Demonstration of dipole-induced transparency using mirrored split-ring resonator metasurface for microwave applications

In this paper, the Dipole-Induced Transparency (DIT) in the microwave frequency regime is proposed and verified using experimental and simulation studies. A single-layer mirrored Split-Ring Resonator (SRR) array configured in the H⊥ excitation scenario is used to create an out-of-phase oscillating electric dipole moment for a normal incident plane wave. The destructive interference between these out-of-phase oscillating electric dipole moments nullifies far-field scattering resulting in the emergence of the transparency window. We used the multipole scattering theory to validate the results computationally. The coupling effects are studied numerically, and the emergence of the transparency window is studied experimentally using transmission measurements inside an anechoic chamber using a vector network analyzer.


Introduction
Electromagnetically induced transparency (EIT) is a quantum interference effect occurring in atomic systems and is responsible for a transparency band within a broad absorption spectrum [1]. This transparency scheme modifies the dispersive nature of the opaque medium under consideration and shows electromagnetic wave slow down, resulting in enhanced light-matter interaction making the scheme suitable for electromagnetic sensing applications. EIT stems from the destructive interference from a multi-level system in which the net electric dipole moment of the atomic system is found to be vanished [2]. Under the EIT conditions, the propagating electromagnetic wave experiences a large positive dispersion, and its group velocity will be significantly reduced. This slow light effect is an essential characteristic of the EIT phenomenon and finds applications in quantum memories. When the light pulse enters an EIT medium, it gets slow down and undergoes spatial compression. The group velocity can be made zero by reducing the control field magnitude, causing the complete stopping of light and storing light within the medium [2].
EIT is also observed in classical coupled resonators in the optical domain [3], in resonator coupled optical waveguides [4], and in metamaterials [5][6][7][8]. In metamaterials, an external plane wave directly excites the bright resonance, which is efficiently coupled to the far field. The dark resonance is a high Q resonance and is weakly coupled to free space. An asymmetry in the unit cell creates resonant anti-parallel currents in the composite resulting in a trapped mode resonance [9][10][11]. The sharp dispersion associated with the trapped mode resonance causes the electromagnetic pulse to be significantly delayed of the order 200 times that of the velocity in free space.
The metasurface is a two-dimensional counterpart of metamaterials whose response is characterized using electric and magnetic polarizabilities and can be used for a wide range of applications [12,13]. In this paper, we experimentally demonstrate the existence of Dipole-Induced Transparency in the microwave regime using a mirrored SRR metasurface. The emergence of the transmission band within the forbidden energy gap is characterized by the dip in the Radar Cross Section (RCS) of the composite. Multipole scattering theory reveals that the emergence of the transparency 1 3 window is associated with scattering suppression due to the resonant out-of-phase oscillation of electric dipole moments excited on the composite. Experimental studies are performed inside an anechoic chamber using a vector network analyzer, and computations are performed using the fullwave electromagnetic simulation software CST Microwave Studio.

The geometry of the problem
The fundamental constituent used in the study is the Split-Ring Resonator (SRR). SRR unit cell is conventionally used to get the mu negative behavior at resonance [14]. The application of a plane wave with polarization parallel to the split with the incident magnetic field parallel to the axis of the SRR creates magnetic dipole moments parallel to the incident magnetic field. This excitation scenario is referred to as the H || excitation [15]. Another excitation is the H ⊥ scheme in which the incident electric field is parallel to the slits, the magnetic field is perpendicular to the axis of the SRR, and the direction of propagation is oriented along the axis of the SRR. This excitation creates strong electric dipole moments on the SRR array, and these in-phase oscillating electric dipole moments create a dielectric bandgap.
We have used the H ⊥ excitation in this study, and the difference is that the used SRR array is asymmetrical. We have used a mirrored array of SRR to create a transparency window within the dielectric bandgap as shown in Fig. 1. The SRR array is printed on an epoxy substrate having a relative dielectric constant of 3.8 and a height of 1.6 mm. The split gap is represented by 's.' The dimensions of the SRR are selected such that its resonant frequency lies within the microwave S-band. The offset parameter is represented as 'g' as shown in Fig. 1.

Results and discussions
The DIT behavior using the proposed mirrored configuration is computationally analyzed using the full-wave CST Microwave Studio software. The parameters of the proposed SRR array are r = 6.7 mm, d = 2 mm, s = 0.8 mm, w = 1 mm, and h = 1.6 mm. The thickness of the metallic implant is 35 µm. The periodicity of the SRR array is p = 20 mm mm both in X and Y directions on both sides of the symmetry line. The asymmetry parameter 'g' is selected to be 1.1 mm. We have also simulated a single layer symmetric SRR array having the same dimensions and periodicity for a comparison study. Both the arrays use a total of 64 SRR elements in the plane. Both the arrays use a total of 64 SRR elements in the plane.
For simulations, both the structures are illuminated with a plane wave traveling perpendicular to the plane of the SRR array with polarization along the Y-axis. We have studied the scattering characteristics of both these arrays using computation. The Radar Cross Section (RCS) of a structure is defined as where R is the distance from the target to the observation point, E inc is the incident electric field measured at the target's position, and E sca is the scattered electric field measured at the observation point. Figure 2 shows the RCS of the symmetric and mirrored SRR arrays. As expected, the symmetric SRR array shows a hike in the scattering spectra at resonance centered on 2.28 GHz. This resonance is characterized by the dominant scattering contribution from the electric dipole (P y ) moments. The RCS value is significantly higher of the order of around 30,425 mm 2 due to this bright electric dipole scattering and is said to be a highly visible resonance.
Interestingly, the RCS of the mirrored array shows low values indicated by the shadow region in comparison with the symmetric SRR array. The scattering reduction region spans over a frequency range from 2. Measurements are performed inside an anechoic chamber using two Ultra-Wide Band horn antennas. One horn antenna is configured in the transmission mode, and the other one is working in the reception mode. Initially, a THRU calibration is performed to nullify the path loss. The metasurface sample is inserted between these antennas to achieve the H ⊥ excitation scenario. The schematic of the measurement setup is shown in Fig. 3a. The resulting transmission coefficients for the symmetric SRR array are illustrated in Fig. 3b. As expected, the symmetric array shows a dielectric band gap centered around the resonant frequency f s = 2.28 GHz, and correspondingly, the transmission coefficient is characterized by a dip showing resonant nature. The simulation and measurement are well matched. This resonance is characterized by strong electric dipole moments P y and is caused due to the time-varying positive and negative charge distributions on the lower and upper unit cells. In the array, these electric dipole moments are oscillating in-phase, as shown in Fig. 3c. The scattering behavior of this SRR array is also studied by exciting the entire array with an external plane wave with polarization along the Y-axis using CST Microwave Studio. At resonance, the structure shows symmetric The symmetric array showing the bandgap is replaced with the mirrored array configuration shown in Fig. 1. Figure 4 illustrates the transmission characteristics of this array. It is evident from the graph that a resonant transparency window is created within the bandgap for the mirrored array. This window is indicated using the shaded regions in the graph. Three resonant frequency points are observed designated as f 1 , f 2, and f 3 . The newly created resonant window is centered at f 2 = 2.21 GHz. The transmission coefficient at this transparency window is found to be -0.6 dB in measurement. The transmission minima are found to be at f 1 = 2.13 GHz and f 3 = 2.32 GHz. The simulation and measurements are well matched.
The measured transmission phase of the two arrays is depicted in Fig. 4b. The transmission phase shows distinctly different characteristics for the small frequency band under study. The symmetric SRR array shows smooth phase advancement across the bandgap. For the lower resonant dip around f 1 , anomalous phase advancement is observed. Since the group delay is calculated as the negative rate of change of phase with frequency = − dΦ d , this region is characterized by a negative group delay (GD). So this resonant dip can be said as a trapped mode, in which the electromagnetic energy is strongly confined within the vicinity of the metasurface. The transparency band centered on f 2 shows a sharp decrease in phase with respect to frequency. Correspondingly, the group delay will be positive, causing a significant delay for the transmitted pulse. The reflection resonance at f 3 is characterized by an abrupt phase jump characterizing a reflective resonance. Since the transparency window is associated with a high group delay, the group velocity of the electromagnetic wave gets reduced. This ensures an enhanced light-matter interaction favorable for dielectric sensing applications. An unknown dielectric material inserted at the symmetry plane will shift the transparency peak to lower frequencies. So this technique could be used as a far-field sensor, in which Monostatic scattering measurements are enough to detect the unknown permittivity of the sample. Since electromagnetic waves around the transparency window are associated with a larger lifetime, the electromagnetic interaction with the sample is enhanced, resulting in a higher sensitivity.
Simulation studies are also performed to find out the nature of electromagnetic power flow across the dispersion band under consideration. Figure 5 shows the Poynting vector distributions of the mirrored array for the three frequency points. The plane wave is traveling along the Z-axis from top to the bottom of the computational domain. Obviously, for the trapped mode resonance centered around 2.16 GHz (Fig. 5a), a transverse flow of electromagnetic power is observed at the discontinuous boundary of the metasurface layer. The circulation of Poynting vector distribution near the metasurface boundary confirms the presence of the trapped mode. At this trapped mode resonance, the electromagnetic waves experience a large lifetime enabling maximum light-matter interaction. For the transparency window centered around 2.21 GHz (Fig. 5b), the pointing vector distributions are normal to the entrance and exit faces indicating a smooth electromagnetic power flow across the boundary.
At this transparency window, the structure shows minimum scattering and is responsible for the RCS dip. This smooth flow of electromagnetic power is similar to that observed in electromagnetic cloaking schemes [16]. The highly reflective resonance shown in Fig. 5a around 2.32 GHz shows a significant perturbation of electromagnetic power flow and shows a high RCS value. It is noted that for the three frequency points, edge diffraction is observed on the left and right boundaries of the metasurface.
The scattering behavior of the mirrored array depicted in Fig. 2a shows a close similarity with a Fano resonance profile [17]. In Fano resonance, the destructive interference is achieved by the combined effect of electric and magnetic resonance to reduce total scattering and show asymmetric scattering profile. However, here the situation is quite different. We used the multipole scattering theory to understand the exact reason behind these peculiar scattering characteristics. Since the H ⊥ excitation scheme induces only the electric dipole moment on the SRR composite, only the power scattered from the electric dipole moment is expected. The induced dipole moments could be calculated by spatial integrating the surface current density excited on the composite as [18] where P, M, T and represent the induced electric, magnetic, and toroidal dipole moments, ⍵ is the angular frequency, J is the volume current density, r is the distance to the far-field observation point.
The normalized scattered power from these dipole moments for the symmetric SRR array is shown in Fig. 6. It is noted that the power radiated from the electric and toroidal dipole moments shows a dip around the transparency window. The radiated power from the electric dipole moment is less than that of the symmetric SRR array for the entire transparency window. For the symmetric array, the H ⊥ excitation scheme causes the separation of resonant positive and negative charges on the top and bottom SRR elements creating a net electric dipole moment (P y ) on the composite. Hence, this resonance is highly reflective, causing a transmission dip and a hike in RCS value around resonance. The mirrored configuration disturbs the uniform phase distribution of this excited electric dipole moment causing destructive interference at the far field. It is to be noted that the power radiated from the toroidal moment for . 4 a Simulated and measured transmission coefficients of the mirrored SRR array, b measured transmission phase of the mirrored and SRR arrays the mirrored array is in comparison with that for the mirrored array. Moreover, the electric dipole moment's radiated power is tremendously higher than that from the toroidal moment for the mirrored array. The magnetic dipole moment is non-resonant because the H ⊥ excitation scenario is incapable of exciting resonant magnetic dipole on the composite. The orientation of the magnetic dipole moment is directed along the direction of propagation (Z-axis), and hence, it is weekly coupled to free space. Hence, it can be concluded that the transparency window emerges due to the cancellation of radiated power from the electric dipole moment. This scattering cancellation effect can be well understood by studying the phase of electric field distributions (E y ) taken over the two arrays, as shown in Fig. 7. It is observed These out-of-phase oscillations between the electric dipole moments cancel the far-field scattered power resulting in the emergence of the transparency window. An equivalent behavior is observed in the cloaking of a sensor or a metallic target [19,20]. In this scenario, the far-field scattering offered by the electric dipole moment of the dipole or the sensor is cancelled by the out-of-phase scattering of the cloaking layer, and hence, the antenna is invisible to a farfield observer without deteriorating the radiation characteristics of the antenna. In the mantle cloaking technique, the electric surface reactance of the cloaking layer is adjusted to cancel the far-field scattering offered by the cloaking layer [21,22]. Parametric analysis has been performed to find out the effect of various parameters on scattering spectra. Figure 8a shows the effect of the gap parameter 'g' on the scattering spectrum. For all these variations, a normal incidence plane wave is considered. It is observed that the scattering dip will be more pronounced when the mirrored elements are brought closer to each other. As 'g' is increased, a redshift in the scattering maximum is observed. When 'g' is increased above 3.1 mm, no significant change in the scattering dip is observed. Parametric studies have also been performed by varying the angle of incidence along the azimuth plane, and these results are shown in Fig. 8b. It is noted that the angle of incidence plays a crucial role on the scattering characteristics. The scattering dip around 2.17 GHz is clearly observed for normal incidence. As the angle of incidence increases in steps of 10°, the structure loses the scattering reduction behavior. When the incident angle is increased beyond 20°, the scattering behavior looks similar to the symmetric SRR array, and the transparency window is found to have vanished.

Conclusion
This paper presents an experimental and computational demonstration of Dipole-Induced Transparency scheme in the microwave regime. Multipole scattering theory has been utilized to find the exact reason behind the emergence of this transparency window. The mirror symmetry in the orientation of the SRR array creates an out-of-phase oscillation of electric dipole moments, resulting in scattering suppression from the composite at the far field. This scattering cancellation scheme is computationally verified using full-wave simulations and found that the transparency window is associated with a dip in the Radar Cross Section of the composite. Parametric studies have also been performed to find out the effect of various parameters on scattering characteristics. The high group delay associated with the transparency window will pave the way for developing an efficient far-field dielectric sensor in the future.
Funding The authors acknowledge the research funding received from the Science and Engineering Research Board (SERB), Department of Science and Technology, for the major research project ECR/2017/002204.

Data availability
Enquiries about data availability should be directed to the authors.

Declarations
Conflicts of interest There are no conflicts of interest.