Topology-imprinting in nonlinear metasurfaces

Abstract

Flat optical components, or metasurfaces, have transformed optical imaging, data storage, information processing, and biomedical applications by providing unprecedented control over light-matter interactions. These nano-engineered structures enable compact, multidimensional manipulation of light's amplitude, phase, polarization, and wavefront, producing scalar and vector beams with unique properties such as orbital angular momentum and knotted topologies. This flexibility has potential applications in optical communication and imaging, particularly in complex environments such as atmospheric turbulence and undersea scattering. However, designing metasurfaces for shorter wavelengths, such as visible and ultraviolet light, remains challenging due to fabrication limitations and material absorption. Here, we introduce an innovative concept called topology imprinting using judiciously designed all-dielectric nonlinear optical metasurfaces to replicate desired waveforms at fundamental and harmonic frequencies, opening promising avenues for advanced photonic applications.

Fig. 1.. Design and characterization of topology imprinting concept.

(A) Diagram of polycrystalline silicon meta-atoms (refractive index n = 3.67 at 1550 nm with height H = 258 nm) on a fused silica substrate with the refractive index of n = 1.45. The INHOM-TH persists in the opaque region of the polycrystalline silicon while carrying the desired imprinted phase on the MS with high fidelity. (B) Designed intensity (left), phase distributions (middle), and the imprinted hologram, which is a combination of a grating intended to maximize the first diffraction order and the optical vortex phase with the TC l = 3 in the case of the fundamental beam being an OAM beam (top) and Hopf-link (bottom). The knotted solution was generated by superposing multiple LG modes carrying specific weightings and indices (9). The final phase masks of the phase-only hologram of OAM and Hopf-link were created through the inverse sinc-function encoding technique, including the amplitude profile onto the phase function (63, 64). (C) Scanning electron microscopy image of the meta-atoms (inset) and the MS structures. (D) Diagram of the experimental setup. The 1550-nm central wavelength laser was split into two paths: One beam was shaped to MS scale via lenses, creating structured first-order diffraction beams, and the other was serving as a reference, delayed for interference pattern generation. A 4f system with an iris filters higher orders. For 3D Hopf-link beam analysis, the camera tracks singularities along the beam’s path. The third harmonic’s interference pattern is achieved by focusing the reference beam onto an unpatterned polycrystalline silicon film, producing a Gaussian TH beam.

Fig. 2.. Linear and nonlinear interference measurement of the optical vortices.

(A) Characteristic doughnut-shaped intensity profile of the fundamental vortex beam. (B) Interference pattern of the fundamental vortex and Gaussian beams. The forks-like pattern converting a single line into the interference plot with three lines indicates that the topology of the TH optical vortex is equal to 3. (C) Characteristic doughnut-shaped intensity profile of the TH vortex beam. (D) Interference pattern of the TH vortex and Gaussian beams. The similar fork-like pattern proves that the topology of the TH optical vortex is equal to 3 and completely preserved. (E) Simultaneous generation of OAM beams with charge l = 3 at both fundamental and TH wavelengths. The difference in diffractive angles between the first-order OAM at FF and TH can be explained by the grating equation: The longer FF wavelength presents a larger diffraction angle than the shorter TH wavelength. The first-order FF OAM exhibited an elliptical profile, likely stemming from the camera’s tilted angle being aligned with the propagation angle of the first-order TH OAM.

Fig. 3.. Linear and nonlinear characterization of 3D complex light beams.

(A) Measured intensity distributions of FF Hopf-link at z = 0 plane. The intensity profile matches the theoretical result in Fig. 1B very well. (B) Interferogram of the Hopf-linked field with Gaussian beams at z = 0 plane. The four red spots indicate the fork-like pattern positions where the singularities are. (C) Locating method via interference. Different transverse planes of the optical field along the beam propagation direction are imaged onto the camera by moving the position of the camera. We can map the vorticity lines in 3D space by connecting the singularity positions from each plane. (D) Isolated Hopf-link configured from interference patterns measured by the scanning method shown in (C). (E) Top view of the isolated Hopf-link structure. The cross between the singularities can be noticed. (F) Intensity distributions of TH Hopf Link beam at z = 0 plane. It shows a similar intensity profile as the FF Hopf link in (A). (G) Interferogram of the TH Hopf linked field with Gaussian beams. The four white spots indicate the fork-like pattern positions where the singularities are. (H) Isolated TH Hopf-link configured from interference patterns measured by the same scanning method used for FF. (I) Top view of the Isolated TH Hopf-link structure.