Arbitrary Space-Time Wave Packet Synthesis

Dielectric metasurfaces, composed of deep-subwavelength nanostructures, can sculpt the phase, amplitude, and polarization of light at the nanoscale. Their multifunctional response at the single-pixel level, combined with compact form-factor and integrability with other CMOS compatible devices make them key components for miniaturized photonic platforms, leading to numerous applications in spatial domain wavefront manipulation of light [1]. Recently, temporal-domain shaping of scalar waveforms of a linearly polarized ultrafast pulse has been demonstrated using dielectric metasurfaces [2, 3]. Here, we show, both theoretically and experimentally, that a single-layer transmission-mode dielectric metasurface can be leveraged to simultaneously and independently tailor the complete spatiotemporal properties of a near-infrared femtosecond pulse. This approach offers the most complete and general control of light field across an ultrabroad bandwidth, enabling synthesis of arbitrary space-time wave packets.<br/>The spatiotemporal profile of a <i>p</i>-polarized femtosecond pulse of ≈10 fs duration (full-width at tenth-maximum bandwidth of ≈ 80 THz, centered at 800 nm) is tailored by manipulating the constituting discrete frequency lines. A 4-<i>f</i> Fourier-transform pulse shaper spatially disperses and focuses the frequency lines at the Fourier plane, where a metasurface is positioned to implement a complex masking function sampled by 200 super-pixels. Each super-pixel contains a two-dimensional (2D) array of rectangular silicon nanopillars orientated at 45° with respect to the horizontal direction, providing parallel phase modulation along the two birefringent axes. In this way, each super-pixel can independently impart a 2D spatial phase function as well as an overall phase-shift to the two orthogonal polarization components of frequency lines that reside within the super-pixel. The shaped frequency lines are then subsequently recombined into a spatiotemporally engineered femtosecond pulse.<br/>This approach, leveraging ultra-high spectral resolution of a Fourier-transform pulse shaper and multifunctional responses at the nanoscale provided by the dielectric metasurface, offers ready design flexibility that can enable the synthesis of a vast variety of complex ultrafast spatiotemporal wave packets. To demonstrate the versatility of this approach, exotic femtosecond pulses, exhibiting a rich set of time-varying instantaneous polarization states and structured wavefronts within a single pulse, are designed and experimentally demonstrated. Comprehensive analysis, including numerical simulations and analytical modeling, are also performed to explain their spatiotemporal evolution.<br/>In conclusion, we have demonstrated tailoring of both the temporal and spatial degrees of freedom of an ultra-broad bandwidth, near-infrared femtosecond pulse using a single-layer transmission-mode dielectric metasurface. Such an approach further promotes the already intriguing applications of metasurfaces, revealing new possibilities in the field of ultrafast science and technology.<br/>[1] N. Yu and F. Capasso, <i>Nature Materials</i> <b>13</b>, 139 (2014).<br/>[2] S. Divitt, W. Zhu, C. Zhang, H. J. Lezec, and A. Agrawal, <i>Science</i> <b>364</b>, 890 (2019).<br/>[3] M. Ossiander, Y.-W. Huang, W. T. Chen, Z. Wang, X. Yin, Y. A. Ibrahim, M. Schultze, and F. Capasso, <i>Nature Communications</i> <b>12</b>, 6518 (2021).