Carrier-envelope phase on-chip scanner and control of laser beams

The carrier-envelope phase (CEP) is an important property of few-cycle laser pulses, allowing for light field control of electronic processes during laser-matter interactions. Thus, the measurement and control of CEP is essential for applications of few-cycle lasers. Currently, there is no robust method for measuring the non-trivial spatial CEP distribution of few-cycle laser pulses. Here, we demonstrate a compact on-chip, ambient-air, CEP scanning probe with 0.1 µm3 resolution based on optical driving of CEP-sensitive ultrafast currents in a metal−dielectric heterostructure. We successfully apply the probe to obtain a 3D map of spatial changes of CEP in the vicinity of an oscillator beam focus with pulses as weak as 1 nJ. We also demonstrate CEP control in the focal volume with a spatial light modulator so that arbitrary spatial CEP sculpting could be realized.


Development of Ir/Al2O3 heterostructures and their properties
Ir/Al2O3 heterostructure (nanolaminate) coatings are grown using the atomic layer deposition (ALD) technique. Amorphous fused silica (FS) with an ultra-flat surface was used as substrates. The typical AFM (1 × 1 µm²) rootmean-square (rms) surface roughness is about 0.26 nm. Their cleaning was performed with a multi-stage, ultrasonicassisted bath cleaning system (Elma Schmidbauer, Singen, Germany) with alternating surfactants and water (H2O) baths, concluded by a deionized, ultra-pure H2O bath. The depositions were performed with a commercial SunALE R-200 Advanced ALD system (Picosun Oy, Masala, Finland) using iridium(III) acetylacetonate (Ir(acac)3) and molecular oxygen (O2), and trimethyl alumium (TMA) and water (H2O) as precursors for Ir and Al2O3, respectively. A heatable wafer chuck ensures a substrate temperature of 380 °C. One Ir ALD cycle consists of 6 s of Ir(acac)3 pulse, 60 s of purge, 2 s of O2 pulse, and 6 s of purge with molecular nitrogen (N2) as purging gas. The corresponding ALD process parameters for Al2O3 are 0.1 s TMA pulse, 4 s N2 purge, 0.2 s H2O pulse and 4 s N2 purge. The growth per cycle (GPC) of Ir and Al2O3 are 0.6 Å/cycle and 0.9 Å/cycle respectively. The development and properties of ALDgrown Ir coatings and Ir/Al2O3 nanolaminates are reported in detail in previous articles [1 -3]. The Ir/Al2O3 ratio is precisely controlled by the number of ALD cycles, which allows to tailor the optical and electrical properties of the heterostructures. Here, a composition with 32 cycles of Ir separated by 35 cycles of Al2O3 and a total thickness of 226.5 nm is used.
The presence of iridium layers is beneficial in terms of the maximum attainable signal J0 of strong-field CEPdependent ultrafast currents. In FigSI. 1 we show how the signal gain increases from bare Al2O3 ALD to iridium containing ALD coating when exposed to similar field strengths. Moreover, the selected nanolaminate medium shows a very good trade-off between stability and magnitude of the signal, see below. We surmise that these advantageous properties of this material stem either from its large nonlinear susceptibility χ (3) [1] or from a conduction band that is not empty. The former increases coupling between the valence and the conduction bands, thus, interband contribution to the current [4,5], while the latter enhances the contribution of intraband oscillations to the current [6,7]. Additionally, the conductivity of the several-atom-thin iridium layers might contribute to the fast recovery between the laser pulses.
FigSI. 2 (a) Illustration of measured lock-in phase φJ and CEP equivalence. The two depicted pulse trains differ in CEP offset by 45°. This projects to the offset of the current oscillation (green line) in the connected circuit leading to the change in the detected lock-in phase φJ by 45°. (b) CEP change sensitivity of a current generated in Ir:Al2O3 target. The plot shows the oscillation of the measured in-phase Jcos and quadrature Jsin components that acquired with lock-in amplifier as amount of glass d is added into a beamline. Secondary abscissa shows an estimated change of CEP calculated from d. (c) Change of magnitude of the current J0 (green) and its phase φJ (pink) that corresponds to the offset of the phase in the pulse train as indicated in (a).

Stability and robustness of CEP measurement
We have investigated the stability of the CEP measurement by investigating the probe design from Fig. 1 in the main manuscript. To show that the chosen nanolaminate of Al2O3 and Ir performs well we made the same electrodes on ALD-deposited Al2O3 without iridium content. We made same probe on this substrate and tested it under same conditions as the probe deposited on the heterostructure. In FigSI. 3 we show the signals from investigated probes. We can see that only in case of Al2O3:Ir probe the stability of the measurement is good enough to make a reliable CEP measurement. During 300 s long measurement with 3 Hz acquisition rate the magnitude of current J0 is constantly settled on a value of 218±17 fA. The phase is accompanied by little oscillation lower than 10° peak-to-peak. However, in one minute interval (180 samples) the standard deviation of the signal is only 3.5°. The noise sample from the Al2O3:Ir probe was measured when the laser illuminated the probe but the lock-in reference loop was disengaged. The current noise was on the order of 20 fA, i.e. 10 % of the typical signal. As expected, the phase jumps quasirandomly. The Al2O3 reference sample without iridium content does not perform very well. Although magnitude of current reaches much higher it is not stable. Also, the noise with the reference loop disengaged is much higher. The measured phase φJ has a weak dependence on the electric field the probe is exposed. This is well visible while performing a power scan (beam attenuation with a reflective ND filter) on a stationary CEP-probe that shows some linear slope of the phase as a function of the electric field, see FigSI. 4(a). This can have some consequences on the CEP scans. As the strength of laser field in the vicinity of beam focus changes fast, there can be some crosstalk between the current and phase. Fortunately, the measurements show that the crosstalk is not higher than -9°nm/V as obtained from a linear fit of the data in FigSI. 4(a). In order to compensate for this crosstalk, we constructed a correction based on the measurement that we used in the data post-processing. The correction is represented by a function mapping the measured current J0 on a phase, see FigSI. 4(b). Measured maps J0(x,y,z) then allow us to make maps of relative offset that we apply on the measured maps of φJ(x,y,z).

Focal spot measurement
The tight focusing geometry of expanded beam is prone to a variety of aberrations. To ensure that the beam is as close as possible to Gaussian TEM00 mode we have characterized it around the focus with an in-situ knife edge method. In this method the beam is cut using a horizontal and vertical edge of the electrode, see Fig. 1

Evaluation of model of focal CEP distribution
In FigSI. 6 we show a few selected examples of CEP distribution in the vicinity of the focus as evaluated with the formula Eq. 12 in [9]. We would like to highlight the property of chirped beam that forms plateaus in the post-and pre-focal regions for negative and positive values of g respectively. Another distinct feature is the crest along the optical axis that is pronounced for the negative chirp.
FigSI. 6 Selected examples of calculated CEP landscape in the vicinity of focus according to eq. (2) in main manuscript (Methods). Waist and Rayleigh length of the considered beam is w0 = 1.5 μm and zr = 8.8 μm respectively. γ is set to zero in all depicted cases. 1D lines represent lineouts along the optical axis z.

Spectral characteristic of laser pulse
Related to the studies of change of CEP landscape as a function of laser pulse chirp, we investigated the spectral phase of the laser pulses. We performed a measurement of the laser spectrum and a d-scan trace to obtain the spectral phase.
Once the d-scan trace is reconstructed we obtain the spectral phase denoted as d = 0.0 mm, see the spectrum (yellow) and the phase (black) in FigSI. 7. We fitted the phase and obtained the polynomial expansion centered at the laser central frequency 2.35 rad/fs (800 nm). The coefficient of the fit at the second power p2 gave us the relative chirp values as Cr = 4ln(2)p2/τ 2 . Interestingly, despite the pulse in state d = 0.0 mm giving the highest currents J0 from the probe there is still a residual phase curvature which in turn leads to a non-zero value of Cr = -0.8 at the point of the central frequency. This justifies the use of negative chirp in the model for the measurements performed with pulse that yielded the highest currents J0. We recall that the model from [1] used for fitting the CEP landscape measurements does not consider the whole spectral phase but deals only with a point estimate at the laser central frequency. This is how we understand slight mismatch between the Cr values reached from the d-scan reconstruction and CEP landscape fitting. Additionally, we show how the point estimate of chirp changes by adding fused silica in the beamline. We calculated an addition to the reconstructed phase of the equivalent of thickness d of the glass, resulting phase is showed in FigSI. 7. One can see that the phase curvature, hence the evaluated Cr can be adjusted and even increased by adding 0.5 mm of fused silica as the Cr in this case reduces almost to zero.

Chromatic aberration of SLM
Measurement of a beam size as a function of the color components of the spectra clearly shows the non-trivial chromatic characteristic of the few-cycle laser beam under investigation. Moreover, on account of the SLM, that is by definition causing the wavelength dependent phase shift, we are able to change the beam size vs. wavelength characteristic. In FigSI. 8 we show a measurement of beam sizes (FWHM in intensity) as a function of frequency (wavelength). The measurement was done with a set of 6 interference filters (10 nm FWHM of transmission bandwidth) at a distance of 1.370 m from the SLM. One can see that the dependence of beam size on frequency changed for beams produced with no SLM pattern and with SLM lensing pattern. The beam presented in FigSI. 8 was used to produce the measurements in the main manuscript in Figs. 2 and 4.

Discussing capabilities of SLM for CEP sculpting for few-cycle lasers based on hollow-core fiber postcompression
We analyzed the possibility to apply the SLM method for few-cycle lasers based on hollow-core fiber postcompression. The key is to address the chromatic aberrations being present in the fibre output beam as they also influence parameters g and γ. Therefore, the SLM should be able to manipulate a certain range of color-dependent phase shifts across the size of the beam. As a representative example, we can consider laser beam characteristics similar to the case presented by Alonso et al. [10]. In FigSI. 9(b) we mimic the case from Fig. 5(b) of that article. The figure shows the wavefront across the beam radius for two selected colors: 600 and 900 nm. One can see that the blue components are more diverging, and the range of the wavefront curvature reaches about 20 radians with a difference of 7.5 radians between the two colors. Applying a curved pattern to the SLM would cause a retardation while in the center the blue components would be more retarded than the red ones, see FigSI. 9(a). (Note that in this example, the pattern is an inverted version of the one used in Fig. 5 of the main manuscript). Consequently, the chromatic aberration can be reduced by application of a curved pattern on the SLM as the SLM induces enough phase shift to invert the difference between the color components, see panel FigSI. 9(c), where the phase difference (black line) between the two colors is flatter than in FigSI. 9(b). At the same time, the SLM pattern can be sculpted further in order to achieve a custom CEP spatial distribution in a similar manner which is presented in Fig. 6 of the main manuscript. In case a system possesses greater aberrations than considered in this example, one would need to find ways to precompensate this by other means, e.g., with lenses.

Laser beam polarization state and probe's linear polarization-orientation dependence
One can expect a polarization sensitivity of the CEP-scanning probe. With this having in mind, we first carefully characterized a polarization state of our linearly polarized laser beam. We performed a rotation scan with a polarizer to obtain the extinction ratio between the minimum and maximum transmitted power yielding 0.2 %, see FigSI. 10(a). Thus, the investigated laser beam was having a clean linear polarization. Then, we investigated the polarization rotation response of the probe. We define θ as the angle between the polarization direction and the sample axis defined as a line connecting the tips of the two opposing electrodes. To measure the dependence of the CEP-dependent current J0 as a function of θ we rotated step-wise the sample about its axis and acquired the current as a function of spatial coordinates x and y, and found a maximum of obtained values J0(x,y). This is necessary as it is difficult to overlay the center of the sample with the rotation axis. As a result, we observe a decreasing current following approximately the relationship J0 ∝ cos(θ), see FigSI. 10(b).
FigSI. 10 (a) Measurement of polarization state of the laser beam used in the experiment. The plot shows the measured power after a polarizer as a function of its rotation α. α = 0 is a horizontal direction in the lab frame. Points are fitted with a cosine function (green line). The extinction was determined to be 0.2 %. (b) Extinction of the CEP-dependent current J0 as a function of the sample orientation θ. The vector connecting the two opposing electrodes is parallel to the laser polarization direction when θ = 0°. The measured points are accompanied with a cos(θ) function as an eye guide.