Abstract

A vertical metallic meander structure with a rectangular corrugated surface profile represents a frequency-selective surface in which the excitation and interaction of localized surface plasmon modes are controlled in a flexible fashion by its geometrical parameters over a large spectral range. In this report we investigate the optical properties of metallic meanders numerically. Although the structure is simple from both the structural geometry and the nanofabrication point of view, its plasmonic band structure manifests rich features that would be very attractive for plasmonic functional devices. In particular, the short-range surface plasmon mode can be tuned by changing the meander depth without altering the long-range surface plasmon mode. To obtain deeper physical insight into the relationship between the structural geometry and its optical response, a transmission line equivalent circuit model is used. It is revealed that circuit parameters that were fitted from numerical scattering parameters have physical relationships with the structural parameters, which can be described by quasi-static or radiative descriptions. In certain frequency ranges, enhanced transmission occurs due to the interaction of magnetic and electric dipole resonances. The calculated effective material parameters reveal that enhanced transmission occurs around the near-zero index frequencies. The application potential of these structures as frequency filters is discussed.

© 2009 Optical Society of America

1. INTRODUCTION

Periodically corrugated metallic films or structured slabs [1, 2, 3, 4, 5, 6, 7, 8] have been studied for decades due to their potential for excitation and interaction of surface plasmon polaritons (SPPs). Recently, intensive studies on these structures have resumed, aiming at novel plasmonic devices including plasmonic bandgap lasers [8, 9, 10], plasmonic Bragg mirrors [11, 12, 13], optical switches [14], as well as enhanced Raman and photoluminescent emission [15, 16]. Due to the coupling between the SPP modes on both surfaces of structured metallic films or slabs and the variety of structural possibilities, the optical responses and band structures are diverse and complicated. In addition, enhanced transmission is often accompanied by the excitation of the SPP modes. Similar to the enhanced transmission in periodic holes or slit arrays perforated in metal films, it was attributed to the coupling of the SPP with localized plasmon modes and resonant tunnelling [17, 18, 19].

In this report we investigate numerically the optical response of a vertical metallic meander structure in vacuum. It is similar to a metal slab with conformal corrugation on both surfaces [6, 7, 20, 21], but rather with a rectangular profile [22, 23]. The structure is more general and simpler for nanofabrication. First we study the plasmonic band structure of the metallic meanders and their corresponding transmittance. Then we use a transmission line (TL) circuit model to interpret both the mode behavior and the enhanced transmittance, which provides an alternative physical interpretation behind the enhanced transmission and mode interactions.

It has been demonstrated that electronic circuit models can be applied to metamaterials in the optical domain [24, 25, 26, 27, 28, 29]. TL circuit models turn out to be more powerful to analyze nanostructured metamaterials or structured metallic surfaces [30, 31, 32]. Using TL circuit models, the tangential magnetic response of the metallic structures can be separated from the tangential electric response [33]. Only via this kind of circuit model can the optical response of metallic structures be reproduced [32], and therefore more physical insight is obtained.

We find that the two lowest coupled SPP modes, which are identified as short-range SPP (SRSPP) and long-range SPP (LRSPP), respectively, can be described by magnetic and electric resonators in a TL model. The parameters of the lumped elements are obtained by directly fitting the response of the circuit model to the numerical results of the structure, whose physical meanings are justified by quasi-static or radiative models with respect to structural parameters. In addition, the effective permeability and effective permittivity of the slabs can be obtained directly from the impedance or admittance of the circuit through the relations Z=Zl=jωμ0μr and Y=Yl=jωε0εr, in which l is assumed to be the effective length of the slab. It might be improper to assign effective material parameters to such a thin slab, because the parameters might be changed when several identical layers are stacked together. Especially, these parameters are connected to an effective length that is difficult to define. However, the effective length does not play a role when μr and εr=0, where the enhanced transmission normally occurs. The enhanced transmission may be well explained from the μr or εr near-zero or equivalent near-zero index point of view, providing simple and straightforward insight. Additionally, through the TL analysis we achieve an alternative explanation for the double Fano-shaped responses [34]. This perspective may help to optimize the structure for different applications.

2. NUMERICAL SIMULATION MODELS AND ANALYSIS METHOD

The metallic meander structure under study is composed of an one-dimensional conformal corrugated metallic film with periodic rectangular ridge profiles, as shown in Fig. 1a . It is characterized by periodicity Px, metal thickness d, and meander depth D. Inverse symmetry along the propagation direction is achieved by setting Wr=Px2d, which is crucial to obtain a strong coupling between the SPP modes on the two interfaces and large enhanced transmission. A fixed film thickness of 30nm is used throughout the report. The structure is placed in vacuum without the loss of generality. In previous studies, this structure was used to produce an effective negative permeability [20, 23]. It is similar to metallic slabs with two corrugated surfaces with a π phase difference and an equal filling factor [5, 8]. However, those structures are more difficult to fabricate when compared with the meanders. The spectra of the structures are calculated by two numerical methods to cross-check and complement each other. One is the commercial Maxwell solver CST Microwave Studio, and the other one is a Fourier modal method (FMM) [35] improved by factorization rules [36] and adaptive spatial resolution [37]. We use silver as the metal due to its low loss at visible frequencies. In order to study the mode behavior in a larger spectral range, a Drude model is used to describe its dielectric dispersion, although the Johnson–Christy dispersion resembles the real metal properties more [38]. In our Drude model, the plasma frequency is 1.37×1016rads and the scattering frequency is 8.5×1013rads, which are fitted values from experiments [39]. In the second method, 61 Floquet–Bloch modes were considered, although fewer modes are sufficient for a good convergence. Only the zeroth diffraction order is presented in the spectra. In Fig. 1b, transmittance spectra of an Ag meander calculated at normal incidence using both methods are compared. Below the Rayleigh frequency, both methods deliver the same spectra. However, some spurious resonances beyond this frequency show up in the solid curve due to numerical inaccuracies of CST Microwave Studio.

3. BAND STRUCTURES OF METALLIC MEANDERS

To excite SPP modes in the corrugated metallic surfaces, an E field component perpendicular to the ridge is needed. In this report we investigate only the relationship of the modes versus the parallel wave vector Kx, namely with TM polarized light, and change the polar angle θ in the xz plane, as shown in Fig. 1. Typical dispersion diagrams with respect to extinction, absorption, and transmission versus the parallel wave vector KxKg of silver meanders with Px=200 and Px=400nm are shown in Figs. 2a, 2b, 2c, 2d, 2e, 2f , respectively. The extinction is defined as ln(T), in which T is the transmittance. Kg is the reciprocal lattice vector defined as Kg=2πPx. Due to the grating scattering, the momentum of the SPPs will be changed according to the relation [15]

Kspp±mKg=Kx=K0sin(θ),
where Kspp is the wave vector of the SPP mode, K0 is the wave vector of the light in free space, and m is an integer that defines the order of the scattering process. These dispersion curves are similar to those shown in [7, 8], where the lowest two branches are attributed to the SRSPP and LRSPP modes scattered by +Kg, respectively. The vertical line shows the position of the first Brillouin zone at KxKg=0.5, and the dashed lines show the free space light scattered by an empty grating.

Figures 2a, 2b, 2c show the dispersion relation for the meander with Px=200nm. The extinction spectra in Fig. 2a demonstrate that two relatively flat bands with large frequency distance occur. At Kx=0, the SRSPP is located around 700THz and the LRSPP around 1000THz. The back-fold branch of the LRSPP is almost flat due to the scattering of the lattice vector Kg, therefore having a high optical density of states [40]. From the absorption spectra shown in Fig. 2b the LRSPP mode is difficult to recognize due to its weak absorption. With the increase of Kx, an increased transmittance up to 90% is observed as shown in Fig. 2c, which behaves similarly as weakly coupled SPPs [5]. The larger frequency distance between the two modes (SRSPP and LRSPP) would be very interesting for realizing plasmonic bandgap lasers, in which the probability to couple the spontaneous emissions from a source into the two modes simultaneously is reduced [10]. Furthermore, at normal incidence both the LRSPP and the SRSPP modes are far away from the grating diffraction mode, revealing that they are localized plasmonic resonances.

Figures 2d, 2e, 2f show the corresponding spectra for Px=400nm. Compared to the dispersion diagram for Px=200nm, both LRSPP and SRSPP modes are redshifted and the frequency difference between the two modes at Kx=0 is decreased. Due to the increased periodicity and decreased Bragg vector, the modes are more dispersive, and more diffraction orders show up in the light cone. In Figs. 2d, 2e intramode and intermode crossings are observed [7, 8]. At Kx=0, intramode band gaps are formed at 650THZ and 750THz, respectively, due to the existence of the 2Kg Fourier component of the grating [7, 41]. At Kx>0 around 800THz, intermode interaction between the SRSPP scattered by +2Kg and the LRSPP scattered by Kg also leads to a bandgap. No intramode interaction is observed between the SRSPP branches scattered by Kg and +2Kg at KxKg=0.5. Figure 2f shows the transmittance spectra versus Kx. With the increase of Kx, the transmittance is increased instead of being decreased [5], while the passband is getting narrower when the dispersion is approaching the grating diffraction line. In order to study the spectra in detail, selected transmittance curves are replotted in Figs. 3a, 3b for the two periodicities, respectively. From Fig. 3a for Px=200nm, we find that the spectra are getting narrower with incident angle from the high frequency side only, namely from the LRSPP mode side. This can be attributed to the cutoff of the Rayleigh frequency, which is induced by the diffraction of the grating. The LRSPP resonance above this line cannot be excited, which makes the high-frequency side of the passband profile sharper. Similarly, the narrowing of the passband at Px=400nm can be interpreted in the same way, as we can see from Fig. 3b.

Figures 3a, 3b show a possibility of how to apply our design for various frequency filters. At a smaller periodicity than Px=200nm [Fig. 3a], the frequency of the passband is less dependent on the incident angle of light, especially when this angle is larger than 40 degrees. It is similar to a radome filter in electrical engineering designed for antennas [42]. Through optimizing the structural parameters, a simple radome filter can be realized [43]. For the meanders at a larger periodicity than Px=400nm [see Fig. 3b], the transmission frequency is selected through changing the incident angle. The passband is getting narrower with almost unchanged transmission amplitude for increased angles, which could result in a frequency filter for a broadband spectrum.

Although both modes are excited through the coupling of the grating with the SPP modes, they behave differently upon a change of their structural parameters. Figure 4a shows the extinction spectra of the meander with varied meander depth D at fixed Px=400nm and d=30nm. We see that the SRSPP branch in (a) can be downshifted from 580THzto460THz when D is changed from 20nmto80nm without changing the frequency of the LRSPP mode. This behavior confirms that the SRSPP mode is strongly localized in the meander loop. It also provides another possibility to move the SRSPP mode away from the LRSPP mode for realizing a plasmonic bandgap laser. The transmittance spectra as a function of meander depth are plotted in Fig. 4b. We see that the enhanced transmission is related to the interaction of the two plasmonic resonances. With the increase of D, the frequency distance between the two modes is increased and the interaction is decreased. This leads to a decreased transmission, as will be further elucidated in the following section.

Contrary to the behavior upon a change of the meander depth, both SPP modes are redshifted with the increase of the periodicity, as shown in Fig. 5 . At larger periodicity the SRSPP mode approaches the LRSPP mode, and both approach the SPP modes in thin metallic films. On the other hand the LRSPP resonance is clipped by the grating diffraction line, and this leads to a narrowed passband. However, the interaction between the two modes remains strong, which leads to a larger enhanced transmission in a broad parameter range, as shown in Fig. 5b. The transmittance achieves its maximum around Px=400nm. At larger D (for instance 80nm—results not shown here), the LRSPP mode maintains the same behavior as in Fig. 5a, but the SRSPP mode shifts more gradually with Px, which again indicates a stronger mode localization in the loop.

4. TRANSMISSION LINE ANALYSIS OF MEANDER STRUCTURES

As shown above, the excited SPP modes and the transmittance of the meander change strongly, not only with Kx but also with meander depth D and periodicity Px when varied within a range that is accessible through standard nanofabrication (also with metal thickness, but it is fixed in this study). Furthermore, the change is not monotonous. In this section, we try to interpret these properties using a TL equivalent circuit model, which gives a novel explanation for the phenomena of the enhanced transmission that we discussed above. In addition, the observed Fano line shapes can also be explained from the response of the TL circuit model [34].

Figure 6a shows the schematic of a meander together with its circuit elements. Figure 6b shows its TL circuit model loaded with frequency-independent L and C elements, which can be constructed using the method introduced in [32]. Resistance R is implemented to describe optical losses. The slab is viewed as a dimensionless impedance sheet perpendicular to the k direction [33] with series and shunt elements. The circuit elements are arranged along a symmetric and reciprocal two-port Π type TL (also equivalent to a T type TL circuit). The length of the TL section is taken as l=D+d, i.e., the physical length of the slab. In the circuit model, L1C1 form a magnetic resonator [44] and L2C2 form an electric resonator due to their position in the TL [33, 45]. The two resonators represent the SRSPP mode and the LRSPP modes, respectively, as will be discussed in the following. The shunt inductance L3 represents the unstructured metallic film when the frequency is smaller than the effective plasma frequency [46]. By fitting the numerical curves of the meander structure using TL equations [47], the proper circuit parameters can be obtained [32]. Figure 7 shows the reflectance/transmittance spectra and the phase spectra of the scattering parameters S11 and S21 (or equivalently, S22 and S12 due to the reciprocity and symmetry of the structure) from numerical simulations (solid curves) and TL calculations (dashed curves) of a meander with Px=500nm and D=40nm at normal incidence. These spectra are typical for Ag meanders, among which the transmittance has a passband with two sharp edges. In principle, the circuit model is also valid for inclined incidence, although the resonances are redshifted due to the weakened electric field coupling. Correspondingly, the circuit parameters are also changed. However, at a larger incident angle, the LRSPP mode might be suppressed by the diffracted light line and makes the fitting procedure difficult, as can be seen from Fig. 2d.

Fitted circuit parameters are listed in Table 1 . Good agreement is obtained not only for the transmittance and reflectance spectra but also for the phase spectra. We have to stress that by using other combinations of circuit elements, one might also be able to obtain the same transmittance and reflectance spectra, but would not be able to obtain the same phase spectra simultaneously. Evidently, the metallic meander can be well represented by the circuit model. Once the inverse symmetry of the meander along the propagation direction is broken, for instance in the presence of a substrate, the circuit parameters might be position dependent along the k direction. In this case a distributed circuit model has to be used in which the circuit parameters cannot be uniquely determined.

To gain more physical insight into the line shapes of the meander response, the transmittance spectra of the TL model shown in Fig. 6b with different combinations of these circuit elements are calculated using the parameters listed in Table 1 for D=40nm. As shown in Fig. 8a , the magnetic resonator (L1C1) induces a stop band resonance and L3 induces a flat transmission spectrum, which is typical for inductive metallic films. The combination of both results in an asymmetrical Fano line-shaped enhanced transmittance with a dip at the low frequency side. Similarly, as shown in Fig. 8b, the electric resonator (L2C2) also induces a stop band resonance. Although its combination with L3 results in an asymmetrical resonance, the dip is at the high-frequency side. Both line shapes can be interpreted by an interference between resonant and nonresonant processes [34]. In the meander the nonresonant response originates from the continuous metallic film. Such a localized plasmonic resonance-induced transparency is also one possible explanation of the macroscopic mechanism for enhanced transmittance with perforated metallic films [48]. They also display a Fano line shape. Finally, when the two resonators are combined together with L3, a typical transmittance line shape of meander structures accompanied by two minima can be obtained, as shown in Fig. 8c.

An interesting observation is the stronger absorption by the magnetic resonance, as indicated in Figs. 8a, 8b, although the ohmic resistance of the two resonances is almost the same as can be seen in Table 1. In fact, the absorption induced by the magnetic resonance alone is not stronger than that of the electric resonance alone. However, the combination with L3 leads to a higher absorption from the magnetic resonance than that from the electric resonance due to the different interaction processes.

The circuit model can be further understood by analyzing field distributions. Figures 9a, 9b, 9c, 9d, 9e, 9f show the distributions of the electric field in the xz plane, the magnetic field Hy, and the current density at the magnetic and electric resonance frequencies 482THz and 585THz, respectively, for the meander shown in Fig. 7. At 482THz, the instantaneous charge distribution manifests that this mode originates from the symmetric SPP mode. Due to the presence of the meander corrugation, the electric field oscillates mainly between the loop edges of A and B. Through the coupling of the magnetic field to the loop, a circular current is induced as shown in Figs. 9c, 9e, revealing that it has the property of a magnetic resonance. This clarifies the origin of L1. The potential difference of the electric field along kz [in Fig. 9a] elucidates the existence of the series capacitance C1. It stems from the instantaneous charge distribution of the induced current. The series inductance L1 and the series capacitance C1 are combined in parallel in the TL and, therefore, lead to a magnetic resonance [32, 44]. At 585THz, the electric field oscillates mainly between the edge points B and C at the top of the meander [Fig. 9b], and the electrically induced current also oscillates mainly between B and C [Fig. 9f]. This is a typical behavior of cut wires and can be described by the shunt L2 and C2 combined in series in TL [32]. On the other hand, L3 originates from the background plasmon oscillation as shown by the current distribution in Fig. 9g at a lower frequency away from any resonances. To see whether the circuit parameters have a physical meaning and to understand the enhanced transmittance, relationships of the circuit parameters with the structural parameters are discussed below.

4A. Variation of Meander Depth

First the meander depth D is varied with fixed Px=400nm, and the dependence of the circuit parameters is shown in Fig. 10 .

For the capacitances shown in Figs. 10a, 10c, C1 and C2 are the parameters obtained by fitting the numerical results, while C1qs and C2qs are the results from the quasi-static equations for a classic parallel-plate capacitor

C1qs=G1Px2dcDDc,
and
C2qs=G2DDcPx2dc,
where G1 and G2 are fitting constants containing the effective length along the y direction. Dc is a fitted correction constant for the meander depth, and dc is the one for the thickness of the metal film. The fitted Dc is around 14nm and dc is around 5nm for both curves. From Fig. 9a we infer that the maximum of the electric field is at a position away from the metal edge. This might explain the formation of Dc and dc. Surprisingly, both C1 and C2 have a quasi-static relationship with the meander depth. However, the corresponding potential difference between the two plates for C1 is along the z direction and for C2 is along the x direction, as has been discussed above. Therefore, the relevant distance for C1 is D, while the relevant distance for C2 is Px2. This fact leads to a completely different dependence of C1 and C2 on D.

The inductances are shown in Figs. 10b, 10d. Both L1 and L3 increase with D, and the relationship is becoming linear at larger D. A quasi-static picture can still be applied to the linear part, because the inductance of a metal loop is proportional to its loop area. L3 has a similar dependence on D as does L1. This could be simply the consequence of the increased metal area when the meander is unfolded into a planar metal film. Contrary to L1, L2 decreases with D oppositely to the quasi-static relation. In order to quantitatively characterize L2, the radiative inductance of the meander is calculated using an analytical formula for planar SRRs given by Meyrath et al. in [27]. Without any modification, the meander dimensions with l1=Px2, l2=D+d2, and a network factor of 0.4 were used. The calculated radiative inductance Lr is plotted in (d) as dashed curve. We conclude that L2 can be reproduced by the radiative model very well.

4B. Variation of Meander Period

The meander period Px was varied with fixed D=40nm. Figure 11 shows the relationship of the circuit parameters with Px. In contrast to the dependence on D, C1 increases with the period while C2 decreases. On the other hand, L1 decreases with Px while L2 increases. L3 first changes little but decreases for larger Px. To check whether the capacitances can still be described by the quasi-static formula, the same fitting parameters (G1,G2,dc,Dc) are put into Eq. (2) and Eq. (3). The calculated C1qs (solid square) and C2qs (solid circle) are shown in Figs. 11a, 11c, respectively. Evidently, C2 can be well understood from the quasi-static picture, while C1 deviates from C1qs substantially, especially at larger Px. The reason for this might stem from the fact that at larger Px the LRSPP modes approach the grating diffraction, which influences the line shape of the response and makes the fitting for the circuit parameters difficult. Lr is calculated based on the same input parameters as for the D variation, and the results are plotted as dashed curve in Fig. 11d. Similarly, L2 can be well described by the radiative inductance.

5. DISCUSSION

From the analysis above we conclude that the interaction of the magnetic and electric resonances induced by localized SPPs results in an enhanced transmission in structured metallic films. This phenomenon can be understood from a simple near-zero index perspective. To elucidate this point, effective permeability and permittivity of meanders with Px=500nm and different D are calculated using the fitted parameters of the circuit elements listed in Table 1 and the TL homogenization method [32]. This method delivers physical effective material parameters for impedance sheets [32], in contrast to the retrieval procedure from scattering parameters [49]. In fact, it is an alternative description for electric and magnetic polarizabilities [45], and it turns out to be very useful in understanding the enhanced transmission in the meanders.

Figures 12a, 13a show the calculated effective permittivity εr and permeability μr homogenized in the physical length of l=D+d with different D. Figures 12b, 13b show the corresponding effective index, which is defined as neff=εrμr. A negative index might be obtained from this calculation. However, it is not relevant for our present discussion and, therefore, only the absolute values of the real part |Re(neff)| are shown in the figures. Both effective parameters have Lorentzian responses. However, due to the background plasmon from the continuous metallic film (L3), εr becomes negative at the low-frequency side. Enhanced transmission occurs in the region where both Re(μr) and Re(εr) are near zero (hatched region). In Fig. 12a, the two transmission peaks are corresponding to the frequencies at which both material parameters are zero, respectively. Consequently, in the same region the effective index is near zero as we can infer from Fig. 12b. For the structure with D=80nm shown in Fig. 13a, although enhanced transmission still occurs, the εr=0 frequency is lower than the μr=0 frequency. This results in an overlap of the εr near-zero region with the strong negative region of the μr (and, therefore, with the strong absorption region, which is not shown here [32]). Although Re(neff) is still near zero [Fig. 13b], the absorption is larger and the transmission amplitude is lower than that by the meander with D=40nm. In addition, only one peak can be seen, although it is induced by two resonances. Therefore, both the shape and the amplitude of the transmission depend on the coupling and oscillation strength of both resonators. At optimized structural parameters, high transmittance with sharp cutoffs at both sides can be obtained, as we have seen in Fig. 4 and Fig. 5.

From this model, some of the observed phenomena can be well understood. For instance, for the dispersion diagram shown in Fig. 2, the coupling of the electric field to the meander is decreased (x component) with increased incident angle of light or increased Kx, while that of the magnetic field into the meander loop does not change. This changes the overlap region of the magnetic and electric resonances and, therefore, the amplitude and shape of the enhanced transmission. This is the same as when changing D or Px. Growing evanescent waves might be obtained in stacked frequency-selective surfaces [50, 51]. Using the TL circuit model and the geometry-related circuit elements, one could design a subwavelength imaging system based on meanders.

The application potential of near-zero index materials have been studied for a long time. Directional emission through such a material can be expected [52, 53]. In earlier work, such a metallic meander structure has been used to enhance the emission and quantum efficiency of GaAs LEDs [54, 55]. At the same time, a directional beam was obtained [54, 55, 56, 57]. Further physical understanding concerning a directional beam is still needed.

6. CONCLUSION

In this report we have studied the optical properties of a vertical metallic meander structure that exhibits rich features in the band diagrams and could be interesting for many applications. The structure can be especially well interpreted using a TL circuit model in which the lowest SRSPP mode is viewed as a magnetic resonance, and the lowest LRSPP mode is viewed as an electric resonance. The enhanced transmittance is well understood from the near-zero index point of view. Through varying the structural parameters, the amplitude, and line shape of the transmission are varied, depending on the incidence angle of the light, the meander depth, and the periodicity. This variation is the consequence of the varied overlap and strength of the magnetic and electric resonances. The double Fano line shapes are also well interpreted by the TL model, which would be an extension to the studies in [34]. Different functional filters can be designed, depending on specific applications. The structure is well suited for nanofabrication. The TL model provides us a way to retrieve the circuit parameters for frequency-selected surfaces, which could become a very powerful tool for designing subwavelength imaging systems.

ACKNOWLEDGMENTS

We thank T. Meyrath for many helpful discussions and acknowledge the support from Deutsche Forschungsgemeinschaft (DFG) grant FOR557, Bundesministerium für Bildung und Forschung (BMBF) grant 3D Metamat 13N10146, and Landesstifung Baden Württemberg (BW) Project OPTIM.

Tables Icon

Table 1. Circuit parameters of the TL model for meanders at Px=400nm and d=30nm

 figure: Fig. 1

Fig. 1 (a) Schematic of a metallic meander with two unit cells in vacuum composed of a corrugated metallic film with a rectangular ridge profile. The structure is characterized by periodicity Px, metal thickness d, and meander depth D. The groove width Wr is set to be Px2d. (b) Transmittance spectra of an Ag meander at normal incidence simulated using time-domain transient solver in CST (solid curve) and using FMM (dashed curve).

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 figure: Fig. 2

Fig. 2 Dispersion diagram of Ag meanders with D=40nm, d=30nm, and different periodicities plotted in extinction, absorption, and transmittance spectra calculated using FMM. (a)–(c) Px=200nm; (d)–(f) Px=400nm. The light dashed lines are diffracted light lines and the dark dashed lines represent the propagating light in free space. The solid lines show the right border of the first Brillouin zone at Kx=Kg2.

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 figure: Fig. 3

Fig. 3 Transmittance versus frequency calculated using FMM at different incident angles for meanders with (a) Px=200nm and (b) Px=400nm. The arrows show the position of the Rayleigh frequency induced by the diffraction of the grating [34].

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 figure: Fig. 4

Fig. 4 (a) Extinction and (b) transmittance spectra of an Ag meander with Px=400nm, d=30nm, and varied meander depth at normal incidence calculated using FMM.

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 figure: Fig. 5

Fig. 5 (a) Extinction and (b) transmittance spectra of an Ag meander with D=40nm, d=30nm, and varied periodicity calculated using FMM.

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 figure: Fig. 6

Fig. 6 (a) Schematic of a metallic meander structure to show the origin of the elements. The dashed arrows show the current flow responsible for the formation of L3. (b) TL circuit model for the meander with the polarization shown in (a). The light gray TL sections represent the free space.

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 figure: Fig. 7

Fig. 7 Comparison of reflectance/transmittance spectra and phase spectra calculated from the TL circuit model with those from the numerical simulation (CST) for a meander with Px=500nm and D=40nm at normal incidence. (a) Reflectance, transmittance, and absorption spectra; (b) Phase S11 and S21 spectra. Dashed curves are from the TL model, solid curves are from the numerical simulation, and the short dashed curve in (a) is absorption. MR, magnetic resonance; ER, electric resonance.

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 figure: Fig. 8

Fig. 8 Transmittance and absorption spectra from the TL circuit model with selective combination of circuit elements: (a) with the combination of the magnetic resonator and L3; (b) with the combination of the electric resonator and L3; (c) combining both the magnetic and electric resonators with L3.

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 figure: Fig. 9

Fig. 9 (a),(b) Instantaneous electric field, (c),(d) normalized magnetic field, and (e),(f) current density distributions of a meander with Px=500nm, D=40nm, and d=30nm at the magnetic resonance (482THz, left column) and electric resonance (585THz, right column), respectively. (g) Normalized current density at the lower frequency side of the magnetic resonance (at 200THz, for instance). Results are taken from CST.

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 figure: Fig. 10

Fig. 10 Dependence of circuit parameters C1, C2, L1, L2, and L3 on meander depth D. Other parameters are fixed with Px=400nm. Solid square curve in (a) and solid circle curve in (c) are results from the quasi-static model [Eqs. (2, 3)]. The dashed curve in (d) represents the radiative model for SRRs.

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 figure: Fig. 11

Fig. 11 Dependence of circuit parameters (C1, L1, C2, L2, and L3) on meander period Px with fixed D=40nm. Solid-square curve in (a) and solid-circle curve in (c) are calculated results using the quasi-static model [Eqs. (2, 3)]. The dashed curve in (d) is from the radiative model for SRRs.

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 figure: Fig. 12

Fig. 12 (a) Effective material parameters and (b) effective index and transmittance versus frequency for Ag meanders with Px=500nm, d=30nm, and D=40nm.

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 figure: Fig. 13

Fig. 13 (a) Effective material parameters and (b) effective index and transmittance versus frequency (b) for Ag meanders with Px=500nm, d=30nm, and D=80nm.

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4. N. Bonod, S. Enoch, L. Li, E. Popov, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003). [CrossRef]   [PubMed]  

5. D. Gerard, L. Salomon, F. de Fornel, and A. V. Zayats, “Analysis of the Bloch mode spectra of surface polaritonic crystals in the week and strong coupling regimes: grating-enhanced transmission at oblique incidence and suppression of SPP radiative losses,” Opt. Express 12, 3652–3662 (2004). [CrossRef]   [PubMed]  

6. I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004). [CrossRef]  

7. Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008). [CrossRef]  

8. T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008). [CrossRef]  

9. T. Okamoto, F. H’Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968–3970 (2004). [CrossRef]  

10. G. Winter and W. L. Barnes, “Can lasing at visible wavelengths be achieved using the low-loss long-range surface plasmon-polariton mode?” New J. Phys. 8, 125 (2006). [CrossRef]  

11. J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352–1359 (2007). [CrossRef]   [PubMed]  

12. M. J. Gonzalez, A. L. Stepanov, J.-C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704–2706 (2007). [CrossRef]   [PubMed]  

13. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55–58 (2008). [CrossRef]  

14. G. Margheri, T. Del Rosso, S. Sottini, S. Trigari, and E. Giorgetti, “All-optical switches based on the coupling of surfaces plasmon polaritons,” Opt. Express 16, 9869–9883 (2008). [CrossRef]   [PubMed]  

15. S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673–3685 (2004). [CrossRef]   [PubMed]  

16. A. Kocabas, G. Ertas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap structures for surface enhanced Raman scattering,” Opt. Express 16, 12469–12477 (2008). [CrossRef]   [PubMed]  

17. A. Degiron and T. W. Ebbeson, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7, 590 (2005). [CrossRef]  

18. S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101–113 (2008).

19. W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000). [CrossRef]  

20. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543–546 (2008). [CrossRef]  

21. C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749–755 (2009). [CrossRef]  

22. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005). [CrossRef]   [PubMed]  

23. H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886–3900 (2007). [CrossRef]  

24. R. Ulrich, “Far infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967). [CrossRef]  

25. N. Engheta, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef]   [PubMed]  

26. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005). [CrossRef]   [PubMed]  

27. T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007). [CrossRef]  

28. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007). [CrossRef]   [PubMed]  

29. S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials 1, 40–43 (2007). [CrossRef]  

30. H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243–1250 (2007). [CrossRef]  

31. L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425–429 (2007). [CrossRef]  

32. L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008). [CrossRef]  

33. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech, 2003).

34. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003). [CrossRef]  

35. T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009). [CrossRef]  

36. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]  

37. G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” J. Opt. Soc. Am. A 16, 2510–2516 (1999). [CrossRef]  

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

39. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006). [CrossRef]   [PubMed]  

40. I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002). [CrossRef]  

41. W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996). [CrossRef]  

42. B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, 2000). [CrossRef]  

43. I. Avrutsky, Y. Zhao, and V. Kochergin, “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25, 595–597 (2000). [CrossRef]  

44. G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51–53 (2003). [CrossRef]  

45. C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials 1, 62–80 (2007). [CrossRef]  

46. R. N. Bracewell, “Analogues of an ionized medium,” Wireless Engineer 31, 320–326 (1954).

47. D. M. Pozar, Microwave Engineering, 3rd. ed. (Wiley, 2005).

48. J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008). [CrossRef]  

49. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002). [CrossRef]  

50. S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293–1300 (2004). [CrossRef]  

51. A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268–272 (2006). [CrossRef]  

52. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002). [CrossRef]   [PubMed]  

53. A. Sihvola and I. Lindell, “EZNZ vs. ENZ metamaterials: anisotropy flavors extreme parameters,” in Proceedings of 2nd European Topical Meeting on Nanophotonics and Metamaterials (NanoMeta, 2009), Seefeld, Austria, January 5–8, 2009.

54. A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAsGaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327–2329 (1990). [CrossRef]  

55. P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748–3750 (1999). [CrossRef]  

56. N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564–570 (2008). [CrossRef]  

57. H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478–479.

References

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  1. U. Schröter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992-4999 (1999).
    [Crossref]
  2. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  3. R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55, 1117-1120 (1985).
    [Crossref] [PubMed]
  4. N. Bonod, S. Enoch, L. Li, E. Popov, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482-490 (2003).
    [Crossref] [PubMed]
  5. D. Gerard, L. Salomon, F. de Fornel, and A. V. Zayats, “Analysis of the Bloch mode spectra of surface polaritonic crystals in the week and strong coupling regimes: grating-enhanced transmission at oblique incidence and suppression of SPP radiative losses,” Opt. Express 12, 3652-3662 (2004).
    [Crossref] [PubMed]
  6. I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004).
    [Crossref]
  7. Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008).
    [Crossref]
  8. T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008).
    [Crossref]
  9. T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
    [Crossref]
  10. G. Winter and W. L. Barnes, “Can lasing at visible wavelengths be achieved using the low-loss long-range surface plasmon-polariton mode?” New J. Phys. 8, 125 (2006).
    [Crossref]
  11. J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
    [Crossref] [PubMed]
  12. M. J. Gonzalez, A. L. Stepanov, J.-C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704-2706 (2007).
    [Crossref] [PubMed]
  13. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
    [Crossref]
  14. G. Margheri, T. Del Rosso, S. Sottini, S. Trigari, and E. Giorgetti, “All-optical switches based on the coupling of surfaces plasmon polaritons,” Opt. Express 16, 9869-9883 (2008).
    [Crossref] [PubMed]
  15. S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673-3685 (2004).
    [Crossref] [PubMed]
  16. A. Kocabas, G. Ertas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap structures for surface enhanced Raman scattering,” Opt. Express 16, 12469-12477 (2008).
    [Crossref] [PubMed]
  17. A. Degiron and T. W. Ebbeson, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7, 590 (2005).
    [Crossref]
  18. S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).
  19. W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
    [Crossref]
  20. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
    [Crossref]
  21. C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
    [Crossref]
  22. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
    [Crossref] [PubMed]
  23. H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
    [Crossref]
  24. R. Ulrich, “Far infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37-55 (1967).
    [Crossref]
  25. N. Engheta, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
    [Crossref] [PubMed]
  26. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
    [Crossref] [PubMed]
  27. T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).
    [Crossref]
  28. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
    [Crossref] [PubMed]
  29. S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials 1, 40-43 (2007).
    [Crossref]
  30. H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
    [Crossref]
  31. L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
    [Crossref]
  32. L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
    [Crossref]
  33. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech, 2003).
  34. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
    [Crossref]
  35. T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
    [Crossref]
  36. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [Crossref]
  37. G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” J. Opt. Soc. Am. A 16, 2510-2516 (1999).
    [Crossref]
  38. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [Crossref]
  39. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
    [Crossref] [PubMed]
  40. I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
    [Crossref]
  41. W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
    [Crossref]
  42. B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, 2000).
    [Crossref]
  43. I. Avrutsky, Y. Zhao, and V. Kochergin, “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25, 595-597 (2000).
    [Crossref]
  44. G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
    [Crossref]
  45. C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials 1, 62-80 (2007).
    [Crossref]
  46. R. N. Bracewell, “Analogues of an ionized medium,” Wireless Engineer 31, 320-326 (1954).
  47. D. M. Pozar, Microwave Engineering, 3rd. ed. (Wiley, 2005).
  48. J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
    [Crossref]
  49. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
    [Crossref]
  50. S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293-1300 (2004).
    [Crossref]
  51. A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268-272 (2006).
    [Crossref]
  52. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
    [Crossref] [PubMed]
  53. A. Sihvola and I. Lindell, “EZNZ vs. ENZ metamaterials: anisotropy flavors extreme parameters,” in Proceedings of 2nd European Topical Meeting on Nanophotonics and Metamaterials (NanoMeta, 2009), Seefeld, Austria, January 5-8, 2009.
  54. A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
    [Crossref]
  55. P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
    [Crossref]
  56. N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
    [Crossref]
  57. H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478-479.

2009 (2)

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
[Crossref]

2008 (10)

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008).
[Crossref]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008).
[Crossref]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
[Crossref]

G. Margheri, T. Del Rosso, S. Sottini, S. Trigari, and E. Giorgetti, “All-optical switches based on the coupling of surfaces plasmon polaritons,” Opt. Express 16, 9869-9883 (2008).
[Crossref] [PubMed]

A. Kocabas, G. Ertas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap structures for surface enhanced Raman scattering,” Opt. Express 16, 12469-12477 (2008).
[Crossref] [PubMed]

S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
[Crossref]

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

2007 (9)

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials 1, 62-80 (2007).
[Crossref]

J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
[Crossref] [PubMed]

M. J. Gonzalez, A. L. Stepanov, J.-C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704-2706 (2007).
[Crossref] [PubMed]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
[Crossref] [PubMed]

S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials 1, 40-43 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

2006 (3)

G. Winter and W. L. Barnes, “Can lasing at visible wavelengths be achieved using the low-loss long-range surface plasmon-polariton mode?” New J. Phys. 8, 125 (2006).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268-272 (2006).
[Crossref]

2005 (4)

A. Degiron and T. W. Ebbeson, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7, 590 (2005).
[Crossref]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

N. Engheta, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

2004 (5)

S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673-3685 (2004).
[Crossref] [PubMed]

T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
[Crossref]

D. Gerard, L. Salomon, F. de Fornel, and A. V. Zayats, “Analysis of the Bloch mode spectra of surface polaritonic crystals in the week and strong coupling regimes: grating-enhanced transmission at oblique incidence and suppression of SPP radiative losses,” Opt. Express 12, 3652-3662 (2004).
[Crossref] [PubMed]

I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004).
[Crossref]

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293-1300 (2004).
[Crossref]

2003 (3)

G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
[Crossref]

N. Bonod, S. Enoch, L. Li, E. Popov, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482-490 (2003).
[Crossref] [PubMed]

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

2002 (3)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[Crossref]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[Crossref]

2000 (2)

I. Avrutsky, Y. Zhao, and V. Kochergin, “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25, 595-597 (2000).
[Crossref]

W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[Crossref]

1999 (3)

U. Schröter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992-4999 (1999).
[Crossref]

G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” J. Opt. Soc. Am. A 16, 2510-2516 (1999).
[Crossref]

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

1996 (2)

W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[Crossref]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
[Crossref]

1990 (1)

A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
[Crossref]

1985 (1)

R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55, 1117-1120 (1985).
[Crossref] [PubMed]

1972 (1)

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

1967 (1)

R. Ulrich, “Far infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37-55 (1967).
[Crossref]

1954 (1)

R. N. Bracewell, “Analogues of an ionized medium,” Wireless Engineer 31, 320-326 (1954).

Alitalo, P.

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293-1300 (2004).
[Crossref]

Alù, A.

A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268-272 (2006).
[Crossref]

Augui, B.

J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
[Crossref]

Avrutsky, I.

Aydinli, A.

Barnes, W. L.

J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
[Crossref]

G. Winter and W. L. Barnes, “Can lasing at visible wavelengths be achieved using the low-loss long-range surface plasmon-polariton mode?” New J. Phys. 8, 125 (2006).
[Crossref]

S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673-3685 (2004).
[Crossref] [PubMed]

W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[Crossref]

Beinstingl, W.

A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
[Crossref]

Bonod, N.

Bouhelier, A.

J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
[Crossref] [PubMed]

Bracewell, R. N.

R. N. Bracewell, “Analogues of an ionized medium,” Wireless Engineer 31, 320-326 (1954).

Brueck, S. R. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Busch, K.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Capasso, F.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Chen, Z.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008).
[Crossref]

Christy, R. W.

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

Colas des France, G.

J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
[Crossref] [PubMed]

de Fornel, F.

Degiron, A.

A. Degiron and T. W. Ebbeson, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7, 590 (2005).
[Crossref]

Del Rosso, T.

Dereux, A.

M. J. Gonzalez, A. L. Stepanov, J.-C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704-2706 (2007).
[Crossref] [PubMed]

J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
[Crossref] [PubMed]

Diehl, L.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Dolling, G.

Dragila, R.

R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55, 1117-1120 (1985).
[Crossref] [PubMed]

Ebbeson, T. W.

A. Degiron and T. W. Ebbeson, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7, 590 (2005).
[Crossref]

Economou, E. N.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Edamura, T.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Eleftheriades, G. V.

G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
[Crossref]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268-272 (2006).
[Crossref]

N. Engheta, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

Enkrich, C.

Enoch, S.

N. Bonod, S. Enoch, L. Li, E. Popov, and M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482-490 (2003).
[Crossref] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Errington, R.

H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478-479.

Ertas, G.

Essig, S.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Fan, J.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Finger, N.

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Frölich, A.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Fu, L.

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

Gerard, D.

Gerthsen, D.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Giessen, H.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

Giorgetti, E.

Gippius, N. A.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
[Crossref]

Gonzalez, M. J.

Gornik, E.

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
[Crossref]

Granet, G.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
[Crossref]

G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” J. Opt. Soc. Am. A 16, 2510-2516 (1999).
[Crossref]

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Guo, H.

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

Hahn, H.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Hauser, M.

A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
[Crossref]

H'Dhili, F.

T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
[Crossref]

Heitmann, D.

U. Schröter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992-4999 (1999).
[Crossref]

Hendry, E.

J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
[Crossref]

Hohenau, A.

Hooper, I. R.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008).
[Crossref]

I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004).
[Crossref]

I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
[Crossref]

Iyer, Ashwin K.

G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
[Crossref]

Johnson, P. B.

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

Kafesaki, M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Kan, H.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Kawata, S.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008).
[Crossref]

T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
[Crossref]

Kellermann, P. O.

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

Kitson, S. L.

W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[Crossref]

Kocabas, A.

Kochergin, V.

Koeck, A.

A. Koeck, E. Gornik, M. Hauser, and W. Beinstingl, “Strongly directional emission from AlGaAs/GaAs light-emitting diodes,” Appl. Phys. Lett. 57, 2327-2329 (1990).
[Crossref]

Koschny, Th.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Krenn, J. R.

Kriegler, C. E.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

Li, J.

S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Li, L.

Lindell, I.

A. Sihvola and I. Lindell, “EZNZ vs. ENZ metamaterials: anisotropy flavors extreme parameters,” in Proceedings of 2nd European Topical Meeting on Nanophotonics and Metamaterials (NanoMeta, 2009), Seefeld, Austria, January 5-8, 2009.

Linden, S.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[Crossref] [PubMed]

Liu, N.

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

Liu, S.

S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Luther-Davies, B.

R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55, 1117-1120 (1985).
[Crossref] [PubMed]

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K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
[Crossref]

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Margheri, G.

Markey, L.

J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
[Crossref] [PubMed]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[Crossref]

Maslovski, S.

S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293-1300 (2004).
[Crossref]

Matthews, D.

H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478-479.

Meyrath, T. P.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).
[Crossref]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Müller, E.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
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Njoh, K.

H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478-479.

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T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008).
[Crossref]

T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
[Crossref]

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J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
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J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

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N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Plet, C.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
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Pozar, D. M.

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Preist, T. W.

W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
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W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
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C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
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Sambles, J. R.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Coupled surface plasmons on thin silver gratings,” J. Opt. A, Pure Appl. Opt. 10, 015007 (2008).
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J. Parsons, E. Hendry, B. Augui, W. L. Barnes, and J. R. Sambles, “Localized modes of subwavelength hole arrays in thin metal films,” Proc. SPIE 6988, 69880Y (2008).
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I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004).
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I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165432 (2002).
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W. L. Barnes, T. W. Presit, S. L. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[Crossref]

Sambles, R. J.

W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[Crossref]

Samson, Z. L.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
[Crossref]

Sarrazin, M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
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Scholz, F.

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

Schrenk, W.

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
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U. Schröter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992-4999 (1999).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[Crossref]

Schweizer, H.

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Synthesis of transmission line models for metamaterial slabs at optical frequencies,” Phys. Rev. B 78, 115110 (2008).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Longitudinal capacitance design for optical left-handed metamaterials,” Phys. Status Solidi B 244, 1243-1250 (2007).
[Crossref]

H. Schweizer, L. Fu, H. Guo, N. Liu, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi A 204, 3886-3900 (2007).
[Crossref]

P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
[Crossref]

Senlik, S. S.

Siddiqui, Omar

G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
[Crossref]

Sihvola, A.

A. Sihvola and I. Lindell, “EZNZ vs. ENZ metamaterials: anisotropy flavors extreme parameters,” in Proceedings of 2nd European Topical Meeting on Nanophotonics and Metamaterials (NanoMeta, 2009), Seefeld, Austria, January 5-8, 2009.

Simonen, J.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77, 115425 (2008).
[Crossref]

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C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials 1, 62-80 (2007).
[Crossref]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[Crossref]

Sottini, S.

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[Crossref] [PubMed]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[Crossref]

Staude, I.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

Stepanov, A. L.

Stockman, M. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
[Crossref]

Summers, H.

H. Summers, D. Matthews, K. Njoh, and R. Errington, “Beam-steering at optical frequencies using metal-grating antennas,” in Proceedings of the 19th IEEE Lasers and Electro-Optics Society Meeting (IEEE, 2006), pp. 478-479.

Tan, W.-C.

W.-C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[Crossref]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Thiel, M.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

Tikhodeev, S. G.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
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Tretyakov, S.

S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials 1, 40-43 (2007).
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S. Maslovski, S. Tretyakov, and P. Alitalo, “Near-field enhancement and imaging in double planar polariton-resonant structures,” J. Appl. Phys. 96, 1293-1300 (2004).
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R. Ulrich, “Far infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37-55 (1967).
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M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

Vigoureux, J.-M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role of wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

von Freymann, G.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
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R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55, 1117-1120 (1985).
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S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Wedge, S.

Weeber, J.-C.

M. J. Gonzalez, A. L. Stepanov, J.-C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704-2706 (2007).
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J.-C. Weeber, A. Bouhelier, G. Colas des France, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7, 1352-1359 (2007).
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Wegener, M.

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapor deposition,” Nature Mater. 7, 543-546 (2008).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[Crossref] [PubMed]

Weiss, T.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, “Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method,” J. Opt. A, Pure Appl. Opt. 11, 114019 (2009).
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P. O. Kellermann, N. Finger, W. Schrenk, E. Gornik, R. Winterhoff, H. Schweizer, and F. Scholz, “Wavelength-adjustable surface-emitting single-mode laser diodes with contradirectional surface-mode coupling,” Appl. Phys. Lett. 75, 3748-3750 (1999).
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S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Yamanishi, M.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
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S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Yu, N.

N. Yu, J. Fan, Q. Wang, C. Pflgl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2, 564-570 (2008).
[Crossref]

Zayats, A. V.

Zentgraf, T.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).
[Crossref]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Zhao, Y.

Zheludev, N. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55-58 (2008).
[Crossref]

Zhou, J.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

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S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Zhu, Y.

S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

Appl. Phys. B: Lasers Opt. (2)

C. E. Kriegler, M. S. Rill, M. Thiel, E. Müller, S. Essig, A. Frölich, G. von Freymann, S. Linden, D. Gerthsen, H. Hahn, K. Busch, and M. Wegener, “Transition between corrugated metal films and split-ring-resonator arrays,” Appl. Phys. B: Lasers Opt. 96, 749-755 (2009).
[Crossref]

L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B: Lasers Opt. 86, 425-429 (2007).
[Crossref]

Appl. Phys. Lett. (4)

S. Wu, Q. Wang, X. Yin, J. Li, D. Zhu, S. Liu, and Y. Zhu, “Enhanced optical transmission: role of the localized surface plasmon,” Appl. Phys. Lett. 93, 101-113 (2008).

T. Okamoto, F. H'Dhili, and S. Kawata, “Towards plasmonic band gap lasers,” Appl. Phys. Lett. 85, 3968-3970 (2004).
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[Crossref]

IEEE Microw. Wirel. Compon. Lett. (1)

G. V. Eleftheriades, Omar Siddiqui, and Ashwin K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wirel. Compon. Lett. 13, 51-53 (2003).
[Crossref]

IEEE Trans. Antennas Propag. (1)

A. Alù and N. Engheta, “Physical insight into the growing evanescent fields of double-negative metamaterial lenses using their circuit equivalence,” IEEE Trans. Antennas Propag. 54, 268-272 (2006).
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Infrared Phys. (1)

R. Ulrich, “Far infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37-55 (1967).
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Figures (13)

Fig. 1
Fig. 1 (a) Schematic of a metallic meander with two unit cells in vacuum composed of a corrugated metallic film with a rectangular ridge profile. The structure is characterized by periodicity P x , metal thickness d, and meander depth D. The groove width W r is set to be P x 2 d . (b) Transmittance spectra of an Ag meander at normal incidence simulated using time-domain transient solver in CST (solid curve) and using FMM (dashed curve).
Fig. 2
Fig. 2 Dispersion diagram of Ag meanders with D = 40 nm , d = 30 nm , and different periodicities plotted in extinction, absorption, and transmittance spectra calculated using FMM. (a)–(c) P x = 200 nm ; (d)–(f) P x = 400 nm . The light dashed lines are diffracted light lines and the dark dashed lines represent the propagating light in free space. The solid lines show the right border of the first Brillouin zone at K x = K g 2 .
Fig. 3
Fig. 3 Transmittance versus frequency calculated using FMM at different incident angles for meanders with (a) P x = 200 nm and (b) P x = 400 nm . The arrows show the position of the Rayleigh frequency induced by the diffraction of the grating [34].
Fig. 4
Fig. 4 (a) Extinction and (b) transmittance spectra of an Ag meander with P x = 400 nm , d = 30 nm , and varied meander depth at normal incidence calculated using FMM.
Fig. 5
Fig. 5 (a) Extinction and (b) transmittance spectra of an Ag meander with D = 40 nm , d = 30 nm , and varied periodicity calculated using FMM.
Fig. 6
Fig. 6 (a) Schematic of a metallic meander structure to show the origin of the elements. The dashed arrows show the current flow responsible for the formation of L 3 . (b) TL circuit model for the meander with the polarization shown in (a). The light gray TL sections represent the free space.
Fig. 7
Fig. 7 Comparison of reflectance/transmittance spectra and phase spectra calculated from the TL circuit model with those from the numerical simulation (CST) for a meander with P x = 500 nm and D = 40 nm at normal incidence. (a) Reflectance, transmittance, and absorption spectra; (b) Phase S 11 and S 21 spectra. Dashed curves are from the TL model, solid curves are from the numerical simulation, and the short dashed curve in (a) is absorption. MR, magnetic resonance; ER, electric resonance.
Fig. 8
Fig. 8 Transmittance and absorption spectra from the TL circuit model with selective combination of circuit elements: (a) with the combination of the magnetic resonator and L 3 ; (b) with the combination of the electric resonator and L 3 ; (c) combining both the magnetic and electric resonators with L 3 .
Fig. 9
Fig. 9 (a),(b) Instantaneous electric field, (c),(d) normalized magnetic field, and (e),(f) current density distributions of a meander with P x = 500 nm , D = 40 nm , and d = 30 nm at the magnetic resonance ( 482 THz , left column) and electric resonance ( 585 THz , right column), respectively. (g) Normalized current density at the lower frequency side of the magnetic resonance (at 200 THz , for instance). Results are taken from CST.
Fig. 10
Fig. 10 Dependence of circuit parameters C 1 , C 2 , L 1 , L 2 , and L 3 on meander depth D. Other parameters are fixed with P x = 400 nm . Solid square curve in (a) and solid circle curve in (c) are results from the quasi-static model [Eqs. (2, 3)]. The dashed curve in (d) represents the radiative model for SRRs.
Fig. 11
Fig. 11 Dependence of circuit parameters ( C 1 , L 1 , C 2 , L 2 , and L 3 ) on meander period P x with fixed D = 40 nm . Solid-square curve in (a) and solid-circle curve in (c) are calculated results using the quasi-static model [Eqs. (2, 3)]. The dashed curve in (d) is from the radiative model for SRRs.
Fig. 12
Fig. 12 (a) Effective material parameters and (b) effective index and transmittance versus frequency for Ag meanders with P x = 500 nm , d = 30 nm , and D = 40 nm .
Fig. 13
Fig. 13 (a) Effective material parameters and (b) effective index and transmittance versus frequency (b) for Ag meanders with P x = 500 nm , d = 30 nm , and D = 80 nm .

Tables (1)

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Table 1 Circuit parameters of the TL model for meanders at P x = 400 nm and d = 30 nm

Equations (3)

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K spp ± m K g = K x = K 0 sin ( θ ) ,
C 1 qs = G 1 P x 2 d c D D c ,
C 2 qs = G 2 D D c P x 2 d c ,

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