## 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 (*7*–*10*) or the frequency domain (*11*–*14*). 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 (*19*–*21*), 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 (*24*–*26*). 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 λ_{min} = 700 nm to λ_{max} = 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 λ_{min} to λ_{max} 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 *w _{x}* = 2.2 cm and

*w*= 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 (

_{y}*27*).

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:*x*) = 2π*c*/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 *S _{k}* (indexed

*k*= 1, 2, …

*N*and centered at position

*x*) is designed to impart phase shift ϕ

_{k}*= ϕ(*

_{k}*x*) and transmission amplitude

_{k}*a*=

_{k}*a*(

*x*) to the

_{k}*k*th wavelength subrange, centered at λ

*= λ(*

_{k}*x*), of the

_{k}*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

*p*) of identical polycrystalline silicon nanopillars of rectangular cross section and equal height

_{k}*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 ϕ

*and transmission amplitude factor*

_{k}*a*imparted by superpixel

_{k}*k*are set respectively by the in-plane dimensions (

*L*

_{x}_{,}

*and*

_{k}*L*

_{y}_{,}

*) and in-plane rotation angle θ*

_{k}*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 (*

_{k}*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 ϕ* _{k}* and transmission amplitude

*a*at each superpixel can be generated independently over the full range of possible values ϕ

_{k}*∈ [–π, π] and*

_{k}*a*∈ [0, 1]. This is achieved, under the simple constraint of a linearly polarized input pulse (electric field oriented along the

_{k}*x*direction), by tailoring each nanopillar to act as a half-wave plate (HWP), which, in combination with the wire-grid polarizer, allows ϕ

*to be controlled only by*

_{k}*L*

_{x}_{,}

*and*

_{k}*L*

_{y}_{,}

*, and*

_{k}*a*to be controlled only by θ

_{k}*. 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):*

_{k}*and ϕ*

_{x}*are the phase shifts for θ = 0° and θ = 90°, respectively, and*

_{y}*x*-polarized incidence is assumed. Introducing the HWP condition ϕ

*– ϕ*

_{x}*= ±π in Eq. 2—through appropriate choice of*

_{y}*L*and

_{x}*L*—leads to an output-wave Jones vector given by

_{y}*x*-polarized output wave of phase shift and amplitude determined by the independent variables ϕ

*and θ, respectively, for which the exit phase shift ϕ*

_{x}*stays constant as the HWP is rotated by θ.*

_{x}Rectangular silicon nanopillars of each superpixel *S _{k}* are designed to approximate HWPs at the pixel central operating wavelength λ

*while also providing the specific phase shift ϕ*

_{k}*targeted for*

_{k}*S*(see fig. S5 for the discussion of the choice of the lattice constant

_{k}*p*). This is achieved by setting, on the basis of rigorous coupled-wave analysis [RCWA (

_{k}*29*)] at each wavelength λ

*, the in-plane pillar dimensions (*

_{k}*L*,

_{x}*L*) to the values that simultaneously yield ϕ

_{y}*= ϕ*

_{x}*and a local minimum of the figure-of-merit function*

_{k}*FOM*given by

*a*and

_{x}*a*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 λ

_{y}*, a parametric curve [*

_{k}*L*

_{x}_{,HWP}(ϕ

*);*

_{k}*L*

_{y}_{,HWP}(ϕ

*)] where ϕ*

_{k}*∈ [–π, π]. The resulting curve, displayed for the case λ*

_{k}*= 800 nm (Fig. 2A), consists of two separate branches (Fig. 2A, dashed and solid black curves). Performing the minimization at all wavelengths λ*

_{k}*∈ [λ*

_{k}_{min}, λ

_{max}] yields two functions,

*L*

_{x}_{,HWP}(ϕ

*, λ*

_{k}*) and*

_{k}*L*

_{y}_{,HWP}(ϕ

*, λ*

_{k}*), where ϕ*

_{k}*∈ [–π, π] (Fig. 2B and fig. S6). Based on the targeted phase shift function ϕ*

_{k}*(λ*

_{k}*), these functions are then used to set the nanopillar in-plane dimensions*

_{k}*L*

_{x}_{,}

*and*

_{k}*L*

_{y}_{,}

*for each superpixel*

_{k}*S*. Finally, to implement the targeted transmission amplitude

_{k}*a*at each superpixel

_{k}*S*, the rotation angle of all HWP nanopillars forming

_{k}*S*is set to θ

_{k}*= cos*

_{k}^{–1}(

*a*)/2. Numerical simulations of ϕ

_{k}*over the nanopillar rotation range θ*

_{k}*∈ [0, 45°] confirm the relative independence of ϕ*

_{k}*from θ*

_{k}*(and hence from*

_{k}*a*), as demonstrated for the specific case of a nanopillar array optimized for HWP operation at λ

_{k}*= 800 nm and targeted phase shift ϕ*

_{k}*= 0 (Fig. 2C).*

_{k}Having mapped the full set of possible phase, transmission amplitude, and wavelength combinations (ϕ* _{k}*,

*a*, and λ

_{k}*) to the corresponding set of nanopillar geometric parameters (*

_{k}*L*

_{x}_{,}

*,*

_{k}*L*

_{y}_{,}

*, and θ*

_{k}*), 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 Δ*

_{k}*t*= 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 – ω

_{0})/Δω], where ω

_{0}= 2π

*c*/λ

_{0}and Δω = 2π/Δ

*t*. 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 dependence

^{I}(λ) and amplitude

*a*

^{I}(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 Δ

*t*= 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 **ϒ**_{P}(*x*) given by*a* ≈ 1, is achieved by setting, for each superpixel *S _{k}*, the nanopillar rotation angle to θ

*= 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*

_{k}*L*

_{x}_{,}

*and*

_{k}*L*

_{y}_{,}

*be set to different values. Setting*

_{k}*L*

_{x}_{,}

*=*

_{k}*L*

_{y}_{,}

*=*

_{k}*L*for all nanopillars of any given superpixel

_{k}*S*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

_{k}*p*= λ/2, the nanopillar-induced complex transmission

*a*exp(

*i*ϕ) is calculated as a function of nanopillar side length

*L*and wavelength λ, where λ ∈ [λ

_{min}, λ

_{max}] 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).

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 ϕ_{in}(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 ϕ^{II}(λ) approximating the function –ϕ_{in}(λ). A least-squares fit assuming ϕ^{II}(λ) = β^{II}[ω(λ) – ω_{0}]^{2}, where ω(λ) = 2π*c*/λ, yields weighting factor β^{II} = –150 fs^{2} · rad^{–1} (Fig. 3D). The metasurface pillar dimensions for each superpixel (fig. S8) are set by computing the function ^{II}(λ* _{k}*) is graphically represented by the solid white line in Fig. 3A, yielding an implemented phase shift of

*S*, where

_{k}*k*= 1 to

*N*. The output pulse emerging from the metasurface-enabled pulse shaper is characterized, as targeted, by a flat spectral-phase function ϕ

_{out}(λ) ≈ [ϕ

_{in}(λ) + ϕ

^{II}(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, ϕ_{targeted}(λ) = β^{III}[ω(λ) – ω_{0}]^{2} + β^{IV}[ω(λ) – ω_{0}]^{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 ^{III} = –200 fs^{2} · rad^{–1} and β^{IV} = –400 fs^{3} · rad^{–2}. Characterization of the spectral-phase shift imparted by the pulse shaper, using a transform-limited pulse as input, yields the spectral dependence ϕ_{out}(λ) ≈ ϕ_{targeted}(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 (ϕ^{III}) and metasurface IV only (ϕ^{IV}) are individually characterized (Fig. 3G), yielding ϕ^{III}(λ) + ϕ^{IV}(λ) ≈ ϕ_{out}(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

This is an article distributed under the terms of the Science Journals Default License.

## References and Notes

**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.