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Abstract
We have theoretically proposed electrical modulation and enhancement of Fano resonance in THz metamaterials. In order to practically realize Fano resonance based devices, resonance dips should be sharp and to be clearly detected. However, realization of Fano resonances with simultaneously high quality factor (Q) and higher spectral contrast remains a major challenge. Therefore we propose a metamaterial based device to overcome the above limitation with active tuning capability. Our simulated results show a large enhancement of surface current and electric field, which results in sharp, extremely narrow bandwidth Fano type resonances. Furthermore, a higher degree of tunability has been achieved for Fano resonance as compared to dipole resonance, which can be useful to realize advanced dynamically reconfigurable devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic wave manipulation and complex light-matter interaction has gained immense interest due to rapid development of numerous novel, wide range of technologies at micro, nanoscale level to control, communicate, detect and monitor information that one can obtain from electromagnetic waves. One of the convenient and efficient way to manipulate and localize electromagnetic (EM) wave is by employing metamaterial based devices. Metamaterial is artificially engineered sub-wavelength structure [1,2] designed in such a way to yield desired resonant response to incident EM radiation. Hence it can be employed in numerous applications like realization of perfect and flat lens, sensors, ultra-compact antennas, slow light, negative refractive index, EM wave modulator, frequency selective surfaces etc. [3–5]. One of the most fundamental metamaterial structure, consists of split ring resonator (SRR), was employed to obtain artificial magnetism and negative index of refraction at microwave frequency domain [1,6]. Typical resonant responses of metamaterial structures follow symmetrical spectral feature described by Lorentzian function. However, due to direct excitation, these metal based resonators predominantly suffer from huge metallic and radiative losses [7,8]. Among them, radiation loss contributes to the largest of metamaterial losses [9]. One of the solutions to minimize radiation loss is with the help of indirect excitation, whose response is characterized by the resonance of asymmetric line-shape, termed as Fano resonance [10,11].
Fano resonance was invented by Ugo Fano in the year 1961 [12], which is excited due to the interaction of broadband continuum with a discrete narrowband scattering event. In metamaterial structure, Fano resonance was first proposed by Fedotov et al. termed as sharp trapped mode, which occurred due to symmetry breaking in metamaterial structure [13]. At the same time, Zhang et al. introduced transparency in plasmonic metamaterials created as a result of destructive interference between super-radiant and sub-radiant resonators [14]. Later on, R. Singh et al. experimentally demonstrated the occurrence of Fano resonance in THz frequency regime using dual gap SRR where structural asymmetry was considered along the direction of the applied electric field [15]. THz frequency range is very useful for biological and chemical label-free sensing, characterization of materials, astronomical observations, security purpose, medical diagnostics, logical operations and environmental monitoring applications [16–19]. Due to indirect excitation and destructive interference between super-radiant (bright) and sub-radiant (dark) mode, Fano resonance is relatively free from high radiation losses. Thus, such high Q, low loss Fano resonances at THz frequency regime are extremely useful for realization of narrowband filters, highly sensitive sensors, slow light devices, and other applications [10].
Numerous metamaterial structures have been proposed so far [13–15,8–22] to realize Fano resonance. In spite of the superior capability of Fano resonance based metamaterial, a trade-off between quality factor (Q) and spectral contrast (or Figure of merit (FOM)) becomes inevitable. As, the structural asymmetry is decreased, Q factor of Fano resonance becomes higher [23]. However, the FOM and spectral contrast also decreases simultaneously with the decrease of structural asymmetry. This causes extreme difficulty to detect Fano resonance and also limit its application possibilities. In addition to that, such passive devices limits the scope of applications and their reconfigurable abilities.
Recently, active metamaterials have attracted enormous interests because of its tunable electromagnetic properties with ultrashort modulation time and on-off switching capabilities. Different techniques have already been proposed by using semiconductors [24,25], superconductors [26], phase change materials [27,28], perovskites [29], graphene [30,31], $V{O_2}$ [32,33], varactor diode [34,35] and electromechanical structures [36] etc. In spite of relatively higher response time in comparison to other techniques, electronic modulation of THz waves has gained much attention due to its low easy integration capability in chip level design [37]. Recently electronic tunability has been realized by using Graphene metasurfaces [29,30]. Although, due to high conductivity of Graphene at THz regime, a higher absorption loss of the resonator eventually degrades the performance of metamaterial devices [31]. An alternative method to tune dipole resonance was proposed by Aydin et al. [38] by using variable capacitors but those are limited to microwave frequency range.
In this paper, we have proposed and theoretically studied modulation performance of Fano resonance using active metamaterials by incorporating variable capacitor operating at THz frequencies. It also shows a highly sharp Fano resonance with Q factor of nearly 380. Our proposed structure is advantageous as it has overcome the trade-off problem between the Q factor and spectral contrast/ FOM of Fano resonance. On the other hand, we’ve demonstrated a detailed and comparative analysis of relative modulation performance of both dipole and Fano resonance with variable capacitors in both the gaps. Our proposed structure can also be capable to suppress the Fano resonance dip completely, which can be employed as THz switches and modulators. Such active tuning of high Q Fano resonance can be extremely useful to realize multi-functional metamaterial devices in the THz frequency domain.
2. Structure and simulation method
The schematic of our proposed structure is shown in Fig. 1. In this study, we’ve taken planar two gap SRR sample with gaps ${G_1}$ and ${G_2}$ in the horizontal arms. Substrate is considered as intrinsic silicon (ɛ=11.68) wafer on top of which 200 nm thick Aluminum resonator (in yellow) has been designed. Typical dimensions are described in the caption of Fig. 1(a). The asymmetry in this structure is introduced by varying the shift parameter ‘d’, which is the axial distance between two split gaps. Electronic tuning capability has been achieved by introducing external capacitors $\; {C_1}$ and ${C_2}$ in the lower and upper gap, respectively.
Fig. 1. Schematic of (a) Unit cell of proposed metamaterial structure with typical dimensions ls = 75 μm, lsrr = 60 μm, w = 6 μm, ${G_1}$ = ${G_2}$ = 3 μm, (b) periodic stack of the proposed structure where external capacitor is introduced only in the lower gap.
To study the electromagnetic responses of the metamaterial, numerical calculations have been carried out using FDTD (finite difference time domain) solver in CST microwave studio software. Here, unit cell boundary condition has been employed to calculate the transmission spectrum. Electric field is applied along the horizontal arms as shown in Fig. 1(a). For such structure, axis of asymmetry has been considered along the direction of E-field. The resonator arm to the left of gaps ${G_1}$and ${G_2}$ is directly excited by incident electromagnetic wave called as super-radiant resonator. The right resonator is very weakly coupled to free space radiation termed as sub-radiant resonator. Destructive interference between the responses of both the resonators results in asymmetric Fano resonance [11].
3. Results and discussions
3.1 Realization of high Q Fano resonance and overcoming the Q factor–FOM trade-off
This numerically simulated results of amplitude transmission spectra for d = 20 μm with (in red) and without (in black) ${C_1}$ are shown in Fig. 2(a). The leftmost resonance dip of both the cases at around 0.98 THz is of symmetrical in shape created due to direct excitation with incident EM radiation known as dipole mode. Other resonant dips around 1.28 THz (without capacitor) and 1.2 THz (with capacitor) are asymmetric in nature, created due to interference phenomena as explained earlier [15], termed as Fano mode. The peak around 1.1 THz is termed as transparency peak (or EIT). Surface current distributions for different resonances are shown in Fig. 2 (b) – (e). It is interesting to note that, for d = 20 μm, the insertion of external capacitor in the lower gap leads to a very high (∼ ‘315’) Q factor (calculated as $Q = {f_0}/{\Delta }f$, where, ${\Delta }f$ is Full width at half maxima (FWHM)), as compared to ∼ ‘10’ in the absence of any external capacitor. In order to understand the origin of such high Q Fano resonance, we also examine the surface current distribution at the Fano dip (Fig. 2). The shape of Fano resonance is given by [39]:
Fig. 2. (a) Variation of amplitude transmission with frequency when external capacitor is loaded in lower gap of the resonator (red curve) and resonator without external capacitor (black curve) for d = 20 μm. Fano dip at f = 1.2 THz (single capacitor in lower gap) and f = 1.28 THz (no capacitor). Surface current distribution at (b) dipole dip for f = 0.98 THz, (c) EIT peak for f = 1.1 THz, (d) Fano dip for f = 1.28 THz when no capacitor is loaded with the resonator (e) Fano dip for f = 1.2 THz ($\; {C_1} = 0.5\; fF$ loaded at lower split gap).
This equation clearly indicates that Fano shape depends on the following 3 factors:
- (i) Fano parameter ‘q’ which is generally taken to be constant for any particular mode.
- (ii) Coupling coefficient ($\kappa $) of both the mode.
- (iii) Phase shift between bright and dark modes in analysis of exactness and accuracy of Fano-like behavior.
Without any external capacitor, all the three factors involves in Eq. (1) will be constant. When external capacitor is added to lower gap, coupling is increased significantly. Induced surface current distribution supports this observation (Fig. 2 (d) & (e)). This figure clearly indicates that stronger surface current is induced at f = 1.2 THz in presence of the external capacitor (max. value ∼ 3.01×105 A/m), which is almost 6.34 times of magnitude larger compared to the case without external capacitor (max. value ∼ 4.74×104 A/m). This strong enhancement in surface current is due to the large displacement current mediated by $ {C_1}$ at the split gap. Higher charge accumulation and electromagnetic energy confinement leads to lower radiation loss which results in high Q Fano resonance.
We have studied further about the effect of asymmetry parameter ‘d’ on the sharpness of Fano resonance with external capacitor ${C_1}$ in lower gap. Figure 3(a) shows the transmission spectra for $ {C_1}$ = 0.5 fF and different d. It’s quite interesting to see that, unlike previous reported results [15,23], the Q factor of Fano dip increases almost linearly with increasing d (asymmetry) (Fig. 3(b)). This is possibly due to the fact that in the presence of capacitor, field confinement in the split gap becomes much higher with increasing d. This results in lower radiation loss with higher asymmetry. Thus, we can achieve Fano resonance simultaneous higher Q factor and higher intensity contrast at the increase of asymmetry parameter d. In order to quantify, the Figure of merit, FOM (= Q×A, where A corresponds to maximum amplitude of Fano resonance). FOM follows the similar behavior as Q factor as shown in Fig. 3(b). Thus, we can achieve a very high Q factor as well as high FOM with the help of external capacitor in higher asymmetry regime.
Fig. 3. (a) Amplitude transmission spectra for different asymmetry (d) with $\; {C_1}$ = 0.5 fF (b) Variation of Q-factor and FOM of Fano dip for different values of asymmetric parameter (d) with $\; {C_1}$ of 0.5 fF loaded in the lower gap.
3.2 Electronic tuning of Fano resonance and FOM optimization
Electronic tuning is achieved through varying the values of the external capacitors. Figure 4(a) & (b) shows resonance tuning with varying external capacitor in the lower gap corresponds to d = 10 and 20 μm respectively. To quantify the resonance tuning, variation of resonance dip position of different modes with different capacitor values are shown in Fig. 4(c). From these graphs, it can be seen that, changing the capacitor value modifies both dipole and Fano resonance position, however the degree of tuning is comparatively larger for Fano resonance in case when only $\; {C_1}$ is present. Although, presence of both $\; {C_1}\; $and $\; {C_2}$ tunes dipole resonance significantly. Also,$\; {C_2}$ causes no significant improvement in tuning of Fano resonance. This is possibly due to the fact that, parallel current distribution on both the side arms of$\; \; {C_1}$ results larger field enhancement (as shown in Fig. 2(e)). While, antiparallel surface current around $\; {C_2}$ doesn’t perturb the field significantly. Electric field distribution for d = 20 μm and $\; {C_1}$ and$\; {C_2}$ of 0.5 fF (shown in Fig. 4(d)), clearly verifies the above argument, as most of the energy confined in the lower split gap. Also, different degree of tuning for dipole and Fano resonances is attributed to the fact that, in addition to the change of resonant frequency of both the arms (arms to the left and right of the split gaps), external capacitor also changes coupling between both the resonators. This has been elaborated more in next section with help of coupled differential equations (Table 1).
Fig. 4. Capacitive tuning of Amplitude Transmission vs frequency spectra for (a) d = 10 μm, (b) d = 20 μm with external capacitor in lower gap only. (c) Resonant dip tuning of various resonance with different capacitor values for d = 10 μm, (d) Electric field distribution at Fano resonant frequency (1.167 THz) for ${C_1}$ = 0.5 fF, (e) Variation of Q-factor and FOM of Fano dip for different values of external capacitor ${C_1}$ and ${C_2}$ for d = 20 μm.
Table 1. Parameters for theoretical fit for d = 10 μm and various values of C1.
Variation of Q factor and Figure of merit (FOM) for different ${C_1}$ and ${C_2}$ values (for d = 20 μm case) are shown in Fig. 4(e). It is shown that, with increase of capacitance values, Q factor and FOM both increase simultaneously (reason explained in previous section) up to C = 0.5 fF. Maximum Q ∼ 380 and FOM ∼ 290.6 for ${C_1}\; $= ${C_2}$ = 0.5 fF are observed which is significantly higher than earlier reported values [40]. Above 0.5 fF, both the parameter values are decreased due to low field confinement and increased loss. Optimized regime for maximum FOM has been shown in Fig. 4(e) (within rectangular box).
Intensity modulation with the help of varying capacitor is shown in Fig. 5(a) where we’ve shown the variation of spectral contrast (= $|({T_{max}}$ -${T_{min}}$)/$({T_{max}}$ +${T_{min}}$)$\; $|) with$\; {C_1}$ and$\; {C_2}$. A maximum spectral contrast of 71% has been achieved with both $\; {C_1}$ and$\; {C_2}$ values of 0.5 fF. With the increment of capacitor, spectral contrast of Fano mode gradually decreases and reaches to almost zero when both$\; {C_1}$ and$\; {C_2}$ becomes 5 fF, which signifies a complete disappearance of Fano resonance. From Ref. [41], it is prevalent that in addition to field enhancement, capacitor with lead wire can also acts as a loop antenna. So, with the increase of capacitor value, radiative loss also increases as shown in the far field pattern in Fig. 5(b). The side lobe level, which quantifies radiation loss, increases with the increment of$\; {C_1}$. This counters the field enhancement effect at Fano resonance frequency and leads to significant decrease of spectral contrast and total suppression of Fano resonance. Such modulation phenomena can be highly useful to realize high Q switching devices, tunable dual band filers, notch filters and tunable broadband transparent devices etc. at THz frequency range.
Fig. 5. (a) Spectral Contrast of Fano dip for d = 20 μm and different values of$\; {C_1}$, (b) Far field radiation pattern corresponding to d = 20 μm and$\; {C_1}$ = 0.5, 1, and 5 fF.
4. Analytical model of Fano resonance
A classical analogy of Fano resonance has been drawn based upon coupled oscillator model. This model consists of super-radiant (bright) resonator which can be directly excited by the incident electromagnetic wave and a sub-radiant (dark) resonator which doesn’t couple to incident wave directly. Eigen mode of those individual resonators (with coupling) is given by ${\omega _0}$ and $({{\omega_0} + \delta } )$, respectively, where $\delta $ represents small deviation of dark resonance (detuning factor) w.r.t bright resonance. The field amplitude of both the modes can be expressed as 2nd order coupled differential equation as [42]:
Fig. 6. Capacitive tuning of Amplitude Transmission spectra for d = 10 μm: analytical modelling using Matlab.
5. Conclusion
Our work proposes Fano resonance based active metamaterial device to realize simultaneously high Q factor and resonance intensity contrast with the help of externally loaded capacitors. Such approach can help to achieve both the frequency and intensity modulations of Fano resonance through proper coupling between the super-radiant and sub-radiant modes. Further, we’ve studied effect of external capacitors $\; {C_1}$ and$\; {C_2}$ to show differential tuning of both the dipole and Fano resonances. We have also demonstrated an analytical approach to obtain the amplitude transmission spectra of variable capacitor loaded Fano metamaterials. For experimental realization of active metamaterials, active materials like semiconductors, graphene, perovskites etc. or electronic devices (varactor, schottky diode) can be employed across the gap where conductivity can be tuned externally. Such conductivity change may also lead to some change of effective capacitance in the split gaps. Our proposed schemes can be beneficial to realize many potential devices like tunable modulators, isolation switches, tunable dual band filters, broadband devices, chemical and biological sensors, nonlinear optical devices and enhanced spectroscopic applications.
Funding
Science and Engineering Research Board (SERB) (EMR/2015/001339).
Acknowledgment
Funding D.R.C. gratefully acknowledges the financial support from the SERB, Department of Science and Technology, India (No. EMR/2015/001339).
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