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Ultrafast optical pulse shaping using dielectric metasurfaces

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Science  31 May 2019:
Vol. 364, Issue 6443, pp. 890-894
DOI: 10.1126/science.aav9632

Metasurfaces get ultrafast pulses into shape

Nanostructured metasurfaces have been designed to function as many passive optical elements. Now, Divitt et al. demonstrate that metasurfaces can also be operated as time-dependent active optical elements. They used an array of dielectric metasurfaces to demonstrate pulse shaping of ultrashort (femtosecond) pulses in the near-infrared by manipulating the phase and amplitude of the frequency components. The results present a path for the development of dynamic metasurfaces as a platform for miniaturized optical technology with advanced time-dependent functionality.

Science, this issue p. 890

Abstract

Advances in ultrafast lasers, chirped pulse amplifiers, and frequency comb technology require fundamentally new pulse-modulation strategies capable of supporting unprecedentedly large bandwidth and high peak power while maintaining high spectral resolution. We demonstrate how dielectric metasurfaces can be leveraged to shape the temporal profile of a near-infrared femtosecond pulse. Finely tailored pulse-shaping operations, including splitting, compression, chirping, and higher-order distortion, are achieved using a Fourier-transform setup embedding metasurfaces able to manipulate, simultaneously and independently, the amplitude and phase of the constituent frequency components of the pulse. Exploiting metasurfaces to manipulate the temporal characteristics of light expands their impact and opens new vistas in the field of ultrafast science and technology.

Developments of ultrafast lasers that produce a train of optical pulses in the time domain, or equivalently a comb of closely spaced spectral lines in the frequency domain, have led to revolutionary advances in areas such as high-field physics (1), quantum optics (2, 3), and frequency metrology (4). These advances are enabled by the development of pulse-shaping techniques that began with dispersion compensation (5, 6) and eventually achieved customizable shaping of pulses through manipulation in either the time domain (710) or the frequency domain (1114). Because of the broadband nature of ultrafast pulses, the most common embodiment of pulse shaping involves some form of dispersion engineering, such as pulse compression for coherent communication (15) or nonlinear microscopy (16), and pulse stretching for chirped pulse amplification (17). Furthermore, optical arbitrary waveform generation through arbitrary control over the amplitude and phase of individual frequency comb lines (18) enables a broad range of applications such as coherent manipulation of quantum mechanical processes (1921), frequency-comb spectroscopy (22), and ultrafast communications (23). Among the various pulse-shaping techniques, Fourier-transform pulse shaping, which synthesizes optical pulses through parallel manipulation of spatially separated spectral components, has been the most widely adopted (11). This form of pulse shaping typically uses a liquid crystal–based spatial light modulator, which offers dynamic control over the optical amplitude and phase. Recently, dielectric metasurfaces—ultrathin, planar optical elements composed of an array of dielectric nanostructures—have emerged as a promising technology for arbitrary control over the amplitude, phase, and polarization of light for spatial-domain wavefront manipulation (2426). By embedding a dielectric metasurface in the focal plane of a Fourier-transform (spectral dispersing-recombining) setup, we implement and demonstrate metasurface-enabled pulse shapers able to tailor the temporal profile of an ultrafast optical pulse. The metasurface is formed from arrays of dielectric nanopillars tailored to impart, simultaneously and independently, a designed phase shift and transmittance specific to each frequency of the spectrally dispersed pulse.

Our Fourier-transform pulse shaper transforms a time-domain waveform f(t) into a targeted waveform g(t) by transmission through a tailored metasurface that physically implements a complex masking function ϒ(ω) relating the respective complex spectra F(ω) and G(ω) of the input and output waveforms according to G(ω) = ϒ(ω)F(ω). The metasurface is designed to operate on near-infrared ultrafast pulses having spectral components contained within an ultrawide wavelength range spanning from λmin = 700 nm to λmax = 900 nm. The various pulse-shaping functions are demonstrated using as inputs either a transform-limited pulse of ~10 fs duration generated by a Ti:sapphire oscillator (full width at 10th-maximum bandwidth of ~80 THz, centered at 800 nm) or its temporally stretched form induced by passage through a 5-mm-thick glass slab. In the Fourier-transform setup (Fig. 1A), the input optical pulse is first spectrally dispersed by a grating. Each angularly separated frequency component of the pulse is then focused by an off-axis metallic parabolic mirror onto a specific lateral position (along the x direction) in the focal plane of the mirror, yielding an elongated focal spot along the x direction, of length ~2.2 cm, where the wavelength varies from λmin to λmax according to a quasi-linear function λ(x) (fig. S1). Along the orthogonal y direction in the focal plane, the beam remains undispersed and confined to an astigmatism-limited maximum width of ~200 μm (fig. S2). A metasurface implementing the targeted masking function ϒ(ω), of rectangular dimensions wx = 2.2 cm and wy = 300 μm, is positioned in the focal plane centered on the beam. After passing through the metasurface and undergoing local phase shift and amplitude transformation, the spectral components of the beam are recombined using a second parabolic mirror and grating, yielding an output pulse of modified temporal shape as characterized by direct electric-field reconstruction using spectral-phase interferometry (27).

Fig. 1 Ultrafast optical pulse shaping using a dielectric metasurface.

(A) Schematic of a Fourier transform pulse-shaping setup, consisting of a pair of diffraction gratings, a pair of parabolic mirrors, and a pulse-shaping metasurface. The metasurface is divided into N superpixels Sk (indexed k = 1, 2, … N) contiguously arranged along the x direction. An input optical pulse upon propagating through this setup is transformed into an output pulse of tailored temporal characteristics. (B) Schematic of metasurface unit cell of superpixel Sk (lattice constant pk) consisting of (i) a rectangular Si nanopillar (of uniform height H = 660 nm), located on one side of a fused-silica substrate, and (ii) an Al wire-grid linear polarizer (wire pitch ppol = 200 nm, wire thickness = 150 nm, duty cycle = 40%) on the other side of the substrate. (C) Schematic of the top view of a metasurface superpixel unit cell indicating the in-plane dimensions Lx,k and Ly,k and the rotation angle θk of a Si nanopillar.

Arbitrary tailoring of the temporal profile of an ultrafast pulse requires control of both the spectral phase and amplitude of the pulse. A metasurface-enabled pulse shaper can achieve this by use of a constituent metasurface that imparts spatially varying phase ϕ(x) and transmission amplitude a(x) to the lateral positions of the focal spot corresponding to different wavelengths, yielding a masking function:ϒ[ω(x)]=a(x) exp[iϕ(x)](1)where ω(x) = 2πc/λ(x) and c is the speed of light in free space. To implement the targeted masking function ϒ[ω(x)], we divide the metasurface into N superpixels contiguously arranged over a 2.2-cm-long distance along the x direction, where each superpixel Sk (indexed k = 1, 2, … N and centered at position xk) is designed to impart phase shift ϕk = ϕ(xk) and transmission amplitude ak = a(xk) to the kth wavelength subrange, centered at λk = λ(xk), of the N consecutive subranges constituting the full spectrum of the pulse. The choice of N = 660 superpixels (each of length 34 μm) defines N independently controllable spectral subranges of respective bandwidth 0.3 nm, ensuring operation at the upper limit of the spectral resolution (~140 GHz) given by the specific design of the Fourier-transform setup (28). Each superpixel consists of a square lattice (lattice constant pk) of identical polycrystalline silicon nanopillars of rectangular cross section and equal height H = 660 nm (Fig. 1B), which act as phase-delay and polarization-manipulating waveguides, and an aluminum wire-grid polarizer (fig. S3), which maps polarization to amplitude. The phase shift ϕk and transmission amplitude factor ak imparted by superpixel k are set respectively by the in-plane dimensions (Lx,k and Ly,k) and in-plane rotation angle θk of the dielectric nanopillars (Fig. 1C). The nanopillars and wire-grid polarizer are fabricated on either side of a fused-silica substrate using electron beam lithography followed by reactive ion etching (28). Polycrystalline silicon was selected for its large refractive index and low optical absorption across the entire near-infrared spectral range (fig. S4); aluminum was selected for its environmental stability, ease of fabrication, and low absorption loss; and fused silica was selected for its low refractive index, low optical dispersion, and optical isotropy.

To generate an arbitrary masking function ϒ of the form described in Eq. 1, we use a scheme in which the phase shift ϕk and transmission amplitude ak at each superpixel can be generated independently over the full range of possible values ϕk ∈ [–π, π] and ak ∈ [0, 1]. This is achieved, under the simple constraint of a linearly polarized input pulse (electric field oriented along the x direction), by tailoring each nanopillar to act as a half-wave plate (HWP), which, in combination with the wire-grid polarizer, allows ϕk to be controlled only by Lx,k and Ly,k, and ak to be controlled only by θk. Note that the polarization state of any local spectral component exiting the polarizer after passage through a metasurface pillar, having arbitrary rectangular profile and rotated by angle θ, can be expressed by the Jones vector (see supplementary text):J=[exp(iϕx)cos2θ+exp(iϕy)sin2θ0](2)where ϕx and ϕy are the phase shifts for θ = 0° and θ = 90°, respectively, and x-polarized incidence is assumed. Introducing the HWP condition ϕx – ϕy = ±π in Eq. 2—through appropriate choice of Lx and Ly—leads to an output-wave Jones vector given byJ=[exp(iϕx)cos(2θ)0](3)This vector describes an x-polarized output wave of phase shift and amplitude determined by the independent variables ϕx and θ, respectively, for which the exit phase shift ϕx stays constant as the HWP is rotated by θ.

Rectangular silicon nanopillars of each superpixel Sk are designed to approximate HWPs at the pixel central operating wavelength λk while also providing the specific phase shift ϕk targeted for Sk (see fig. S5 for the discussion of the choice of the lattice constant pk). This is achieved by setting, on the basis of rigorous coupled-wave analysis [RCWA (29)] at each wavelength λk, the in-plane pillar dimensions (Lx, Ly) to the values that simultaneously yield ϕx = ϕk and a local minimum of the figure-of-merit function FOM given byFOM(Lx,Ly)=|ax(Lx,Ly) exp[iϕx(Lx,Ly)]ay(Lx,Ly) exp[iϕy(Lx,Ly)]exp(iπ)|2(4)where ax and ay represent the transmission amplitude of a given pillar at θ = 0° and θ = 90°, respectively. The result of this minimization operation yields, at each wavelength λk, a parametric curve [Lx,HWPk); Ly,HWPk)] where ϕk ∈ [–π, π]. The resulting curve, displayed for the case λk = 800 nm (Fig. 2A), consists of two separate branches (Fig. 2A, dashed and solid black curves). Performing the minimization at all wavelengths λk ∈ [λmin, λmax] yields two functions, Lx,HWPk, λk) and Ly,HWPk, λk), where ϕk ∈ [–π, π] (Fig. 2B and fig. S6). Based on the targeted phase shift function ϕkk), these functions are then used to set the nanopillar in-plane dimensions Lx,k and Ly,k for each superpixel Sk. Finally, to implement the targeted transmission amplitude ak at each superpixel Sk, the rotation angle of all HWP nanopillars forming Sk is set to θk = cos–1(ak)/2. Numerical simulations of ϕk over the nanopillar rotation range θk ∈ [0, 45°] confirm the relative independence of ϕk from θk (and hence from ak), as demonstrated for the specific case of a nanopillar array optimized for HWP operation at λk = 800 nm and targeted phase shift ϕk = 0 (Fig. 2C).

Fig. 2 Pulse-shaping metasurface enabling simultaneous and independent control of spectral phase and amplitude.

(A) HWP figure of merit (FOM) versus nanopillar in-plane dimensions (Lx, Ly), plotted in logarithmic scale at a targeted wavelength λ = 800 nm. Loci of optimal performance (Lx,HWP and Ly,HWP), indicated by dashed and solid black paths, are given by the local minima of FOM. The optimal locus yielding the targeted phase shift ϕ = 0 at λ = 800 nm is indicated by the red star (Lx = 185 nm and Ly = 114 nm). (B) Color maps depicting the values of Lx and Ly minimizing FOM versus phase shift ϕ ∈ [–π, π] and wavelength λ ∈ [700 nm, 900 nm]. The dashed and solid black lines at λ = 800 nm are the optimal values (Lx,HWP and Ly,HWP) transposed from (A); the red stars, also transposed from (A), indicate the loci of targeted phase shift ϕ = 0. (C) Superpixel-conferred amplitude ak and phase ϕk versus nanopillar rotation angle θ, assuming λ = 800 nm and in-plane nanopillar dimensions Lx = 185 nm and Ly = 114 nm as calculated by RCWA. (D) Schematic of a metasurface (labeled I), implemented to split an optical pulse into two time-separated replicas with separation Δt = 30 fs. The metasurface (length wx = 2.2 cm and width wy = 300 μm) consists of N = 660 superpixels each consisting of an array of nanopillars with rectangular in-plane cross section and specific angular orientation (represented by orange cuboids) backed by an Al wire-grid polarizer (represented by blue vertical lines). Each superpixel is illuminated by a specific spectral component of the pulse (represented by blue, green, and red arrows). (E) A representative scanning electron microscopy (SEM) image of metasurface I showing a detail of the arrays of Si nanopillars at the boundary between superpixels S34 and S35. Scale bar, 1 μm. (F to H) Experimental demonstration of pulse splitting targeting Δt = 30 fs, for an input Gaussian pulse of length 10 fs. The targeted spectral phase ϕkI and transmission amplitude akI required to achieve the desired Δt are displayed in (F) and (G), respectively (solid blue lines). The lateral in-plane nanopillar dimensions (Lx,kI and Ly,kI) to achieve targeted ϕkI for each superpixel are obtained using the color map in (B) (via overlaid solid white line). The rotation angle θkI for each superpixel is set to cos1(akI)/2 to achieve the targeted akI. The metasurface designed and implemented with these dimensions yields simulated (dotted red lines) and measured (solid red lines) spectral phases (F) and transmission amplitudes (G) that closely match the targeted values. (H) represents the temporal profile of targeted, simulated, and measured output pulses (solid blue, dotted red, and solid red lines, respectively) emerging from a pulse shaper incorporating metasurface I, along with that of the input pulse (solid yellow line).

Having mapped the full set of possible phase, transmission amplitude, and wavelength combinations (ϕk, ak, and λk) to the corresponding set of nanopillar geometric parameters (Lx,k, Ly,k, and θk), we implement, as an illustrative example of the flexibility of simultaneous spectral-phase and amplitude manipulation, a HWP-based metasurface (designated as metasurface I) that enables the Fourier-transform pulse shaper to split a single optical pulse into two replicas time-separated by an interval Δt = 30 fs (Fig. 2, D and E). The corresponding time-shift operation can be implemented via a sinusoidal masking modulation ϒ(ω) = cos[π(ω – ω0)/Δω], where ω0 = 2πc0 and Δω = 2π/Δt. The metasurface implementation of the required positive and negative excursions for ϒ(ω) is achieved via combination of a targeted stepwise phase function alternating between 0 and π with dependenceϕkI=ϕI(λk)=arg[ϒ(2πc/λk)] (Fig. 2B, white line, and Fig. 2F) and an always-positive, targeted transmission amplitude akI=aI(λk)=|ϒ(2πc/λk)| (Fig. 2G). The metasurface pillar dimensions and their rotation angles (fig. S5) for each superpixel are respectively derived through lookup (Fig. 2B) of the functions Lx,kI=Lx,HWP[ϕI(λk),λk] and Ly,kI=Ly,HWP[ϕI(λk),λk], and by settingθkI=cos1(akI)/2. RCWA simulations based on these dimensions confirm the targeted phase and amplitude functions (Fig. 2, F and G). The fabricated metasurface is characterized, respectively, by a measured spectral-phase shift ϕI(λ) and amplitude aI(λ) that closely match the targeted and simulated values (Fig. 2, F and G). Time-domain reconstruction assuming a Gaussian input pulse of length 10 fs yields simulated and measured output pulses (Fig. 2H) having two distinct peaks separated, respectively, by Δt = 30.9 fs and 30.7 (±0.8) fs. Although the peak separation in each case is close to the targeted value, the advanced peak is attenuated with respect to the retarded peak in both the simulated and measured cases, as a result of suboptimal HWP implementation at the edges of the pulse spectrum.

A common embodiment of pulse shaping in ultrafast science involves compression or stretching of an optical pulse. This can be achieved by using a metasurface designed to impart a constant transmission amplitude a independent of position (i.e., frequency) and a spatially varying phase ϕ(x), yielding a phase-only masking function ϒP(x) given byϒP[ω(x)]=a exp[iϕ(x)](5)Near-unity transmission amplitude, a ≈ 1, is achieved by setting, for each superpixel Sk, the nanopillar rotation angle to θk = 0. Eliminating the wire-grid polarizer, which is no longer required for a phase-only masking function, furthermore helps to maximize the absolute transmission amplitude. Finally, phase-only operation relaxes the restriction that the nanopillars act as HWPs, and therefore the requirement that Lx,k and Ly,k be set to different values. Setting Lx,k = Ly,k = Lk for all nanopillars of any given superpixel Sk simplifies the metasurface design procedure by reducing the parameter optimization space to one dimension, and yields a metasurface with a polarization-independent masking function. Using RCWA simulations that assume a value for the lattice constant p = λ/2, the nanopillar-induced complex transmission a exp(iϕ) is calculated as a function of nanopillar side length L and wavelength λ, where λ ∈ [λmin, λmax] and L ∈ [0, λ/2]. This calculation yields a near-unity amplitude transmission function a(ϕ, λ) (fig. S7), along with a phase shift function ϕ(L, λ) that spans the full range [0, 2π] and can be inverted to provide a nanopillar dimension lookup function L(ϕ, λ) (Fig. 3A).

Fig. 3 Pulse-shaping metasurfaces enabling control of only the spectral phase.

(A) Color map depicting the values of nanopillar side length L versus phase shift ϕ ∈ [0, 2π] and wavelength λ ∈ [700 nm, 900 nm], calculated using the RCWA method. (B) Schematic of a phase-control metasurface (labeled II), implemented to compress a positively chirped optical pulse of length ~73 fs to its transform limit. The metasurface (length wx = 2.2 cm, width wy = 300 μm) consists of N = 660 superpixels, each consisting of an array of nanopillars with square in-plane cross section (represented by orange cuboids). (C) A representative SEM image of metasurface II showing a detail of the array of Si nanopillars within superpixel S67. Scale bar, 500 nm. (D) Characterization of salient spectral phases of pulse compression enabled by metasurface II. ϕin, measured (solid yellow line): spectral phase of the positively chirped input pulse to the pulse shaper. ϕout, targeted (solid blue line): spectral phase of targeted transform-limited output pulse. ϕkII, targeted (dashed green line): quadratic metasurface phase map approximating –ϕin to achieve targeted ϕout. The corresponding in-plane nanopillar dimensions (LkII) to achieve targeted ϕout for each superpixel are obtained using the color map in (A) (via overlaid solid white line). ϕII, measured (solid green line): experimentally characterized metasurface-induced spectral-phase shift closely matching targeted ϕkII. ϕout, measured (solid red line): spectral phase of the pulse emerging from the pulse shaper closely matching targeted ϕout representative of a transform-limited pulse. (E) Temporal profile of the targeted and measured output pulse (solid blue and solid red line, respectively) emerging from the pulse shaper incorporating metasurface II given the positively chirped input pulse (solid yellow line). (F) Schematic of a cascaded sequence of phase control metasurfaces, respectively quadratic (labeled III) and cubic (labeled IV), implemented to impart a third-order polynomial phase function to a transform-limited optical pulse of length ~10 fs. (G) Characterization of salient spectral phases for distortion of a transform-limited pulse enabled by metasurfaces III and IV individually and in a cascaded configuration. ϕout, targeted (solid blue line): given by ϕout(λ) = βIII[ω(λ) – ω0]2 + βIV[ω(λ) – ω0]3, where βIII = –200 fs2 · rad–1 and βIV = –400 fs3 · rad–2. ϕIII and ϕIV, measured (dashed magenta and cyan lines, respectively): measured spectral-phase shifts induced by metasurfaces III and IV individually, designed to match ϕkIII=βIII[ω(λk)ω0]2 and ϕkIV=βIV[ω(λk)ω0]3, respectively. ϕIII, measured + ϕIV, measured (solid green line): spectral-phase shift mathematically predicted for cascaded metasurfaces III and IV. ϕout, measured (solid red line): spectral phase of the pulse emerging from the pulse shaper, closely matching targeted ϕout. (H) Temporal profile of the targeted and measured output pulses (solid blue and red lines, respectively) emerging from the pulse shaper incorporating cascaded metasurfaces III and IV given a transform-limited input pulse (solid yellow line).

Having determined L(ϕ, λ), we implement and demonstrate, as an example of metasurface-enabled dispersion engineering, a phase-control metasurface (designated as metasurface II) that can compress a positively chirped optical pulse to its transform limit (Fig. 3, B and C). Such an input pulse is generated by passing a 10-fs-wide transform-limited pulse through a 5-mm-thick glass slab, yielding a spectral phase ϕin(λ) with an upward-opening, approximately quadratic shape (Fig. 3D)—characteristic of normal material dispersion—and a time-stretched, chirped pulse of length ~73 fs (Fig. 3E). This dispersion can be compensated to the lowest order using a phase-control metasurface with a quadratic phase function ϕII(λ) approximating the function –ϕin(λ). A least-squares fit assuming ϕII(λ) = βII[ω(λ) – ω0]2, where ω(λ) = 2πc/λ, yields weighting factor βII = –150 fs2 · rad–1 (Fig. 3D). The metasurface pillar dimensions for each superpixel (fig. S8) are set by computing the function LkII=L[ϕII(λk),λk], where ϕIIk) is graphically represented by the solid white line in Fig. 3A, yielding an implemented phase shift of ϕkII=ϕII(λk) for each superpixel Sk, where k = 1 to N. The output pulse emerging from the metasurface-enabled pulse shaper is characterized, as targeted, by a flat spectral-phase function ϕout(λ) ≈ [ϕin(λ) + ϕII(λ)] (Fig. 3D) and a temporal pulse width ≈ 10.6 (±0.3) fs, approximating recompression of the pulse to its transform-limited state prior to passage through the glass slab (Fig. 3E). The pulse compression achieved here demonstrates the ability of a single phase-control metasurface to compensate for normal dispersion via a tailored anomalous dispersion transformation.

Ultrafast pulses with phase functions having both quadratic and higher-order terms are widely exploited in applications such as quantum coherent control (30) and pulse stretching (31). We demonstrate how a metasurface-enabled pulse shaper embedding a series of cascaded phase-control metasurfaces can implement an arbitrary higher-order polynomial phase function, where each term of the polynomial is implemented by one of the metasurfaces. As an illustrative example, a targeted third-order spectral-phase function, ϕtargeted(λ) = βIII[ω(λ) – ω0]2 + βIV[ω(λ) – ω0]3, is implemented by inserting into the focal volume of the pulse shaper two cascaded metasurfaces (designated as metasurfaces III and IV; Fig. 3F) having the same number of superpixels (k = 1 to N) and respectively configured to confer quadratic and cubic spectral-phase shifts ϕkIII=βIII[ω(λk)ω0]2 and ϕkIV=βIV[ω(λk)ω0]3 at each superpixel, where βIII = –200 fs2 · rad–1 and βIV = –400 fs3 · rad–2. Characterization of the spectral-phase shift imparted by the pulse shaper, using a transform-limited pulse as input, yields the spectral dependence ϕout(λ) ≈ ϕtargeted(λ), confirming implementation of the targeted third-order polynomial phase function (Fig. 3G). The time-domain waveforms (Fig. 3H) reveal stretching and anomalous dispersion of the output pulse with respect to the input pulse (attributable to the quadratic component of the phase function), along with higher-order distortion as evidenced by the appearance of wiggles at the leading edge of the pulse (attributable to the cubic phase component). For reference, the spectral phases for metasurface III only (ϕIII) and metasurface IV only (ϕIV) are individually characterized (Fig. 3G), yielding ϕIII(λ) + ϕIV(λ) ≈ ϕout(λ), consistent with the assumption of linearity underlying the cascaded-metasurface pulse-shaping scheme. Given the elongated shape of a pulse-shaping metasurface in the x direction, it is then straightforward to implement a multi-masking function (MMF) sample formed of multiple metasurfaces arrayed in the y direction on the same fused-silica substrate. This allows, for example, implementation of two MMF samples consisting, respectively, of parallel arrays of quadratic and cubic metasurfaces with different weighting factors β. Cascading the two samples in the focal volume of the pulse shaper and translating a specific metasurface of each sample into the beam enables reconfigurable synthesis of a finely tailored third-order polynomial phase function (fig. S9).

By further configuring the metasurface pixel array to accommodate and process spectra dispersed to two spatial dimensions (14), we expect that the number of individually controllable spectral features can be increased by several orders of magnitude, thereby allowing line-by-line shaping of frequency combs with ultranarrow comb spacing and ultrawide bandwidth. Expanding metasurfaces into the realm of time-domain manipulation will amplify the impact of their application as two-dimensional wavefront shapers and will open new vistas in the field of ultrafast science and technology.

Supplementary Materials

science.sciencemag.org/content/364/6443/890/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S9

References (3234)

References and Notes

  1. See supplementary materials.
Acknowledgments: S.D., W.Z., C.Z., H.J.L., and A.A. thank N. Zhitenev, J. Strait, Lu Chen, T. Xu, Y. Liang, A. Solanki, F. Habbal, and Lei Chen for valuable discussions. Funding: S.D., W.Z., C.Z., and A.A. acknowledge support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Physical Measurement Laboratory, award 70NANB14H209, through the University of Maryland. Author contributions: All authors contributed to the design of the experiments. The measurements were performed by S.D., W.Z., and A.A. Simulations were performed by S.D., W.Z., and C.Z. with further analysis by H.J.L. and A.A. Device fabrication were performed by W.Z. and C.Z. All authors contributed to the interpretation of results and participated in manuscript preparation. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are available in the manuscript or the supplementary materials.
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