Abstract

In this paper we explore the existence of electromagnetic surface bound modes on a perfect metal wire milled with arrays of subwavelength grooves. The surface modes are axially symmetric transverse magnetic (TM) waves and have the same polarization state with the dominant propagating surface plasmon polaritons on the real metal wires. The dispersion of the fundamental surface mode has close resemblance with the dispersion of the surface plasmon polaritons. Moreover, we note that for TM polarization this metallic structure can be equivalent to a dielectric coated metal wire with defined geometrical parameters and effective refractive index of the dielectric coating. This metallic structure is expected to have some potential applications in the optical research in microwave or THz region.

©2006 Optical Society of America

Introduction

Recently, surface plasmon polaritons (SPPs) have attracted great attention for their relevant roles in subwavelength optics [1–6] and their applications in waveguides [7–14]. As we know, SPPs are surface-bound waves that only propagate along the surface of a conductor with finite conductivity [15] and the surface of a perfect electric conductor (PEC) which has infinite conductivity usually does not support surface plasmons. However, it has been shown that both one dimensional and two dimensional structured PEC surfaces can support surface-bound waves [16–20]. Further more, it was recently demonstrated that these surface waves have strong similarities with SPPs on the real metal surfaces [21–23].

In this letter, we explore the existence of surface bound states on a perfect metal wire with infinite periodic arrangement of subwavelength grooves. These grooves are circumferentially milled in the surface of the metal wire. This metallic structure can support axially symmetric transverse magnetic (TM) surface modes which have the same polarization state with the dominant propagating surface polaritons (DPSP) traveling along the real metal wires [24–26]. The dispersion of these surface modes has close resemblance with the dispersion of DPSP on the real metal wires. Interestingly, for TM polarization, this wave-guiding system can be regarded as a dielectric coated metal wire with defined geometrical parameters and effective refractive index of the dielectric coating. It is possible to use the structure to create a three dimensional (3D) effective dielectric medium with a high positive refractive index [18]. We also propose some potential applications for this metallic system in the optical research.

2. Theoretical analysis

First, consider arrays of grooves circumferentially milled in the surface of a perfect metal wire (see Fig. 1), the periodic structure is assumed to be infinite along the metal wire. d is the width of grooves and p the period of the array, 2a and 2b are the outer and inner diameter respectively, the depth of the grooves is defined as h=a-b. We assume vacuum for the groove regions and ambient environment around the metal wire. Because this system is a cylindrical structure, it is convenient to analyze the electromagnetic (EM) problem in the cylindrical coordinates.

 figure: Fig. 1.

Fig. 1. The metal wire milled with periodic array of subwavelength grooves

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We consider the eigenproblem for TM polarization, the magnetic filed component Hz =0 indicates the TM polarization state. The procedure for solving the dispersion relation of surface modes supported by the system is the following. First the EM fields inside the grooves (in region 1) can be expressed as a superposition of circular parallel-plate waveguide modes supported by the grooves. As we assume that the wavelength of light is much larger than the width of the grooves, in the modal expansion of the fields inside grooves we only consider the fundamental waveguide mode. It is a propagating TEM mode with the electric field pointing in the z direction and the EM fields inside grooves hold the relations Hz =0 and Er =Eφ =0. Substitute the relations into Maxwell’s equations [27], we find that ∂H/∂φ=0 and ∂E/∂φ=0 which indicate that the EM fields inside grooves are independent of φ and have homogeneous angular distribution, thus have axially symmetric property. The magnetic field component Hφ in the mth groove has the following form

Hφm(r,z)=[Am(z)Hν(1)(ωcr)+Bm(z)Hν(2)(ωcr)]
forzmpd2bra

Where ω is the frequency, C is the speed of light. Am and Bm are amplitudes of forward (in the r direction towards the z axis) and backward (in the r direction and deviates from the z axis) propagating TEM cylindrical waves inside the mth groove. Hν(1)(ωcr) and Hν(2)(ωcr) represent νth order Hankel functions for the first and second kind respectively. Here, we emphasize that in any waveguide system with cylindrical symmetry, the angular momentum is a conserved quantity and denoted by ν (ν=0, 1, 2…). In our case, the EM fields inside grooves are of homogeneous angular distribution, so ν=0.

Then, the EM fields outside the metal wire (in region 2, in the vacuum ambient environment) can be expressed as sum of diffractive waves. Because we are interested in surface modes which are bound state, all diffracted waves outside the metal wire are evanescent in the transverse direction in vacuum. The EM fields of each diffraction order has a form Kν (·) (modified Bessel functions) which decays in the region 2 from the metal-vacuum interface. As the angular momentum ν keep conservation in this system, the value of ν outside the metal wire should keep the same as that inside grooves. The magnetic field component Hφ outside the metal wire has the form

Hφoutside(r,z)=n=CnK0(iτnr)eiβnz
forra

Where Cn is the coefficient associated with the diffraction order n. βn=β+2πnp(n=,...0,...) , which is the momentum in the z direction of the nth diffraction orders, β=kz is the propagation constant along the z axis. τn=k02βn2 is the transverse momentum, here k 0 is the wave vector in vacuum. For evanescent diffractive waves, k 0<βn so the transverse momentum τn is purely imaginary. By substituting the relation: Hz =0, ∂H/∂φ=0 and ∂E/∂φ=0 into Maxwell’s equations, one can determine all EM field components

Hz=Hr=0
Hφ=iμk0(ErzEzr)
Eφ=0
Ez=iεk01r(rHφ)r
Er=iεk0Hφz

Here, we denote by ε and μ the relative permittivity and relative permeability respectively, for vacuum ε=μ=1. From the above Eq. (6) and Eq. (7), we can determine the electric fields in terms of the magnetic field component Hφ . By matching the boundary conditions (at r=b, Ez must be zero; at r=a, continuity of Ez at every point of the unit cell, and continuity of Hφ only at the grooves location), we find the eigenmodes satisfy the dispersion relation

1iψ=[J0(ωca)N0(ωcb)N0(ωca)J0(ωcb)J1(ωca)N0(ωcb)N1(ωca)J0(ωcb)]

Where J and N are Bessel function and Newmann function, respectively. f=d/p, gn=sinc(βn·d2) .

ψ=n=f(ωc)·K1(iτna)τnK0(iτna)·gn2

From the above discussion we know that the surface waves supported by this structure have axially symmetric property and only one magnetic field component Hφ , so they are axially symmetric transverse magnetic (TM) modes (we also call them azimuthally symmetric zeroth order TM modes [25, 26]).

 figure: Fig. 2.

Fig. 2. The dispersion relation ω(kz ) of the surface bound states supported by a metal wire milled with arrays of sub-wavelength grooves obtained from Eq. (8). The geometrical Parameters are d/p=0.1, b/p=2.6, a/b=1.3.

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It is worth commenting on the similarities between the surface modes in this case and dominant propagating SPPs (DPSP) along the real metal wires. In fact, the DPSP is the fundamental mode. Higher order SPPs modes can also be excited on the real metal wires, however, most of the field energy of these higher order modes is inside the metal, their attenuation are much larger than the DPSP [24]. The DPSP is the azimuthally symmetric zeroth order TM mode [24, 25] which has the same polarization state with the surface modes supported by the structure in our case. In Fig. 2, we plot the dispersion relation of the surface modes by numerically solving Eq. (8) for the case d/p=0.1, b/P=2.6, a/b=1.3. The dispersion has close resemblance with the dispersion of the DPSP supported by the real metal wires [28–30]. In the low frequency range, both of the dispersion curves approach the air line; while at large propagating constant kz , in the DPSP band the eigen frequencies ω approach the surface plasmon frequency ωsp [31]; whereas in our case ω approach the frequency ωCM which is the frequency location of a cavity waveguide mode inside the circular grooves. The frequency locations of the different cavity waveguide modes approximately correspond to the condition

J1(ωca)N0(ωcb)N1(ωca)J0(ωcb)J0(ωca)N0(ωcb)N0(ωca)J0(ωcb)=0

In the limit h=a-b<<b, and d<<p, by using the asymptotic approximation of Bessel function and Newmann function, from the Eq. (10) the resonant frequencies of the cavity waveguide modes approximately satisfy the condition cot(ωch)=0 , it coincides with the cavity waveguide modes inside the rectangular metallic grooves [21, 32].

3. Equivalent dielectric coated metal wire

It is interesting to note that for TM polarization the wave-guiding properties of the system can be equivalent to a dielectric coated metal wire with defined geometrical parameters and an effective refractive index of the dielectric coating (see Fig. 3). In the dielectric coated metal wire the TM modes are also axially symmetric waves and satisfy the dispersion relation [33].

1iϕ=[J0(Ta)N0(Tb)N0(Ta)J0(Tb)J1(Ta)N0(Tb)N1(Ta)J0(Tb)]
ϕ=n02TK1(τa)n2τK0(τa)

The thickness of the dielectric coating is(a′-b′), the radius of the coated metal wire is a′. n 2 and n02 are refractive index of the dielectric coating and vacuum respectively. T 2+β 2=(ωn)2, β 2-τ 2=ωn 0)2,in which β=kz denotes the propagation constant of the surface modes.

In the dielectric coated wire, the cutoff of surface modes is due to the condition τ=0, which indicates that the surface waves are no longer bound states and become radiative modes. The cutoff frequencies of these modes correspond to the condition

J0(Ta)N0(Tb)N0(Ta)J0(Tb)=0

In our case (the structured metallic system), by tuning the geometrical parameters of the structured metal wire, fundamental and higher order surface modes (TM0n, n=0, 1, 2…,) can be excited, and the modal cutoff is due to the condition τn =0 (n=0), which implies that when the zeroth-order diffracted wave outside the metal wire is not evanescent, there will exist a channel for light getting rid of the confinement around the metal wire. The cutoff frequencies satisfy the condition

J0(ωca)N0(ωcb)N0(ωca)J0(ωcb)=0

We define the effective refractive index n=pd for the dielectric coating of the equivalent coated wire. In order to make the modal cutoff frequencies of the equivalence keep the same with those of the structured metal wire, the geometrical parameters of the equivalent should have the relations a=an21 and b=bn21 [see Fig. 3(b)]. Figure 4 shows the dispersion curves of the first two modes (TM00 and TM01) in the first Brillouin zone of the structured metal wire and its equivalent dielectric coated wire. As the effective n=pd increases, the dispersion curves of the equivalent system asymptotically approach those of the structured metal wire.

 figure: Fig. 3.

Fig. 3. The metal wire milled with array of subwavelength grooves (a) and its equivalent dielectric coated wire (b). The geometrical parameters of the equivalent dielectric coated wire have the relations a=an21 and b=bn21 . The effective refractive index n=pd is defined for the dielectric coating.

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 figure: Fig. 4.

Fig. 4. Dispersion curves of the first two surface modes (TM00 and TM01) in the first Brillouin zone. The black lines represent the surface modes of the structured metal wire; the red lines represent the modes of equivalent dielectric coated wire. The dashed lines are the light lines in vacuum and in the dielectric coating, respectively. b/p=1.7, a/b=2. (a) p/d=2.5; (b) p/d=20.

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 figure: Fig. 5.

Fig. 5. Profile view of the Hφ field distributions of the fundamental surface modes of the metellic structure [shown in (a)] and the corresponding dielectric coated wire [shown in (b)] for b/p=1.7, a/b=2,the effective refractive index of the dielectric coating is n=p/d=2.5. The fundamental surface modes in these two systems are azimuthally symmetric TM waves, the red color indicates the positive amplitude, and the blue color indicates the negative amplitude. The black lines in (a) and (b) show the interface between the guided systems and their ambient environment (vacuum). The normalized excitation frequency is ω=0.05 in units of 2πCp . The arrows indicate the modal wavelength (the periodicity of the modal field) of the surface waves.

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Figure 5 shows the modal patterns of the fundamental surface modes (TM00 mode) of the structured metal wire and the equivalent dielectric coated wire with an effective refractive index n=2.5. The normalized frequency of the surface mode is ω=0.05 in units of 2πCp , which is in the overlap region of the dispersion curves in Fig. 4(a). From Fig. 5(a) we can see that waves travel along the metal wire which is milled with arrays of subwavelength grooves, these waves are bounded around the metal wire and decay outside the grooves. Through evanescent coupling from one groove to the next, energy of light can create groove-to-groove propagation. By comparing with the equivalent dielectric coated wire, it is found that the two systems have almost the same external fields and modal wavelength (the spatial periodicity) of the surface modes. If the modal wavelength is much larger than the periodicity p of the array of grooves, the surface waves will be insensitive to the periodic geometry on the metal wire and the array of subwavelength grooves can be regarded as a quasi uniform effective medium along the propagation direction. This effective dielectric medium model is very valid in the long wavelength limit to characterize the wave-guiding properties along the periodic structures [18, 21].

4. Applications

The analysis and results presented in this paper are based on the perfect electric conductor (PEC) model. For frequencies range from microwave to THz regime, the PEC model is a feasible approximation for analyzing the propagation of surface modes supported by the structured metal surfaces, since the absorption loss and plasmonic effects in this frequency range can be largely neglected and it is valid to disregards the Zenneck wave solution for the structured metal surfaces [34].

The wave-guiding properties of the surface modes supported by the metallic system may have some potential applications. For example, quite recently researchers found that a simple metal wire which supports THz SPPs can be used as effective THz waveguides [12, 13]. However, the polarization mismatch between the light source and SPPs on the metal surface lead to a very low coupling efficiency [25, 26, 35], because the electric fields of light sources are generally linearly polarized but the DPSP on the metal surface is axially symmetric TM mode, the electric field is approximately radially polarized [25]. The polarization mismatch may be improved by the array of subwavelength grooves as a coupler integrated in the simple metal wire, since the SPP-like waves can be excited on the structured metal wire by the external light source. It is necessary to note that the notions of the improved input coupler and effective SPPs on the structured metal surfaces for THz radiation were hinted at by the group of Ajay Nahata in their recent works [36, 37, 38]. Notably, in the works of Ajay Nahata et al. they proposed a very promising method to facilitate the fabrication of the metal wires with subwavelength features: By fabricating arrays of linear grooves into the surface of a metal sheet and rolling the sheet about the axis perpendicular to the groove length, one can have a solid cylindrical metal conductor with circular grooves [38]. The micro fabrication techniques on surfaces of the planar structure are much easier than the fabrication on the cylindrical surfaces [39]. Here, we would like to point out that the theoretical analysis in our paper is based on the structures with infinite periodic elements (or the structures have great many periodic elements and can be approximately treated as infinite). So the theoretical treatment in our paper may not be suitable for the cases in the papers of Ajay Nahata et al., in which the structures have several finite periodic elements.

Another application is as waveguide filters integrated on the simple metal wire waveguides, since there exist stop-band between guided bands of the surface modes (see Fig. 4), waves with frequencies in the stop-band region can not propagate along the metal wire. Moreover, this system can be regarded as a dielectric coated conducting wire and can create 3D effective dielectric medium with a very high positive refractive index [see Fig. 4(b)], this implies that this system can support extra-slow speed for the surface wave propagation, and may be used as optic delay-line systems.

Moreover, at microwave or THz frequencies, the dispersion relation and sub-wavelength confinement of the effective SPPs on the structured metal wires do not rely on the finite conductivity of the metal, but are basically due to the geometrical parameters of the surface structure. In this way, the propagation characteristics of these effective SPPs can be controlled by the periodic surface geometry. Highly localized SPPs on the structured metal wires can be sustained in the THz region to overcome the considerable radiation loss due to bends, non-uniformities or nearby objects in the weakly-guided THz bare metal wires. More interestingly, by tapering the corrugated metal wires, the energy concentration and wave-guiding properties of these effective SPPs can be effectively and dramatically changed. This conical geometry may open up a new way for channeling THz radiation to micron-scale volumes for near-field imaging, spectroscopy and sensing applications [40, 41].

5. Conclusion

In conclusion, we have shown that the axially symmetric SPP-like waves can be exited on a perfect metal wire milled with arrays of subwavelength grooves. Moreover, for TM polarization, this system can be equivalent to a dielectric coated metal wire with defined geometrical parameters and an effective refractive index of the dielectric coating. This metallic structure is expected to have some potential applications for the optical research at microwave or THz frequencies. The results presented here are valid and can be directly applied in the wavelength range from microwave to THz region.

Acknowledgments

We wish to thank Dr. J. B. Pendry from Imperial College for his encouragement and the careful reading of our manuscript, and we acknowledge careful reading of this manuscript and helpful suggestions by Dr. Weili Zhang and Dr. Jiaguang Han from Oklahoma State University. This work was supported by the National Key Basic Research Special Foundation of China (Grant Nos. 2003CB314904 and 2006CB806000), the National Natural Science Foundation of China (Grant No. 60678012) and National Natural Science Foundation of China (Grant No. 60578037).

References and links

1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

2. H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]  

4. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001). [CrossRef]   [PubMed]  

5. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999). [CrossRef]  

6. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004). [CrossRef]   [PubMed]  

7. W. L. Barnes, T. W. Preist, S. C. 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]  

8. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996). [CrossRef]   [PubMed]  

9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997). [CrossRef]   [PubMed]  

10. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface” Opt. Lett. 29, 1069–1071 (2004). [CrossRef]   [PubMed]  

11. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005). [CrossRef]  

12. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004). [CrossRef]   [PubMed]  

13. T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005). [CrossRef]  

14. T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006). [CrossRef]  

15. H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

16. L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948). [CrossRef]  

17. R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

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

19. M. Qiu “Photonic band structures for surface waves on structured metal surfaces” Opt. Express 13, 7583–7588 (2005). [CrossRef]   [PubMed]  

20. F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005). [CrossRef]   [PubMed]  

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23. A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005). [CrossRef]   [PubMed]  

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28. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974). [CrossRef]  

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30. K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006). [CrossRef]   [PubMed]  

31. The surface plasmon frequency ωsp is determined by ωsp=ωpεair+1 where ωp is the bulk plasma frequency of metal

32. T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984). [CrossRef]  

33. R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).

34. S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006). [CrossRef]  

35. J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006). [CrossRef]  

36. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005). [CrossRef]   [PubMed]  

37. A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13, 3535–3542 (2005). [CrossRef]   [PubMed]  

38. H. Cao and A. Nahata, “Coupling of terahertz pulsed onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005). [CrossRef]   [PubMed]  

39. S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766 [CrossRef]  

40. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012 [CrossRef]   [PubMed]  

41. Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

References

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  1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).
  2. H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [Crossref]
  4. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
    [Crossref] [PubMed]
  5. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
    [Crossref]
  6. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
    [Crossref] [PubMed]
  7. W. L. Barnes, T. W. Preist, S. C. 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]
  8. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
    [Crossref] [PubMed]
  9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997).
    [Crossref] [PubMed]
  10. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface” Opt. Lett. 29, 1069–1071 (2004).
    [Crossref] [PubMed]
  11. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
    [Crossref]
  12. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
    [Crossref] [PubMed]
  13. T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
    [Crossref]
  14. T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
    [Crossref]
  15. H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)
  16. L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
    [Crossref]
  17. R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).
  18. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
    [Crossref] [PubMed]
  19. M. Qiu “Photonic band structures for surface waves on structured metal surfaces” Opt. Express 13, 7583–7588 (2005).
    [Crossref] [PubMed]
  20. F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
    [Crossref] [PubMed]
  21. 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, S97–S101 (2005).
    [Crossref]
  22. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
    [Crossref] [PubMed]
  23. A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
    [Crossref] [PubMed]
  24. G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119–1128 (1950).
    [Crossref]
  25. Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005).
    [Crossref] [PubMed]
  26. K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
    [Crossref]
  27. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, Oxford, 1975).
  28. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
    [Crossref]
  29. U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
    [Crossref]
  30. K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
    [Crossref] [PubMed]
  31. The surface plasmon frequency ωsp is determined by ωsp=ωpεair+1 where ωp is the bulk plasma frequency of metal
  32. T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
    [Crossref]
  33. R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).
  34. S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
    [Crossref]
  35. J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
    [Crossref]
  36. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
    [Crossref] [PubMed]
  37. A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13, 3535–3542 (2005).
    [Crossref] [PubMed]
  38. H. Cao and A. Nahata, “Coupling of terahertz pulsed onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005).
    [Crossref] [PubMed]
  39. S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
    [Crossref]
  40. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
    [Crossref] [PubMed]
  41. Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

2006 (4)

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
[Crossref]

2005 (12)

H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
[Crossref] [PubMed]

A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13, 3535–3542 (2005).
[Crossref] [PubMed]

H. Cao and A. Nahata, “Coupling of terahertz pulsed onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005).
[Crossref] [PubMed]

Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005).
[Crossref] [PubMed]

K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
[Crossref]

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
[Crossref]

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

M. Qiu “Photonic band structures for surface waves on structured metal surfaces” Opt. Express 13, 7583–7588 (2005).
[Crossref] [PubMed]

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

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, S97–S101 (2005).
[Crossref]

2004 (4)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[Crossref] [PubMed]

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[Crossref] [PubMed]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface” Opt. Lett. 29, 1069–1071 (2004).
[Crossref] [PubMed]

2001 (2)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[Crossref]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

1997 (1)

1996 (2)

W. L. Barnes, T. W. Preist, S. C. 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]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

1984 (1)

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

1974 (1)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[Crossref]

1954 (1)

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

1950 (1)

G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119–1128 (1950).
[Crossref]

1948 (1)

L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
[Crossref]

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

Agrawal, A.

Andrews, S. R.

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Barlow, H. M.

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

Barnes, W. L.

W. L. Barnes, T. W. Preist, S. C. 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]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, Oxford, 1975).

Brillouin, L.

L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
[Crossref]

Cao, H.

Cao, Q.

Catrysse, P. B.

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

Collin, R.

R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).

Cullen, A. L.

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

Davis, C. C.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

de Abajo, F. J. Garcia

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

Deibel, J. A.

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
[Crossref]

Dereux, A.

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[Crossref]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[Crossref]

Elliott, R. S.

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

Escarra, M. D.

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
[Crossref]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Fan, S.

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

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
[Crossref]

Garcia-Vidal, F. J.

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, S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Goubau, G.

G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119–1128 (1950).
[Crossref]

Gramotnev, D. K.

Grischkowsky, D.

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[Crossref] [PubMed]

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Jacobsen, S. C.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

Jahns, J.

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. 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]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

Kobayashi, T.

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Lopez-Rios, T.

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

Maier, S. A.

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Maier, S.A.

Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

Martin-Moreno, L

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, S97–S101 (2005).
[Crossref]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Mittleman, D. M.

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
[Crossref]

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
[Crossref]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[Crossref] [PubMed]

Morimoto, A.

Nahata, A.

Ngai, K. L.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[Crossref]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Pendry, J B

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, S97–S101 (2005).
[Crossref]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Pfeiffer, C. A.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[Crossref]

Pile, D. F. P.

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
[Crossref]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. 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]

Qiu, M.

Qu, D.

Raether, H.

H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

Saenz, J. J.

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

Sambles, J. R.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. 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, J. Roy

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Schröter, U.

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K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
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[Crossref]

Wood, J. E.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
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R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

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T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
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T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
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S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
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Nature (2)

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Optical Express. (1)

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
[Crossref]

Phys. Rev. B (3)

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[Crossref]

Phys. Rev. Lett. (6)

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
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L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
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[Crossref] [PubMed]

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[Crossref] [PubMed]

Proc. R. Soc. London (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
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T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

Other (8)

R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, Oxford, 1975).

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

The surface plasmon frequency ωsp is determined by ωsp=ωpεair+1 where ωp is the bulk plasma frequency of metal

H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

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Figures (5)

Fig. 1.
Fig. 1. The metal wire milled with periodic array of subwavelength grooves
Fig. 2.
Fig. 2. The dispersion relation ω(kz ) of the surface bound states supported by a metal wire milled with arrays of sub-wavelength grooves obtained from Eq. (8). The geometrical Parameters are d/p=0.1, b/p=2.6, a/b=1.3.
Fig. 3.
Fig. 3. The metal wire milled with array of subwavelength grooves (a) and its equivalent dielectric coated wire (b). The geometrical parameters of the equivalent dielectric coated wire have the relations a = a n 2 1 and b = b n 2 1 . The effective refractive index n = p d is defined for the dielectric coating.
Fig. 4.
Fig. 4. Dispersion curves of the first two surface modes (TM00 and TM01) in the first Brillouin zone. The black lines represent the surface modes of the structured metal wire; the red lines represent the modes of equivalent dielectric coated wire. The dashed lines are the light lines in vacuum and in the dielectric coating, respectively. b/p=1.7, a/b=2. (a) p/d=2.5; (b) p/d=20.
Fig. 5.
Fig. 5. Profile view of the Hφ field distributions of the fundamental surface modes of the metellic structure [shown in (a)] and the corresponding dielectric coated wire [shown in (b)] for b/p=1.7, a/b=2,the effective refractive index of the dielectric coating is n=p/d=2.5. The fundamental surface modes in these two systems are azimuthally symmetric TM waves, the red color indicates the positive amplitude, and the blue color indicates the negative amplitude. The black lines in (a) and (b) show the interface between the guided systems and their ambient environment (vacuum). The normalized excitation frequency is ω=0.05 in units of 2 π C p . The arrows indicate the modal wavelength (the periodicity of the modal field) of the surface waves.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

H φ m ( r , z ) = [ A m ( z ) H ν ( 1 ) ( ω c r ) + B m ( z ) H ν ( 2 ) ( ω c r ) ]
for z m p d 2 b r a
H φ outside ( r , z ) = n = C n K 0 ( i τ n r ) e i β n z
for r a
H z = H r = 0
H φ = i μ k 0 ( E r z E z r )
E φ = 0
E z = i ε k 0 1 r ( r H φ ) r
E r = i ε k 0 H φ z
1 i ψ = [ J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) J 1 ( ω c a ) N 0 ( ω c b ) N 1 ( ω c a ) J 0 ( ω c b ) ]
ψ = n = f ( ω c ) · K 1 ( i τ n a ) τ n K 0 ( i τ n a ) · g n 2
J 1 ( ω c a ) N 0 ( ω c b ) N 1 ( ω c a ) J 0 ( ω c b ) J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) = 0
1 i ϕ = [ J 0 ( T a ) N 0 ( T b ) N 0 ( T a ) J 0 ( T b ) J 1 ( T a ) N 0 ( T b ) N 1 ( T a ) J 0 ( T b ) ]
ϕ = n 0 2 T K 1 ( τ a ) n 2 τ K 0 ( τ a )
J 0 ( T a ) N 0 ( T b ) N 0 ( T a ) J 0 ( T b ) = 0
J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) = 0

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