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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 17719–17728
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Transmission resonances in periodic U-shaped metallic nanostructures

Srinivasan Iyer, Sergei Popov, and Ari T. Friberg  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 17719-17728 (2010)
http://dx.doi.org/10.1364/OE.18.017719


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Abstract

The spectral response of crescent-like metallic nanostructures, a sub-class of U-shaped split-ring resonators, on a glass substrate at normal incidence is studied numerically. Also, the interpretation of transmission resonances arising from periodic conventional standard split-ring resonators with rectangular edges (SSRR) at normal incidence is revisited. In particular, we focus on one specific transmission resonance which is present for nano-crescents (NC) but absent in the case of SSRRs used for metamaterials. It is proposed that for a U-shaped metallic structure of arbitrary geometry, coupling of plasmonic eigen modes at all the surfaces of the three-dimensional structure is essential to be considered. The manner in which the coupling takes place between plasmonic modes at all the surfaces of the three-dimensional structure is what completely characterizes transmission resonances, and it is unique for each given resonance.

© 2010 OSA

1. Introduction

In 1999, Pendry and associates proposed two fundamental constituents for the construction of a left- handed metamaterial (LHM) – an artificial medium exhibiting a negative refractive index, wherein the electric field E, magnetic field H, and wave vector k follow the left-hand rule. One of the constituents consists of arrays of thin metal wires, which gives negative permittivity (ε) [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]

]. The other constituent comprises metallic structures called split-ring resonator (SRR) that provide negative permeability (μ) [2

2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

]. By combining these two, a metamaterial can be obtained that shows a negative index of refraction within a certain wavelength range. This metamaterial appears to the incident electromagnetic radiation as a homogeneous medium with an effective ε and μ, instead of a collection of components, i.e., wires and SRRs, provided the wavelength is much larger than the size and spacing of the individual components. Recently, a magnetic response from periodic arrays of U-shaped single-slit split-ring resonators (SSRRs) was demonstrated at optical and telecommunication wavelengths [3

3. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

5

5. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006). [CrossRef] [PubMed]

]. The SSRR, which forms the 'magnetic atom' of the LHM, can be viewed as an LC circuit with the metal represented by the inductance L of a single winding coil and the gap by a capacitance C between the ends of the coil [3

3. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

]. An oscillating current can flow through the LC circuit due to time-varying E and H fields. At resonance, the magnitude of the oscillating current in the LC loop is the strongest and it gives rise to a large magnetic moment in the gap, which is crucial to obtain negative permeability [3

3. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

6

6. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004). [CrossRef]

]. This LC resonance frequency (or magnetic resonance frequency ωr) can be tuned since it scales inversely with the lateral size of the SSRRs until the limits of size scaling are reached [5

5. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006). [CrossRef] [PubMed]

].

The electrical LC analogy can also be invoked for the more general crescent-shaped nanostructures, the nano-crescents (NCs), which are nano-particles that have been extensively studied over the last few years owing to their field enhancement properties [12

12. J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antenna,” Adv. Mater. 17(17), 2131–2134 (2005). [CrossRef]

16

16. B. M. Ross and L. P. Lee, “Plasmon tuning and local field enhancement maximization of the nanocrescent,” Nanotechnology 19(27), 275201 (2008). [CrossRef] [PubMed]

]. Although the NCs have not been used for the construction of magnetic atoms in LHM, it is very likely that they could be used since both, the NCs and the SSRRs, have a common U-shaped geometry. In this paper, we study the optical transmission properties of NCs with rectangular inner boundaries ('NCR' geometry) at normal incidence, in the visible and near-IR wavelengths, using numerical simulations. In particular, we analyze the principal resonant modes arising in the transmission spectrum of periodic arrays of such NCR structures and compare them to those in the conventional, rectangular-edged SSRR transmission spectra. One can observe an extra tunable resonance peak in the transmission spectrum of the NCRs that does not exist for the SSRRs with similar dimensions and periodicity. All the resonance conditions in the visible and near-IR region are characterized with the help of the associated near-field distributions of the electric and magnetic fields, so as to analyze their origin and understand their physical properties. Our results suggest that sometimes it becomes necessary to also consider the plasmonic mode pattern at the metal-glass interface, along with the air-metal interface, to explain certain far-field transmission resonances occurring with a U-shaped metal nanostructure. Thus, for a general three dimensional U-shaped metallic structure, the transmission resonances can be explained as a result of coupling between plasmonic modes excited at all the metal-(air/dielectric) interfaces, namely front, back, top, bottom, inner surfaces as well as lateral sides.

2. Modeling

The propagation of light (plane waves) through periodic arrays of gold (Au) SSRRs and NCs on dielectric substrates is examined by the full, three-dimensional (3D) vector finite-element method (FEM) using COMSOL Multiphysics. The advantage of using FEM is that it can model and mesh irregular, curved geometries like NCs with great accuracy. The dielectric substrate chosen, in our case, is glass (nsub = 1.5 unless specified otherwise). The refractive index of Au in the visible and near-IR range is obtained from literature [17

17. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. Figure 1
Fig. 1 Unit cells of two different types of periodic U-shaped nanostructures: (a) single-slit split-ring resonator (SSRR), (b) nano-crescent with rectangular inner boundaries (NCR). Incident light is linearly polarized along the x axis and propagates in the + z direction.
shows the unit cells of the two types of U-shaped structures considered, namely the SSRR and NCR. Both structures are first made in 2D and then extruded a distance t in the z direction. The NCR has an elliptical outer boundary and a rectangular inner boundary. It can be constructed in 2D by immersing a rectangle of width wx into the ellipse from the top until the desired value of depth dr is reached. Then, the intersection of the two 2D geometries is taken and the resultant is extruded to give a 3D NCR. A similar approach is followed to construct a 3D SSRR, but here the outer boundary is a rectangle of dimensions lx x ly.

The parameters of the SSRR array are kept the same as those in the published experimental work of Klein et al [5

5. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006). [CrossRef] [PubMed]

]: lx = 110 nm, ly = 95 nm, wx = 34 nm, dr = 45 nm, t = 45 nm, and a square lattice with lattice constant a = 240 nm (Fig. 1). This is done so as to confirm the results of our computations and to facilitate the comparisons between resonances. The whole NCR geometry is completely inscribed into the SSRR's outer dimensions and the gap width wx is kept the same as in the SSRR. Plane waves are incident onto the periodic nanostructures from air (n = 1) and it propagates in the + z direction. The discussion in this paper is limited to horizontally (x) polarized light. Periodic boundary conditions are applied at the sides of the unit cell, i.e., yz and xz planes, to simulate a square periodic array of Au SSRRs/NCRs. Please note that the above dimensions of lx, ly, wx, and t are kept the same throughout the manuscript for, both, SSRRs and NCRs.

3. Analysis of the transmission spectrum

3.1. Dependence of transmission resonances on lateral depth

The lateral depth parameter (dr) is varied and the transmission and reflection spectra are calculated as a function of wavelength for horizontally polarized incident light. Figure 2
Fig. 2 (a) Comparison between transmission spectra of periodic NCR (crescent shaped structures with a rectangular inner void) and conventional SSRR structures of same lateral depth (dr = 45 nm). Figures (b) and (c) show the transmission and reflection spectra for NCRs with different values of dr. The numbers 1, 2 and 3 are labels for the different resonances arising in the transmission/reflection spectra.
shows the comparison of the transmittance and reflectance spectra for periodic NCR structures of three different dr values and an SSRR array (dr = 45 nm) in the visible-NIR range.

One can observe three distinct and significant modes (or peaks) at the same wavelengths in the transmittance and reflectance spectrum, labeled as 1, 2, 3, of NCRs (Fig. 2). But for the SSRR, only two modes are present, namely 1 and 3 [Fig. 2(a)]. Mode 1 is the resonance that occurs approximately at frequency ωr predicted by the electrical LC theory. Since the light is normally incident onto the glass substrate with the SSRRs/NCRs, an oscillatory current is induced by E-field coupling [6

6. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004). [CrossRef]

,7

7. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547–2549 (2005). [CrossRef]

] and flows throughout the 'U' in a closed loop. At mode 1 condition, the magnitude of the current is maximal and the net magnetic moment in the gap is large. This explains the low transmission at mode 1. In the case of the SSRR, the wavelength of this mode can be tuned further by varying dr while keeping the overall size fixed. Enkrich et al [7

7. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547–2549 (2005). [CrossRef]

] experimentally demonstrate a gradual blue shift in mode 3 by decreasing dr. When dr = 0, i.e., the gap vanishes, mode 1 coincides with mode 3 giving rise to a single broad resonance peak (not shown). The blue shift can be explained in simple terms by following the LC analogy, in which the inductance and the capacitance of the SSRR change as the lateral depth is varied. Since both the NCs and the SSRRs are U-shaped, we expect to observe similar effects for mode 1 in the NCR structures. Hence, as dr is decreased from 60 nm to 30 nm for the NCR, resonance 3 moves from 1010 nm to 770 nm. Its magnitude also remains effectively constant [Fig. 2(a)], consistent with the results in [7

7. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547–2549 (2005). [CrossRef]

].

Resonance 3 can be explained by the formation of a higher-order mode at that wavelength and it will be considered in detail later (in section 3.3). There is virtually no change in the wavelength of mode 3 (580 nm) as dr is altered from 30 nm to 60 nm. The most interesting aspect about the NCR geometry is the presence of a new peak, i.e., mode 2, that is otherwise absent in case of the SSRR. It can be observed that as dr ranges from 60 nm to 30 nm, the magnitude of mode 2 gets stronger and its peak becomes narrower. The spectral tuning of mode 2 also closely resembles that of mode 1 outlined above, as it experiences a gradual blue shift with decreasing dr.

3.2. Dependence of transmission resonances on the refractive index of substrate

The refractive index of the substrate is varied from 1.5 to 1 and the NCR depth dr is fixed at 45 nm. Figure 3
Fig. 3 Behavior of transmission resonances(denoted as 1, 2 and 3) of NCR (t = dr = 45 nm) with a variation in the refractive index of substrate (nsub).
shows the changes that occur in the different transmission modes when substrate index is brought closer to that of air.

3.3. Discussion

In order to understand the origin of the new resonance (i.e., mode 2) arising in the NCR structures, the magnetic and normal electrical near-field distributions are analyzed at the three mode conditions described above, for the NCR with dr = 45 nm. The vector-valued H field is projected onto fictional planes 1' and 2' cutting through the cross-section of the vertical arms and the horizontal part of the NCR respectively, as shown in Fig. 4(a)
Fig. 4 (H)-field (array of red cones on left-side pictures) and Ez-field (colored map in right-side patterns) distribution of the NCR with thickness t = dr = 45 nm at different resonance conditions. (a) Two slices 1' (xz plane) and 2' (yz plane) onto which the vector magnetic field is projected. Points A and B denote the sharp edges of the NCR structure, whereas C is the cross-section of the bottom part. (H)-field projections on planes 1' and 2', and Ez distribution (from left to right) are shown for (b) mode 1, (c) mode 2, and (d) mode 3, respectively. The sizes of the red cones are proportional to the magnitude of projected (H) field. The white arrows merely represent the current flow direction in the respective arms of the NCR as deduced by the (H)-field projections for modes 1 and 2. The Ez component is color-coded, with red corresponding to positive and blue to negative values, respectively.
. The H-field projections provide valuable information about current flow direction in the respective parts of the U shaped structure. The Ez plot, on the other hand, is basically a snapshot of the Ez distribution (total E field in the z direction). The character of the various plasmon modes at the front air-metal interface (xy plane) can be visualized by the Ez distribution as it is the component perpendicular to the metal surface [10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

]. The Ez plot is calculated on a xy plane, 20 nm before the surface of the NCR/SSRRs in air. The color scale that depicts the amplitude of Ez – positive (red) and negative (blue) – provides useful phase information of the near field.

At mode 1, circulatory magnetic fields are observed on planes 1' and 2', which is a signature of an oscillating current flowing in the respective arms of the NCR [Fig. 4(b)]. By the right-hand thumb rule, the direction of the current can be deduced and it is shown by white arrows in the Ez plots. The Ez pattern shows a single maximum that oscillates from one vertical arm (field is concentrated at the tip) to the other and resembles a dipole. However, the Ez plot for mode 3 [Fig. 4(d)] reveals the presence of a higher-order quadrupole mode with two diagonally opposite maxima and minima. The results for both modes 3 and 1 are consistent with the work in recent publications in which the plasmonic character of the resonance is discussed [8

8. J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15(26), 17881–17890 (2007). [CrossRef] [PubMed]

,10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

,11

11. C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express 15(14), 8871–8883 (2007). [CrossRef] [PubMed]

]. Mode 1, due to its dipole resemblance, is called the lower-order plasmonic mode and mode 3 is a higher-order plasmonic mode. At mode 2 [Fig. 4(c)], however, circulatory magnetic fields with a closed loop around the vertical arms (1') can be seen, but not around the horizontal bottom arm (2'). Thus, there is no evidence of a unidirectional current in the bottom arm of the NCR. As stated before, this resonance (mode 2) is absent in conventional SSRRs with rectangular edges. Also, the Ez plot at mode 2 looks nearly identical to that at mode 1. This suggests that the formation of plasmonic eigenmodes at the air-metal interface alone, especially just the front interface of the metal nanostructure as in the work of Rockstuhl et al [10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

,11

11. C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express 15(14), 8871–8883 (2007). [CrossRef] [PubMed]

], cannot explain all the resonances arising in a U-shaped nanostructure.

The H-field projection on plane 1' at mode 2 condition is compared for the NCR structures with dr = 30 nm, 45 nm, and 60 nm (Fig. 5
Fig. 5 (H)-field distribution on plane 1' (as shown in Fig. 3(a)) for NCR structures with different lateral depths (dr): (a) 30 nm, (b) 45 nm, and (c) 60 nm at mode 2 condition.
).

Mode 2 occurs at 670 nm (dr = 30 nm), 710 nm (dr = 45 nm), and 730 nm (dr = 60 nm) for the cases analyzed (as seen in Fig. 2). It is observed that the strength of this resonance becomes stronger as dr decreases. It is found that the H-field strength in the gap is largest for dr = 30 nm and it decreases as the lateral depth increases. This effect is consistent with the change in transmission magnitude of the NCR structures with greater lateral depths. But still, the reason behind the reversal of currents, as we move from mode 1 to mode 2, despite identical Ez distributions at the front surface of the U-shaped nanostructure is unanswered at this point.

As the incident light is x-polarized, Ex is the superposition of the incident and the scattered electrical field, while Ey and Ez are generated purely by the scattering of the incident light. The component Ez is responsible for plasmon generation for the front (air-metal interface) and back (metal-glass) surfaces, Ey for the top-bottom (air-metal) surfaces, and Ex for the lateral surfaces (air-metal). Before discussing the NCR geometry, it will be interesting to first consider the case of a conventional SSRR. Figure 6
Fig. 6 Plasmonic mode distribution (total Ez field) at the front (metal-air) and back (metal-glass) interface at different mode conditions of SSRR (dr = t = 45 nm). Labels z1 and z2 denote xy planes situated at a distance of 20 nm from the SSRR, in air and glass, respectively.
contains the Ez plots at points z1 (in air) and z2 (in glass) along the z axis for a SSRR with dr = 45 nm. These points are situated at 20 nm before and after the metal nanostructure. We clarify that the Ez plots in Fig. 4 are indeed calculated at z = z1.

It is observed that for SSRR, the plasmonic distribution maintains the same character (i.e., dipolar for mode 1 and quadrupolar for mode 2) at the front and back interfaces for a given incident wavelength, but they are phase-shifted by π radians with respect to each other. Also, the Ey (Ex) distribution at the top-bottom (lateral) surfaces of the SSRR is interesting at the two mode conditions (Fig. 7
Fig. 7 Plasmonic mode distribution at the top-bottom and lateral surfaces of the SSRR: (a) Ey plots for the top (y = y1) and bottom (y = y2) surface of the SSRR at different far-field resonance conditions. Planes y1 and y2 are 20 nm away from the respective metal surfaces. (b) Respective Ex plots for the lateral surfaces of the SSRR at the same resonance conditions.
). The distribution is plotted over xz planes (for Ey) and yz planes (for Ex) set 20 nm away from the air-metal interfaces. Since the lateral sides are symmetric, the Ex plots are the same for both lateral surfaces at a given wavelength (Fig. 7(b)). Looking at Ey and Ex plots, it can be clearly observed that the plasmonic modes occurring at the front air-metal interface and the back metal-glass interface couple via the top surface for mode 1 (910 nm). However, the coupling is via the bottom surface for the higher order mode 3 (610 nm). This suggests that even though the plasmon distribution at the front air-metal interface (Ez plot) is enough for us to make a distinction for different resonance conditions of SSRRs, it does not fully explain the physics behind the occurrence of peaks in the far-field transmission spectrum. The resonances are, in fact, a result of an intricate coupling process between plasmonic modes excited at all the surfaces of the 3D-metal nanostructure. And, it is the manner of coupling that is unique to every transmission resonance.

The above results are consistent with the Ez plots for the NCR at different mode conditions (Fig. 8
Fig. 8 Plasmonic mode distribution (total Ez field) at (a) the metal-air (z1) and metal-glass (z2) interfaces at different mode conditions of the NCR structure (t = dr = 45 nm). Kindly note the mismatch in the mode pattern at z1 (dipolar) and z2 (quadrupolar) for mode 2 condition.
below).

The only peculiarity, however, is the plasmonic mode distribution at the mode 2 condition (at 710 nm). It can be seen that the distribution is dipolar for the front air-metal interface but quadrupolar for the metal-glass interface. This mismatch, which arises from the NCR geometry, to some extent explains why the current directions are different in the vertical arms of the NCR structure despite the Ez plots being identical, at mode 1 and mode 2, at the front air-metal interface [Fig. 4(b) and 4(c)]. The current flowing through the different arms of the NCR (and SSRR) actually depends on the net E-field distribution – vector sum of Ex, Ey and Ez – near all its surfaces and not just on the Ez distribution at the front surface. It is in turn a function of the plasmonic modes occurring at all the surfaces and their associated coupling which is evidently different for mode 1 and mode 2. Even the observed blue shift in all the resonances accompanied by a change in the magnitudes of mode 2 and mode 3 when the substrate index is varied (Fig. 3) from 1.5 to 1, is in line with this reasoning since the properties of different plasmonic modes excited at the back metal-substrate interface changes.

As it was shown in case of SSRRs (Figs. 6 and 7), the manner in which coupling takes place between the dominant plasmonic modes at the front (air-metal interface) and back (metal-glass interface) surfaces, is what completely characterizes any transmission resonance. If we compare the geometries of SSRR and NCR, the top two flat surfaces (SSRR) are reduced to sharp edges (NCR), and the lateral and bottom surfaces (SSRR) merge to form one single elliptical surface (NCR). This changes the plasmonic eigen mode conditions of the lateral elliptical surface and deeply influences the manner in which the coupling takes place between those at the front and the back surfaces of the NCR. The change in the manner of coupling manifests itself as mode 2 for the NCR geometry. As the rectangular inner surfaces of the NCR is modified into a circular or elliptical surface to form a natural crescent structure, we end up destroying the hitherto mode 2 condition and the transmission spectrum from such a structure is completely different to that of a NCR (not presented here). This observation backs our aforementioned qualitative explanation regarding the effect of geometrical shape of the 'U' on the coupling dynamics. However, more intense investigation is required to precisely clarify what all parameters of the geometrical shape can be modified to freely tune the positions of different transmission resonances.

4. Conclusions

Acknowledgements

Our research is financially supported by the Swedish Foundation for Strategic Research (SSF) and the Academy of Finland (SA).

References and links

1.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]

2.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

3.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

4.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

5.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006). [CrossRef] [PubMed]

6.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004). [CrossRef]

7.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547–2549 (2005). [CrossRef]

8.

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15(26), 17881–17890 (2007). [CrossRef] [PubMed]

9.

T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008). [CrossRef] [PubMed]

10.

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

11.

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express 15(14), 8871–8883 (2007). [CrossRef] [PubMed]

12.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antenna,” Adv. Mater. 17(17), 2131–2134 (2005). [CrossRef]

13.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005). [CrossRef] [PubMed]

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J. Kim, G.L. Liu, Y. Lu, and L.P. Lee, “Numerical study of Au nano-crescent with giant local field enhancement within the biological window,” Frontiers in Optics, OSA Technical Digest Series, paper FWR5 (2005).

15.

J. Kim, G. L. Liu, Y. Lu, and L. P. Lee, “Intra-particle plasmonic coupling of tip and cavity resonance modes in metallic apertured nanocavities,” Opt. Express 13(21), 8332–8338 (2005). [CrossRef] [PubMed]

16.

B. M. Ross and L. P. Lee, “Plasmon tuning and local field enhancement maximization of the nanocrescent,” Nanotechnology 19(27), 275201 (2008). [CrossRef] [PubMed]

17.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

OCIS Codes
(160.4760) Materials : Optical properties
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(260.5740) Physical optics : Resonance

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 24, 2010
Revised Manuscript: July 26, 2010
Manuscript Accepted: July 27, 2010
Published: August 2, 2010

Citation
Srinivasan Iyer, Sergei Popov, and Ari T. Friberg, "Transmission resonances in periodic U-shaped metallic nanostructures," Opt. Express 18, 17719-17728 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17719


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References

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