Split Ring Ressonator
http://mcvictimsworld.ning.com/forum/attachment/download?id=2301601%3AUploadedFi38%3A12410Phase modulation using dual split ringresonatorsIftekhar O. Mirza*, Shouyuan Shi, and Dennis W. PratherDept of Electrical and Computer Engineering, University of Delaware, 151 Evans Hall Newark, Delaware 19716See the attached file below with the full Descripiton of Phase Modulation using duel Split Ring-*iomirza@udel.eduhttp://www.ece.udel.edu/Abstract: In this paper, we studied phase modulation numerically usingmetamaterials such as stacked structures of dual split ring resonators(DSRRs). To demonstrate the modulation, a vertical and a planar designwere considered, where the wave vectors were parallel and perpendicular tothe proposed structures creating 70 degrees and 80 degrees of phase change,respectively. In both of the designs modulation was brought about bychanging the effective index of the structure through switching between theopen and short states of the DSRRs while maintaining high transmission.One of the attractive features of our design was the thin layers of DSRRs,where for the vertical and planar models the DSRRs layers were 5 mm and2.28 mm respectively. The numerical results obtained by simulationmatched well with the theoretical prediction.© 2009 Optical Society of AmericaOCIS codes: (160.3918) Metamaterials; (060.5060) Phase Modulation; (070.5753)Resonators.References and links1. V. G. Veselago, The electrodynamics of substances with simultaneously negative values of permittivity andpermeability, Sov. Phys USPEKHI 10, 509 (1968).2. R. A. Shelby, D.R. Smith, and S. Schultz, “Experimental verification of negative index of refraction,Science 292, 77-79, (2001).3. Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, “Three-dimensionalsubwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,”Phys. Rev. Lett. 95, 153901(4) (2005).4. Z. Sheng and V. Varadan, “Tuning the effective properties of metamaterials by changing the susbstrate,” J.Appl. Phys. 101, 014909-1, (2007).5. D. K. Ghodgaonkar, V.V. Varadan, and V. K. Varadan, “Free-space measurement of complex permittivityand complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas.39, 387-394, (1990).6. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis and E. Ozbay, “Investigation of magneticresonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).7. K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis and E. Ozbay, “Effect of disorder on magneticresonance band gap of split-ring resonator structures,” Opt. Express 12, 5896 (2004)8. A. A. Zharov, I. V. Shadrivov, and Y.S. Kivshar, “Nonlinear properties of left handed materials,” Phys.Rev. Lett. 91, 037401 (2003)9. H. T. Chen, W. J. Padilla, J. Zide, A. Gossard, A. Taylor and R. Averitt, “Active terahertz metamaterialdevices.” Nature 444, 597-600, (2006).10. V. J. Logeeswaran, A. Stameroff, M. Islam, W. Wu, A. Bratkovsky, P. Kuekes, S. Wang and R. Williams,“Switching between positive and negative permeability by photoconductive coupling for modulation ofelectromagnetic radiation,” Appl. Phys. A 87, 209-216, (2007).O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84, 1198, (2004).11.12. P. He, P. Parimi, C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electon. Lett.43, (2007).13. A. Velez, J. Bonache, “Varactor-loaded complementary split ring resonators (VLCSRR) and theirapplication to tunable metamaterial transmission lines,” IEEE Microwave and Wirel. Compon. Lett. 18, 28-30, (2008).#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 508914. D. Smith, S. Schultz, P. Markos and C. M. Soukoulis “Determination of effective permittivity andpermeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104-1,(2002).15. H-T. Chen, J. Ohara, A. Azad, A. Taylor, R. Averitt, D. Shrekenhamer and W. J. Padilla, “Experimentaldemonstration of frequency-agile terahertz metamaterials,” Nature Photonics 2, 295-298, (2008).16. M. K. Karkkainen and P. Ikonen, “Patch antenna with stacked split-ring resonators as artificial magneto-dielectric substrate,” Microwave Opt. Technol.Lett. 46, 554–556, (2005).17. S. Oh, L. Shafai, “Artificial magnetic conductor using split ring resonators and its applications toantennas,” Microwave Opt. Technol.Lett. 48, 329–334, (2006).18. S. Maslovski, P. Ikonen, I. kolmakov and S. Tretyakov, “Artificial magnetic materials based on the newmagnetic particle: metalsolenoid” Prog. Electromag. Res. 54, 61-81, (2005).19. N. Katsarakis, T. Koschny and M. Kafesaki, “Electric coupling to the magnetic resonance of split ringresonators,” Appl. Phys. Lett. 84, 2943-2945, (2004).20. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780-1782,(2006).21. M. Kafesaki, T. Koschny, R. Penciu, T. Gundogdu, E. Econonou and C. Soukoulis, “Left-handedMetamaterials: detailed numerical studies of the transmission properties, J. Opt. A: Pure andAppl. Opt. 7, S21-S22, (2005).22. D. Dudley, W. Duncan, J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc.SPIE 4985, 14-25 (2003).23. K. Aydin, E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl.Phys. 101, 024911-5, (2007).24. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer and H. Giessen, “ Three-dimensional photonicmtamaterials at optical frequencies,” Nature Materials 7, 31-37, (2008).25. C. Balanis, Antenna Theory, third edition (John Wiley & Sons, 2005), Chap. 6.26. T. Hand, S. Cummer, “Controllable magnetic metamaterial using digitally addressable split-ringresonator,” IEEE Ant. Propag. Lett. (to be published).1. IntroductionRecently metamaterials have drawn a lot of attention in the research arena [1, 2, 20]. Theability of this class of materials to respond to an electromagnetic field and bring aboutchanges in a material’s fundamental properties has opened up doors for new applications suchas flat lens, antenna miniaturization and artificial magnetic conductors to name a few [3, 16,17]. One of the advantages of these artificial materials is that they can also be tuned over afrequency range by effectively changing the substrate properties, the geometry of theresonating metamaterial structure, or by changing the external fields with non lineardielectrics [4, 6, 7, and 8]. Another effective way of tuning resonating metamaterials such asthe split ring resonators is by changing the resistance properties of the rings using capacitorsthat can be controlled by an applied voltage [11]. As these tunable structures are scalable withthe wavelength, they can be used for modulation for any desired frequency range. Inparticular, a Terahertz modulator was demonstrated where the metamaterials were grown on aconductive substrate and the amplitude of the incoming wave was modulated using electricalcontrols to change the resistivity of the metamaterial on a GaAs substrate [9, 15]. Alsorecently, another research group demonstrated phase shifting with tunable negative refractiveindex metamaterials using variable external magnetic field [12]. Similar work was also donewith negative index material by means of photoconductive coupling [10]. Complementarysplit ring resonators and their applicability in tuning frequency has also been studied [13].Although these works had been successful in bringing out the idea of frequency andamplitude modulation, little investigation has been carried out in terms of phase modulationusing metamaterials. Also a major challenge in working with metamaterials has been theinherent loss that arises from their resonating nature. To address such issues, in this paper wedemonstrated phase only modulation using tunable metamaterials, namely the DSRRs. Wemitigated the issue of material loss by employing thin resonating metamaterials operating atan off-resonant frequency to demonstrate a high degree of phase modulation with veryminimal loss. Particularly, in our paper we demonstrated phase modulation using two#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5090different polarizations for the DSRRs: in the first configuration, the polarization of magneticfield, H, was perpendicular to the DSRRs as shown in Fig. 1 (a), whereas in the secondconfiguration, shown in Fig. 1(b), the wave vector k was perpendicular to the ring. TheDSRRs consisted of single split rings packed very closely where the adjacent rings’ split gapswere alternated in orientation. The key advantage of the DSRRs in the first configuration wasthat the rings could provide an off-resonance high permeability value when excited by themagnetic field [18]. Whereas in the second configuration the symmetric nature of thealternate rings could avoid electric coupling from the magnetic resonances that might lead tocross-polarization effects [21] when excited by the electric field .The key advantages in bothof our designs were the constituent elements which could be readily manufactured usingstandard lithography processes and simple electrical connections could be used to regulatebetween the two states of the modulation using very thin layers of DSRRs in the propagationdirection. Compared to conventional phase modulators, metamaterial-based phase modulatorsoperating in transmission mode, promise to produce enhanced phase modulation in terms ofexhibiting a high degree of phase change within a small volume. Moreover, being physicallysmall it can ensure ease of structural integration and can offer scalability with wavelength thatcan reduce design constraints while operating in different frequencies. We believe thesemodulators can be the building block for spatial light modulators in the microwave frequencyregime that can add significant advantage over conventional modulators by simplifying futureDigital Micromirror Devices (DMD) and phased array antenna design by controlling eachelement of the array or pixel electronically [22, 25].The first step in the recipe to build a tunable phase modulator was to design the DSRRsthat could provide the resonant frequency around which the phase modulation would occur.Standard numerical techniques were used to retrieve the constitutive parameters and theeffective refractive index information of the unit cell of the DSRRs for the two different statesof modulation: electrically open and closed rings [5]. The difference in the value of theeffective index for the two different states was used to calculate the phase change. We alsocalculated the change in phase using the volumetric field data obtained inside thecomputational region and explained the differences with the calculated theoretical result. Inthe following sections we will provide the details of the numerical setup, extraction of therelevant parameters to calculate the modulation and discuss the simulated results with aconclusion for improvement and our plan for experimental verification.EkEkHHTransmission plane Reflection plane Transmission planeReflection plane3.81 mm5 mmzyx15 mm15 mmy1mm(a) (b)3.63 mmzxFig. 1. (a). Configuration 1: H-field perpendicular to the DSRR. (b) Configuration 2: k vectorperpendicular to the DSRR#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 50912. Design and modelingThe DSRRs needed to be designed in such a way so that it could operate for a particularfrequency where the values of the effective permeability and permittivity of the DSRR’swould meet the following criteria: a) numerically large to create appreciable phase changethrough a change in the effective index, b) impedance matched interface, and c) minimize thepower loss. This is formalized in terms of the Figure Of Merit (FOM) = nreal / nimaginary, wherenreal and nimaginary are the real and imaginary parts of the refractive index respectively. Thegoal will be to achieve a high FOM for each state for both of the configurations.In order to meet these requirements we carried out several numerical simulation using thecommercial software HFSS to obtain an optimal design. Two different orientations of theDSRRs with respect to the wave vector were considered: case1) wave vector, k, parallel to thestructure and case 2) wave vector, k, perpendicular to the structure. The setup in Fig. 1(a),shows the unit cell analysis for the configuration 1 which will be discussed in the following.The dimensions of the DSRR were 3 mm x 3 mm with a gap and strip width of 0.33 mm. Thethickness of the metal was 0.02 mm printed on a 0.25 mm thick Duroid substrate (ε = 2.2).The unit cell of dimension 5 mm x 1 mm x 3.63 mm was placed in between the waveportswith a perfect magnetic conductor (PMC) boundary condition in the y-direction andperpendicular to the ring and a perfect electric conductor (PEC) boundary condition in the z-direction and parallel to the ring. By doing so, we were able to simulate a two dimensionalperiodic structure along both y and z directions with minimal computation. A similar setupwas used in [4]. Based on this orientation, the DSRRs were excited by the magnetic fieldwhich was perpendicular to the DSRRs. The dense stack of DSRRs acted as metalsolenoidwhich helped to concentrate the magnetic flux inside the structure giving rise to a strongmagnetic resonance. Similar design was considered and discussed in [18] where it washighlighted that the main benefit of this design was that a high value of permeability could beobtained away from the resonance. The large off-resonance permeability value leads to alarge effective index at the same frequency for the DSRRs which could be exploited formaximum phase modulation. The reflection/transmission spectra results obtained from thesimulation were used to extract the effective index of the DSRR using the formulationdescribed in [4, 5].For a normally incident wave in free-space, at the air-sample boundary the scatteringparameters, namely the S11 and S21 can be related to the reflection ( Γ ) and transmission (T)coefficients [5] as:Γ = R ± R2 −1 (1)where, S 2 − S 2 +1R = 0.5 11 21 (2)S11 and S + S −Γ T = 11 21 (3) 1 − ( S11 + S21 )Γ ncomplex = nreal + nimag ,Following this, the complex refractive index can be formulated as2mπ − arg(T ) − log(| T |)nreal = and nimag = . The parameter d indicates the slabwheredk0 dk02π, where λ0 is the operationalthickness in the direction of propagation and k0 =λ0#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5092wavelength in free space. In our studies, m was set to zero as the wavelength inside theDSRRs was larger than the slab thickness. Detailed discussion of the parameter m can befound in [4]. The extracted data are shown in Fig. 2(a), where the real and imaginary parts ofthe effective index for the open and closed cases of the DSRRs were plotted. From the graph,at 4 GHz the real part of the effective index was 5.9 for the open state DSRRs while for theclosed state the value of the real part of the effective index was 1.6. The closed state had a flatreal part response and minimal loss since the DSRRs were off-resonance within the frequencyrange of 3.5 – 4.5 GHz. The closed state for the DSRR was achieved by effectively shortingthe gaps in the DSRRs by placing a piece of metal inside the gap. Due to the large indexdifference between the two states, we chose a frequency band centered at 4 GHz for our phasemodulation application. Although, at resonance the real index was at a maximum whichwould provide the maximum phase modulation, the imaginary part which indicated the loss ofthe structure was also very high that could potentially degrade the overall performance of thedevice. In particular, the transmission data as shown in Fig. 3(a) indicated that forconfiguration 1 the transmission was -1.6 dB and -2.8 dB for the open and short caserespectively. The value of the imaginary parts for both the cases at this frequency wasnegligibly low and the difference in the real parts of the effective index was calculated as 5.9-1.6 = 4.3. The calculated FOM for the open state was 5.9/0.325 = 18.2 and for the closed statethe FOM was 1.6/0.0003 = 5.3 x 103. As expected the FOM was much higher for the closedstate because of the absence of a resonance.Freq: 4GHz
Comments