Sculpting ultrafast mid-infrared light for solid-state high harmonic generation

Abstract

The ability to sculpt light in space, time, and polarization has revolutionized studies of light-matter interaction and enabled breakthroughs in optical communication, imaging, and ultrafast science. Among the many degrees of freedom of light, orbital angular momentum (OAM) further expands these capabilities by unlocking new regimes of control in information encoding, particle trapping and manipulation, and symmetry-driven selection rules. However, exploiting OAM to drive nonlinear, non-perturbative effects in solids remains challenging, especially in the mid-infrared (MIR) spectral regime-a key region for accessing these effects in ambient air, where spatial light modulators do not operate. Here, we circumvent this limitation by generating femtosecond, few-cycle MIR Bessel-Gauss vortex (BGV) and perfect optical vortices (POVs), using a robust, static spatial-shaping strategy. By utilizing these beams to drive nonlinear optical processes such as second-harmonic generation (SHG) and high-harmonic generation (HHG) in various solid-state materials, we show that the resulting harmonic beams faithfully inherit the structural characteristics of the drivers: the constant-intensity ring of the POVs is preserved across harmonic orders, while the BGV harmonic beams retain their intrinsic topological charge-dependent intensity profiles. Furthermore, by verifying the linear OAM up-scaling law, we confirm the conservation of OAM during SHG and HHG in solids. These results establish strong-field HHG in solids as a robust platform for synthesizing ultrafast structured harmonic light with controllable, high-value OAM.

Figures (4)

• Figure 1: Simplified experimental setup for the generation and characterization of fs BGV and POV beams. Here, we illustrate the generation of a fs Gaussian beam, centered at $\lambda=$ 3.2 $\mu$m, followed by the generation of the LGV and BGV beams by means of a spiral phase plate (SPP) and an axicon (AX), respectively. The generation is followed by the characterization of both fundamental and POV harmonic beams. (a) conceptualization of the experimental setup that realized the theoretical ideas supporting the experiment design. (d) Resulting spectrum and temporal intensity extracted from the FROG traces frog showing the temporal duration of the pulse after the axicon optical element. SPP: Spiral phase plate, VB: Vortex beam, PK: pickup mirror, $f_f$: focusing lens, $f_c$: collimation lens, SP: spectrometer and CCD: beam profiler.
• Figure 2: Intensity distribution of the fs MIR BGV and POV beams. (a1)-(a5) Intensity distribution of fs BGV beams with values of the TC $l_0=-3,-2$,1,2 and 3. (b1)-(b5) Their corresponding HG intensity distribution after the transformation by a CL, from where we extracted the beam's TC. (c1)-(c5) Intensity distribution of fs POV beams generated from the BGV beams shown in (a1)-(a5). Notice that we used the same beam size value for the BGV beam generated with $l_0=1$ and $l_0=-1$ for completeness, since the latter values were not measured. (d), Comparison between the POV and BGV beam size results for the different TC. Notice that we divided the POV beam radius values by 4 for a better comparison with the BGV beam. The intensity bar on the right side corresponds to the measured temperature produced by the beam in the MIR camera.
• Figure 3: Second-harmonic generation in ZnO and GaSe for fundamental POV and BGV (after background subtraction). (a1)-(a3) and (b1)-(b3) Normalized intensity distribution of the SH BGV and POV beams for a ZnO target, respectively. The driving field carried $l_0=1,-3$, and -5. (c) and (d), SH in GaSe for a fundamental field with values of the TC $l_0=3,5$ and 6. (e) and (f) Summary of the results for ZnO and GaSe, showing the SH POV beam size (full lines) and the SH BGV beam size (dashed lines). We divided the beam radius of the SH POV by 4 to make easily to compare the sizes of the vortex beams. The error bar for all the values corresponds to 5 $\mu$m.
• Figure 4: Non-perturbative harmonics. (a) and (b), The $5^{\text{th}}$ POV and BGV harmonic beams, generated in GaSe, respectively. (c) Comparison between the beam size for different harmonic orders showing that the POV harmonic beams conserve similar beam radius values for a very large range of TCs. (d)-(e) Topological charge measurements in GaSe and ZnO, respectively. For the case of GaSe, we obtained harmonic vortices $q=6$ and 7, with TC as large as $l_q=35$ and 36, when the solid-state HHG process is driven by a fundamental field with $l_0=5$ and 6. There results clearly demonstrate that the up-conversion process can produce harmonics in the infrared-to-visible wavelength spectral range. Additionally, the linear trend followed by the harmonic TC as a function of the fundamental vortex beam TC, supports the conservation of OAM and extend its validity for this particular type of vortex beams. We divided the beam radius of the SH POV by 3 to make easily to compare the sizes of the vortex beams. The error bar for all the values corresponds to 5 $\mu$m.