 59