OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 1072–1080
« Show journal navigation

Planar terahertz waveguides based on complementary split ring resonators

Gagan Kumar, Albert Cui, Shashank Pandey, and Ajay Nahata  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 1072-1080 (2011)
http://dx.doi.org/10.1364/OE.19.001072


View Full Text Article

Acrobat PDF (1026 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We experimentally demonstrate planar plasmonic THz waveguides using metal films that are periodically perforated with complementary split ring resonators (CSRRs). The waveguide transmission spectra exhibit numerous transmission resonances. While the geometry is commonly used in developing negative index materials, the excitation geometry used here does not allow for conventional metamaterial response. Instead, we show that all of the observed resonances can be determined from the geometrical properties of the CSRR apertures. Surprisingly, the Bragg condition does not appear to limit the frequency extent of the observed resonances. The results suggest that metamaterial-inspired geometries may be useful for developing THz guided-wave devices.

© 2011 OSA

1. Introduction

Although the conductivity of conventional metals is finite, metals are often approximated as perfect electrical conductors (PECs) in the far-infrared and beyond. Under this approximation, planar metal films are not capable of supporting surface plasmon-polaritons (SPPs). However, there have been a number of theoretical studies demonstrating that patterning the surface of a PEC can alter the dielectric properties of the effective medium, which, in turn, can be manipulated by simply altering the geometrical parameters of the pattern [1

1. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

6

6. Y. Shin, J. So, J. Won, and G. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

]. This concept has potential utility in a broad range of applications, including the development of guided-wave devices. An early embodiment of this concept is a plasmonic slab waveguide demonstrated by Williams et al. [7

7. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

]. In their demonstration, they used a two-dimensional periodic array of square blind holes (i.e. holes that do not perforate the metal film). More recently, we have shown that a one-dimensional array of rectangular apertures that do perforate the metal film can be used to create a variety of guided-wave devices, including a straight waveguide, a y-splitter, and a 3 dB coupler [8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

]. Subsequently, there have been several theoretical papers suggesting the use rectangular and wedge-shape protrusions [10

10. A. I. Fernández-Domínguez, E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz wedge plasmon polaritons,” Opt. Lett. 34(13), 2063–2065 (2009). [CrossRef] [PubMed]

12

12. W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express 18(20), 21498–21503 (2010). [CrossRef] [PubMed]

]. In each of these cases, relatively simple shapes have been used. This raises the obvious question of whether more complex structuring would allow for greater control of the propagation parameters or offer any new or unexpected capabilities.

In this submission, we experimentally demonstrate low-loss guided-wave capability using one-dimensional array of CSRRs periodically perforated in free-standing metal films. We measure the propagation properties of the devices using THz time-domain spectroscopy. In contrast to our earlier studies on waveguides based on rectangular apertures, devices based on CSRRs exhibit much richer spectral characteristics over a broader frequency range than expected. Using a simple effective cavity resonance model and finite-difference time-domain (FDTD) simulations, we explain the origin of the various modes. A surprising feature of the measurements is the fact that the Bragg condition does not appear to limit the frequency extent of the observed resonances. We also measure the propagation properties for a linear waveguide. The observed modes appear to be somewhat less well confined than observed using simple rectangular apertures [8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

]. Nevertheless, the use of metamaterial inspired geometries appears to be a promising approach for developing new THz guided-wave devices.

2. Experimental details

We fabricated a number of straight plasmonic THz waveguides by periodically perforating 300 µm thick stainless steel foils with CSRRs using conventional laser micromachining (i.e. the apertures go completely through the metal sheet). A schematic diagram of a section of the waveguide is shown in Fig. 1
Fig. 1 (a) Schematic diagram of a terahertz waveguide based on CSRR apertures. A semi-circular groove is used to couple a broadband THz waveform to the patterned structure. For clarity, a small section of the waveguide structure is expanded in the figure panel. The CSRR design parameters are s = 500 µm, b = 300 µm, a = 50 µm, g = 100 µm and h = 300 µm. The center-to-center spacing, d, between individual CSRRs is 400 µm. (b) a photograph of an individual CSRR fabricated in a 300 µm thick stainless steel foil.
, along with a photograph of an individual structure. The typical CSRR dimensions were s = 500 µm, b = 300 µm, a = 50 µm, g = 100 µm and h = 300 µm. The center-to-center spacing, d, between individual CSRRs was 400 µm. Normally incident broadband THz radiation was coupled to a broadband THz SPP using a chemically etched semi-circular groove at the one end of the waveguide. The groove had a radius of 1 cm and rectangular cross-section (500 µm wide by 100 µm deep) and was chemically etched at the input side of each waveguide, with the origin of the circle lying at the center of the first CSRR. This groove coupled and subsequently focused freely propagating THz pulses to SPP waves propagating along the waveguide [7

7. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

,8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,18

18. W. Zhu, A. Agrawal, and A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express 15(16), 9995–10001 (2007). [CrossRef] [PubMed]

].

We used a modified THz time-domain spectroscopy setup to characterize the waveguiding properties of the periodically spaced apertures, which has been described in detail elsewhere [4

4. S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using Plasmon-polariton-like surface modes on structures conductive surface,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]

]. For completeness, we provide a brief description here. Broadband THz radiation was generated using a 1 mm thick <110> ZnTe crystal, which was then collected and collimated using an off-axis paraboloidal mirror. The collimated THz radiation was normally incident on the semi-circular groove fabricated on the waveguide samples and was subsequently coupled to SPP waves propagating towards the input end of the CSRR array. Using a second <110> ZnTe crystal, we measured the out-of-plane component of the surface electric field via electro-optic sampling. It should be noted that the vector components of the surface electric field could be measured at any point above the metal surface by moving the optical probe beam and the ZnTe detector simultaneously [19

19. A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007). [CrossRef] [PubMed]

].

In the numerical FDTD simulations of the propagation properties, the metal was modeled as a perfect electrical conductor, which is a reasonable approximation for real metals in the THz regime, and the surrounding dielectric medium was air. We used a spatial grid size of 10 µm, which is sufficient to ensure convergence of the numerical calculations, and perfectly matched layer absorbing boundary conditions for all boundaries. For the input electric field, we used the derivative of a Gaussian pulse that had the same bandwidth (and similar pulse shape) as what was available in the experimental work. All simulated results were obtained using measurements taken at specific spatial points, typically centered on the waveguide (except for y-axis measurements) in order to match the experimental measurements.

3. Experimental results, simulations and discussion

In Fig. 2(a)
Fig. 2 (a) The experimentally measured and numerically simulated waveguide transmission spectra. Both spectra are normalized relative to the corresponding input spectra. (b) the simulated AR frequencies of the lowest order plasmonic mode (filled circles). The solid black trace corresponds to a fit to Eq. (1) with m = 1 and n = p = 0.
, we show both the experimentally measured and simulated waveguide transmission spectra for a 7 cm long linear waveguide measured 2 mm after the last CSRR aperture. There are a number of characteristics that are immediately apparent. In contrast to predictions for waveguides based on ultrathin CSRRs, the transmission spectra associated with CSRRs fabricated in thick metal films do not appear to support broadband propagation of THz radiation. This is particularly evident from the numerical simulations. It is also clear that the experimentally measured transmission resonances are considerably broader than those observed in simulations. As we pointed out above, in the numerical simulations, the metal was modeled as a PEC with idealized geometrical properties. Since metals are characterized by a finite conductivity, there is an associated loss at THz frequencies, which leads to linewidth broadening. Furthermore, imperfections in the individual apertures, as well as variations between apertures, are also expected to broaden the resonances.

In both the experimental data and the simulation results shown in Fig. 2(a), it is clear that there are a number of transmission resonances, characterized by both resonance and anti-resonance (AR) frequencies (i.e. the frequencies corresponding to the sharp dips on the high frequency side of each resonance). In order to analyze the data, we examine the anti-resonance frequencies, as opposed to the resonance peaks. We have previously shown that AR frequencies remain fixed even when the other geometrical parameters (a and d, in the present case) are varied [8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

], demonstrating the fundamental nature of the AR frequencies. From the data, there are four clear transmission resonances in common between the two spectra, with associated AR frequencies occurring at 0.12 THz, 0.35 THz, 0.58 THz, and 0.76 THz. The simulation results show additional amplitude dips, discussed below, that are not apparent in the experimental data.

While the CSRR aperture shape is obviously more complex than a simple rectangular aperture, we find that the all of the AR frequencies can be determined by considering the entire unwrapped CSRR length, L, rather than any subsections of the structure. The AR frequencies correspond to effective cavity resonance frequencies, since the top and bottom of each aperture is open, and are approximately given by
νmnp=c2π(mπL)2+(nπa)2+(pπh)2,
(1)
where, m, n, and p are integers (m = 1,2,3… and n, p = 0,1,2…). Using this approach, the lowest order resonance discussed above can be indexed as m = 1, n = 0, and p = 0. Therefore, ν100 = c/2L = νc = 0.12 THz. With the theory of Pendry and associates in mind [9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

,10

10. A. I. Fernández-Domínguez, E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz wedge plasmon polaritons,” Opt. Lett. 34(13), 2063–2065 (2009). [CrossRef] [PubMed]

], since ν100 = νc for the “unwrapped” aperture, we refer to it as the plasmonic mode [9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

]. Based on FDTD simulations, where we vary the number of CSRR apertures in the waveguide, we find that the lowest order mode diminishes in amplitude with increasing number of apertures at a rate that is faster than the other resonances. This may occur because the associated wavelength (0.12 THz corresponds to a wavelength of ~2.5 mm) is significantly larger than the CSRR structures and may result in greater loss due to interaction with the unstructured metal region adjacent to the waveguide. In what follows, we will index the modes as (m,n,p).

In contrast to transmission spectrum for a rectangular aperture-based waveguide [8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

], the present CSRR-based waveguide exhibits richer spectral characteristics. In addition to the ARs at 0.35 THz, 0.58 THz, and 0.76 THz, the simulated spectrum shows two additional ARs at 0.69 THz and 0.81 THz. All of these frequencies lie above νc and correspond to dielectric slab modes, where energy can flow into the apertures and bounce back and forth between the interfaces like Fabry-Perot resonances. Using Eq. (1), these AR frequencies can be indexed as (3,0,0) at 0.35 THz, (5,0,0) at 0.58 THz, (6,0,0) at 0.69 THz, (7,0,0) at 0.81 THz, and (5,0,1) at 0.76 THz. Since the aperture array is symmetrically excited by the semi-circular groove (i.e. the groove is symmetrically etched about the waveguide), we would normally expect that only symmetric modes where m is an odd integer, such as the (1,0,0), (3,0,0), (5,0,0), (7,0,0) and (5,0,1) modes, could be excited. However, clearly, the (6,0,0) mode is also observed in the numerical simulations. We discuss this in greater detail below. Furthermore, while the dip associated with the (5,0,1) mode is evident, dips associated with the (1,0,1) mode at 0.51 THz and the (3,0,1) mode at 0.61 THz are not. The dip associated with the (3,0,1) resonance appears very weakly in the simulated spectrum, while the (3,0,1) AR frequency is very close to the (5,0,0) AR frequency, making it difficult to differentiate between the two.

The mode designations above arise from fitting the observed AR frequencies to Eq. (1) and are in excellent agreement. Nevertheless, more evidence is necessary to validate these assignments. To do so, we used FDTD simulations with a sinusoidal input corresponding to each individual AR frequency and computed the steady state electric field distributions for each mode. In Fig. 3
Fig. 3 Steady state total electric field distribution in the xy plane using a sinusoidal input frequency of (a) 0.12 THz corresponding to the (1,0,0) mode (b) 0.35 THz corresponding to the (3,0,0) mode (c) 0.58 THz corresponding to the (5,0,0) mode and (d) 0.69 THz corresponding to the (6,0,0) mode and (e) 0.76 THz corresponding to the (5,0,1) mode and (f) 0.81 THz corresponding to the (7,0,0) mode.
, we show the simulated total electric field in the xy plane for the six different modes shown in Fig. 2(a). These distributions clearly show the value of the index, m. Specifically, we expect to observe m-1 nodes in the electric field distribution. Thus, for m = 1, no nodes should be evident in the xy electric field distribution.

There are several important points to note about these field distributions. First, using the aforementioned FDTD simulations, we have verified that n = 0 for all of the modes and that p = 1 only for the (5,0,1) mode (not shown). Second, as we noted above, the symmetric nature of the coupling mechanism leads to the suppression of modes when m is even. Nevertheless, in the simulated spectrum shown in Fig. 2(a), the AR frequency associated with the TM600 mode is evident. While modes with even values of m are not expected due to symmetry considerations theoretically, they may arise in numerical simulations, albeit with very low associated magnitudes. For example, the magnitude of the (6,0,0) mode, shown in Fig. 3(d), is approximately 30 dB lower in magnitude than the other modes shown in Fig. 3. In addition, the AR frequencies associated with the (2,0,0) mode at 0.23 THz and (4,0,0) mode at 0.46 THz occur in spectral regions where the transmission amplitude is already low and, therefore, are not expected to be visible. Field distributions associated with these two modes exhibit even weaker field strengths than were computed for the (6,0,0) mode. Finally, the xy plane field distributions for the (5,0,0) and (5,0,1) modes do not look the same. However, since the electric field distributions along each of the three axes are not wholly independent, there is no reason to believe that the (5,0,0) and the (5,0,1) modes will look the same.

In order to further examine this phenomenon, we simulated the transmission properties of complementary closed ring resonators (i.e. CSRR apertures with g = 0 and all other parameters the same as in Fig. 1) and periodically spaced rectangular apertures with s = 500 µm, a = 50 µm and d = 400 µm. The complementary closed ring resonator waveguide and the CSRR waveguide both exhibited well-defined transmission resonances well beyond the Bragg condition, while the rectangular waveguide did not. Apparently, the more complex electric field properties within each ring resonator, caused by the center metal region in each aperture, allows for higher frequency operation. Further work is necessary to fully elucidate this effect.

Finally, we examined the waveguiding characteristics of a linear device based on periodically spaced CSRRs, as summarized in Fig. 5
Fig. 5 The measured electric field amplitude |Ez| (a) along the x-axis at different positions along the length of the waveguide. (b) along the y-axis approximately 4 cm from the waveguide input. (c) along the z-axis at different heights above the sample surface.
. Since the lowest order (1,0,0) (plasmonic) mode is extremely weak, we measured the propagation properties of the (3,0,0) mode, which was the most prominent resonance. Due to the orientation of the crystal and the polarization of the THz and optical probe beam, we were sensitive only to the out-of-plane (Ez) component of the propagating surface field, rather than the Ex and Ey field components, which dominate within the apertures. In Fig. 5(a), we show the magnitude of the Ez field component measured along the length (x-axis) of the waveguide. From these measurements, we find that the loss is ~0.0166 mm−1, corresponding to a 1/e propagation length of 60 mm. This value is smaller, but comparable, to the loss observed in other planar waveguide geometries [8

8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,9

9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

]. However as previously mentioned, the structure of a split ring resonator allows for a broader range of higher order modes that can be supported with low loss.

In Fig. 5(b), we show the magnitude of the Ez field component measured along the y-axis of the waveguide, 4 cm from the waveguide input. The lateral field distribution at the cross-section exhibits a Gaussian mode profile with a full-width at half maximum (FWHM) mode size of ~9.8 mm. When rectangular apertures were used, we observed a much tighter Gaussian mode profile. The change in mode profile may arise from the more complex aperture geometry, including the fact that there is metal at the center of the CSRR aperture. In Fig. 5(c), we show the magnitude of the Ez field component as a function of distance above the waveguide surface (along the z-axis). The field decays exponentially from the metal dielectric interface with a 1/e decay length of ~4 mm. While the field confinement along the y and z axes is greater than observed using rectangular apertures, it is important to note that these measurements do not correspond to the lowest order mode. Measurements on the TM100 mode are expected to show a greater level of field confinement. With that in mind, we have previously found that the 1/e decay length for an unstructured planar metal film was ~4-5 mm or ~4-5 λ at ~0.3 THz (corresponding to λ = 1 mm) [19

19. A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007). [CrossRef] [PubMed]

].

4. Conclusion

In conclusion, we have demonstrated that a one-dimensional array of complementary split ring resonators can act as effective terahertz waveguides. In contrast to what has been predicted for CSRRs in ultrathin metal films [16

16. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef] [PubMed]

], we find that CSRR-based planar waveguides in free-standing thick metal films support a number of well-defined narrowband modes. The observed mode frequencies extend well beyond what is expected based upon the Bragg condition. Each of the observed modes can be ascribed to an effective cavity resonance of the unwrapped CSRR aperture. We have demonstrated guided-wave propagation in a linear waveguide device that exhibits low loss. Based on these results, we believe that other metamaterial inspired geometries offer promising approaches for developing new THz guided-wave devices.

Acknowledgements

We gratefully acknowledge support of this work through National Science Foundation (NSF) grants ECCS-0824025 and DMR-0415228.

References and links

1.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

2.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

3.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

4.

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using Plasmon-polariton-like surface modes on structures conductive surface,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]

5.

Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]

6.

Y. Shin, J. So, J. Won, and G. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

7.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

8.

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

9.

W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.

10.

A. I. Fernández-Domínguez, E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz wedge plasmon polaritons,” Opt. Lett. 34(13), 2063–2065 (2009). [CrossRef] [PubMed]

11.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express 18(2), 754–764 (2010). [CrossRef] [PubMed]

12.

W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express 18(20), 21498–21503 (2010). [CrossRef] [PubMed]

13.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

14.

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

15.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

16.

M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef] [PubMed]

17.

B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). [CrossRef] [PubMed]

18.

W. Zhu, A. Agrawal, and A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express 15(16), 9995–10001 (2007). [CrossRef] [PubMed]

19.

A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007). [CrossRef] [PubMed]

20.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator metamaterial,” J. Appl. Phys. 100(2), 024507 (2006). [CrossRef]

21.

R. Yang, Y. Xie, X. Yang, R. Wang, and B. Chen, “Fundamental modal properties of SRR metamaterials and metamaterial based waveguiding structures,” Opt. Express 17(8), 6101–6117 (2009). [CrossRef] [PubMed]

22.

N. Marcuvitz, Waveguide Handbook (New York: McGraw-Hill, 1951).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(260.3090) Physical optics : Infrared, far
(160.1245) Materials : Artificially engineered materials
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Metamaterials

History
Original Manuscript: October 26, 2010
Revised Manuscript: December 20, 2010
Manuscript Accepted: January 5, 2011
Published: January 10, 2011

Citation
Gagan Kumar, Albert Cui, Shashank Pandey, and Ajay Nahata, "Planar terahertz waveguides based on complementary split ring resonators," Opt. Express 19, 1072-1080 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1072


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  2. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
  3. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]
  4. S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using Plasmon-polariton-like surface modes on structures conductive surface,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]
  5. Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]
  6. Y. Shin, J. So, J. Won, and G. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]
  7. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]
  8. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]
  9. W. Zhu, A. Agrawal, A. Cui, G. Kumar, and A. Nahata. “Engineering the propagation properties of planar plasmonic terahertz waveguides,” IEEE J. Sel. Top. Quantum Electron. (2010), in print.
  10. A. I. Fernández-Domínguez, E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz wedge plasmon polaritons,” Opt. Lett. 34(13), 2063–2065 (2009). [CrossRef] [PubMed]
  11. D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express 18(2), 754–764 (2010). [CrossRef] [PubMed]
  12. W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express 18(20), 21498–21503 (2010). [CrossRef] [PubMed]
  13. V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
  14. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
  15. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]
  16. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef] [PubMed]
  17. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). [CrossRef] [PubMed]
  18. W. Zhu, A. Agrawal, and A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express 15(16), 9995–10001 (2007). [CrossRef] [PubMed]
  19. A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007). [CrossRef] [PubMed]
  20. D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator metamaterial,” J. Appl. Phys. 100(2), 024507 (2006). [CrossRef]
  21. R. Yang, Y. Xie, X. Yang, R. Wang, and B. Chen, “Fundamental modal properties of SRR metamaterials and metamaterial based waveguiding structures,” Opt. Express 17(8), 6101–6117 (2009). [CrossRef] [PubMed]
  22. N. Marcuvitz, Waveguide Handbook (New York: McGraw-Hill, 1951).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited