Electromagnetically induced transparency (EIT) arises from the interplay between coherent electromagnetic fields and atomic energy level systems, representing a quantum interference phenomenon^[1,2]. EIT-like effects, often rooted in Fano-type linear destructive interference^[3–5], are extensively observed in classical electromagnetic systems, including coupled resonators^[6,7], circuits^[8], and plasmon structures^[9–16]. These systems, providing transparency and high dispersion to dielectrics, enable slow-light effects and amplify nonlinear interactions^[9,17], facilitating applications in slow-light photonic components^[18–22], high-sensitivity sensors^[23–29], and electromagnetically induced absorption analogs^[30–33]. Integrating slow-light devices with on-chip nanophotonic devices in sectors such as optoelectronics^[34], ultrafast information technology^[35], and imaging and sensing^[23,24] requires exploring novel optical materials and structural designs to effectively harness slow-light phenomena.

Metamaterials offer a novel platform for exploring the slow-light effect^[36–43], enabling tailored optical responses through strategic design and functional arrangement. Plasmonic structures, providing strong optical responses in sub-wavelength configurations, prompt study into plasmon metamaterials simulating the atomic EIT effect. On-chip integrated plasmonic metamaterials serve as effective platforms for EIT-like effect simulation research, leading to the development of classical optics analogs of quantum interference mechanisms inherent in atomic EIT systems. These structures, typically composed of coupled sub-wavelength resonators, such as cut wires (CWs) and split-ring resonators (SRRs), facilitate the EIT-like effect^[9,44]. Advancements involve incorporating various active optical materials, such as liquid crystals^[45,46], semiconductors^[47–50], two-dimensional materials^[51–53], and phase change materials^[54,55], to transition from passive to actively controllable PIT structures, enhancing versatility and tunability for applications in integrated optical filters^[56,57], optical switches^[47], and biological detection^[23–26]. Although optically controlled active metamaterials have received significant attention, research has primarily focused on configuring PIT structures and investigating the optical resonance properties of metamaterials to achieve ultrafast mode conversion and strong dispersion properties^{[9,29,58–61]}. However, the limited exploration of near-field coupling flip phenomena specific to PIT metamaterials in the current literature hinders the structural design and performance optimization of active PIT metamaterials.

Our work investigates the coupling mechanism responsible for the EIT-like effect in actively modulated structures. Initially, we embed photosensitive silicon into the gaps of metal SRRs and vary its conductivity in simulations to actively control dispersion characteristics and coupling strength. Utilizing the Lorentz coupling resonator model, we parameterize the transmission spectrum of the PIT structure under various conductivities and extract the group delay. Adjusting parameters d and g allows modulation of the coupling strength, which influences spectrum features. We analyze the relationship between group delays and coupling states in correlation with varying spacing parameters and delve into the regulatory mechanisms of these parameters on resonant frequency detuning δ and the transparency window Δf and their influence on the PIT effect.

In our investigation of the EIT-like effect, we employ a classical coupling structure of bright and dark modes, as shown in Fig. 1(a). The PIT unit-cell structures consist of a metallic CW paired with symmetrically metallic SRRs. Silicon islands are integrated within the gaps of the SRRs. In the configuration, the CWs function as the bright mode, while the SRRs serve as the dark mode. The resonance features of both components depend intrinsically on their geometric dimensions. The structural dimensions, with x- and y-periods of 80 and 120 µm, respectively, are precisely chosen and placed on a 500-µm-thick quartz substrate. The coupling components, CWs and SRRs, are made from 0.2 µm thick gold, supplemented with an equally thin layer of photosensitive silicon. The subwavelength scale of the unit-cell geometry is crucial, ensuring that terahertz waves interacting with the PIT structure avoid multi-order diffraction.

A comprehensive numerical simulation is conducted using the commercial software CST Microwave Studio to explore the qualitative relationship between carrier excitation and the attenuation of the dark mode in SRRs within the context of the PIT effect. The quartz substrate is modeled as a lossless dielectric with a dielectric constant of εquartz=3.75, while the dielectric constant of silicon is 11.9, and the conductivity of gold is 4.56×107S/m. Terahertz wave excitation with normal incidence and y-polarization is applied to the PIT samples. The transmission spectrum of the CW resonator array displays a pronounced absorption dip at 1.06 THz, indicating a localized surface plasmon (LSP) resonance. In contrast, the inductor-capacitor (LC) resonance characteristic of the SRR array remains unexcited by the incident wave near 1.06 THz, with the CW and SRR acting as the bright and dark modes, respectively. In the formation of the PIT structures, the CWs directly couple with the incident electric field, initiating the LSP resonance due to the electric field’s polarization parallel to the CWs. Meanwhile, the SRRs, not coupling directly with the incident electric field, engage in near-field coupling with the CW resonator, exciting the LC resonance. This interaction leads to a destructive interference between the LSP and LC resonances, resulting in a distinct transparency window at 1.03 THz against the 1.06 THz absorption background.

To investigate the impact of critical spacings d (the distance between the CW and the SRR) and g (the gap between the SRRs) on the coupling mechanism across varying strengths, PIT structures are endowed with active tuning functionality. Active tuning of PIT sample transmission characteristics is achieved through varying irradiated light power. In our numerical analysis, the conductivity σ of photosensitive silicon is varied from 0 to 10,000 S/m to simulate different light power excitation conditions. The impact of these silicon islands on the PIT transmission spectrum at various conductivity σ values is shown in Fig. 2. Without light excitation (σ≈0S/m), a distinct PIT is discernible at 1.03 THz with a transmission amplitude of 0.86. With increasing simulated light excitation power and escalating conductivity, the PIT transparency window undergoes significant modulation. Notably, at a conductivity σ of 3000 S/m, the transmission amplitude diminishes to 0.52, and at 10,000 S/m, the PIT transparency window is entirely obliterated, leaving only the LSP resonance absorption attributable to the CWs visible in the transmission spectrum. The observation underscores that as light power intensifies, the PIT peak is actively modulated from the ‘ON’ to ‘OFF’ states, corresponding to a shift in the conductivity σ of photosensitive silicon from 0 to 10,000 S/m.

Analyzing the electric field distribution at the PIT resonance frequency in numerical simulations reveals the attenuation change process of the dark mode. As shown in Fig. 3, the electric field distribution at conductivity σ values of 0, 5000, and 10,000 S/m corresponds to the states of complete conduction, partial attenuation, and full attenuation of the PIT peak, respectively. At σ=0S/m, the electric field within the CW is suppressed, concentrating around the gaps of the SRRs with an opposing phase, leading to the emergence of a PIT transparency window at a specific frequency. Increasing conductivity to 5000 S/m results in reconfiguration of the electric field distribution, diminishing field intensity at the SRR openings while intensifying at the top of the CW. Further elevation of conductivity to 10,000 S/m almost entirely suppresses the electric field at the SRRs, concentrating it at the ends of the CW and leading to the disappearance of the PIT peak. PIT resonance modulation is rooted in the optically tunable conductivity of the silicon islands, driven by the photodoping effect^[9].

The design of the PIT structure is conceptually analogous to the transition path among the ground state, excited state, and metastable state in atomic EIT systems. To elucidate the physical mechanisms underlying the PIT effect, we consider a three-level atomic EIT system model encompassing the ground state |0⟩, the metastable state |1⟩, and the excited state |2⟩. In the framework, the |0⟩→|2⟩ transition path, which is dipole-allowed, correlates with the LSP bright mode resonance in the CWs. Conversely, the |0⟩→|1⟩ transition path is dipole-forbidden, mirroring the LC dark mode resonance in the SRRs. In the absence of the pump light, the detection light frequency ω02 matches the transition resonance frequency between |0⟩ and |2⟩, stimulating electron transitions and resulting in resonance absorption. Introduction of the pump light, set to frequency ω12 and matching the transition resonance frequency between |1⟩ and |2⟩, elevates electron population in |2⟩ relative to |1⟩, initiating a preferential transition from |2⟩→|1⟩. The transition is analogous to the coupling between the CWs and the SRRs, introducing destructive interference and yielding significant dispersion in a narrow frequency band with pronounced loss suppression. The destructive interference resulting from the near-field coupling between the bright and dark modes in the PIT structure can be qualitatively described using the Lorentz oscillator coupling model^[9,44], as {x¨1+γ1x˙1+ω02x1+κx2=G·Ex¨2+γ2x˙2+(ω0+δ)2x2+κx1=0.(1)

The Lorentz oscillator model describes this destructive interference, where (x1, x2) and (γ1, γ2) denote amplitudes and damping rates of the bright and dark modes, respectively. Resonance frequencies are represented by ω0 for the bright mode and ω0+δ for the dark mode, with δ indicating frequency difference. Here, the coupling coefficient κ represents the strength of the coupling between the bright and the dark modes, while G denotes the coupling between the bright mode and the incident electromagnetic field. Under minimal detuning conditions (δ≪{γ1,γ2,κ}), magnetic susceptibility χ of the PIT structure can be deduced by solving Eq. (1), χ=χr+iχi∝(ω−ω0−δ)+iγ22(ω−ω0+iγ12)(ω−ω0−δ+iγ22)−κ24.(2)

Given that the energy loss in the system is proportional to the imaginary component of the magnetic susceptibility χi, the transmittance of the PIT structure can be estimated using the following approximation: T∝1−χi=1−Gχi.(3)

The transmission spectra of the PIT structure, corresponding to varying conductivity values, have been theoretically analyzed and fitted using Eqs. (2) and (3). These fitting results are represented as blue dotted lines in Fig. 2. The fitting data demonstrates a good consistency with the results obtained from numerical simulations. Additionally, the variation in fitting parameters in relation to different conductivity σ values is presented in Fig. 4.

Figure 4 illustrates that with increasing conductivity σ of the photosensitive silicon, parameters γ1, δ, and κ exhibit minimal variation, while the non-radiative damping rate γ2 of the dark mode SRRs significantly increases. Specifically, γ2 escalates from 0.01 THz at σ=0S/m to 0.35 THz at σ=10,000S/m. At conductivity values of 0, 500, 1500, 3000, and 5000 S/m, κ remains greater than the mean of γ1 and γ2, indicating a strong coupling state in the PIT structure^[44,62]. Conversely, at σ=10,000S/m, where κ=0.2 becomes smaller than the mean of γ1=0.1 and γ2=0.35, the PIT structure enters a weak coupling state. These results indicate that the active modulation of the PIT metamaterials depends on the variation of the damping rate γ2 of the dark mode SRRs. An increase in the conductivity σ of the photosensitive silicon enhances the non-radiative loss in the dark mode of the SRRs, thereby transitioning the PIT structure from a strong to a weak coupling state. This transition hinders destructive interference between the bright and dark modes. Specifically, at the maximum conductivity σ of 10,000 S/m, γ2 becomes large enough to fully suppress dark mode excitation. Consequently, the PIT structure is in a weak coupling state, ultimately leading to the disappearance of the PIT resonance peak.

The conductivity σ of the photosensitive silicon plays a key role in actively tuning the slow-light properties of the PIT effect. The group delay (tg) of the terahertz pulses traversing the PIT structure is calculated using tg=−dφdω (where φ represents the phase and ω denotes the angular frequency). Figure 5(a) shows the variation of group delay tg with conductivity. It is observed that as the conductivity increases, tg progressively diminishes, indicating a corresponding weakening in the dispersion intensity of the PIT structure. Upon reaching a conductivity of 10,000 S/m, the PIT structure loses its distinctive slow-light characteristics, exhibiting typical LSP group delay properties. Consequently, the conductivity σ serves as an effective regulator for the PIT transparency window, enabling active control over its slow-light capability. Furthermore, to elucidate the influence of coupling between the CW and the SRR, as well as the interplay between the SRRs on the slow-light attributes of the PIT structure, two parameters d and g are introduced. By maintaining a constant photosensitive silicon conductivity σ at either 0 S/m or 1500 S/m and varying the parameters, the group delay tg at the peak frequency of the PIT structural transparency window exhibits corresponding changes with these parameters, as shown in Fig. 5(b). With the conductivity set at 0 S/m and with g maintained at 32 mm, an increase in d results in a corresponding initial increase in the group delay tg, achieving a maximum of 0.66 ns at d=18mm. Additionally, at a conductivity of 1500 S/m, an increase in d leads to a peak group delay tg of 0.28 ns, occurring when d is equal to 10 mm. Beyond d=18mm or d=10mm, the tg gradually decreases with further increments in d. Additionally, maintaining d at 7 mm, the relation between g and tg is investigated. As g increases, the overall amplitude change in the tg is less pronounced. This reveals that when conductivity σ remains unchanged, the parameter d predominantly governs the regulation of the slow-light characteristics of the PIT structure.

To further understand the two coupling regulation mechanisms represented by parameters d and g, a detailed numerical simulation and fitting analysis of the PIT structure are conducted. This analysis elucidates the relationship between the fitting parameters (γ1, γ2, δ, and κ) and the parameters d and g, as illustrated in Fig. 6. Figure 6(a) presents the variation of fitting the parameters with the parameter d while keeping the parameter g fixed at 32 mm. As d incrementally increases, γ1, γ2, and δ remain relatively constant, whereas κ exhibits a notable decrease, dropping from 0.43THz2 at d=1mm to 0.015THz2 at d=21.6mm. This trend suggests that the near-field coupling strength between the CW and the SRR diminishes as d increases. When d is sufficiently large, κ approaches zero, indicating an absence of near-field coupling between the CW and the SRR, resulting in the PIT structure and exhibiting a typical bright-mode LSP resonance. Conversely, keeping d constant at 7 mm, Fig. 6(b) explores the changes in parameters (γ1, γ2, δ, and κ) as g is adjusted. In this scenario, γ1, γ2, and κ remain largely unchanged, while the absolute value of δ decreases slightly, transitioning from −0.15THz at g=4mm to −0.01THz at g=51mm. This indicates a gradual reduction in the resonant frequency detuning between the bright and dark modes as g increases, trending towards a zero-detuning situation. Notably, during the adjustment of d and g, the resonant frequency detuning amount (δ) between the bright and dark modes predominantly depends on g and is not significantly influenced by d. Furthermore, as g increases with d held constant, κ remains relatively unaffected, signifying that the coupling strength between the SRR and the CW is primarily determined by d. In the control process of d and g, neither γ1 nor γ2 undergoes significant changes, suggesting that they primarily govern the loss associated with the mode.

The influence of parameters d and g on Δf is also a significant aspect of our work. When maintaining a constant conductivity σ, the corresponding variations in Δf with the parameters d and g are illustrated in Figs. 7(a) and 7(b). For different conductivity σ values, Δf shows negligible alteration during changes in the parameter g, aligning with the limited influence of g on the coupling strength κ. Conversely, the dependency of Δf on d under varying conductivity σ is more pronounced. As d increases, Δf progressively diminishes, approaching zero. The trend of Δf aligns with the regulatory mechanism of parameter d on coupling strength κ. Notably, higher conductivity values cause Δf to converge towards zero more rapidly with increasing d, as shown in Fig. 7(c). The observation underscores the pivotal role of the parameter d not only in regulating the coupling strength κ but also in significantly influencing Δf.

Integrating photosensitive silicon into the gaps of SRRs enables active tuning of the coupling strength in PIT structures. Through manipulation of spatial parameters d and g across varying conductivity values, we explore the flip from strong to weak coupling states. Our simulations yield several key insights: (1) The control over tg is primarily governed by parameter d; (2) The variation of Δf is predominantly influenced by parameter d; (3) Parameter g chiefly affects the resonant frequency detuning (δ) between the bright and dark modes. Our theoretical fitting analysis, employing the Lorentz resonator coupling model, supports these findings. Notably, at d=18mm, the maximum tg aligns with κ(=0.034) being approximately equal to γ1γ2(=0.039)^[44]. Regarding coupling parameter regulation, d plays a dominant role in the transition of the PIT structure from strong to weak coupling states, thereby controlling κ and subsequently Δf. Conversely, throughout the adjustment of parameter g, the PIT structure consistently maintains a strong coupling state, as the mean value of γ1 and γ2 consistently remains lower than κ. Thus, g has limited capability in modulating κ and primarily adjusts δ. Our research sheds light on the intricate interplay of the coupling mechanisms within PIT structures and their flip features. These insights offer valuable guidance for advancing active control devices in slow-light technologies, optical switches, modulators, and related applications.