Polarization and incidence insensitive dielectric electromagnetically induced transparency metamaterial

In this manuscript, we demonstrate numerically classical analogy of electromagnetically induced transparency (EIT) with a windmill type metamaterial consisting of two dumbbell dielectric resonator. With proper external excitation, dielectric resonators serve as EIT bright and dark elements via electric and magnetic Mie resonances, respectively. Rigorous numerical analyses reveal that dielectric metamaterial exhibits sharp transparency peak characterized by large group index due to the destructive interference between EIT bright and dark resonators. Furthermore, such EIT transmission behavior keeps stable property with respect to polarization and incidence angles. ©2013 Optical Society of America OCIS codes: (160.3918) Metamaterials; (230.4555) Coupled resonators; (260.5430) Polarization. References and links 1. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. 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Introduction
Recently, metamaterial microstructures have been employed to mimic electromagnetically induced transparency (EIT) behavior of atomic system [1][2][3][4][5][6].A sharp transmission peak along with steep normal dispersion results in large value of group index, which is of great interest to the enhancement of group delay and slow light control [7].To resemble classical EIT behavior, various metamaterial based approaches including "trapped mode" [1][2][3][4] and destructive interference between isolated bright and dark elements were proposed [5,6,[8][9][10][11][12][13][14][15][16][17][18][19].For the latter case, bright and dark elements generally have same resonance frequencies, around which bright element can be excited by the incident beam directly while dark elements do not coupled directly to external wave, but can be excited by local field of bright element resonance via near field coupling.
Up to now, most previous studies of EIT metamaterials employ metallic split ring resonator (SRR) and related planar structures [8][9][10][11][12][13][14][15][16][17][18] based on conduction currents oscillation of induction-capacitance (LC) resonance.Anisotropic properties of conventional planar EIT metamaterial microstructures results in strict requirement on polarization angle, which becomes problematic in potential applications.The local field coupling between dark and bright elements enhances the difficulties to realize polarization insensitivity even in symmetrical wires and SRR system [19].Alternatively, Mie resonance of dielectric particle exhibits abrupt sign change for effective permittivity/permeability around electric/magnetic resonance, providing ideal candidate means to realize metamaterial [20][21][22][23].In contrast to LC resonance of metallic microstructure, Mie resonance is only accompanied by displacement current oscillation.Furthermore, due to the lack requirement of the capacitance gap, the main source for anisotropic influence of metallic planar structure, it is more convenient to design polarization and incidence independent metamaterial via dielectric Mie resonance.However, there are few attentions given on dielectric EIT metamaterial [24,25].
In the letter, we propose a windmill type dielectric EIT metamaterial at terahertz regime.Instead of isolated dark and bright elements for EIT metamaterial, herein elementary unit is a unified cell composed of two orthogonal dumbbell dielectric resonators, which serves as bright and dark elements via electric and magnetic Mie resonance, respectively.Rigorous numerical results reveal a typical EIT transmission peak along with large group index occurs around 0.5 THz.Besides, such behavior shows independent property to incidence angle and polarization.

Results and discussion
Figure 1 depicts schematically configuration for dielectric EIT metamaterial.A windmill configuration is proposed as a combination of two identical dumbbell type twisted by 90°.Each dumbbell cell consists of two square bricks separated by a dielectric bar.The whole dielectric metamaterial array is patterned on a fused quartz substrate (ε Quartz = 3.794 + 0.003i) [26].Dielectric layer is assumed as Titanium oxide (TiO 2 ) with a relative large permittivity and moderate dielectric loss at terahertz frequencies (ε TiO2 = 114, tanδ TiO2 = 0.01) [27].The geometrical parameters are given in the caption of Fig. 1.The scattering response of EIT metamaterial is calculated by using 3D full wave frequency domain package, High Frequency Structure Simulator (HFSS).At the first stage, we carry out investigations on transmission characteristic of single dielectric dumbbell cell with various excitations, as shown in Fig. 2(a).When a single dielectric dumbbell type metamaterial cell is under normal illumination with electric field parallel to dielectric bar (upper inset of Fig. 2(a)), a visible transmission dip with a quality factor Q = 101 occurs at 0.495 THz.This resonance arises from electric Mie resonance via longitudinal displacement currents oscillation along the whole dumbbell, as displayed in top panel of Fig. 2(b).However, for a grazing incident beam with electric field perpendicular to dielectric bar, a sharp resonance with higher quality factor (Q = 139) than previous case under normal incidence is strong overlapping of the electric resonance.From the local field distribution (bottom panel of Fig. 2(b)), a magnetic Mie resonance, resulting from circular displacement current loop concentrated inside two dielectric bricks of dumbbell resonator, is responsible for this transmission dip.Moreover, such Mie resonance is mainly determined by the dielectric bricks, while the connection dielectric bar only leads minor frequency shift.It is noted that magnetic resonance cannot be observed under normal incidence with same polarization (not shown here), indicating the possibility to serve as EIT dark element.According to two-resonator-model for EIT metamaterial [5,6], it is obvious that two dumbbell resonators are required.That means one dumbbell is electrically coupled directly to the incident beam as bright element and the other one, whose resonance cannot be observed directly for normal incidence, acts as a dark element.Finally, a windmill type configuration is formed by two dumbbell resonators for EIT metamaterial design.Figure 2(c) presents the scattering parameters of windmill metamaterial under normal incidence with electric polarization along x axis.Clearly, a typical EIT-like transmission spectrum with one sharp peak located at 0.483 THz and two transmission dips at 0.465 and 0.528 THz can be observed.Compared to the resonance frequency of bright/dark element, slightly frequency shift of EIT peak mainly attributes to the overlap of middle parts of twisted dumbbell resonators.
To look insight the underlying physics for such dielectric metamaterial, local electric field distributions of transmission peak and dips are monitored and given in Fig. 3.At the transmission dips around EIT windows, as shown in Figs.3(a) and 3(c), linearly oscillated displacement currents are excited along the vertical dumbbell resonator, which is directly coupled to incident electric field, hence, leading to vanishing transmission.Subsequent local magnetic field produced by displacement currents along vertical dumbbell further induces anti-orientation circular displacement currents distribution inside two square bricks of horizontal dumbbell.At the transmission peak frequency, as presented in Fig. 3(b), most local displacement currents are localized inside two square bricks of horizontal dumbbell and mere displacement currents are observed along the vertical dumbbell, due to destructive interference between resonance modes of dark and bright resonators.Employing a well-established retrieval algorithm [28], electromagnetic parameters including effective index, n, can be obtained.The group index, n g = n + ωdn/dω, is further calculated and presented in Fig. 4. Within the EIT transmission window, the group index experiences strong dispersion.The peak value over 100 for group index and low value of imaginary part of effective index reveal great interest of potential application in slow light control.Figure 5(a) presents the transmission spectra as a function of frequency and polarization angle off to x axis.Electric polarization angle off to x axis varying 180° were investigated, even though only four polarization angles were plotted.As incident polarization varies, transmission spectra difference is so minor that can be negligible, clearly demonstrating the polarization independence property of dielectric EIT metamaterial.Local electric field distribution at EIT transmission peak under various polarization excitations were given in Figs.5(b) and 5(c).When the incident polarization is off to x axis, accumulation of local field is no longer concentrated inside two dielectric bricks of single dumbbell resonator, despite the amplitude distribution mainly depends on polarization angle.This is because two orthogonal dielectric bars can be excited by incident electric field components along x and y axes, consequently, such electromagnetic energy can be finally transferred into corresponding dielectric brick resonators.Actually, local field interference between bright elements plays an important role to design a polarization insensitive property.As reported in Ref. 25, construction/destruction interference of local fields of two orthogonal bright elements can result in the enhancement or elimination of EIT effect, when polarization angles are 135° and 45°, respectively.On the contrary, dielectric brick resonators' locations at the vertex of dielectric bar in this manuscript ensure these dark elements can only be excited by single bright element under various polarizations.Furthermore, symmetric configuration of windmill microstructure leads to unchanged resonance frequencies of bright and dark elements.As a consequence, EIT behavior is independent of varying polarization.6, for normal incidence, dumbbell metamaterial shows the same EIT transmission characteristics for TE and TM polarizations.With increasing incident direction angle off to z axis, θ, EIT peaks shows a stable behavior for both TE and TM modes.A maximum frequency shift is around 0.03 THz, accounting for 6% with respect to central frequency.Even though, EIT transmission feature remains under oblique incident up to 75° off to z axis.Obviously, this shows the advantage of dielectric metamaterial in the realization of planar isotropic EIT structure.

Conclusions
In conclusion, we present a full dielectric windmill type EIT metamaterial at terahertz frequency.With proper design, electric and magnetic Mie resonances of dumbbell resonator enable superradiant and subradiant resonance nature under different excitation.Rigorous numerical analyses verify such planar dielectric metamaterial exhibits typical EIT transmission peak along with large value of group index.Due to symmetry configuration, windmill type EIT metamaterial possesses a nearly independent characteristic of EIT transmission feature on polarization and incidence angle.Furthermore, recent advance on magnetic sputtering approach and lithography [29] to prepare dielectric film enables the feasibility of dielectric EIT metamaterial at terahertz as proposed in this manuscript.Considering strict requirement for polarization independence in real application, it can be expected that this work will be useful to promote the development of EIT metamaterial and slow light device.

Fig. 2 .
Fig. 2. (a) Transmission spectra of dielectric resonator under electric and magnetic field excitation.The insets show schematically dumbbell resonator under normal (upper) and grazing incidences (bottom).(b) Local electric field distribution of dielectric resonator around electric (upper panel) and magnetic resonances (bottom panel).(c) Transmission spectra for windmill type dielectric EIT metamaterial.

Fig. 4 .
Fig. 4. Group index and imaginary part of phase index for dielectric windmill type EIT metamaterial.

Fig. 5 .
Fig. 5. (a) Transmission spectra as a function of frequency and polarization angle.Local electric field distribution at EIT peak frequency f = 0.485 THz under incidence polarization of (b) φ = 30°and (c) φ = 135°.Inset shows the electric polarization varies with respect to x axis.

Figure 6
Figure6displays EIT metamaterial transmission spectra as a function of frequency and incident angle under TE and TM modes.As shown in Fig.6, for normal incidence, dumbbell metamaterial shows the same EIT transmission characteristics for TE and TM polarizations.With increasing incident direction angle off to z axis, θ, EIT peaks shows a stable behavior for both TE and TM modes.A maximum frequency shift is around 0.03 THz, accounting for 6% with respect to central frequency.Even though, EIT transmission feature remains under oblique incident up to 75° off to z axis.Obviously, this shows the advantage of dielectric metamaterial in the realization of planar isotropic EIT structure.

Fig. 6 .
Fig. 6.Oblique incidence as a function of frequency for dielectric EIT metamaterial.(a) TE and (b) TM mode.