Electromagnetically induced transparency (EIT) is a quantum interference effect that renders a medium transparent within a narrow spectral range around an absorption line^[1]. Much attention has been paid to achieve the EIT-like effects in classical oscillator systems, such as coupled resonators^[2,3], electric circuits^[4], and plasmonic metamaterials^[5–7]. These structures have an EIT-like phenomenon attributed to the Fano resonance in the structure^[8,9]. Slow light is a dramatic reduction in the group velocity of light passing through the medium^[10] and has an important impact on optical science, as it can enhance light–matter interactions^[11,12]. In particular, it has great promise in optical communication and computation. Therefore, many metasurfaces were designed to achieve the slow light effect^[13–15]. Among them, structures with EIT-like phenomena exhibit a very large group refractive index, so they have shown great promise in slowing down the group velocity of light^[16–18].

For practical applications, it is desirable that the group velocity of electromagnetic waves can be actively controlled. For this purpose, a controllable EIT metasurface is an excellent candidate. Many efforts have been devoted to the tunable EIT metasurfaces^[19–24] by various means, such as thermal^[19,20] and optical^[21,22] methods. Furthermore, Kim et al.^[24] demonstrated electrically tunable EIT-like spectral properties by integrating single-layer graphene onto the functional unit cells. However, manipulation speed in the available work is slow. As slow light has the potential in the optical delay device, the ultrafast control of EIT-like metasurfaces and thus ultrafast modulation of slow light are desirable.

In this paper, we propose ultrafast tunable slow light metasurfaces based on a bright-bright mode coupling EIT-like structure. The unit cell of the metasurfaces consists of a gold (Au) cut wire (CW) and two Au split-ring resonators (SRRs). In order to achieve ultrafast control of slow light, we integrate P+-implanted Si CW into the SRRs. Due to the intrinsic Si having a long carrier recombination life time on the order of milliseconds, the Si in our experiments is implanted with P+ to produce lattice defects of Si and further reduce the carrier lifetime of Si. Compared with previous optically tunable EIT metasurfaces^[21,25–27], in the work of Hu et al.^[25], the switching time of the EIT surface under the irradiation of near-infrared pump light is 1 ns. Our EIT metasurface with P+ implantation achieves much faster control of the two states (with EIT and without EIT) of the device. We experimentally demonstrate the transmission spectra of the ultrafast EIT metasurface in the terahertz (THz) range by using optical-pump THz-probe (OPTP) spectroscopy. By changing the pump–probe delay time, we demonstrate that the group delay of THz light can be controlled in an ultrafast manner, with one switch cycle taking only 200 ps. Then, the coupled oscillator model is also used to explain the origin of the ultrafast controllability of the device. This ultrafast EIT metasurface has the potential to be used as an ultrafast THz band optical delay device.

The schematic illustration of the ultrafast EIT metasurface is shown in Figs. 1(a) and 1(b). As shown in Fig. 1(b), the unit cell of the EIT metasurface consists of a CW and two SRRs, which are made of Au, and there is a CW made of n−Si between the CW and each SRR. The parameters of the structure are given: the length of Au CW L=85μm, the width of Au CW and SRR w=5μm, the side length of SRR l=29μm, and the periods of the structure P1=120μm, P2=80μm. The size of the unit cell ensures that no diffraction happens, and thus the EIT metasurface behaves as an effective medium. The structure was fabricated on the Si-on-sapphire (SOS) wafer comprised of 600 nm thick Si and 530 μm thick sapphire, with a microscopy image shown in Fig. 1(c). Firstly, the Si layer of SOS was ion implanted with P+ at a dose of 1013cm−2 and an energy of 100 keV. Then, the CW of Si was fabricated by the standard UV photolithography and reactive ion etching on the SOS substrate. Finally, the Au CW and Au SRRs are overlaid on the Si structure using the lift-off method.

We firstly utilized the commercial software COMSOL Multiphysics 5.2 to simulate the transmission spectra. In our simulation, the propagation of the incident electromagnetic wave is perpendicular to the surface of the structure, while the (E, H) plane is parallel to the surface of the structure, as shown in Fig. 1(a). The incident wave is generated by the port boundary conditions (in our simulation, the power of the incident wave is 1 W, and the absolute value of the corresponding electric field intensity can be calculated as 2.8×105V/m), and the periodic boundary conditions are employed. The transmission coefficient S21 can be obtained from the simulations, and the transmission T is extracted by T=|S21|2. In our simulation, the sapphire substrate was treated as a lossless dielectric with nSap=3.42^[21]. The permittivity of Au is described by the Drude model εAu=1−ωp2ω2+iγω, where ωp=1.37×1016Hz and γ=4.07×1013Hz^[28]. The permittivity of the doped Si can be described well by the Drude model as^[29]ε=ε∞−ωp2ω2+iω/τd, where ε∞=11.7, ωp=Ninie2/ε0mopt* is the plasma frequency of the unexcited Si, mopt*=(me*−1+mh*−1)−1=0.15me is the optical effective mass of the carriers, and τd=80fs is the Drude damping time^[30]. Since 1/τd≫ω (0.2–1.2 THz), the permittivity of the doped Si can be written as ε≈ε∞+iτdωp2ω=ε∞+iσωε0, where σ denotes the conductivity of doped Si. To clarify the mechanism of the EIT effect, we simulated the Au CW and SRR structures separately. As shown in Fig. 2(a), the Au CW shows a resonance peak at 0.7 THz, and the SRR structure shows a resonance peak at 0.89 THz, with the corresponding electric fields shown in Figs. 2(b) and 2(c). The results show that both Au CW and SRRs can be coupled with the incident THz waves directly, meaning that these two structures are both bright modes in our design. In the EIT sample, the near-field coupling between the Au CW and SRRs excites a resonance. The destructive interference between these two resonances in Au CW and SRRs leads to a sharp transparency peak at 0.76 THz. Furthermore, the conductivity of Si CW is set from 200 S/m to 60,000 S/m to simulate the effect of optical excitation. In Fig. 2(d), the transmission spectrum presents an EIT peak at 0.76 THz when σSi=200S/m. Figure 2(e) shows the electric field at 0.76 THz, where both the SRRs and the Au CW are simultaneously excited by the incident wave. When σSi=60,000S/m, the electric field around the Au SRRs is completely suppressed, and the field distribution is localized at the Au CW at 0.76 THz, as given in Fig. 2(f). These results show that the EIT peak can be suppressed when carriers in Si CW are excited by the pump light.

Then, we characterized the fabricated EIT metasurface by a homemade OPTP spectrometer, with the experimental setup described in detail elsewhere^[31]. The output laser pulse from a Ti:sapphire regenerative amplifier with a pulse width of 35 fs, a central wavelength of 800 nm, and a repetition rate of 1 kHz was split into three parts: two for THz generation and detection and the other one for optical excitation. THz radiation was generated by the optical rectification in a 0.5 mm thick (110)-oriented ZnTe nonlinear crystal and was focused on the sample by the off-axis parabolic (OAP) mirrors. The THz beam electric field signal is measured by the electro-optic sampling using another 0.5 mm thick (110)-oriented ZnTe crystal. The optical-pump pulse was focused on the sample with a diameter of 10 mm at an incidence angle of about 20°. The variation in the pump–probe delay was implemented using a motion stage by changing the pump beam optical path. Under various pump–probe delay, the transmitted THz pulses through the EIT metasurface and the blank sapphire reference were measured in the time domain at the pump fluence of 1.4mJ·cm−2. The transmission spectra were obtained by performing fast Fourier transformation of time-domain signals and normalized to those of the reference. The OPTP system is shown in Fig. 3.

The differential change in the transmitted THz peak signal (ΔT/T) was measured as a function of pump–probe delay, with the results shown in Fig. 4(a). It can be seen that the THz peak signal firstly reduces rapidly, resulting from the photogenerated carriers in the Si CW. Until the time delay reaches 5 ps, the THz peak signal starts to recover due to the recombination of carriers in Si. It can return to be the initial state within 200 ps. Additionally, the transmission spectra of the EIT metasurface at different pump–probe delays are shown in Fig. 4(b). When the time delay is −20ps, there is no photoexcitation, and the corresponding transmission spectra show an EIT peak at 0.78 THz, while the EIT peak is totally suppressed when the time delay reaches 5 ps. As the time delay increases from 5 ps to 180 ps, the EIT peak appears again. One cycle of switching from the EIT suppressing to the EIT reappearing takes within 200 ps.

In the following, ultrafast modulation of the slow light behavior is further demonstrated. The EIT metasurface changes the group refractive index by changing the dispersion of the metasurface. Since the increasing group refractive index increases the time of THz waves passing through the metasurface, the slow light effect of the metasurface can be characterized by this time value. Therefore, we use Δtg to describe the slow light capability of our device^[21], which refers to difference in tg for THz waves to pass through the EIT metasurface and air of equivalent thickness. So, tg=−dφ/dω, where φ is the phase, and ω is the angular frequency of the THz pulse. The retrieved Δtg from the experiment is shown in Fig. 4(c). When the pump–probe time delay is −20ps, the wave packet with a central frequency of 0.78 THz is delayed by 6 ps, which is equivalent to the time delay of a 1.8 mm free space propagation. However, when the time delay is 5 ps, the wave packet is delayed by 4 ps (caused by the substrate), which means that the EIT metasurface gradually loses its slow light characteristic. As the time delay increases to 180 ps, the slow light effect appears again. It is worth noting that there are spectral regions where the delays are negative, which would seem to allow faster-than-light wavepacket transfer. But, this phenomenon does not violate the law of causality. Superluminal group velocity can result from pulse shaping due to anomalous dispersion^[32]. Δtg plotted as a function of pump–probe time delay at 0.78 THz is shown in Fig. 4(d).

Experimental transmission spectrum mapping as a function of pump–probe time delay is shown in Fig. 5(a) to more clearly illustrate the switching characteristics of the device. As indicated by the dashed black line, one cycle of switching on and switching off the EIT peak is within 200 ps. Additionally, to illustrate the effect of ion implantation on carrier lifetime and thus the manipulation speed of the EIT metasurface, we measured the differential change of the transmitted THz peak signal for different Si films with doping doses of 1013cm−2, 1015cm−2, and 1015cm−2 but annealed (rapid thermal annealing at 1000°C for 30 s), respectively. The transient differential transmission trace is fitted by a single exponential expression ΔT/T=A+Be−t/τ, and the relaxation time τ is obtained, as shown in Fig. 5(b). The sample with an implantation dose of 1015cm−2 and without annealing presents a shorter relaxation time but a lower modulation depth than that of the 1013cm−2 implanted Si film and without annealing. This is due to a higher implantation dose that results in more crystal defects, which heavily reduces the carrier lifetime of Si. However, the annealing post-procession can repair the crystal defects and activate the implanted P+, thus improving the carrier density and extending the carrier lifetime. So, the annealing sample has a much higher modulation depth, but much longer relaxation time. Therefore, in our experiment, a Si film with a doping dose of 1013cm−2 but without annealing was selected to fabricate the metasurface, taking into account that it has a good modulation depth and also a relatively short carrier lifetime.

To explain the physical origin of the EIT behavior, we use the coupled oscillator model^[33] to analyze the interaction between two bright modes in the EIT structure, with the model expressed as x1″+γ1x1′+ω12x1−Ω2exp(iφ)x2=f1,(1)x2″+γ2x2′+ω22x2−Ω2exp(iφ)x1=f2,(2)where x1, x2, γ1, and γ2 are the amplitudes and damping rates of the two bright modes, respectively. Ω2exp(iφ) is the coupling coefficient between two resonators. f1 and f2 are the external force. Here, the discussion is only restricted to the case that φ=0 and f1=f2=f. Under this condition, Eqs. (1) and (2) can be solved as x1=Ω2+(ω22−ω2−iωγ2)(ω12−ω2−iωγ1)(ω22−ω2−iωγ2)−Ω4f,(3)x2=Ω2+(ω12−ω2−iωγ1)(ω12−ω2−iωγ1)(ω22−ω2−iωγ2)−Ω4f.(4)

The electric current density J and the surface conductivity σe of the metasurface can be expressed as J=−ineω(x1+x2)=σeE,(5)where ne and E denote the average electron density and spatially averaged electric field on the metasurface, respectively. If assuming f∝E, σe=−ineω2Ω2+(ω12−ω2−iωγ1)+(ω22−ω2−iωγ2)(ω12−ω2−iωγ1)(ω22−ω2−iωγ2)−Ω4.(6)

The transmission coefficients of the metasurface can be calculated from Eq. (6): t=22+Z0σe,(7)where Z0 is the wave impedance of the external waves.

The simulated transmission spectra with Si conductivity that varied between 200 S/m and 60,000 S/m are presented by red dotted line in Figs. 6(a)–6(e). When the Si conductivity is set to be 200 S/m, the EIT peak is activated, similar to the experimental result at −20ps in Fig. 4(b). The EIT phenomenon is suppressed when the Si conductivity increases to 60,000 S/m, which is the same as the experimental one at 5 ps. Therefore, it can be concluded that the ultrafast manipulation of carrier density of Si CW and thus conductivity of Si contributed to the ultrafast control of the EIT peak.

The equation of |t2| is used to fit the simulation results in Figs. 6(a)–6(e), with fitted results shown by black lines in Figs. 6(a)–6(e). The fitting parameters with the Si conductivity are plotted in Fig. 6(f).

As can be seen from Fig. 6(f), γ1 and ω1 change slightly because the Au CW resonators are hardly affected by the change of Si conductivity. A significant change in γ2 and ω2 can be seen due to the change of Si conductivity that can affect the damping rate of the SRRs and the effective length of the electric dipole (SRRs). The value of Ω changes a little because the effective distance between these two resonators also varies a little due to the change of Si conductivity. From the above analysis, we can see that the whole process is indeed due to the ultrafast change of Si conductivity, which has a great influence on the SRRs and destroys the interference between the bright-bright mode couplings.

In summary, by incorporating P+-implanted Si CW into the EIT metasurface unit cell, we have experimentally demonstrated an ultrafast dynamic control of slow light in THz metasurfaces. The transition from the state with the slow light effect to the state without the slow light effect occurs at an ultrafast time of 5 ps, and the recovery to the slow light effect state takes 200 ps. A coupled oscillator model has been used to explain the origin of the controllability. The ultrafast manipulation of conductivity of Si CW affects the damping rate and the effective electric dipole length of the SRRs, and thus destroys the interference between the bright-bright mode couplings. The structure we designed may be applied to an ultrafast THz band optical delay device.