Active dual-control electromagnetically induced transparency analog in metal- vanadium dioxide-photosensitive silicon hybrid metamaterial

We investigate an active dual-control metamaterial leveraging electromagnetically induced transparency (EIT), exploiting near-field interactions between electric and magnetic dipole resonances. Our hybrid strip element, combining metal and vanadium dioxide, generates electric dipole resonance, while split-ring resonators integrating metal and photosensitive silicon induce magnetic dipole resonance. Simulations confirm coupling validity and demonstrate dynamic adjustability of EIT via temperature and light intensity changes. EIT modulation transitions between transparent and non-resonant states due to temperature fluctuations, or resonant states with varying light intensity. Temperature adjustments dominate when both factors are altered. Analysis via a coupled oscillator model reveals modulation of damping rates as the origin of disappearance curve variations. This innovative design enhances tunable EIT metamaterial versatility, with implications for high transmission ratios and adaptable slow-light effects in terahertz applications.

Currently, efforts to enhance the practicality of EIT metamaterials have focused on actively modulating these materials.Active modulation involves adjusting EIT phenomenon by external factors-such as light intensity, voltage, or temperature-without changing the inherent structural dimensions.Common approaches include integrating active modulation materials like graphene, vanadium dioxide (VO 2 ), or photosensitive silicon into conventional EIT metamaterials.These materials possess controllable electromagnetic properties, enabling adjustment of the EIT phenomenon.Researchers have extensively explored this avenue [20][21][22][23][24][25][26][27][28][29].For instance, Xiao et al explored the dynamic control of an EIT-like phenomenon in hybrid metamaterials by placing a monolayer of graphene beneath a metal-based dark resonator.Their study illustrated how adjusting the gate voltage of graphene can influence the EIT-like effect [21].Jin et al developed a terahertz EIT metamaterial using a pair of metal-based U-shaped split ring resonators and a metal cut wire resonator.By integrating a photosensitive silicon cell within the U-shaped resonator, they achieved active optical manipulation of the EITlike effect [26].Zhang et al explored an EIT analogue using terahertz metamaterial embedded with vanadium oxide, effectively regulating the EIT peak by varying temperature [28].However, it's crucial to note that current designs primarily demonstrate modulation from the EIT phenomenon towards disappearance, transitioning into a state characterized by a resonance curve.Instances of achieving modulation from the EIT phenomenon towards reduction and transition into a state characterized by a non-resonance curve, with higher transmission coefficients, are rare.The development of EIT metamaterials capable of selectively transitioning from the EIT phenomenon towards diminishment and into either a resonance curve or a non-resonance curve is yet to emerge.
To the best of the author's knowledge, currently, there is no existing solution for achieving both modulation effects using a single modulation method.In order to accomplish the capability of selectively transitioning from the EIT phenomenon towards diminishment and into either a resonance curve or a non-resonance curve, we present a dual-control EIT metamaterial accomplished via the near-field interaction between electric dipole and magnetic dipole resonances.The basic component features a hybrid strip combining metal and vanadium dioxide, specifically designed to generate electric dipole resonance.Additionally, a pair of split-ring resonators incorporating metal and photosensitive silicon are introduced to induce magnetic dipole resonance.Through simulations, we validate the transition of electromagnetic energy, thus inducing an EIT-like phenomenon.Our research demonstrates that the EIT-like effect can be manipulated, transitioning from an EIT-like state to a nonresonant curve state by adjusting temperature.Similarly, alterations in light intensity enable modulation of the EIT-like phenomenon from transparency to a resonant curve state.This design will enrich the schemes of actively tunable EIT metamaterials, holding paramount significance for terahertz applications requiring high transmission ratios and actively adaptable slow-light effects.Additionally, it holds crucial importance for advancing the development of slow-light switch devices within this domain.According to existing research findings, the parameters specified above can be successfully implemented in practical applications [30].We utilize finite-difference time-domain (FDTD) method to evaluate how the proposed EIT metamaterial couples.In our simulation configuration, a plane wave is incident on the hybrid metamaterial along the z-direction with polarization oriented along the y-direction.Employing Drude model, we characterize the properties of aluminum, setting the plasma frequency at rad s 2. 24  10 16  ´/ and the damping constant at rad s 1. 22  10 14  ´/ [21,31].Furthermore, we calculate the terahertz range permittivity of VO 2 using the Drude model [32,33]:

Analogue designs and simulations
e w e = - Here, e ¥ is fixed at 12, the damping coefficient, denoted as , g is set to a value of rad s 5.75 10 ,

13
´/ and the plasma frequency is described by the equation: .´/ to 2 10 s m 5 ´/ [34][35][36], and w signifies the angular frequency.The conductivity of photosensitive silicon ( Si s ) exhibits the highest sensitivity with laser pumping at a wavelength of 800 nm, and the value of Si s can be adjusted from 1 10 s m 2 ´/ to 3 10 s m 5 ´/ [37].The permittivity of SiO 2 is specified as 3.9.

Results and discussions
To ascertain the coupling mechanism underlying the proposed EIT phenomenon, we initially compute the transmission spectra of two isolated resonators, as depicted in figure 2. For this analysis, we set the initial value of ´/ while Si s is set to 3 10 s m. 5 ´/ Figure 2 shows that the isolated HS resonates directly at 1.33 THz, operating as bright resonator, as opposed to the isolated HSRR, which exhibits inactive when exposed to the same incident wave, serving as a dark mode resonator.However, upon their simultaneous operation, at 1.27 THz, a slender transparency peak emerges, sandwiched amidst transmission dip I (1.20 THz) and dip II (1.38 THz), as illustrated in figure 2.
To provide additional insight into the coupling mechanism, figure 3 presents the individual field distributions of the isolated HS and HSRR at 1.33 THz, as well as the field distribution of EIT scheme at 1.27 THz.In figure 3(a), the electromagnetic energy is primarily concentrated at the ends of HS, which supports the typical behavior associated with electric dipole resonance, indicating that HS is being excited by the incident wave.In contrast, figure 3(b) illustrates the passive response of the isolated HSRR to the incident wave.Upon their simultaneous operation, the original inactive HSRR is excited indirectly through interference with HS, resulting in the transfer of electromagnetic energy, as illustrated in figure 3(c).The field distributions depicted in figures 3(c)-(e) correspond to the characteristics of magnetic dipole resonance, revealing the envisaged EIT phenomenon originates from the detrimental interaction amidst electric dipole and magnetic dipole resonance.
As noted earlier, the suggested EIT-like phenomenon can be dynamically modified by varying the conductivity of VO 2 ( VO2 s ) (by varying temperature) and the conductivity of photosensitive silicon ( Si s ) (by ´/ and Si s varying from 3 10 s m 5 ´/ to 1 10 s m, 2 ´/ the transparency peak experiences a slight shift towards higher frequencies, accompanied by a reduction in amplitude.The bandwidth of the transparency window decreases, and the coupling strength of EIT diminishes.Ultimately, the EIT-like effect vanishes, and the transmission spectra transition to a state characterized by a resonance curve. In order to delve deeper into the regulatory mechanism driving the adjustable EIT phenomenon, we utilize a theoretical framework known as the two-coupled oscillator model.This approach is chosen to correlate with the transmission curves obtained from simulations.The system's behavior is captured by a series of interconnected differential equations that dictate the effective mass (m), amplitude (x), damping rate (g ) of the two harmonic oscillators under the incident wave E E e i t 0 = w - [34,38]: Here, oscillator 1 represents the HS, while oscillator 2 corresponds to HSRR.κ represents the coupling coefficient, g and ω signify geometric attribute and resonance frequency, respectively.Notably, g 2 is set to 0 since HSRR operates as a dark mode oscillator.After resolving the differential equation, the susceptibility of the  metamaterial is delineated by the subsequent equation: Where, K is scaling coefficient, A g g , = =¥ B m m .

=
As effi c characterizes the system's absorption, and the absorption of system is derived by 1-R-T.Here, T is the transmission and R is reflection of system.Thus, the transmission spectra can be fitted using 1effi c and the reflection spectra.Figure 5 depicts the fitted transmission spectra of the EIT metamaterial at various VO2 s and , Si s closely matching the simulated results.
Figure 6 illustrates the fitted values of 1 g and , 2 g as well as the coupling coefficient κ at different VO2 s and .
Si s As shown in figure 6(a), when reducing the conductivity , VO2 s there is a notable rise in the value of , 1 g coupled with a significant reduction in the coupling coefficient κ, while 2 g remain constant.Similarly, as depicted in figure 6(b), when decreasing the conductivity , Si s there is a notable rise in the value of , 2 g coupled with a significant reduction in the coupling coefficient κ, while 1 g remain constant.Due to 1 g and 2 g representing the bright mode resonator's damping rate and dark mode resonator's damping rate respectively, we can conclude that when increasing the bright mode resonator's damping rate, the EIT phenomenon tends towards curves indicating non-resonant states; whereas when increasing the dark mode resonator's damping rate, the EIT phenomenon tends towards curves indicating resonant states.Moreover, a distinguishing feature of the EIT phenomenon is its slow light effect.Consequently, the group delay of the incident wave [39], an essential parameter that characterizes this phenomenon, is evaluated at various VO2 s and .
Si s As illustrated in figure 7, when VO2 s is set to2 10 s m 5 ´/ and Si s is 3 10 s m, 5 ´/ the transparency peak's group delay is measured at 8.32 ps.Furthermore, as VO2 s or Si s is decreased, the group delay diminishes accordingly, thus confirming the conclusion of reduced coupling strength.
To further validate the preceding analysis, figure 8 presents the electric field distribution when the EIT phenomenon dissipates.As depicted in figure 8(a), when Si s fixed at 3 10 s m 5 ´/ and VO2 s is reduced to ´/ and Si s decreases to 1 10 s m, 2 ´/ near-field coupling is constrained, resulting in the continuous concentration of electromagnetic energy on the bright mode resonator, consistent with the transmission spectra exhibiting a resonant curve characteristic.Next, we demonstrate the variations in the EIT phenomenon when simultaneously adjusting VO2 s and .

Si s
As depicted in figure 9, when reducing the conductivities of both VO2 s and Si s simultaneously, several changes occur: the peak frequency of transparency undergoes a redshift, the amplitude of the transparency peak initially decreases before increasing, the frequencies of dip I and dip II also undergo a redshift, and the coupling strength decreases.Ultimately, the EIT-like phenomenon is adjusted until it disappears, manifesting as a transmission spectrum resembling a non-resonance curve state, which is similar to the phenomenon observed when solely adjusting the bright mode resonator's damping rate.Therefore, when simultaneously adjusting the bright mode resonator's damping rate (by varying temperature) and dark mode resonator's damping rate (by varying light intensity), the adjustment of the bright mode resonator's damping rate (by varying temperature) plays a more dominant role.´/ and Si s is 1 10 s m

Conclusions
In summary, we present an innovative dual-control EIT analog utilizing near-field coupling transitioning between electric and magnetic dipole resonances.This approach employs a bright oscillator, initiated by aluminum and vanadium dioxide strips, and a dark oscillator generated by aluminum and photosensitive silicon split-ring resonators.Through active manipulation, our design facilitates dynamic alterations in EIT, responsive to temperature and light intensity adjustments.Simulation results demonstrate selective transitions from EIT to diminishment and either resonance or non-resonance curves.Temperature variations primarily dominate when adjusting both factors simultaneously.Theoretical analysis employing a two-harmonic oscillator model clarifies the adjustable trait's fundamental mechanism, indicating the role of damping rates.Our study enriches the landscape of actively tunable EIT metamaterials, holding significant implications for slow-light switch device development.

Figure 1
Figure 1 provides a schematic representation of the proposed EIT metamaterial.As depicted in figure 1(a), this metamaterial is a periodic arrangement, where each unit cell contains two distinct components crafted on a SiO 2 substrate: a hybrid aluminum-photosensitive silicon split-ring resonator (HSRR) and a hybrid aluminumvanadium dioxide strip (HS).The HS is situated within the HSRR, and the center point of HSRR aligns with the central of unit cell.In figure 1(b), the periodic dimensions are P x = P y = 100 μm.The dimensions of the VO 2 strip are D 2 = 44 μm in length and w = 5 μm in width, while the horizontal aluminum strips of HS have dimensions L 2 = 26 μm in length and w = 5 μm in width.Two photosensitive silicon elements are positioned at the center of the metal strip in the HSRR.The dimensions of the HSRR are as follows: L 1 = 60 μm, D 1 = 19 μm, D = 74 μm, L 3 = 2 μm, and w = 5 μm.The distance s between the center of HS and unit cell in horizontal direction is set to 5 μm.The thicknesses of VO 2 , aluminum, photosensitive silicon, and SiO 2 are all 5 μm.According to existing research findings, the parameters specified above can be successfully implemented in practical applications[30].

Figure 1 .
Figure 1.Diagram arrangement: (a) Three-dimensional schematic perspective and (b) overhead representation of a unit cell.
s denotes the conductivity of VO 2 , which is modulated by temperatures within the range from 2 10 s m 2

Figure 2 . 2 ´
Figure 2. Transmission curves of isolated HS, isolated HS and EIT scheme when VO2 s is 2 10 s m, 5 ´/ Si s is 3 10 s m

Figure 3 .
Figure 3.The field distributions of the isolated HS and HSRR at 1.33 THz, as well as the field distribution of EIT scheme at 1.27 THz: (a) electric field of isolated HS; (b) electric field of isolated HSRR; (c) electric field of EIT scheme; (d) magnetic field of EIT scheme; (e) surface current of EIT scheme.

Figure 4 .
Figure 4. Transmission curves of EIT scheme at various conductivity:(a) Si s is 3 10 s m, 5 ´/ VO2 s is various; (b) VO2 s is 2 10 s m, 5´/ Si s is various.

Figure 5 .
Figure 5. Fitting transmission curves of EIT scheme at various conductivity:(a) Si s is 3 10 s m, 5 ´/ VO2 s is various;(b) VO2 s is 2 10 s m, 5´/ Si s is various.

Figure 6 . 1 g 2 g
Figure 6.Fitting values of , 1 g 2 g and κ at various conductivity:(a) Si s is 3 10 s m, 5 ´/ VO2 s is various;(b) VO2 s is 2 10 s m, 5 ´/ Si s is various.

2 10 s m, 2 ´fixed at 2 10 s m 5
/ neither HS nor HSRR show any response to the incident wave, consistent with the characteristic of the transmission spectra being a non-resonant curve.Similarly, figure 8(b) illustrates that when VO2 s

Figure 7 .
Figure 7. Incident wave's group delay at various conductivity:(a) Si s is 3 10 s m, 5 ´/ VO2 s is various;(b) VO2 s is 2 10 s m, 5´/ Si s is various.

Figure 8 .
Figure 8.The electric field distribution when the EIT phenomenon dissipates:(a) Si s is 3 10 s m 5´/ and VO2 s is 2 10 s m;2´/ (b) VO2 s is 2 10 s m 5

Figure 9 .
Figure 9. Transmission curves of EIT scheme when simultaneously adjusting VO2 s and Si s .