Metamaterials for sensing and slow light applications

Metamaterials for Sensing and Slow Light Applications Sher-Yi Chiam June 30, 2012 Abstract This thesis details research carried out at the Center of Ion Beam applications in the field of metamaterials from 2005 to 2010. In this work, we used a proton beam based lithography process (Proton Beam Writing) to fabricate high aspect ratio metamaterial structures as shown in fig 1. Our work focused on two areas : the use of metamaterials for sensing applications, and for slowing light by exploiting a metamaterial analogue to the the quantum phenomenon of Electromagnetically Induced Transparency (EIT). This work was carried out in the technologically relevant Terahertz (THz) regime. THz Time Domain Spectroscopy Technique (THz-TDS) was used to study the electromagnetic properties of our structures and these measurements where supported by numerical simulations. Figure shows an example of the metamaterial structures successful fabricated for this work. While the Split Ring Resonator structures shown here were already well studied at the time, the Proton Beam Writing (PBW) fabrication technique allowed us to study high aspect ratio versions of this well-know structure. Most fabrication techniques result in flat arrays of structures with very limited height perpendicular to the sample plane. This can be overcome by PBW, which as evidenced by the scanning electron micrograph (SEM) in fig. 1(b), can produce structures with highly vertical and smooth sidewalls of great height. Despite the intense research that has been carried out in the field of metamaterial, not much research has been carried out on high aspect ratio structures like these. Figure 1: Optical (a) and scanning electron (b) micrographs of the gold Split Ring Resonators (SRRs) fabricated for this work using the PBW technique. The substrate is Silicon. The smoothness and height (about µm) of these SRRs are clearly seen in (b). These structures are designed to have resonances in the THz regime. By carrying out a systematic study of the effects of aspect ratio and substrate thickness, we were able to conclude that high aspect ratio SRRs result in larger frequency shifts upon the application of a dielectric layer, thus offering enhanced sensitivity for sensing applications. In the process, we also carried out a detailed investigation into the dielectric effects of the substrate on the metamaterial resonance. An intriguing aspect of metamaterials is their ability to mimic effects known in quantum and atomic physics. In this work, we also demonstrated a metamaterial analogue to the quantum phenomenon of EIT, which normally occurs in metallic vapors. To achieve this, we proposed a slightly modified SRR design (fig. 2(a)), fabricated using PBW. Using THz-TDS, we showed that such a structure possessed a narrow transparency window within a broad absorption band - a characteristic feature of quantum EIT. Figure 2: (a) Scanning electron micrograph of the modified SRR sample fabricated by PBW. The inset shows details of the region marked in the main panel (scale bar µm). The width of the arms is about 800 nm, and the height is over µm. (b) Measured amplitude transmission amplitude for the fabricated sample as a function of frequency for two polarization states of the illumination by the external beam. Inset shows the orientation of the E field for the two orthogonal polarizations : E parallel to the gap side of the inner ring, (blue, solid), and E perpendicular to the gap side of the inner ring (red,dashed). The narrow transparency window is present for only one polarization. Using the phase data from the THz-TDS measurements, we experimentally confirmed that the transparency window is coincident with a steep normal dispersion, which results in a drastic slowing down of a light pulse at that frequency. These results were as predicted by numeral simulations. Unlike previous work on this topic, this work used a structure whereby two independent resonances were coupled to produced an EIT-like effect. We have thus used a high aspect ratio lithography tool to fabricate metamaterials structures and studied two current applications for metamaterials. Preface The work in presented in this thesis resulted from experimental work carried out mainly from January 2006 to June 2009. Publications Parts of the work presented in this thesis has been published in the following journals: 1. Sher-Yi Chiam, Ranjan Singh, Weili Zhang and Andrew A Bettiol, Controlling Metamaterial resonances via dielectric and aspect ratio effects, Applied Physics Letters, 97, (2010) 196906 2. Sher-Yi Chiam, Ranjan Singh, Carsten Rockstudhl, Falk Lerderer, Weili Zhang and Andrew A Bettiol, Analogue of Electromagnetical Induced Transparency in a Terahertz Metamaterial, Physical Review B, 80, (2009) 153103 3. S. Y. Chiam, Ranjan Singh, J. Gu, J Han, W. Zhang and A. A. Bettiol, Increased Frequency Shifts in High Aspect Ratio Metamaterials, Applied Physics Letters, 97, (2010) 196906 Other recent publications the author contributed to: 1. W. Yue, S.Y. Chiam, Y Ren, J. A. van Kan, T. Osipowicz, L Jian, H. O. Moser and F Watt, The Fabrication of X-ray Masks using Proton Beam Writing, Journal of Micromechanics and Microengerineering, 18, (2008), 085010 2. A.A. Bettiol, S.Y. Chiam, E.J. Teo, C. Udalagama, S.F. Chan, S.K. Hoi, J.A. van Kan, M.B.H. Breese and F. Watt, Advanced applications in microphotonics using proton beam writing, Nuclear Instruments and Methods in Physics Research B, 267 (2009) 2280-2284 3. J. A. van Kan, F. Zhang, S. Y. Chiam, T. Osipowicz, A. A. Bettiol and F. Watt, Proton beam writing: a platform technology for nanowire production, Microsystem Technologies, 14 (2008), 1343-1348 4. S.Y. Chiam, J.A. van Kan, T. Osipowicz, C.N.B. Udalagama and F. Watt, Sidewall quality in Proton Beam Writing, Nuclear Instruments and Methods in Physics Research Section B, 260 (2007), 455-459 5. F. Zhang, J. A. van Kan, S.Y. Chiam and F. Watt, Fabrication of Free Standing Resolution Standards Using Proton Beam Writing, Nuclear Instruments and Methods in Physics Research Section B, 260 (2007), 460-463 6. J.A. van Kan, A.A. Bettiol, S.Y.Chiam, M.S.M. Saifullah, K.R.V. Subramanian, M.E. Welland and F. Watt, New Resists for Proton Beam Writing, Nuclear Instruments and Methods in Physics Research Section B, 260 (2007), 474-478 Earlier publications the author contributed to (during B.Sc. and M.Sc. degrees): 1. T. Osipowicz, S.Y. Chiam, F. Watt , G. Li and S.J. Chua, Channelling Contrast Microscopy of GaN and InGaN Thin Films, Nuclear Instruments and Methods in Physics Research Section B, 158 (1999), 653-657 2. I. Orlic, S.Y. Chiam, J.L. Sanchez and S.M. Tang, Quantitative Analysis of Cascade Impactor Samples Revisited, Nuclear Instruments and Methods in Physics Research Section B, 150 (1999), 465-469 3. Y.K. Lee, K.M. Latt, S. Li, T. Osipowicz and S.Y. Chiam, Characterization of Interfacial Reactions between Ionized Metal Plasma DepositedAl-0.5 wt.% Cu and Ti on SiO2 , Materials Science and Engineering B, 77 (2000), 101-105 4. Y.K. Lee, K.M. Latt, K. Jaehyung, T. Osipowicz T, S.Y. Chiam and K Lee, Study of Interfacial Reactions in Ionized Metal Plasma (IMP) deposited Al-0.5%wt Cu/Ti/SiO2 /Si structure, Journal of Materials Science, 35 (2000), 5857-5860 5. Y. K. Lee, K.M. Latt, T. Osipowicz and S.Y. Chiam, Study of diffusion barrier properties of ternary alloy (Tix Aly Nz ) in Cu/Tix Aly Nz /SiO2 /Si thin film structure, Materials Science in Semiconductor Processing, (2000), 191-194 6. Y. K. Lee, K.M. Latt, J H Kim, T Osipowicz, S.Y. Chiam and K Lee, Comparative analysis and study of ionized metal plasma (IMP)-Cu and chemical vapor deposition (CVD)-Cu on diffusion barrier properties of IMP-TaN on SiO2 , Materials Science and Engineering, B: Solid-State Materials for Advanced Technology, B77 (2000), 282-287 International Conferences Parts of the presented in this thesis was presented at the following international conferences: 1. 10th International Conference on Nuclear Microprobe Applications and Techniques (ICMNAT 2006) July 2006, Singapore, organized by the Centre for Ion Beam Applications, NUS • Oral presentation on “Sidewall morphology in Proton Beam Writing” 2. 1st Topical Conference on Nanophotonics and Metamaterials (Nanometa 2007) January 2007, Seefeld, Austria, organized by European Physical Society. • Poster presentation on “Proton Beam Writing for Metamaterials” 3. International Conference on Materials for Advanced Technologies 2007 (ICMAT 2007) July 2007, Singapore, organized by Materials Research Society, Singapore • Oral presentation “Proton Beam Writing for the fabrication of Electromagnetic Metamaterials” • Contributing author on oral presentation “Proton Beam Writing for X-Ray Mask Fabrication” 4. Photonics West 2008 January 2008, San Jose, California, USA, organized by SPIE • Oral presentation on “Spectral Properties of Thick Split Ring Resonators in the THz regime” 5. International Conference on Materials for Advanced Technologies 2011 (ICMAT 2011) July 2011, Singapore, organized by Materials Research Society, Singapore • Poster presentation “Thin Substrates for Enhanced Metamaterial Sensing Applications” Collaborators and author’s contributions The author carried out all fabrication work presented in his thesis, as well as all the simulations and analysis carried out with CST Microwave StudioTM . With his supervisor and collaborators, he developed the ideas that led to the work presented here. The author is grateful for the help received from his collaborators. Ranjan Singh (currently at Los Alamos National Laboratories) and Prof. Weili Zhang conducted the Terahertz Time Domain Spectroscopy measurements presented in this work. These measurements were carried out at the School of Electrical and Computer Engineering, Oklahoma State University at Stillwater, Oklahoma, USA. They helped to interpret the results and discussed and contributed to the manuscript of our joint publications. The author is also grateful to Carsten Rockstudhl of the Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universt¨at at Jena, Germany for this assistance in the computational and theoretical aspects of parts of this work. He discussed and contributed to the manuscript of our joint publication. Acknowledgements It was Thomas Osipowicz who made that fateful phone call that led me back to CIBA, and set me on the path that led to this thesis. Jeroen van Kan then taught me all the essentials and intricacies of fabrication and Proton Beam Writing. Finally, Andrew Bettiol led me down the exciting path of metamaterials. To all my supervisors, thank you for an wonderful journey. It has been a long one, but I dare say I enjoyed most of it. Special thanks goes to Andrew for his patience and for setting a world record in vetting a thesis. Thanks also to all of you for being wonderful mentors and friends. To my collaborators, Ranjan and Carsten, without you, the thesis could not have been the same. I am so glad to have worked with, and look forward to working with you again. Chammika, Sook Fun, Ee Jin, Siew Kit and Isaac were the wonderful friends that made my life so much more interesting and fun. Thanks for all the occasions you gave up beam time to me, shared that desperately needed Silicon wafer, and most touching of all, allowed me to take you SEM slot! You have been great friends and colleagues! To the wonderful technical team, Choo and Armin, thanks for keeping the accelerator humming and beaming, and for attending to my last minute requests. To the colleagues at the NUS High School, thanks for tolerating my occasional absence from lessons when a conference was going on, and for company in the evenings and weekends as I wrote this thesis. And last but not least, to Joycelyn, for tolerating my absence on evenings and weekends, and for staring intently at the screen even when home. Thanks for being there for me. Contents Introduction 1.1 10 Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1.1 Historical review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Negative Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Optical Properties of Metals and Wire Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 The Split Ring Resonator (SRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.1 Overview of SRR properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.2 SRRs under normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.3 Electrical Response of SRRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.4 Single vs Double Split Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Research Trends in Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.1 Frequency Regimes and Fabrication Techniques . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 Evolution in magnetic metmaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.3 Applications for metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.4 Metamaterial Analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.5 Three-dimensional metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5 1.6 Motivation and focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characterization and Numerical Studies of Terahertz Metamaterials 2.1 2.2 2.3 29 30 Terahertz Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 Terahertz Time Domain Spectrometry (THz-TDS) . . . . . . . . . . . . . . . . . . . . 31 2.1.3 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Simulation and Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 The Simulation Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.2 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.3 Simulation Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.4 Application of Auto Regressive Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabrication with Proton Beam Writing 45 46 3.1 Overview of the fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 Proton Beam Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.1 Features of PBW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.2 The Accelerator Facility at CIBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.3 The PBW beam line at CIBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.4 Ion Beam Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2.5 PBW Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Supporting Fabrication Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.1 Substrate Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.2 Spin Coating of PMMA resist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3.3 Deep Ultra-Violet (DUV) Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.4 Development of exposed PMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.5 Gold Electroforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.6 Seed layer etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Fabrication Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.4.1 High aspect ratio metamaterials for THz applications . . . . . . . . . . . . . . . . . . 62 3.4.2 Metamaterials for higher frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3 3.4 141 The higher penetration power of X-rays allow thick resist layers to be patterned if a mask of sufficient contrast is available. The PBW technique thus compliment each other very well. The ability of the PBW writing technique to fabricate high contrast X-ray masks consisting of thick gold structures on a thin SiN membrane has been demonstrated [100]. Thus, a worthwhile future direction would be to explore the possibility of using X-ray lithography using a PBW mask to fabricate metamaterials on a larger scale. Another possibility would be the use of PBW to make a mold or stamp for nano-imprint lithography [101]. 6.2.2 Metamaterials for higher frequencies Another important future direction would be to further study the kind of high aspect ratio metamaterials as shown in fig. 6.1(a) (also shown in fig. 3.11). As these high aspect ratio SRRs have heights in excess of their diameters, we call them Split Cylinder Resonators (SCR). Initial studies using Fourier Transform Infra-Red spectroscopy have shown that the structures shown there support a resonance at about 26 THz under normal incidence (i.e. with the wave vector along the cylinder axis). This is manifested in the form of a reflection dip when the electric field of the polarized beam is parallel to the gap bearing side (fig. 6.1(b)). Simulations have shown that this is due to a unique three-dimensional resonance that comes about because of the very high aspect ratio of the structures (fig. 6.1(c)). Reflectance (Arbitrary Units) 1.0 0.8 0.6 0.4 Measured Parallel o 30 o 60 Perpendicular SRR depth = 4.8 0.2 0.0 20 22 24 26 28 30 32 34 36 38 Frequency (THz) (a) (b) (c) Figure 6.1: (a) Electronmicrograph of very high aspect ratio SRRs with sub-micron minimum feature size. (b) Measure reflection spectra (normal incidence) with a polarized light source shows a dip when the electric field vector is parallel to the gap bearing side (black curve). This dip gradually weakens and is absent when the electric field vector is perpendicular to the gap side (blue curve). (c) Simulated surface currents at the resonance. As can be seen in fig. 6.1 (c), there is a complex three dimensional current resonance that includes strong 142 currents in the direction of the cylinder axis at the gap edges. The current at the two edges are anti-parallel. This leads to an intense magnetic fields in between the gaps. As the direction of the magnetic fields would be parallel to the external electromagnetic radiation, it means that these structures have a magnetic response. This resonance is complex and could suggest a new approach for three-dimensional metamaterials. It would be a fascinating topic for further work. 6.2.3 EIT-like metamaterials In this work, we demonstrated an EIT-like effect using a design consisting of a split ring within a closed outer ring. A deserving topic for further study for this structure would be to vary the parameters of this structure - such as by breaking the vertical symmetry, or otherwise varying the position of the inner ring with respect to the outer ring. Some preliminary studies have been made and the results are discussed in the appendix. It would also be meaningful to explore an active version of the structure, one whereby the EIT-iike effect can be turned on and off by dynamically varying the conductivity of the gap substrate using a scheme similar to that of Chen et al [11]. This would be a necessary first step in developing a practical device for selective slowing of light. Another worthwhile topic for future study would be to investigate ways to replace the inner split ring with a resonator with a higher quality factor. This would increase the difference between the quality factors of the resonators. It should lead to a narrower transparency window and thereby result in a steeper dispersion and further slowing of the light pulse. 6.2.4 Metamaterials for sensing applications One area that deserves to be explored is the fabrication and experimental study of metamaterials on thin substrates. The possibility of fabricating metallic structures on thin SiN films has been demonstrated before [100]. In particular, this would allow us to experimentally verify the possibility of applying analyte films to the substrate side of the metamaterial sample. Sensing at higher frequency regimes can also be explored. 143 6.3 Epilogue In a review paper in 2010, Zheludev presented the “Metamaterial Tree of Knowledge” (see fig. 6.2) whereby he identified mature fields in metamaterial (ripe, red apples), fields where research was currently flourishing (yellow apples) and emerging fields (green apples) [102]. Figure 6.2: The metamaterial tree of knowledge, as published in [102] This review was published at about the time at which experimental work for this thesis was coming to a close. From the “Tree of Knowledge” we see that the work in this thesis has been in the area of “Designer Dispersion” (a yellow apple) and “Sensor Metamaterials” (a green apple). The work in this thesis has thus been in the growing research areas of metamaterials, and relevant to other researchers. Looking back on the work carried out in this thesis, it is satisfying to know that we have chosen to focus on flourishing areas with potential for future work. Bibliography [1] Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006). [2] Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006). [3] Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. 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A.1 Varying coupling strength We expect that the distance between the bright and the dark resonators of an EIT-like metamaterial would be an important parameter that can significantly affect the peak transmission and other properties of the EIT-like metamaterial. This was studied in the case of the single bar and pair bar structures [79, 83] as well as the paired SRRs [52,82]. In all cases, it was found that decreasing the separation between the resonantors increased the coupling strength and increased the peak transmission of the transparency window. In our structure, the dark resonator is located within the bright one, and it is less clear what would constitute the separation between the resonators. Figure A.1 below shows the simulated S21 spectrum when the inner split ring is displaced the upwards and downwards by µm. We see that when the inner ring is displaced upwards such that the gap side is brought closer to the side of the closed ring, the transparency window is 153 154 strengthened - the peak amplitude in the transparency window is significantly increased. When the inner split ring is displaced downwards, the transparency window can be sufficiently weakened so as to disappear completely. We also note that moving the inner split ring has the effect of shifting the frequency of the transparency window downward to a slightly lower frequency - a upwards displacement of the inner ring by µm results in a shift in the peak of the transparency window from about 1.20 THz to 1.12 THz. Figure A.1: Simulated S21 spectra of the EIT-like metamaterial with inner split ring displace upwards (red line), centered within the larger closed ring (black line) and displaced downwards (red line). All spectra are for parallel polarization (electric field vector parallel to gap bearing side). Under perpendicular polarization (electric field vector perpendicular to gap bearing side) one observes only a broad transmission dip, very similar to the red line, for all three structures. Evidently, the interaction of between the two resonances in increased by having the gap side of the inner ring as close to one of the edges of the outer ring as possible. Thus, the critical parameter here is distance between the gap bearing side of the inner split ring and the closed outer ring. This is an effect that deserves further study. It indicates that the design we have studied in chapter can be further optimized to yield a higher transparency. The result in fig A.1 should also be further modeled and explained using a RLC circuit model. Such a model should be able to explain details like the frequency shift we noted in fig. A.1. This would lead to a better understand of the phenomena and even lead to a more refined RLC model of the structure. 155 A.2 Effects of symmetry breaking One unique feature of our design is that symmetry breaking is not required for the dark mode to be excited, as the dark mode is directly accessible under parallel polarization. Up to this point, we have not considered the effects of breaking symmetry along the vertical axis for our structure. In the previous section, while we have displaced the inner ring along the vertical, the structure had retained its symmetry along the vertical axis. When the vertical symmetry is retained, the LC resonance of the split inner ring remains inaccessible under perpendicular polarization (electric field vector perpendicular to gap bearing side). A transparency window remains absent under perpendicular polarization and one observes a broad absorption dip regardless of the vertical position of the inner ring. It is useful to study the effects of symmetry breaking in our design, by shifting the inner split ring horizontally to one side. The simulated results of such a structure are shown in figure A.2 below for both the parallel and the perpendicular polarization. Figure A.2: Simulated S21spectra of the closed and split ring structure with inner ring displaced horizontally. Spectra are shown for parallel (solid blue curve and perpendicular polarization. insert shows the orientation of the electric field vector relative to the structure We see that symmetry breaking makes the dark mode indirectly excitable under perpendicular polarization. A transparency window is observed for both polarizations, and the simulated electric field patterns indicate 156 that the LC resonance of the inner ring is excited under perpendicular polarization (see fig. A.3(a) and (b)). The result is thus very much like that for the other structures where an inaccessible dark resonator is excited by virtue of its coupling to a nearby bright resonator. The difference is that while symmetry breaking is essential in the other structures, it is optional in our structure. It is also apparent that dipole resonance of the outer ring is suppressed under perpendicular polarization in the centre of the transparency window (compare fig. A.3(c) and (d)). Another important effect is the dipole resonance of the outer ring appears to be converted into a more complex asymmetrical resonance. This is evident from the plots of the electric field patterns obtained from the simulations (fig. A.3(c) and (d)). A further detailed study will have to be carried out. Figure A.3: Simulated electric field patterns for 1.07 THz (dip in S21) and at 1.15THz (peak of transparency) window for perpendicular polarization. Arrows in the plots indicate the direction of Ex and Ey . [...]... or negative refractive index at higher frequencies As research progressed, effort started to focus on the use of metamaterials for practical applications 24 Sensing Applications One application that received much attention was the use of metamaterials for sensing Sensing applications for metamaterials are generally based on detecting the change in the spectral properties as a substance is brought in... 64 66 4 Metamaterials for sensing applications : enhancing sensitivity via aspect ratio and dielectric effects 67 4.1 Metamaterials for sensing applications 68 4.2 Fabrication 70 4.3 Characterization and Numerical Studies 72 4.4 Effects of SRR height and dielectric environment... few sources, detectors and other optical components available for this regime Thus, the Terahertz regime is where metamaterials can have many potential applications sensing, and in the control and manipulation of radiation As we shall demonstrate, the Proton Beam Writing technique that we use for this work meets the requirements of fabricating high aspect ratio metamaterials for the Terahertz regime... height normal to the sample plane, study their properties and their potential for applications There has been limited research on the fabrication and characteristic of high aspect ratio metamaterials Most metamaterials studied are flat, two-dimensional arrays with only limited height perpendicular to the sample plane • Focus on applications for metamaterials in the technologically relevant Terahertz regime... Transparency 140 Directions for future work 140 6.2.1 6.2.2 Metamaterials for higher frequencies 141 6.2.3 EIT-like metamaterials 142 6.2.4 6.3 Fabrication of high aspect ratio metamaterials 140 Metamaterials for sensing applications 142... materials”, in reference to the simultaneously negative values of µ and They are also called “left handed materials” due to the fact that in the vectors E, B and k form a left-handed trio The term metamaterials is also strongly associated with a negative refractive index However, we shall not restrict the use of the term metamaterials to left-handed materials 1.2 Negative Refraction While this thesis does... frequency This information can yield insight into material characteristics for a wide range of applications, as many materials have strong signatures in the THz regimes A number of methods exist for performing THz spectroscopy Fourier transform spectroscopy (FTS) is perhaps the most well know technique used for 30 31 studying molecular resonances It has the advantage of an extremely wide bandwidth, enabling... to detect, for example, the presence of a thin dielectric film Section 4.1 of this thesis provides an overview of research into this field 25 Active Terahertz Metamaterials Important potential applications for metamaterials can be found in the THz regime In the THz regime, the devices and components necessary to effectively manipulate Terahertz radiation still require substantial development, and lag behind... board material The rings and wires are on opposite sides of the boards, and the boards have been cut and assembled into an interlocking lattice so as to form a wedge Adapted from [3] medium to the radiation, and can be described using an effective, or average value of µ and for the entire wedge In this case, the effective values of µ and depend not on the materials that the wedge is composed of, but instead... [2–4] There has been much interest and effort in fabricating and studying metamaterials intended for higher frequency regimes This is achieved by fabricating the metamaterial unit cells at a smaller scale, so that the resulting structures couple to electromagnetic radiation of shorter wavelength and thus resonate at higher frequencies 21 SRRs and single split rings for higher frequency regimes The SRR . Metamaterials for Sensing and Slow Light Applications Sher-Yi Chiam June 30, 2012 Abstract This thesis details research carried out at the Center of Ion Beam applications in the field of metamaterials from. . . . . . . . . . . . 66 4 Metamaterials for sensing applications : enhancing sensitivity via aspect ratio and di- electric effects 67 4.1 Metamaterials for sensing applications . . . . . . structures as shown in fig 1. Our work focused on two areas : the use of metamaterials for sensing applications, and for slowing light by exploiting a metamaterial analogue to the the quantum phenomenon