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Subwavelength confined terahertz waves on planar waveguides using metallic gratings |
Optics Express, Vol. 21, Issue 5, pp. 6009-6019 (2013)
http://dx.doi.org/10.1364/OE.21.006009
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– Abstract
1. Introduction
2. Configuration of the planar hybrid plasmonic waveguide
3. Subwavelength confinement on the metal grating waveguide
4. Conclusion
– References and links
– Abstract
1. Introduction
2. Configuration of the planar hybrid plasmonic waveguide
3. Subwavelength confinement on the metal grating waveguide
4. Conclusion
– References and links
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Abstract
A terahertz plasmonic waveguide is experimentally demonstrated using a plastic ribbon waveguide integrated with a diffraction metal grating to approach subwavelength-scaled confinement and long-distance delivery. Appropriately adjusting the metal-thickness and the periodical slit width of a grating greatly improves both guiding ability and field confinement in the hybrid waveguide structure. The measured lateral decay length of the bound terahertz surface waves on the hybrid waveguide can be reduced to less than λ/4 after propagating a waveguide of around 50mm-long in length. The subwavelength-confined field is potentially advantageous to biomolecular sensing or membrane detection because of the long interaction length between the THz field and analytes.
© 2013 OSA
1. Introduction
Various plasmonic waveguides have been demonstrated to achieve electromagnetic (EM)-field confinement in subwavelength scales, and have proved popular for near-field microscopy and sensing applications [1–3]. EM-waves can be transferred to surface-conduction electrons at the metal-dielectric interface via the plasmonic structures of waveguides. When excited by EM waves, these transferred surface-conduction electrons are known as surface-plasmon-polaritions (SPPs), and subwavelength-confined SPPs are advantageous in near-field detection with an optical resolution beyond the diffraction limit [3]. Terahertz (THz) waves have EM frequencies which are considerably lower than the intrinsic plasmon frequency of metal materials, and are prevented from penetrating into metals to directly excite SPPs. Hence, EM-fields in the THz region propagate in a delocalized manner on metal surfaces as so-called Sommerfeld-Zenneck surface waves [4,5].
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Recently, new concepts for the engineering of metal surfaces to generate surface plasmons have been proposed to confine weakly guided THz Sommerfeld-waves, including the two-dimensional hole array [6], periodical slits [7] and various patterns of metamaterials [8–10]. The structured-metal surfaces can be considered as a material with a high dielectric constant that enables parts of THz-EM fields to penetrate into the patterned metal-surface in a way that resembles the behavior of SPPs in an optical regime to enhance THz lateral confinement [8]. Various geometry-controlled SPPs, expressed as spoof SPPs, are theoretically demonstrated with a strong THz-field confinement on the corrugated metal surfaces [11]. However, the spoof SPPs usually suffer from severe attenuation due to the high confinement of the THz-field causing the transmitted amplitudes to quickly decay [12]. For example, a metallic waveguide has been theoretically demonstrated to guide THz-SPPs with a lateral decay length of around 0.2λ, but the proven propagation length is as short as several wavelengths [13]. On the other hand, a low loss plasmonic waveguide, composed of one-dimensional (1D) periodic slits on a metal sheet, has recently been demonstrated to guide THz-SPPs for a long distance of around 60mm at 0.3THz. However, the guided field is loosely bounded with a mode size about three times larger than the THz-wavelength [7], where the field confinement is not sufficient for sensing or imaging applications. To achieve subwavelength confinement and long-distance delivery of THz spoof-SPPs in a waveguide, it is essential to overcome the coupling loss between the SPPs- and waveguide-modes resulting from the waveguide-index mismatch, along with the extremely high absorption loss of the highly confined THz surface waves in metal structures [14,15]. To decrease the coupling loss, a diffraction metal grating with periodic corrugations or slits on a metal surface is demonstrated to easily couple free-space THz radiation into THz-SPPs with a coupling efficiency as high as 20% [16], and the effective index of a grating approaches that of air. This diffraction-grating-based structure can be multi-functionally manipulated to control THz SPPs for SP reflection, SP beam splitting, SP focusing, etc [17–19]. Integrating the structure of a diffraction grating with a low loss THz waveguide effectively excites the SPP mode from a propagated waveguide mode due to easy control of index/phase matches between the two modes [17], and prevents severe SP coupling loss [14,15]. To further confine THz-SPPs on the metal surface, a thin dielectric layer can be attached to the metallic surface or dielectric materials can be inserted in the periodic slits of the patterned metal structure, thus greatly reducing the mode size of the THz-SPPs based on the increased effectiveness of the waveguide-index [20]. This method does not result in increased metallic absorption loss, thus allowing for long-distance propagation.
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]
W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]
F. J. Garcia-Vidal, L. Martín-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]
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]
F. J. Garcia-Vidal, L. Martín-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]
S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006). [CrossRef] [PubMed]
L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]
D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Waveguided spoof surface plasmons with deep-subwavelength lateral confinement,” Opt. Lett. 36(23), 4635–4637 (2011). [CrossRef] [PubMed]
W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]
A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optical-fiber-based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef]
M. Weisser, B. Menges, and S. M. Neher, “Refractive index and thickness determination of monolayers by multi-mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. 56(3), 189–197 (1999). [CrossRef]
M. Martl, J. Darmo, K. Unterrainer, and E. Gornik, “Excitation of terahertz surface plasmon polaritons on etched groove gratings,” J. Opt. Soc. Am. B 26(3), 554–558 (2009). [CrossRef]
L. S. Mukina, M. M. Nazarov, and A. P. Shkurinov, “Propagation of THz plasmon pulse on corrugated and flat metal surface,” Surf. Sci. 600(20), 4771–4776 (2006). [CrossRef]
G. Gaborit, D. Armand, J. L. Coutaz, M. Nazarov, and A. Shkurinov, “Excitation and focusing of terahertz surface plasmons using a grating coupler with elliptically curved grooves,” Appl. Phys. Lett. 94(23), 231108 (2009). [CrossRef]
L. S. Mukina, M. M. Nazarov, and A. P. Shkurinov, “Propagation of THz plasmon pulse on corrugated and flat metal surface,” Surf. Sci. 600(20), 4771–4776 (2006). [CrossRef]
A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optical-fiber-based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef]
M. Weisser, B. Menges, and S. M. Neher, “Refractive index and thickness determination of monolayers by multi-mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. 56(3), 189–197 (1999). [CrossRef]
M. Gong, T. I. Jeon, and D. Grischkowsky, “THz surface wave collapse on coated metal surfaces,” Opt. Express 17(19), 17088–17101 (2009). [CrossRef] [PubMed]
In the presentation, we demonstrate a THz waveguide capable of high field-confinement and long-distance delivery based on the concept of spoof surface plasmons. The proposed THz plasmonic waveguide consists of a diffraction metal grating with a 1D periodic slit-array attached to a plastic ribbon for subwavelength modal confinement and the long-distance delivery of THz SPPs on the waveguide. A subwavelength-thick plastic ribbon waveguide is demonstrated as a low loss THz-waveguide [21–23] with large portions of power extending to the air cladding. Its effective waveguide-index approaches that of air, making it suitable for integration with a diffraction grating to generate THz-SPPs due to their similar effective index. The weakly confined ribbon waveguide mode can be successfully transferred into a THz surface wave, which is tightly bound and propagated on the metallic grating by optimizing the thickness and the slit-widths of a diffraction grating. The dependence of the lateral decay lengths of the bound THz surface waves on different grating dimensions is characterized. The confined decayed length is less than λ/4 and the experimental propagation length can be up to 50mm, which is sufficiently long among spoof-SPPs waveguide devices [6,7]. Based on the characteristics of subwavelength confinement and long-distance delivery, the proven plasmonic THz waveguide could potentially be applied to bio-chemical sensing and near-field THz imaging, such as for the sensitive detection of membranes or molecular binding [24,25] at air-metal interfaces, due to the enhanced field at the interface and the sufficiently long interaction-length between the EM-field and analytes.
A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008). [CrossRef] [PubMed]
C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt. 44(28), 5937–5946 (2005). [CrossRef] [PubMed]
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]
W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]
M. Nagel, F. Richter, P. Haring-Bolívar, and H. Kurz, “A functionalized THz sensor for marker-free DNA analysis,” Phys. Med. Biol. 48(22), 3625–3636 (2003). [CrossRef] [PubMed]
A. Hassani and M. Skorobogatiy, “Surface plasmon resonance-like integrated sensor at terahertz frequencies for gaseous analytes,” Opt. Express 16(25), 20206–20214 (2008). [CrossRef] [PubMed]
2. Configuration of the planar hybrid plasmonic waveguide
Figure 1
shows the schematic drawing of a hybrid THz plasmonic waveguide consisting of a 220mm-long dielectric planar waveguide and a 50mm-long metallic diffraction grating. The dielectric planar waveguide is made from a polyethylene (PE) ribbon 15mm wide, 220mm long and 20μm thick. The THz wave propagating behavior along the 20μm-thick PE ribbon resembles that of a waveguiding mechanism [22,23] of a subwavelength plastic wire with a large portion of evanescent powers outside of the ribbon, and the extended power ranges in the Y-direction could approach one-wavelength, λ. The subwavelength ribbon waveguide has advantages of high coupling efficiency and low transmission loss [22,23]. The metallic diffraction grating comprises a chain of cut-through slits, which are machined on a brass sheet with a latticeconstant of 1.5mm and a slit-width of 1mm, as shown in Fig. 1. The diffraction grating is attached on one side near the output end of the ribbon waveguide. As shown in Fig. 1, the diffraction grating is 50mm long and 15mm wide, with a thickness h. Previous studies have theoretically demonstrated the use of the 1D-metal grating to generate and deliver transverse-magnetic (TM)-polarized THz spoof plasmons, and their waveguide loss and dispersion properties have been well characterized [12], indicating that the slit-width and the slit-depth of a diffraction grating have a significant impact on both the confinement and propagation distance of THz fields guided onto the metal surfaces [11,12]. In the experiment, we use the brass gratings with three different thicknesses (100μm, 200μm and 400μm), and two different slit-widths (1mm and 0.5mm) to optimize the power transmission and field confinement along the Y-axis direction of the waveguide. The THz fields in the X-axis direction are not constrained because the width of the PE is much greater than its thickness.
L. J. Chen, H. W. Chen, T. F. Kao, J. Y. Lu, and C. K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed]
C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt. 44(28), 5937–5946 (2005). [CrossRef] [PubMed]
L. J. Chen, H. W. Chen, T. F. Kao, J. Y. Lu, and C. K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed]
C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt. 44(28), 5937–5946 (2005). [CrossRef] [PubMed]
L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]
S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006). [CrossRef] [PubMed]
L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]
Fig. 1 A schematic drawing of the planar hybrid plasmonic waveguide, where the diffraction grating composed of periodically-spaced rectangular slits is represented in orange and the subwavelength-thick PE ribbon is cyan. The TM-polarized THz waves are coupled from the ribbon edge to the ribbon waveguide.
To deliver THz waves in the hybrid waveguide structure, polarization of THz waves propagated along the PE-ribbon waveguide should be matched with that along the metal grating. It is demonstrated that a dielectric ribbon waveguide can support TM-polarized THz waves [23,26] while the input THz polarization is perpendicular to the ribbon surface (as shown in Fig. 1), and the proposed hybrid plasmonic waveguide consequently enables the transmission of THz waves that are straightforwardly coupled from the PE-ribbon waveguide. TM-polarized THz waves are edge-coupled to one end of the planar ribbon waveguide by a pair of parabolic mirrors, forming the weakly confined waveguide mode to propagate through a 170mm-long waveguide length [22]. The stabilized waveguide mode would then directly enter a 50mm-long integrated metallic grating waveguide. When the loosely confined THz waves are illuminated on the metal grating, they are partially transmitted and partially reflected due to the modal and index mismatch. We used the waveguide-based THz time-domain spectrometer (THz-TDS) [27] to characterize the transmitted THz waves at the output end of the hybrid grating waveguide.
C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt. 44(28), 5937–5946 (2005). [CrossRef] [PubMed]
R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88(7), 4449–4451 (2000). [CrossRef]
L. J. Chen, H. W. Chen, T. F. Kao, J. Y. Lu, and C. K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed]
B. You, J. Y. Lu, T. A. Liu, J. L. Peng, and C. L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 96(5), 051105 (2010). [CrossRef]
The frequency of the reflected THz surface waves from the diffraction grating can be determined by the momentum conservation relation,where the vectors of Kin, KR and KΛ are, respectively, the propagation constants of the input and reflected THz waves along the ribbon waveguide as well as a grating-wave-vector. The grating-wave-vector, KΛ, is equal to 2πm/Λ, where m and Λ are, respectively, the Bragg diffraction order and lattice constant of periodically spaced slits. The directions of propagation constants, Kin and KR, are opposite but have the same value, 2πνneff/C, for THz waves with a frequency of ν, propagated along the ribbon waveguide, where C and neff are, respectively, the speed of light in a vacuum and a waveguide-effective-refractive index. Therefore, the diffraction grating can reflect THz waves exactly at Bragg frequencies in different orders, derived as mC/2neffΛ, based on the momentum conservation relation.
Figure 2(a)
shows the THz power transmittance after propagating the 50mm-long grating waveguides with different metal thicknesses. The transmittance is obtained from comparing the transmission power behind of the 220mm-long ribbon waveguide with and without attaching the metal gratings. In Fig. 2(a), the THz transmission spectrum from the waveguide with a 100μm-thick grating is broad and the transmittance is rather high. However, the deliverable spectral ranges of the 200μm- and 400μm-thick grating waveguides, defined as a transmittance larger than 0.1, are restricted in the low frequency ranges, with respective bandwidths of less than 0.285THz and 0.250THz. In addition, two transmission-dips around 0.300THz and 0.400THz are observed for all the three gratings, caused by Bragg reflections in the periodical slits of the grating waveguide under the phase-matching condition and corresponding to the 3rd- and 4th-order Bragg frequencies for the 1.5mm-long lattice constant. The spectral depths of these transmission dips increase with the metal thickness, but the dip-positions are red-shifted as shown in Fig. 2(a). For example, the 3rd- and 4th-order transmission dips for the 100μm-thick grating waveguide are, respectively, at 0.300THz and 0.400THz and both exhibit shallow spectral depths compared with those for the 200μm- and 400μm-thick grating waveguides. For the 200μm-thick grating, the two transmission dips are shifted respectively to 0.296THz and 0.396THz with a lower transmittance of about 0.005 and 0.002. When the metal thickness is increased to 400μm, the transmission dips are further red-shifted to 0.280THz and 0.380THz, with the smallest transmittances of about 0.003 and 5x10−5. The decreased transmission and red-shift effect of the minimum transmittance for large grating thicknesses both result from the raised scattering cross section [28] because the large slit-depth (or the increased metal thickness) causes stronger scattering and also deflects the lower-frequency THz-waves. In Section 3, we show that, as they approach the transmission-dip frequencies, the deflected THz waves are more easily coupled into the grating structure to form the confined surface waves.
J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93(25), 256804 (2004). [CrossRef] [PubMed]
Fig. 2 (a) Power transmittance of a 50mm-long grating waveguide with different grating thicknesses and the same grating structure. (b) THz transmittance of a 50mm-long integrated grating waveguide with different slit-widths but the same lattice constant of 1.5mm and metal thickness of 200μm.
In the following, we discuss the THz spectral dependence on different slit-widths of the grating. The 200μm-thick grating is used as an example in which the slit-width of the grating is changed from 1.0mm to 0.5mm based on the same lattice constant of 1.5mm, with their transmittances compared in Fig. 2(b). The transmittances of the 3rd- and 4th-order Bragg frequencies at 0.296THz and 0.396THz are both clearly raised about one order of magnitude in the grating waveguide with 0.5mm-long slit-widths, as compared with 1mm-long slit-widths. This indicates that the wider slit-width causes the larger scattering cross section, resulting in reduced transmittance. Based on the measured results, the larger slit-width of the hybrid grating waveguide makes it easier to transfer considerably more evanescent power from the ribbon-waveguide-mode into the THz-SPP modes that are confined on the periodical metal structure (see Section 3 below). Therefore, suitably tailoring the geometrical parameters of the hybrid waveguide, such as metal thickness and slit-width, allows for the coupling of the ribbon-guided THz-waves to the tightly bound surface waves on the patterned metal surface.
3. Subwavelength confinement on the metal grating waveguide
The periodical metal structure of the grating waveguide not only affects the THz spectral property but also introduces phase retardation on the electric-field oscillation. The induced phase retardation changes the effective waveguide indices, and consequently influences the spatial modal confinement. Figure 3
shows the THz electric-field oscillations guided on the 220mm-long ribbon waveguide with and without attaching a metal grating, where the grating dimensions are those shown in Fig. 1, with the same lattice constant of 1.5mm and different metal thicknesses. Figures 3(a)-3(d) respectively show THz waveforms after propagation through a bare ribbon waveguide, and a hybrid grating waveguide with 100, 200, and 400μm-thick gratings. When the thickness of the attached grating is increased, the duration of the THz pulse increases and the second peak of the waveform shifts to the larger time-delay, indicated by the dashed line in Figs. 3(a)-3(d). The pulse-broadening and the increased time-delay both reveal that additional phase retardations are produced from 50mm-long diffraction gratings with different thicknesses integrated on the ribbon waveguide.
Fig. 3 (a) Electric-field oscillations of a THz pulse propagates along a 220mm-long ribbon waveguide without an attached grating, and with the attachment of various gratings with metal thicknesses of (b) 100μm, (c) 200μm, (d) 400mm. (e) Phase-variation spectrum for different metal thicknesses contributed by the metal grating. (f) Effective-index-variation spectrum for different metal thickneses contributed by the metal grating.
The phase information of different grating waveguides can be extracted by Fourier transformation of the time-domain oscillation in Figs. 3(b)-3(d), and compared with that of the blank ribbon waveguide in Fig. 3(a) to obtain the induced phase difference, ΔΦ, of the grating waveguide shown in Fig. 3(e). The phase difference is contributed only from the 50mm-long metallic grating without including the plastic ribbon waveguide, because it is obtained from the relation ΔΦ = ΦG -ΦBlank, where ΦG and ΦBlank are, respectively, the phases of the THz electric-field propagation through a 220mm-long ribbon waveguide with and without the attachment of a 50mm-long metallic grating. The relation between the phase difference (Δϕ) and refractive-index variations (Δn) is defined as Δn = C.Δϕ/(2π.ν.L), where C, ν, L, are, respectively, the speed of light in a vacuum, the frequency of a THz wave, and the length of a metal grating. From the above relation, the phase difference spectrum of Fig. 3(e) for different metal gratings can be transferred to the refractive-index-variation spectrum as shown in Fig. 3(f). In Figs. 3(e) and 3(f), the phase difference (ΔΦ) and refractive-index-variation (Δn) from the 100μm-thick grating are both smaller than those from the 200μm- and 400μm-thick gratings and increased slowly with the THz-wave frequency. The positive value of Δϕ results from the positive value of Δn because the effective refractive index of the hybrid waveguide is higher than that of the bare ribbon waveguide. For the 200μm-thick grating in Fig. 3(e), the zero-phase difference at 0.300THz and 0.400THz represents ΦBlank = ΦG, which is phase-matching between the input THz ribbon-waveguide mode (Kin) and the reflected SPP-modes of the hybrid-waveguide (KR) via the periodic structure of the metal grating (KΛ), as described in Eq. (1). In other words, at these frequencies of zero-phase difference, the transmitted ribbon-waveguide-modes are completely transferred to the reflected SPP-modes through the Bragg reflection of the metal grating, which corresponds to the zero-refractive-index-variation shown in Fig. 3(f) for index matching between the two modes. In the 400μm-thick grating waveguide, Figs. 3(e) and 3(f) respectively show the zero phase-difference and refractive-index-variation. The phase matching condition between the ribbon-waveguide and the SP modes also occurs around 0.300THz, but its spectral width between 0.287~0.300THz is broader than that of the 200μm-thick grating. The phase information of the 400μm-thick grating beyond 0.400THz is not available because, at such frequencies, the guided THz-field is nearly dissipated after the 50mm-long propagation, resulting in an extremely low signal-to-noise ratio (SNR). Therefore, the measured spectral positions of the phase-matching frequencies (or zero-phase differences) are dependent on the grating periods, and the spectral range of phase-matching is increased with the slit-depth of the metallic waveguide due to the larger scattering cross section. This is the reason why the 100μm-thick metal grating has difficulty coupling the weakly bound ribbon waveguide modes to the periodical metal structure to generate confined surface waves at the frequency approaching phase matching point, as illustrated in Fig. 2(a), although a small amount of the THz field is indeed reflected from the 100μm-thick grating surface at Bragg frequencies. In other words, a large portion of the THz field still transmits and is weakly bound around the 100μm-thick grating waveguide, where a small amount of the field is coupled inside the periodical metal slits.
As shown in Figs. 3(e) and 3(f), the high phase-difference results in the high effective-refractive indices of the grating waveguide. Consequently, the effective mode indices of the metal grating are slightly larger than those of a blank ribbon waveguide and increase with frequency except at phase-matching frequencies. Thus, the high effective refractive indices lead to low phase velocities. Based on waveguide theory [6], the high effective-refractive indices of the waveguide concentrate EM fields in the waveguide core to form a smaller spatial mode. As a result, THz waves along the metal grating resemble propagation on a dielectric waveguide except at phase-matching frequencies. Among the three gratings, the 400μm-thick grating has the largest scattering cross section, causing the largest phase difference and effective waveguide index at frequency ranges of 0.300~0.360THz and less than 0.260THz, as indicated in Figs. 3(e) and 3(f). Compared with the 200μm-thick grating, the 400μm-thick grating thus generates more closely-confined THz SPPs.
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]
To verify the deduction of the modal confinement mentioned above, we theoretically analyze the THz-field distribution at the output end of the grating waveguide based on the finite-difference time-domain (FDTD) method using Rsoft software. The input half-spatial mode size of the THz wave for coupling to the grating is determined by the knife-edge method [29] measured at one side of the ribbon and at 170mm from the ribbon input-end, as shown in Fig. 1. The measured half-spatial mode sizes along the Y-axis are respectively 0.96mm, 0.74mm and 0.58mm for the 0.200THz-, 0.250THz- and 0.278THz-waves, but along the X-axis the value is 2.00mm for all three frequencies. These asymmetric modal dimensions are considered to be the theoretical input modal sizes at the input-end of the metallic grating waveguide. The simulated modal patterns following the propagation of the 50mm-long metal grating waveguide are shown in Fig. 4
in which the complex permittivity of the brass material is assumed as ε = −3E4 + (1E6)i [30]. We take the 200μm-thick grating waveguide as an example to characterize the frequency dependence of THz-field confinement on a diffraction grating.Figure 4(a) illustrates the simulated and measured transmittance through the 50mm-long propagation of the 200μm-thick grating waveguide with a slit-width of 1mm and a lattice constant of 1.5mm. The trend of the calculated and measured THz transmitted spectrum is rather consistent especially at Bragg-reflection frequencies of around 0.300 and 0.400THz. For THz waves above 0.250THz, the measured transmittance obviously drops; this drop is theoretically anticipated even though the transmittance value is not exactly matched. Figures 4(b)-4(d) respectively show the cross sections of a THz-field propagated on the 200μm-thick grating waveguide at frequencies of 0.200THz, 0.250THz and 0.278THz, where the metal grating structure is located at 0 ~0.20mm on the Y-axis and −7.50 ~7.50mm on the X-axis. The PE-ribbon shown in the simulation results is located at 0 ~−0.02mm on the Y-axis and −7.50 ~7.50mm on the X-axis. In this presentation, we only discuss the half-THz field distribution which is on the top side of the metal grating, i.e. in + Y-axis part, without considering field distributions below the ribbon waveguide, i.e. in the –Y-axis part. As shown in Fig. 4(b), the simulated modal pattern of the 0.200THz-wave is significantly expanded outside the 200μm-thick grating waveguide over the Y-axis scale of 0.60mm, and the field confinement can be improved for the 0.250THz-wave to make the entire THz-field inside the Y-axis scale of 0.60mm, as shown in Fig. 4(c). Figures 3(e) and 3(f) indicate that the induced phase difference of the 0.250THz-wave is around two times larger than that of the 0.200THz-wave, and the effective waveguide index of the 0.250THz-wave is larger than that of the 0.200THz-wave, which results in 0.250THz exhibiting improved modal field confinement over 0.200THz, as shown in Figs. 4(b) and (c). When the frequency of a THz wave is further increased to 0.278THz with a further large phase difference as indicated in Fig. 3(e), the field distribution along the Y-axis is highly confined inside the grating structure, shown in Fig. 4(d).
S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1–6), 22–26 (1998). [CrossRef]
M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]
Fig. 4 (a) Simulated and measured THz-wave transmittance of 200μm-thick metal grating waveguide. (b) ~(g) THz field distribution of different frequencies at the output end of grating waveguides with various metal thicknesses. (b) 200μm-thick grating at 0.200THz. (c) 200μm-thick grating at 0.250THz. (d) 200μm-thick grating at 0.278THz. (e) 100μm-thick grating at 0.250THz. (f) 400μm-thick grating at 0.250THz. (g) 200μm-thick grating at 0.300THz.
As shown in Fig. 3(e), in the phase difference of a certain THz frequency there are distinct deviating Bragg frequencies for the propagation along metal gratings with different thicknesses, and the field confinement could also be different. We take the 0.250THz-wave as an example to discuss the field confinement ability of THz surface waves guided along different gratings with thicknesses of 100μm, 200μm, and 400μm, respectively shown in Figs. 4(e), 4(c) and 4(f). Compared with the simulation results of 200μm- and 400μm-thick grating waveguides shown in Figs. 4(c) and 4(f), the field distribution for the 100μm-thick grating waveguide in Fig. 4(e) is unable to sufficiently confine the 0.250THz-wave in the Y-axis, which is consistent with the predictions shown in Figs. 2(a), 3(e) and 3(f). In comparisons of the Y-axis field distribution between the 400μm- and 200μm-thick grating waveguide at a frequency of 0.250THz, the former ranges from 0.4 ~0.6mm with a half-transverse modal size less than 0.20mm (Fig. 4(f)) while the latter has an extended half-modal size of about 0.40mm, ranging from 0.2mm to 0.6mm (Fig. 4(c)). Obviously, the hybrid waveguide with a 400μm-thick grating possesses a confinement ability of the THz surface wave superior to those of the 100μm- and 200μm-thick grating waveguides. This simulation result indicates that the subwavelength-confinement of the THz surface wave can be achieved by adding the metal grating thickness of the hybrid waveguide, which is equivalent to increasing the effective refractive indices of the waveguide. Figure 4(g) shows the cross section of the field distribution at a Bragg frequency of 0.300THz propagated on the 200μm-thick grating waveguide, revealing that the surface wave can be well confined within the grating structure. At Bragg frequencies, THz-waves are strongly reflected with low transmittances (Fig. 2(a)) and they produce a zero-phase variation (phase match) along the 50mm-long grating waveguide (Fig. 3(e)). The low transmittance at Bragg frequencies originates from the strong coupling of the ribbon waveguide mode with the grating structure due to phase matches, which causes multiple reflections of the ribbon waveguide modes from the periodic grating slits and forms strong field confinement within the slits [31]. Therefore, the transmission ability of the phase-matching waves is comparatively weak, in contrast to those waves neighboring Bragg frequencies. Based on the simulation results shown in Fig. 4, it is possible to efficiently couple the PE-ribbon waveguide mode into the THz surface waves guided along the hybrid grating waveguide with a subwavelength modal field confinement by either suitably adjusting the grating thickness or operating THz waves near the Bragg frequencies of the grating waveguide.
E. S. Lee, D. H. Kang, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, D. S. Kim, and T. I. Jeon, “Bragg reflection of terahertz waves in plasmonic crystals,” Opt. Express 17(11), 9212–9218 (2009). [CrossRef] [PubMed]
In the experiment, we used the knife-edge method to verify the confinement ability of various grating waveguides with different grating thicknesses. A metal blade was used to conduct a one-dimensional probe of the guided waves along the Y-axis to measure the decay lengths of evanescent fields around the grating waveguide. The decay-length of the evanescent wave, denoted as ΔY, is determined from the power differences between 90%- and 10%-THz transmissions in the Y-axis [29] as schematically sketched in the inset of Fig. 5
without accounting for the metal thickness. For comparison, we also measured the modal size of the THz evanescent field at the output end of a 220mm-long PE ribbon as a reference. Figure 5 shows the measured and simulated decay lengths on one side of the bare ribbon and different hybrid grating waveguides. The decay lengths show a decreasing trend for the bare ribbon waveguide and all hybrid grating waveguides as the THz frequency increases. The experimental minimum decay length of the blank ribbon is about 0.56mm at frequencies beyond 0.300THz, as shown by the black solid line in Fig. 5. When a 100μm-thick grating is attached to the ribbon waveguide, the THz surface wave is only loosely guided on the metal grating surface and the decay length of the guided wave is thus apparently extended, especially for frequencies below 0.350THz. When the grating thickness is increased to 200μm and 400μm, the decay length of the guided wave shrinks, especially at frequencies approaching 0.300THz and 0.250THz, respectively indicated by the green and blue lines in Fig. 5. The measured decay lengths of 100 μm-, 200μm- and 400μm-thick gratings are in good agreement with the simulated results based on the FDTD method.
S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1–6), 22–26 (1998). [CrossRef]
Fig. 5 Experimental and theoretical power decay lengths of a blank ribbon and grating-waveguides integrated with different grating thickness.
In Fig. 5, the best THz confinements for the 200μm- and 400μm-thick gratings respectively occur at frequencies of 0.278THz and 0.240THz. At 0.278THz, the THz waves propagate on a bare ribbon waveguide with a measured power-decay length of 0.61mm but this dropped to 0.26mm when the guided waves are transferred to a 200μm-thick grating waveguide, in which the modal confinement can be achieved at about λ/4 corresponding to a 60%-shrink ratio. For the 400μm-thick grating, the decay lengths of a bare ribbon waveguide and the grating waveguide measured at 0.240THz are reduced from 0.77mm to 0.23mm, corresponding to a λ/5-confinement and 70%-shrink ratio. The decay lengths of THz frequencies above 0.278THz and 0.240THz propagated respectively on the 200μm- and 400μm-thick grating waveguide cannot be measured because, at those frequency ranges, their SNRs in knife-edge measurement are too low to form reliable data. In our current knife-edge measurement, the detection limit of THz transmittance is as low as 0.1. Further improvement of the SNR in THz-TDS system would enable measurement of the modal field of THz waves which approached the phase-matching frequencies and are much more tightly confined on the grating surface. For example, the simulated decay length of the 0.285THz-wave in the 200μm-thick grating waveguide is about 0.16mm, which is smaller than that of the 0.278THz-waves (Fig. 5) which indicates that the confinement is further improved from λ/4 down to λ/6.
Figure 6(a)
shows the simulated power-distribution in the Y-Z plane for a 0.278THz-wave propagated along the 200μm-thick and 50mm-long grating waveguide. The input power is excited from the left-hand side and its intensity is assumed to be one unit. Following a 50mm- long propagation, the intensity of the 0.278THz-wave remains 0.1-unit, which is consistent with the measured result shown in Fig. 2(a) (green line), and its high confinement at the output end of waveguide agrees well with the measurement shown in Fig. 5. Figure 6(b) shows the power distribution of 0.300THz-wave which is interrupted after about a 40mm-long propagation because of the low transmittance (about 0.03) at the waveguide’s output end, as shown in Fig. 2(a) and thus falls outside the measurable dynamic range. Beyond the Braggfrequency of the 200μm-thick grating waveguide (0.296THz), the measured transmittance rises to 0.1 at 0.318THz as indicated in Fig. 2(a). Figure 6(c) shows the simulated power-distribution of the 0.318THz-wave at the output end of 200μm-thick grating waveguide, indicating that this frequency is able to transmit through the 50mm-long grating waveguide and its confinement is better than that of the 0.278THz-wave. Therefore, the THz frequency approaching the Bragg frequency of 0.296THz from a high frequency range can also be highly confined inside the 200μm-thick grating waveguide and its transmission length can be as long as 50mm.
4. Conclusion
We have experimentally demonstrated a THz plasmonic waveguide with subwavelength-scaled confinement and long-distance delivery. A diffraction metal grating integrated with a plastic ribbon waveguide is able to couple the evanescent field to the periodical metal structure to form tightly bound THz-SPPs waves. The coupling strength from the air cladding into the grating structure is dominated by the metal thickness and slit-width of the grating. Aside from the phase-matching frequencies, phase retardation analysis shows that better modal field confinement results from the larger phase difference, which corresponds to the larger effective waveguide index. To guide the highly confined THz waves on the hybrid grating waveguide over a long distance, the guided waves should be operated close to the phase-matching frequency. Our measured decay length is shown to be less than λ/4 at 0.278THz and the longest delivery distance is approximately 50mm, which is competitive with existing spoof-SPPs devices. The demonstrated THz hybrid plasmonic waveguide provides advantages to minute molecular sensing because the THz field can be strongly confined on the metal surface and it also provides sufficient interaction length between the EM field and analytes. The metallic grating could potentially be integrated in a plastic wire to derive circular confined modes for the realization of a near-field THz microscope.
Acknowledgment
This work was supported by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 100-2221-E-006 -174 -MY3) of Taiwan.
References and links
S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef] | |
E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett. 7(2), 334–337 (2007). [CrossRef] [PubMed] | |
E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed] | |
T. I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88(6), 061113 (2006). [CrossRef] | |
T. I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005). [CrossRef] | |
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] | |
W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed] | |
F. J. Garcia-Vidal, L. Martín-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] | |
C. R. Williams, M. Misra, S. R. Andrews, S. A. Maier, S. C. Palacios, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Dual band terahertz waveguiding on a planar metal surface patterned with annular holes,” Appl. Phys. Lett. 96(1), 011101 (2010). [CrossRef] | |
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] | |
S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006). [CrossRef] [PubMed] | |
L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed] | |
D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Waveguided spoof surface plasmons with deep-subwavelength lateral confinement,” Opt. Lett. 36(23), 4635–4637 (2011). [CrossRef] [PubMed] | |
A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optical-fiber-based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef] | |
M. Weisser, B. Menges, and S. M. Neher, “Refractive index and thickness determination of monolayers by multi-mode waveguide coupled surface plasmons,” Sens. Actuators B Chem. 56(3), 189–197 (1999). [CrossRef] | |
M. Martl, J. Darmo, K. Unterrainer, and E. Gornik, “Excitation of terahertz surface plasmon polaritons on etched groove gratings,” J. Opt. Soc. Am. B 26(3), 554–558 (2009). [CrossRef] | |
L. S. Mukina, M. M. Nazarov, and A. P. Shkurinov, “Propagation of THz plasmon pulse on corrugated and flat metal surface,” Surf. Sci. 600(20), 4771–4776 (2006). [CrossRef] | |
M. Nazarov, J. L. Coutaz, A. Shkurinov, and F. Garet, “THz surface plasmon jump between two metal edges,” Opt. Commun. 277(1), 33–39 (2007). [CrossRef] | |
G. Gaborit, D. Armand, J. L. Coutaz, M. Nazarov, and A. Shkurinov, “Excitation and focusing of terahertz surface plasmons using a grating coupler with elliptically curved grooves,” Appl. Phys. Lett. 94(23), 231108 (2009). [CrossRef] | |
M. Gong, T. I. Jeon, and D. Grischkowsky, “THz surface wave collapse on coated metal surfaces,” Opt. Express 17(19), 17088–17101 (2009). [CrossRef] [PubMed] | |
A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008). [CrossRef] [PubMed] | |
L. J. Chen, H. W. Chen, T. F. Kao, J. Y. Lu, and C. K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed] | |
C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt. 44(28), 5937–5946 (2005). [CrossRef] [PubMed] | |
M. Nagel, F. Richter, P. Haring-Bolívar, and H. Kurz, “A functionalized THz sensor for marker-free DNA analysis,” Phys. Med. Biol. 48(22), 3625–3636 (2003). [CrossRef] [PubMed] | |
A. Hassani and M. Skorobogatiy, “Surface plasmon resonance-like integrated sensor at terahertz frequencies for gaseous analytes,” Opt. Express 16(25), 20206–20214 (2008). [CrossRef] [PubMed] | |
R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88(7), 4449–4451 (2000). [CrossRef] | |
B. You, J. Y. Lu, T. A. Liu, J. L. Peng, and C. L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 96(5), 051105 (2010). [CrossRef] | |
J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93(25), 256804 (2004). [CrossRef] [PubMed] | |
S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1–6), 22–26 (1998). [CrossRef] | |
M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed] | |
E. S. Lee, D. H. Kang, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, D. S. Kim, and T. I. Jeon, “Bragg reflection of terahertz waves in plasmonic crystals,” Opt. Express 17(11), 9212–9218 (2009). [CrossRef] [PubMed] |
OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(130.2790) Integrated optics : Guided waves
(240.6690) Optics at surfaces : Surface waves
(300.6495) Spectroscopy : Spectroscopy, teraherz
ToC Category:
Optics at Surfaces
History
Original Manuscript: November 29, 2012
Revised Manuscript: February 5, 2013
Manuscript Accepted: February 22, 2013
Published: March 4, 2013
Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics
Citation
Borwen You, Ja-Yu Lu, Wei-Lun Chang, Chin-Ping Yu, Tze-An Liu, and Jin-Long Peng, "Subwavelength confined terahertz waves on planar waveguides using metallic gratings," Opt. Express 21, 6009-6019 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6009
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References
- S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007). [CrossRef]
- E. Verhagen, L. Kuipers, and A. Polman, “Enhanced nonlinear optical effects with a tapered plasmonic waveguide,” Nano Lett.7(2), 334–337 (2007). [CrossRef] [PubMed]
- E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
- T. I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett.88(6), 061113 (2006). [CrossRef]
- T. I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett.86(16), 161904 (2005). [CrossRef]
- 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. Photonics2(3), 175–179 (2008). [CrossRef]
- W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express16(9), 6216–6226 (2008). [CrossRef] [PubMed]
- F. J. Garcia-Vidal, L. Martín-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]
- C. R. Williams, M. Misra, S. R. Andrews, S. A. Maier, S. C. Palacios, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Dual band terahertz waveguiding on a planar metal surface patterned with annular holes,” Appl. Phys. Lett.96(1), 011101 (2010). [CrossRef]
- 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]
- S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006). [CrossRef] [PubMed]
- L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express16(5), 3326–3333 (2008). [CrossRef] [PubMed]
- D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Waveguided spoof surface plasmons with deep-subwavelength lateral confinement,” Opt. Lett.36(23), 4635–4637 (2011). [CrossRef] [PubMed]
- A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optical-fiber-based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B24(6), 1423–1429 (2007). [CrossRef]
- M. Weisser, B. Menges, and S. M. Neher, “Refractive index and thickness determination of monolayers by multi-mode waveguide coupled surface plasmons,” Sens. Actuators B Chem.56(3), 189–197 (1999). [CrossRef]
- M. Martl, J. Darmo, K. Unterrainer, and E. Gornik, “Excitation of terahertz surface plasmon polaritons on etched groove gratings,” J. Opt. Soc. Am. B26(3), 554–558 (2009). [CrossRef]
- L. S. Mukina, M. M. Nazarov, and A. P. Shkurinov, “Propagation of THz plasmon pulse on corrugated and flat metal surface,” Surf. Sci.600(20), 4771–4776 (2006). [CrossRef]
- M. Nazarov, J. L. Coutaz, A. Shkurinov, and F. Garet, “THz surface plasmon jump between two metal edges,” Opt. Commun.277(1), 33–39 (2007). [CrossRef]
- G. Gaborit, D. Armand, J. L. Coutaz, M. Nazarov, and A. Shkurinov, “Excitation and focusing of terahertz surface plasmons using a grating coupler with elliptically curved grooves,” Appl. Phys. Lett.94(23), 231108 (2009). [CrossRef]
- M. Gong, T. I. Jeon, and D. Grischkowsky, “THz surface wave collapse on coated metal surfaces,” Opt. Express17(19), 17088–17101 (2009). [CrossRef] [PubMed]
- A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express16(9), 6340–6351 (2008). [CrossRef] [PubMed]
- L. J. Chen, H. W. Chen, T. F. Kao, J. Y. Lu, and C. K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett.31(3), 308–310 (2006). [CrossRef] [PubMed]
- C. Yeh, F. Shimabukuro, and P. H. Siegel, “Low-loss terahertz ribbon waveguides,” Appl. Opt.44(28), 5937–5946 (2005). [CrossRef] [PubMed]
- M. Nagel, F. Richter, P. Haring-Bolívar, and H. Kurz, “A functionalized THz sensor for marker-free DNA analysis,” Phys. Med. Biol.48(22), 3625–3636 (2003). [CrossRef] [PubMed]
- A. Hassani and M. Skorobogatiy, “Surface plasmon resonance-like integrated sensor at terahertz frequencies for gaseous analytes,” Opt. Express16(25), 20206–20214 (2008). [CrossRef] [PubMed]
- R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys.88(7), 4449–4451 (2000). [CrossRef]
- B. You, J. Y. Lu, T. A. Liu, J. L. Peng, and C. L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett.96(5), 051105 (2010). [CrossRef]
- J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93(25), 256804 (2004). [CrossRef] [PubMed]
- S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1–6), 22–26 (1998). [CrossRef]
- M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt.22(7), 1099–20 (1983). [CrossRef] [PubMed]
- E. S. Lee, D. H. Kang, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, D. S. Kim, and T. I. Jeon, “Bragg reflection of terahertz waves in plasmonic crystals,” Opt. Express17(11), 9212–9218 (2009). [CrossRef] [PubMed]
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