Ultrafast all-optical tuning of direct-gap semiconductor metasurfaces

Optical metasurfaces are regular quasi-planar nanopatterns that can apply diverse spatial and spectral transformations to light waves. However, metasurfaces are no longer adjustable after fabrication, and a critical challenge is to realise a technique of tuning their optical properties that is both fast and efficient. We experimentally realise an ultrafast tunable metasurface consisting of subwavelength gallium arsenide nanoparticles supporting Mie-type resonances in the near infrared. Using transient reflectance spectroscopy, we demonstrate a picosecond-scale absolute reflectance modulation of up to 0.35 at the magnetic dipole resonance of the metasurfaces and a spectral shift of the resonance by 30 nm, both achieved at unprecedentedly low pump fluences of less than 400 μJ cm–2. Our findings thereby enable a versatile tool for ultrafast and efficient control of light using light.

photodiode was lock-in detected. Recorded values for each wavelength and angle of incidence were divided by the values obtained for a silver mirror. The experimental reflectance spectra are presented in Supplementary Figure 1

Supplementary note 2
Role of two-and three-body recombination in fast relaxation of e-h plasma Eq.(2) of the main text, which represents the plasma recombination dynamics in GaAs, was solved numerically by Wolfram Mathematica. In order to estimate the possible effect of two-and three-body processes on the relaxation time, we perform calculations of the initial relaxation rate as a function of injected electron-hole plasma density in the absence of the enhanced surface recombination, i.e., A = 0. Using the known parameters B = 1.7 · 10 −10 cm 3 s −1 [1] and C eff = 7 · 10 −30 cm 6 s −1 [2], one obtains the dependence of Γ on the initial plasma density, as shown in Fig. 2. It can be seen that for the estimated plasma density ranges found in experiments, the fastest high-order-process relaxation is more than a-Si metasurface [3] 0. Supplementary note 4

Dynamics of the refractive index of photoexcited gallium arsenide
Here, we provide the ansatz behind the refractive index dynamics in GaAs metasurfaces. Upon FC injection, the refractive index change relies on three main components [10]: the Drude term, the band filling effect and the band shrinkage effect; the resulting index modulation is given by: The Drude term can be expressed as follows: where N e and N h are the densities of electrons and holes, respectively (we assume N e = N h = N/2); m e , m lh , and m hh are the masses of electrons, light holes and heavy holes, respectively; ε 0 is the permittivity of vacuum, and n 0 is the unperturbed refractive index.
The band filling effect on the refractive index is defined by the decline of the interband transitions due to occupation of the electron and hole states in the conductance and valence bands, respectively. In the parabolic band approximation, the interband absorption is given by the following expression: where C hh = 3.1 · 10 6 cm −1 eV 1/2 and C lh = 1.6 · 10 6 cm −1 eV 1/2 , and E g = 1.42 eV is the band gap width of GaAs at room temperature. The decrease in interband absorption for photon are the Fermi-Dirac distributions in for electrons and holes, respectively. The quasi-Fermi levels are given by approximate expressions: and Note a misprint in Eq.(8b) of Ref. [10]. N c and N v are the densities of states in the conduction and valence bands, respectively: where m dh = (m is the density-of-states effective mass of holes. Because of the parabolicity of the bands, the excess energies E ah,al,bh,bl are directly connected to the excitation energy E through momentum and energy conservation: We obtain the modulated absorption constant by substituting Eqs. (5)(6)(7)(8)(9)(10)(11)(12) into Eq.(4). It is important to note, that, since the injected plasmas are hot, we are interested in Eq. (4) as a function of the non-equilibrium FC temperature. We estimate the average initial temperature to be about T max = 15000 K for the given initial plasma density after Ref. [11].
This value is larger than the initial excess energy of the carriers and, therefore, Fermi-Dirac statistics is not applicable, and our numerical results are an approximation. Thermalization of FCs to this temperature takes place during the first 200 fs after the pump pulse arrives, which is considered as an instantaneous process. Also, the time constant of the carrier-lattice cooling through optical phonon scattering is less than 1 ps given the large initial plasma temperature [12]. The law of plasma cooling is phenomenologically set to be as follows: where τ T is set to be 0.3 ps.
Having omitted the band shrinkage addition, for its effect on n is more than order of magnitude lower than the other contributions at our plasma densities, one can use the time dependence of ∆n(t) in order to calculate the reflectance spectra of the metasurface as a function of time. The results are given in Fig. 4 of the main manuscript text.