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Gradual cross polarization conversion oftransmitted waves in near field coupled planarterahertz metamaterialsS. JAGAN MOHAN RAO,1,4 RAKESH SARKAR,1 GAGAN KUMAR,1

AND DIBAKAR ROY CHOWDHURY2,3

1Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, India2Mahindra Ecole Centrale, Jeedimetla, Hyderabad, 500043, India3dibakarrc@gmail.com4suraboinajmr@gmail.com

Abstract: In this work, we examine gradual cross polarization conversion using two coupledcircular split ring resonators (SRRs) in the terahertz (THz) frequency regime. In the proposedgeometry, a metamolecule (unit cell) is comprised of two circular split ring resonators havinga single split gap. One resonator is rotated with respect to the other from 0° to 180° in thesteps of 15° and thereby, co- and cross-polarization components of the transmitted terahertz areinvestigated. The cross polarization component is observed to be maximum when resonator splitgaps are orthogonal to each other; however, in the co polarization resonance, a strong split isobserved. Based upon the angle of rotation between the resonators, the study reveals that the crosspolarization conversion can be tuned from minimum to maximum and then back to the minimum.We have employed a semi-analytical model to understand the polarization conversion arisingfrom the coupling between the resonators and found that it corroborates numerical findings. Theability to control linear polarization conversions can be significant in the development of THzpolarimetric devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The field of terahertz has seen a rapid growth in last few years because of its significancein diversified applications such as imaging, sensing and communications. For most of theseapplications, not only efficient terahertz sources are required, but also very high-speed terahertzcomponents and devices to control and manipulate the terahertz waves are essential. Thosecomponents include switches, modulators, polarization converters, antennae, sensors etc. [1,2].Most of the natural materials do not respond to terahertz radiations, therefore it is important toexplore alternate methods to make devices in terahertz domain. By utilizing the metamaterials(MMs) concept [3], efficient terahertz devices can be realized [4]. Metamaterials exhibit severalfascinating features and applications including negative refractive index [5], invisibility clocking[6], perfect lens to overcome the diffraction limits [7] etc. Metamaterials research began with J.Pendry’s seminal 1999 paper on split ring resonators (SRRs) [8]. At the resonance frequencyof metamaterials, a strong localization of electromagnetic energy takes place in the resonatorwhich results enhancement of amplitude at the resonance frequency. The feature is important toseveral applications in the terahertz regime. Additionally, circular currents can be induced in thesplit ring resonators giving rise to an inductance in the designed resonators. The combination ofcapacitive and inductive nature of SRRs leads to strong inductive capacitive resonance, termedas fundamental resonance [9]. Several studies have been reported on THz transmission in twodimensional MMs using single SRR as the unit cell [9–13]. When two SRRs are broughtsufficiently close to each other, they can couple strongly through magnetic and electric fieldlines gives rise to several interesting phenomena including mode hybridization effect, broadband

#349941 https://doi.org/10.1364/OSAC.2.000603Journal © 2019 Received 1 Nov 2018; revised 21 Dec 2018; accepted 22 Dec 2018; published 25 Feb 2019

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modulation, wave modulation, plasmon induced transparency (PIT) [14–17] etc. In this contextbroadly two types of SRRs are investigated, they are broad side coupled SRRs (BC-SRRs) [18]and edge coupled SRRs (EC-SRRs) [19–21]. In both the cases, the SRRs are placed orthogonalto each other in a metamaterial unit cell. Upon incidence of a linearly polarized light, one SRRis directly excited and it is termed as bright resonator, whereas the other resonator is excitedindirectly through the bright resonator, hence called as dark resonator [22,23]. In case of MMsconfiguration, where both the SRR gaps are aligned parallel to incident electric field, the brightmodes are excited simultaneously in both the resonators [24,25].Polarization rotation is an important phenomena in many applications [26–34]. Generally

polarization rotation is achieved by using conventional methods like prism rotators using totalinternal reflection principle and the wave retarders which alter the polarization of light based uponthe principle of birefringence. Their performance is wavelength-specific and they have their ownlimitations. Therefore, more convenient and flexible approaches are desirable to fully manipulatethe polarization state of an electromagnetic wave. Recently, near field coupled metamaterialsexhibited great promise to realize polarization rotation [35–38]. Many schemes have beenimplemented to rotate the polarization state at THz frequencies using novel metamaterialconfigurations. Grady et al. have reported the rotation of linearly polarized light to its orthogonalstate using ultrathin, broadband and highly efficient MM configuration [39]. Cong et al. studiedthe rotation of a linearly polarized broadband terahertz wave using tri-layer metasurfaces [40]. Inanother study, polarization conversion in reflection mode was accomplished using metamaterialunit cell composed of a metallic disk and split-ring resonator placed near to the ground planeand separated by a polyamide layer. This configuration can result in the rotation of a linearlypolarized light by 90° with an extended operation bandwidth [41]. Wen et al. studied polarizationrotation in reflection mode using three layers of planar structures on the top of a two-dimensionalarray of tilted coupled split rings (TCSRs) [42]. Xia et al.demonstrated a linear polarizationconverter composed of two metal layers and a dielectric spacer [43]. Chen et.al investigated themagnetic interactions of edge coupled twisted split ring resonator pairs as a function of theircoupling strength to control the polarization conversion in both the transmission and reflectionmode [35]. Very recently a linear polarization conversion of transmitted terahertz wave withdouble-layer meta-grating surfaces in transmission mode is also demonstrated [44]. Yang et al.studied broad band polarization conversion in reflection mode by using the hybrid metamaterialunit structure consisting of a split-ring metal pattern and a metal sheet separated by a dielectricresonator spacer [45]. So far, many works have been reported on linear polarization rotationsusing relatively simple and complex metamaterial geometries, however, polarization rotationat relatively small angles is overlooked. In this work, we have studied gradual control of linearpolarization rotation with a simple planar metamaterials capable of working in the terahertzfrequency regime.

In this work, we propose a metamaterial unit cell comprising of two near field coupled circularresonators on a silicon substrate with the ability to gradually rotate and control linearly polarizedlight. We study the polarization rotation in transmission mode using the designed MMs in the0.2 THz to 0.8 THz frequency range. The terahertz transmissions of the coupled structures arestudied by varying rotation angle of one resonator with respect to the other one. We examine theco- and cross-polarization transmission for different rotation angles of one resonator with respectto another resonator. In the first section, the design of MM geometry has been discussed alongwith the effect of rotation angle on the coupling of fundamental LC resonances. The numericalresults are discussed in detail in the next section. Further, we discuss lumped-element RLCcircuit model in order to validate the numerical results. Finally, the results are summarized in theconclusion section.

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2. Metamaterial design and numerical simulation details

Design of THz metamaterial is very crucial in order to accomplish variable magnitude of the coand cross polarization responses. In our proposed metamaterial configuration, metamolecule(unit cell) is comprised of two circular split ring resonators (SRRs) and separation between tworesonators is fixed at 1 µm throughout this study. A schematic of the proposed configuration isshown in Fig. 1. We have assumed silicon of thickness 50 µm as the substrate with a permittivity

Fig. 1. Schematic of a planar THz metamaterial geometry consisting of SRRs on siliconsubstrate. A single unit cell consists of two circular split ring resonators of gold metal.The yellow regions represent the metallic gold areas while gray region represents siliconsubstrate. Each of circular resonators has outer radius of 20 µm and inner radius r=16 µm.The w = 4 µm and g = 4 µm in the schematic stand for the line width and split gap of theresonators respectively. S (Separation between two resonators) = 1 µm and the parameter θrepresents rotation angle, which can be varied from 0° to 180°. Fig 1(a) Schematic view ofTHz transmission through metamaterial sample. Fig 1(b) represents unit cell of metamaterialwith varying rotation angles.

of ε = 11.9 and negligible loss. Other dimensions of substrate are assumed to be, length xbreadth = 100 µm x 60 µm. The unit cell is chosen to be much bigger in size compared tothe resonators pair in order to avoid any inter metamolecular coupling. The circular SRRs asdepicted in the Fig. 1(b) are 20 µm and 16 µm in outer and inner radius, respectively, and made ofgold layer of 200 nm thickness. The capacitive gap (g) and line width (w) of both the resonatorsare taken to be, same i.e. 4 µm. The geometrical parameters are kept constant throughoutthe analysis. In Fig. 1(b), θ is the angle between the split gaps of left and right SRR and ischanged from 0° to 180° during this study. We fix the right side resonator and rotate the left sideresonator from 0° to 90° and further 90° to 180°, in an anticlockwise fashion at an interval of15° and observed co-polarization as well as cross polarization transmissions corresponding tovarious relative orientations (Fig. 1). For our numerical study, we have employed commerciallyavailable numerical software, CST Microwave Studio and used tetrahedral meshing in order toaccurately measure the response of geometry. We have used waveguide ports for the source anddetector. In all simulations, plane wave excitation is used with normal incidence, containingmodes linearly polarized in either x or y direction. Periodic boundary conditions are used to

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simulate an infinite two-dimensional periodic array, with unit cell and structural dimensionsspecified in Fig. 1(b). The transmission results are normalized w.r.t. the transmission from a baresubstrate and plotted in Fig. 2. These plots represent transmissions, Tyy and Txy that contain bothy- and x-polarization components, respectively, excited by the incident field linearly polarizedin y direction. In this study, the polarization of the incident THz beam is assumed to be alongthe split gap of the right resonator in order to excite the fundamental LC resonance. The splitresonances result from the coupling of right side split ring resonators with the left side resonatorsthrough a combination of magnetic and electric flux because of edge coupling of the twistedcircular resonators [23,46]. The amplitude transmission shows a resonance split and results inmaximum polarization conversion (Fig. 2) due to a comparatively strong inductive coupling ofthe fundamental resonances of right and left circular resonators. The results of the terahertztransmission for both polarizations through inductively coupled THz metamaterial systems arediscussed elaborately in the next section.

Fig. 2. Numerically simulated transmission of the metamaterials. (a) Co polarizationamplitude transmission for left SRR rotation from 0° to 180° (b) Cross polarization amplitudetransmission results for left SRR rotation from 0° to 180°.

3. Results and discussions

In order to examine the terahertz co and cross polarization transmission properties of the nearfield coupled metamaterial responses, we rotate the LHS SRR with respect to the RHS SRR in theanticlockwise direction. The results are shown in Fig. 2 and in Fig. 3. In Fig. 2(a), we plot the THzco polarization transmission amplitude versus frequency and in Fig. 2(b), we plot the THz crosspolarization transmission amplitude versus frequency for 0°, 45°, 90°, 135°, and 180°. At θ = 0,transmission shows single resonance at 0.5246 THz with cross polarization amplitude almostzero. As the relative SRR rotation is changed through the rotation angle from 0° to 15°, 30°, 45°,60°, 75°, and 90°, we observed the gradual decrease in co-polarization transmission amplitudeaccompanied by a gradual increase in cross-polarization transmission amplitude. For θ lessthan 45°, the single resonance appears nearly at 0.5246 THz in co-polarization transmission andbeyond θ = 45 till 90°, resonance split appears in co-polarization transmission with the lowerresonance appearing near 0.4802 THz and the higher resonance at 0.5276 THz (see Fig. 2(a)).At θ = 90, clear resonance split takes place with resonance dips at 0.4922 THz and 0.5222 THzin cross polarization transmission. At this configuration maximum polarization conversion isachieved with conversion amplitude as 0.33 (see Fig. 2(b)). Further, LHS SRR is rotated withrespect to RHS SRR from θ = 90 to 180°. For the range of θ = 90 till 120°, resonance split inco-polarization transmission amplitude exists with the lower resonance close to 0.4802 THz andhigher frequency resonance close to 0.5276 THz. From θ = 135 to 180°, a single resonance dip

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occur at 0.4802 THz in co-polarization transmission. With the change in rotation angle fromθ = 90 to 180°, a gradual increase in co-polarization transmission amplitude is observed alongwith a gradual decrease in cross-polarization transmission amplitude and finally at θ = 180,linear polarization rotation conversion reaches to zero. Further the intrinsic resonance of the SRRis observed at 0.4964 THz (Fig. 3a). However, the split resonances are observed centering theintrinsic resonance. In order to understand the phenomenon behind the co and cross polarizationtransmissions elaborately, we have provided the qualitative analysis below. In our studied MMs,two circular split ring resonators are placed side by side to each other on silicon substrate. Whenthe incident electric field is linearly polarized along the y-direction, the fundamental resonancemode of the right side SRR is always directly excited [9,12]. The incident electric field parallelto split gap creates circular current in right SRR with the accumulation of charges at the splitgap (Fig. 5). With θ = 0 bright mode in both the resonators are excited. However there is astrong inductive coupling changing the effective inductance of the resonators, therefore shiftingthe resonance from its intrinsic position (Fig. 2). As the LHS resonator rotates (θ increasing), theLHS resonator slowly moves from bright regime (θ = 0) to dark regime (θ = 90). In case ofθ = 90 the LHS is excited indirectly through the RHS bright resonator which is followed by interresonator coupling to give rise to resonance mode splitting [23]. At this position the radiationof dark resonator is completely orthogonal to the incoming wave, hence we observe maximummagnitude of cross polarization. With further rotation (θ > 90°), the LHS resonator graduallycomes out of dark mode regime to bright regime. In the process the orthogonal polarizationconversion diminishes and finally at θ = 180 both the resonators are excited directly through theincident electric field, hence no polarization conversion takes place. However the resonance dipappears at a different frequency than intrinsic case because of the effective inductance of theresonators. The induced circulating currents are in opposite direction resulting in different valueof effective inductance.

Fig. 3. Comprehensive numerical simulation transmission amplitudes for θ varying from 0°to 180°. (a) Contour plot for co polarization amplitude transmission for left SRR rotationfrom 0° to 180° (b) Contour plot for cross polarization amplitude transmission results forleft SRR rotation from 0° to 180°.

For an elaborate understanding of co and cross polarization amplitudes, comprehensivesimulation results are shown through contour plot (Fig. 3). Figure 3(a) and (b) represents contourplots for co and cross polarization transmissions, respectively. In Fig. 4(a), rotation angle isplotted against the resonance frequencies for the co-polarization transmission amplitudes. Blueline represents fundamental resonance of the intrinsic resonator, whereas the red and greenlines represent the lower and higher order resonance frequencies for the coupled resonators,respectively. Figure 4(b) depicts the polarization conversion amplitude with rotation angleof the LHS resonator. With an increase in the rotation angle, cross polarization amplitude

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increases gradually till it reaches 90° where the linear polarization conversion attains maximumvalue. With further increase in θ, cross polarization decreases, and at 180° rotation angle, thecross polarization conversion amplitude reaches to zero. From our study, it is evident that thecross polarization conversion can be tuned from zero to maximum depending upon the relativeorientation of the resonators.

Fig. 4. (a) Rotation angle vs resonance frequency plot for co polarization amplitudetransmission. Left SRR rotation from 0° to 180° (b) Rotation angle vs cross polarizationconversion amplitude plot. Left SRR rotation from 0° to 180°.

We have further studied the electric field profiles and surface current profiles for 0°, 90° and180° cases. The induced surface current and electric field distributions are shown in Fig. 5 atthe resonance dips. At 0.5246 THz for 0° case, the induced currents are in phase for both theresonators. This is the situation when both the resonators behave like the bright resonators.Electric field distribution depicts the bright mode excitation in both the resonators (Fig. 5(a)and (b)). Surface current and electric field profiles for θ = 90 at lower and higher resonancemodes are shown in Fig. 5(c), (d), (e) and (f), respectively. Figure 5(c) and (d) illustrates that theinduced currents are out of phase whereas induced currents are in phase as revealed by Figs. 5(e)and (f). In Fig. 5(g) and (h), electric field distribution and surface current distribution are shownfor 180° situation. However, the nature of induced currents are different in two resonators.

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Fig. 5. Simulated surface current and electric field profiles for 0°, 90°, and 180°, (a) &(b) represents electric field and surface current profiles for 0° at 0.5246 THz. (c) & (d)represents electric field and surface current profiles for 90° at lower resonance frequency0.4802 THz. (e) & (f) represents electric field and surface current profiles for 90° at higherresonance frequency 0.5276 THz. (g) & (h) represents electric field and surface currentprofiles for 180° at resonance frequency 0.4766 THz.

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Fig. 6. Schematic of the RLC circuit model. The electrical components R1, L1, C1 representthe resistance, inductance, capacitance describing the fundamental LC resonance of the rightmeta-resonator and R2, L2, C2 describe the resonance for the second left resonator. I1 andI2 represent the excited currents in right and left resonators respectively. The parameter M isresponsible for the coupling between the resonators.

4. Theoretical model

In order to validate the co and cross polarization transmission results obtained through coupledmetamaterials, we have employed a semi-analytical RLC circuit approach (Fig. 6) [35,47]. Thismodel has the ability to give us insight into the resonant co and cross polarization transmissionbehavior through the proposed coupled metamaterials system. In this semi-analytical approach, asingle SRR is modeled with an equivalent RLC circuit which exhibits resonance at a specificfrequency depending upon the shape and size of the split ring resonator. For our case, we assumedtwo RLC circuits with resistances, inductances and capacitances as R1, L1, C1 and R2, L2, C2corresponding to the right and left resonators, respectively (Fig. 6). When incident electric filed(Ein =

Vg , where V is voltage and g is the split gap of SRR) is linearly polarized along y direction,

the fundamental resonance mode of only the right SRR is excited (because right SRR capacitivegap oriented along y direction). This is considered as a primary loop where circulating current isI1. The fundamental mode of left SRR can not be excited due to its different orientation. So, leftSRR will be excited because of right SRR through near field inductive coupling and the couplingparameter is mutual inductance (M). This is called a secondary loop and circulating current is I2.Using Kirchhoffs voltage law, we can write equations for primary loop and secondary loop asbelow

[R1 + jωL1 +1

jωC1]I1 + jωMI2 = V (1)

jωMI1 + [R2 + jωL2 +1

jωC2]I2 = 0 (2)

Using Cramer’s rule, if you solve I1 and I2

I1 =V[R2 + jωL2 +

1jωC2]

[R1 + jωL1 +1

jωC1][R2 + jωL2 +

1jωC2] − ω2M2j2

(3)

I2 =VjωM

[R1 + jωL1 +1

jωC1][R2 + jωL2 +

1jωC2] − ω2M2j2

(4)

Where j is the imaginary unit and ω is the angular frequency of the incident electromagneticwaves. The induced electric dipoles are proportional to the charge accumulation at the splitgaps, i.e. P1,2 is proportional to

∫I1,2dt. From above analysis, we know I1 is responsible for

co-polarization and I2 is responsible for cross polarization transmission. Now from I1 and I2,we can derive total impedance for co and cross polarization transmissions. We know Z = V

I ,

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then Zco =VI1 and Zcross =

VI2 now we can write total impedance for co and cross polarization

transmissions.Zcross =

Z1Z2 − (Zm)2

Zm(5)

Zco =Z1Z2 − (Zm)

2

Z2(6)

whereZ1 = R1 + jωL1 +

1jωC1

(7)

Z2 = R2 + jωL2 +1

jωC2(8)

Zm = jωM (9)

Normalized transmission formula [12,48] for co and cross polarization is

t(ω) =Ztotal(Zs + Z0)

Zs(Ztotal + Z0) + (ZtotalZ0)(10)

Where, Zs (impedance of Si substrate) = 103 Ω and Z0 (impedance of free space) = 377 Ω.We have used equation 10 to get co and cross polarization transmission results. For co-

polarization transmission results, we have substituted equation 6 in place of Ztot into equation10 and varies R, L, C and M values. At particular values of R, L, C and M, we calculatedco-polarization transmission plots (See Table 1 for R, L, C and M values). The results ofamplitude transmission through RLC-circuit model for co-polarization are shown in Fig. 7(a).The corresponding values of coupling parameter M are given in table-1. We observe increase inM value with an increase in rotation angle of left SRR from 60° to 90° and from 90° to 120° Mvalue got decreased. The calculated amplitude transmission is found in good agreement with thenumerical simulations. Next, for cross-polarization transmission results, equation 5 is substitutedin place of Ztot in equation 10. Using final transmission (equation 10) expression and at particularR, L, C and M values (See Table 2), we calculated the cross polarization transmissions. Theseresults too match well with our numerical simulations (shown in Fig. 7(b)). Mutual inductance(M) values (Table 1 and Table 2) for both the co and cross polarizations cases show a certaintrend i.e. till 90° it increases and beyond 90° till 120° it decreases gradually. From this, wecan conclude that at 90° mutual inductance attains highest value. Since mutual inductance Mrepresents coupling strength, this indicates that at 90° , the resonators are maximally coupledthrough mutual inductance. Beyond this point, if left SRR is rotated in anti-clockwise fashionwith respect to the right SRR, the coupling strength decreases as can be confirmed from mutualinductance values.

Table 1. R, L, C and M values for Co-Polarization transmission

Rotation angle (θ) R1 (ohm) L1 (pH) C1 (fF) R2 (ohm) L2 (pH) C2 (fF) M (pH)

60° 35 245 0.38 34 165 0.64 12

75° 52 245 0.4 32 165 0.63 19

90° 52 282 0.38 32 200 0.5 20

105° 40 342 0.32 32 194 0.5 14

120° 35 282 0.4 32 180 0.2 12

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Fig. 7. Terahertz amplitude transmission through the coupled resonators in planar THzmetamaterials obtained from RLC circuit model for various rotations of left split ringresonator w.r.t right SRR. The results affirm numerical observations. (a) Co-polarizationtransmission. (b) Cross-Polarization transmission.

Table 2. R, L, C and M values for Cross-Polarization transmission

Rotation angle (θ) R1 (ohm) L1 (pH) C1 (fF) R2 (ohm) L2 (pH) C2 (fF) M (pH)

60° 250 145 0.4 312 125 0.2 179

75° 250 125 0.4 312 125 0.2 205

90° 250 141 0.4 312 125 0.2 224

105° 250 156 0.4 312 125 0.22 220

120° 250 205 0.4 312 125 0.2 210

5. Conclusion

To summarize, we have presented a gradual linear polarization convertor with a double split ringresonator based metamaterials system operating in the terahertz regime without changing themetamolecule unit cell size. We have tuned cross polarization and co polarization transmissionsby changing the relative rotation angle of one resonator with respect to the other from 0° to 180°.We have demonstrated that the cross polarization transmission amplitude gradually changes fromzero to maximum and then back to zero. At the same time, the co-polarization transmissionamplitude varies from single resonance dip to split resonance dips and then back to singleresonance dip. With the rotation angles at 90°, the maximum cross polarization conversion isachieved. When the left side circular resonator split gap rotation angles are close to θ = 0 or180°, minimum cross polarization conversion is achieved along with a single resonance in copolarization transmission because of the absence of mode hybridization where resonators behaveclose to the intrinsic resonators. We have monitored electric field and surface current profiles toconfirm our observations. Further, an RCL theoretical model is employed to validate the couplingmechanisms in detail. We considered the circular SRRs as lumped element RLC resonant circuitsand calculated the induced currents within the circular SRR loops. Finally, we calculated the coand cross polarization transmissions. Our theoretical outcomes are in good agreement with ournumerical results. The present work for our studied near field coupled metamaterials boosts theunderstanding of near field resonator coupling within the composite metamolecules, which canlead to realization of polarization manipulation devices in terahertz regime.

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Funding

Board of Research in Nuclear Sciences (BRNS) (34/20/17/2015/BRNS); Science and EngineeringResearch Board (SERB) (EMR/2015/001339); Ministry of Human Resource Development(MHRD).

Acknowledgments

GK gratefully acknowledges the financial support from the Board of Research in Nuclear Sciences(BRNS), India (34/20/17/2015/BRNS). DRC gratefully acknowledges the financial support fromthe SERB, Department of Science and Technology, India (EMR/2015/001339). SJM Rao and RSarkar would like to acknowledge the financial support from the Ministry of Human ResourceDevelopment, Government of India for a research fellowship.

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