June 1, 2015 / Vol. 40, No. 11 / OPTICS LETTERS
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Spoof surface plasmon-based stripe antennas with extreme field enhancement in the terahertz regime Zhanghua Han,1,* Yusheng Zhang,1 and Sergey I. Bozhevolnyi2 1 2
Center for Terahertz Research, China Jiliang University, Hangzhou 310018, China
Department of Technology and Innovation, University of Southern Denmark, Odense M DK-5230, Denmark *Corresponding author: [email protected] Received April 3, 2015; accepted May 1, 2015; posted May 8, 2015 (Doc. ID 237183); published May 21, 2015
Retardation-based stripe antennas due to the excitation of spoof surface plasmons on a corrugated metal stripe are proposed and numerically studied in the terahertz regime, revealing sharp Fabry–Perot resonances in scattering cross-section spectra with strongly enhanced local fields. The order of the resonance exhibiting the sharpest scattering cross section and strongest field enhancements (FEs) is found to coincide with the number of grooves, due to the hybridization of the antenna resonance with the individual groove resonance. The proposed (spoof surface plasmon-based) antennas with narrow resonances and large FE open up new possibilities for metamaterial design and seem very promising for sensing applications in the terahertz frequencies. © 2015 Optical Society of America OCIS codes: (250.5403) Plasmonics; (040.2235) Far infrared or terahertz; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.40.002533
In the optical frequencies, a metal–dielectric interface may support the well-known surface plasmon (SP) modes, which result from the coupling of electromagnetic (EM) fields with coherent oscillations of the metal’s free electrons and exhibit strong (on the sub-wavelength scale) field confinement. It should be noted that the phenomenon of SPs can typically be classified into two different types: surface plasmon polaritons (SPPs), which are propagating modes that exist on the extended interface of metal and dielectric or waveguide structures, and localized surface plasmons (LSPs), which are resonance modes supported by small metal particles [1]. Taking advantage of their sub-wavelength nature, waveguide structures supporting SPPs are excellent candidates for the further miniaturization of photonic circuit elements [2]. LSPs or, more generally, retardation-based optical nanoantennas [3], have long been of intense interest for increasing applications in surface-enhanced Raman spectroscopy [4], and in chemical and biological sensing [5], etc., owing to the large field enhancement (FE) occurring at the resonances. However, the aforementioned exciting properties of SPs cannot directly be transferred to low frequencies using metals, including terahertz and microwave frequencies, because metals with large imaginary and negative real parts of the permittivity can only sustain very loosely bound EM modes and thus behave as perfect electric conductors (PECs). Besides the use of highly doped semiconductors as terahertz plasmonic materials [6], the concept of spoof (or designer) surface plasmons (SSPs) [7] allows one to circumvent this problem. Propagating SSPs supported by a structured metal surface composed of grooves or holes perforated in a flat metal surface have been experimentally demonstrated at microwave [8] and terahertz frequencies [9]. Since then, further research has been conducted on exploiting these artificial surface waves, and various waveguides and devices [10] have been proposed and studied in the terahertz and microwave regimes. 0146-9592/15/112533-04$15.00/0
More recently, the concept of localized spoof plasmons, which resemble the LSPs in the optical frequencies, was realized with periodically textured, closed surfaces [11], and closed, textured cavities [12] have been proposed and experimentally demonstrated at microwave frequencies [13]. Multi-band localized spoof plasmons have also been numerically investigated by decorating periodically textured cylinders and closed, textured cavities [14]. However, a very basic structure of SSP-based stripe antennas operating at low frequencies has so far not been studied, especially with the aim of realizing a large FE. Actually, a local FE is very important in the terahertz regime, in which the fingerprint sensing of biological and chemical materials is the most promising application. An enhancement of the interaction between the terahertz radiation and the specimen will help achieve a high sensitivity, quite similar to the principal of surface-enhanced infrared absorption [15]. In this Letter, we propose a novel antenna based on the excitation of SSP modes supported by a corrugated stripe structure composed of limited periods of grooves. The proposed antenna, although conceptually simple, exhibits a large sharp-scattering cross-section resonance and a huge FE. Some characteristics of the proposed antennas, including the scattering cross section (SCS) and the FE due to the excitation of the SSP, are presented and compared with those of a regular antenna. A threedimensional counterpart of the proposed antenna is also presented with the characteristics given. The unit cell of the groove is schematically shown in Fig. 1(a), where a rectangular groove with width W and depth H is perforated into a metal stripe with a remaining base thickness of t. The grooves form a one-dimensional array with a period of P. In this Letter, the relationship between these geometrical parameters are assumed to be W 0.5 P and t 0.25 P, where P is chosen as 50 μm so that the resulting reference frequency will be in the terahertz regime. The index of the surrounding background © 2015 Optical Society of America
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studied using the FEM technique. A linearly polarized plane wave with the electric field along the x direction to excite the transverse electromagnetic mode (TEM) in the individual grooves in Fig. 1(b) is incident downward from the top. The EM response of this structure can be described by the SCS, which is calculated by σ sc
Fig. 1. (a) Schematic of the unit cell of the PEC corrugated groove used for the spoof plasmon polaritons with the groove depth H and width W and the periodicity P. (b) Stripe antenna with three corrugated groove unit cells. The total length is represented by L; the metal bottom thickness is represented by t. (c) The calculated dispersion curve for the SSP mode, supported by an infinite number of grooves with different groove heights.
medium nd is assumed to be 1.45. As is well known, an array composed of infinite periods of such grooves will be able to support a well-confined surface mode with a relatively low propagation loss [7]. The dispersion relation for the SSP waveguide mode supported by this periodic structure is calculated using a finite-element method (FEM) based eigenfrequency solver and the results are shown for different groove heights in Fig. 1(c), where the straight line is given for the light in the background medium for comparison. In the calculations of the dispersion, the metal is assumed to be a PEC to facilitate the selection of the calculated frequency at a certain wavenumber. It is clearly seen [see Fig. 1(c)] that the corrugated (grooved) surface exhibits a well-pronounced SP-like behavior. The wave vector of the SSP modes deviates from that of the light in the surrounding medium as the frequency increases, and the dispersion curve of the SSP mode becomes flat when the frequency asymptotes to a certain value. The dispersion curve moves to the right when the groove height increases, showing a trend of tighter modal confinement. When the waveguide is truncated to consist of a few grooves, the resulting structure should then be expected to operate as a stripe antenna, in a geometrically similar way to a metal stripe optical nanoantenna. Note that with optical (plasmonic) nanoantennas, the SPs on both sides of the metal stripe surface will couple to each other to form the slow-SPP mode [16], while the considered structure only supports the SSP mode on one side of the metal stripe, where it is corrugated. Since the SSP wave vector is found to the right of the light wave vector in Fig. 1(c), one can expect that this novel antenna based on the retardation effect of the SSP mode will have a shorter length than the regular (radiowave) dipole antenna. In our structure, the number of grooves is assumed to be N, so that the total length of the antenna with a metallic closure at both ends [as depicted in Fig. 1(b)] will be L N 0.5P. Because the resonance frequencies scale with the reciprocal size of the structure, the period P is hereafter used as the unit length when presenting the results of numerical simulations. The properties of the proposed antenna, including the SCS and the FE in the terahertz regime, are numerically
1 I in
Z
1 ˆ E × H sc · ndS; 2 sc
(1)
where I in is the intensity of the incident wave, E sc and H sc are the scattered electric and magnetic fields, respectively, and the integration is performed over a sphere surrounding the stripe antenna, with nˆ being the outward unit vector normal to the sphere. We first start with a groove number N of 3. In Fig. 2(a), the normalized SCS to the real length of the antenna L is presented as a function of the frequency (the solid lines) for different groove heights. The metal is assumed to be a PEC first, and the frequency is normalized so that it has a unit of f 0 c∕P, where c is the velocity of the light in the vacuum. From the SCS spectrum, it is clearly seen that with each solid line, there are two peaks that must be related to the resonant EM behaviors of this stripe antenna. The first resonance has a broader normalized SCS, while the second SCS resonance is much sharper and has a feature of a Fano resonance. The Fano resonance is attributed to the coupling between the second SCS resonance to the first resonance, because the first resonance is quite broad, leading to the positioning of the second resonance still within the first one. A similar behavior was experimentally observed in plasmonic nanorods [17]. For different groove heights, it is seen that when H increases, both resonances not only shift to the left, but also become narrower. This is due to the tighter modal confinement for a larger groove depth, as shown by the dispersion curves in Fig. 1(c).
Fig. 2. (a) Normalized SCS. (b) Average FE for the terahertz antenna with groove number N 3 and different groove height (solid lines). The dashed lines in (a) are for a bare dipole antenna with loss considered. (c), (d) H z distributions for the two resonances when groove height is P.
June 1, 2015 / Vol. 40, No. 11 / OPTICS LETTERS
These resonances in the SCS curves are due to the excitation and propagation of the SSP modes, similar to those supported by the nanostripe antennas working in optical frequencies [16,18]. Propagating SSPs back and forth along the corrugated metallic stripe will have reflections at both terminations, and the constructive interference of the SSP waves can be achieved when the following phase condition is fulfilled [16]: kSSP L Φ mπwhere m 1; 2; 3…;
(2)
where kSSP is the wavevector of the SSP mode, L is the length of stripe antenna, m is an positive integer indicating the resonance order, and Φ is the reflection phase at both terminations due to the partial scattering of the SSP modes into free space. Figures 2(c) and 2(d) illustrate the distributions of the magnetic field (H z ) in this stripe antenna at the two resonances when the antenna groove height H is equal to P. One can easily see that the order m of the two resonances is 1 and 3. The first resonance has a mode profile quite resembling a regular dipole mode, resulting from a small deviation of the SSP wavevector to that of the light at this frequency. The SSP mode at the second resonance is more confined within the grooves, due to this frequency being closer to an asymptotic frequency. The resonance with the even order of m 2 is not excited at the normal incidence, due to symmetry reasons. One of the most remarkable properties of optical nanoantennas is the FE at the resonant frequencies. To illuminate this property of the proposed SSP-based antennas, the electric field in the simulated structure is alsoR characterized. An average FE factor, defined by FE jEjdl∕L∕jE 0 j, where jEj is the amplitude of the electric field and jE 0 j is that for the incident light, is used to eliminate the influence of the corner effect. The integration is performed along the upper surface of the antenna, and the results are shown for different groove heights in Fig. 2(b). It is seen that at the first resonance, where a broad, normalized SCS is shown, the average FE does not exhibit any resonant behavior, probably because its mode profile resembles that of a dipole resonance. Notably, at the second resonance, the FE increases for a larger groove height, and FEs up to 12 and 22 are achieved, respectively, for groove heights of P and 1.5 P. Then, the local electric field intensity is enhanced by two orders of magnitude compared to the incident plane wave. In the above calculations, the metal is assumed to be a PEC for simplicity. To make sure our results have more guidance for real applications, a stripe antenna that is composed of copper to take into account the Ohmic loss has also been investigated. The permittivity of copper is characterized by a Drude model εω 1 − ωp ∕ ω2 iωγ, where ω is the angular frequency, ωp 1.123 × 1016 Hz is the plasma frequency, and γ 1.379 × 1013 Hz is the collision frequency [19]. Although the metal loss is expected to deteriorate the properties of the antennas, the results for the antenna made from copper with a groove height of P shown as the dotted lines in Figs. 2(a) and 2(b) demonstrate that the characteristics of both the SCS and FE remain almost unchanged for the first resonance, while for the second resonance, both
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results are decreased only by a few percents. Actually, the average FE at the second resonance due to the excitation of SSP mode is still up to 10.5 times. To highlight the properties of the proposed antennas, the normalized SCS for a regular dipole antenna made of copper (with the absorption loss being considered) is shown as the dashed line in Figs. 2(a) and 2(b) for comparison. It is evident that only a single resonance with a broad bandwidth at around 0.1 f 0 is present. At this frequency, the dipole works as a half-wave antenna. The almost flat FE is due to an average of the field, although it is known that at the resonance, the dipole antenna has some local FE. Even higher orders of resonances can also be found when more grooves are used in the antenna design. The normalized SCS and FE for the antennas with the groove numbers of 5 and 7 are presented in Figs. 3(a) and 3(b), respectively. Here, the groove height is fixed to be H P. It is evident that the higher orders appear as m 1, 3, and 5 for N 5 and m 1, 3, 5, and 7 for N 7. For a specific antenna, the SCS resonance is sharper, and the FE is stronger for higher orders of resonances. It is worth noting that the highest FE also happens when the resonance number is equal to the number of grooves. We attribute this phenomenon to the hybridization of the antenna resonance, with the individual groove resonance formed by the standing TEM mode supported by individual grooves. It is seen that the position of this (sharpest) resonance, while being dependent on the groove depth, is practically independent on the number of grooves (cf. Figs. 2 and 3). The structure given in Fig. 1(b) is a two-dimensional case, which is easier to use to demonstrate the principal of the proposed antenna. In practice, it corresponds to a groove array with a much longer dimension in the z direction. To facilitate the use of the proposed antenna structure in real applications, the three-dimensional planar structure schematically shown as the inset in Fig. 4 is used. Actually, the use of this structure has been used for the propagation of SSP modes [20]. In our simulation, the thickness of the metal stripe h is assumed as 0.2 P, and the other parameters are same as those in the two-dimensional situation. A linearly polarized plane wave with the electric field along the x direction is used for excitation. As is shown in Fig. 4, a similar FE resonance achieved at the top surface of the antenna can be obtained from this finite, thick-stripe antenna, and surprisingly, the FE factor is even higher than that its two-dimensional counterpart, with the average FE factor of the second resonance as high as 50. This implies that the local electric field
Fig. 3. (a) Normalized SCS. (b) Average FE for the terahertz antennas with groove numbers N 5 and 7.
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have a significant impact on the applied research in the terahertz or microwave regimes.
Fig. 4.
Average FE, with a thickness of h 0.2 P.
intensity can be enhanced by three orders of magnitude. The ease of fabrication, together with the ultra-high FE, makes this stripe antenna an ideal platform for highsensitivity sensing applications in the terahertz and microwave regimes. Sharp resonances supported by SSP-based stripe antennas imply enhanced field-matter interactions and, thereby, new possibilities for improving environmental sensitivity and single-molecule detection in the terahertz regime. That is to say, the proposed SSP-based antennas with extreme FEs hold high potential in applications such as surface-enhanced terahertz absorption spectroscopy. Both the application scope and sensitivity of the conventional technique of terahertz time-domain spectroscopy will be improved substantially. In conclusion, we have shown that a corrugated metallic stripe with a few grooves can be utilized to realize novel SSP-based antennas that work in the terahertz regime. Resonances based on the retardation effect of the propagating SSP modes exhibit sharp, normalized scattering cross sections and enhanced average electric fields. Extremely sharp (high-order) SSP resonances associated with strongly confined and enhanced local fields, which have been identified and exploited in this work, provide new design perspectives for terahertzoriented metamaterials and sensing configurations. As a result, we believe that the proposed novel antennas will
References 1. S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007). 2. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008). 3. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005). 4. F. J. García-Vidal and J. Pendry, Phys. Rev. Lett. 77, 1163 (1996). 5. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, Nat. Mater. 7, 442 (2008). 6. Y. Zhang and Z. Han, AIP Adv. 5, 017113 (2015). 7. F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A 7, S97 (2005). 8. A. P. Hibbins, B. R. Evans, and J. R. Sambles, Science 308, 670 (2005). 9. C. R. Williams, S. R. Andrews, S. A. Maier, A. L. FernándezDomínguez, L. Martín-Moreno, and F. J. García-Vidal, Nat. Photonics 2, 175 (2008). 10. S. A. Maier and S. R. Andrews, Appl. Phys. Lett. 88, 251120 (2006). 11. A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012). 12. Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, Appl. Phys. Lett. 104, 251601 (2014). 13. X. Shen and T. J. Cui, Laser Photon. Rev. 8, 137 (2014). 14. Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, Appl. Phys. Lett. 104, 101603 (2014). 15. L. V. Brown, K. Zhao, N. S. King, H. Sobhani, P. Nordlander, and N. J. Halas, J. Am. Chem. Soc. 135, 3688 (2013). 16. S. I. Bozhevolnyi and T. Søndergaard, Opt. Express 15, 10869 (2007). 17. N. Verellen, F. López-Tejeira, R. Paniagua-Domínguez, D. Vercruysse, D. Denkova, L. Lagae, P. Van Dorpe, V. V. Moshchalkov, and J. A. Sánchez-Gil, Nano Lett. 14, 2322 (2014). 18. E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, Opt. Express 16, 16529 (2008). 19. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, Appl. Opt. 24, 4493 (1985). 20. X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, Proc. Natl. Acad. Sci. USA 110, 40 (2013).
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Spoof surface plasmon-based stripe antennas with extreme field enhancement in the terahertz regime Zhanghua Han,1,* Yusheng Zhang,1 and Sergey I. Bozhevolnyi2 1 2
Center for Terahertz Research, China Jiliang University, Hangzhou 310018, China
Department of Technology and Innovation, University of Southern Denmark, Odense M DK-5230, Denmark *Corresponding author: [email protected] Received April 3, 2015; accepted May 1, 2015; posted May 8, 2015 (Doc. ID 237183); published May 21, 2015
Retardation-based stripe antennas due to the excitation of spoof surface plasmons on a corrugated metal stripe are proposed and numerically studied in the terahertz regime, revealing sharp Fabry–Perot resonances in scattering cross-section spectra with strongly enhanced local fields. The order of the resonance exhibiting the sharpest scattering cross section and strongest field enhancements (FEs) is found to coincide with the number of grooves, due to the hybridization of the antenna resonance with the individual groove resonance. The proposed (spoof surface plasmon-based) antennas with narrow resonances and large FE open up new possibilities for metamaterial design and seem very promising for sensing applications in the terahertz frequencies. © 2015 Optical Society of America OCIS codes: (250.5403) Plasmonics; (040.2235) Far infrared or terahertz; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.40.002533
In the optical frequencies, a metal–dielectric interface may support the well-known surface plasmon (SP) modes, which result from the coupling of electromagnetic (EM) fields with coherent oscillations of the metal’s free electrons and exhibit strong (on the sub-wavelength scale) field confinement. It should be noted that the phenomenon of SPs can typically be classified into two different types: surface plasmon polaritons (SPPs), which are propagating modes that exist on the extended interface of metal and dielectric or waveguide structures, and localized surface plasmons (LSPs), which are resonance modes supported by small metal particles [1]. Taking advantage of their sub-wavelength nature, waveguide structures supporting SPPs are excellent candidates for the further miniaturization of photonic circuit elements [2]. LSPs or, more generally, retardation-based optical nanoantennas [3], have long been of intense interest for increasing applications in surface-enhanced Raman spectroscopy [4], and in chemical and biological sensing [5], etc., owing to the large field enhancement (FE) occurring at the resonances. However, the aforementioned exciting properties of SPs cannot directly be transferred to low frequencies using metals, including terahertz and microwave frequencies, because metals with large imaginary and negative real parts of the permittivity can only sustain very loosely bound EM modes and thus behave as perfect electric conductors (PECs). Besides the use of highly doped semiconductors as terahertz plasmonic materials [6], the concept of spoof (or designer) surface plasmons (SSPs) [7] allows one to circumvent this problem. Propagating SSPs supported by a structured metal surface composed of grooves or holes perforated in a flat metal surface have been experimentally demonstrated at microwave [8] and terahertz frequencies [9]. Since then, further research has been conducted on exploiting these artificial surface waves, and various waveguides and devices [10] have been proposed and studied in the terahertz and microwave regimes. 0146-9592/15/112533-04$15.00/0
More recently, the concept of localized spoof plasmons, which resemble the LSPs in the optical frequencies, was realized with periodically textured, closed surfaces [11], and closed, textured cavities [12] have been proposed and experimentally demonstrated at microwave frequencies [13]. Multi-band localized spoof plasmons have also been numerically investigated by decorating periodically textured cylinders and closed, textured cavities [14]. However, a very basic structure of SSP-based stripe antennas operating at low frequencies has so far not been studied, especially with the aim of realizing a large FE. Actually, a local FE is very important in the terahertz regime, in which the fingerprint sensing of biological and chemical materials is the most promising application. An enhancement of the interaction between the terahertz radiation and the specimen will help achieve a high sensitivity, quite similar to the principal of surface-enhanced infrared absorption [15]. In this Letter, we propose a novel antenna based on the excitation of SSP modes supported by a corrugated stripe structure composed of limited periods of grooves. The proposed antenna, although conceptually simple, exhibits a large sharp-scattering cross-section resonance and a huge FE. Some characteristics of the proposed antennas, including the scattering cross section (SCS) and the FE due to the excitation of the SSP, are presented and compared with those of a regular antenna. A threedimensional counterpart of the proposed antenna is also presented with the characteristics given. The unit cell of the groove is schematically shown in Fig. 1(a), where a rectangular groove with width W and depth H is perforated into a metal stripe with a remaining base thickness of t. The grooves form a one-dimensional array with a period of P. In this Letter, the relationship between these geometrical parameters are assumed to be W 0.5 P and t 0.25 P, where P is chosen as 50 μm so that the resulting reference frequency will be in the terahertz regime. The index of the surrounding background © 2015 Optical Society of America
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studied using the FEM technique. A linearly polarized plane wave with the electric field along the x direction to excite the transverse electromagnetic mode (TEM) in the individual grooves in Fig. 1(b) is incident downward from the top. The EM response of this structure can be described by the SCS, which is calculated by σ sc
Fig. 1. (a) Schematic of the unit cell of the PEC corrugated groove used for the spoof plasmon polaritons with the groove depth H and width W and the periodicity P. (b) Stripe antenna with three corrugated groove unit cells. The total length is represented by L; the metal bottom thickness is represented by t. (c) The calculated dispersion curve for the SSP mode, supported by an infinite number of grooves with different groove heights.
medium nd is assumed to be 1.45. As is well known, an array composed of infinite periods of such grooves will be able to support a well-confined surface mode with a relatively low propagation loss [7]. The dispersion relation for the SSP waveguide mode supported by this periodic structure is calculated using a finite-element method (FEM) based eigenfrequency solver and the results are shown for different groove heights in Fig. 1(c), where the straight line is given for the light in the background medium for comparison. In the calculations of the dispersion, the metal is assumed to be a PEC to facilitate the selection of the calculated frequency at a certain wavenumber. It is clearly seen [see Fig. 1(c)] that the corrugated (grooved) surface exhibits a well-pronounced SP-like behavior. The wave vector of the SSP modes deviates from that of the light in the surrounding medium as the frequency increases, and the dispersion curve of the SSP mode becomes flat when the frequency asymptotes to a certain value. The dispersion curve moves to the right when the groove height increases, showing a trend of tighter modal confinement. When the waveguide is truncated to consist of a few grooves, the resulting structure should then be expected to operate as a stripe antenna, in a geometrically similar way to a metal stripe optical nanoantenna. Note that with optical (plasmonic) nanoantennas, the SPs on both sides of the metal stripe surface will couple to each other to form the slow-SPP mode [16], while the considered structure only supports the SSP mode on one side of the metal stripe, where it is corrugated. Since the SSP wave vector is found to the right of the light wave vector in Fig. 1(c), one can expect that this novel antenna based on the retardation effect of the SSP mode will have a shorter length than the regular (radiowave) dipole antenna. In our structure, the number of grooves is assumed to be N, so that the total length of the antenna with a metallic closure at both ends [as depicted in Fig. 1(b)] will be L N 0.5P. Because the resonance frequencies scale with the reciprocal size of the structure, the period P is hereafter used as the unit length when presenting the results of numerical simulations. The properties of the proposed antenna, including the SCS and the FE in the terahertz regime, are numerically
1 I in
Z
1 ˆ E × H sc · ndS; 2 sc
(1)
where I in is the intensity of the incident wave, E sc and H sc are the scattered electric and magnetic fields, respectively, and the integration is performed over a sphere surrounding the stripe antenna, with nˆ being the outward unit vector normal to the sphere. We first start with a groove number N of 3. In Fig. 2(a), the normalized SCS to the real length of the antenna L is presented as a function of the frequency (the solid lines) for different groove heights. The metal is assumed to be a PEC first, and the frequency is normalized so that it has a unit of f 0 c∕P, where c is the velocity of the light in the vacuum. From the SCS spectrum, it is clearly seen that with each solid line, there are two peaks that must be related to the resonant EM behaviors of this stripe antenna. The first resonance has a broader normalized SCS, while the second SCS resonance is much sharper and has a feature of a Fano resonance. The Fano resonance is attributed to the coupling between the second SCS resonance to the first resonance, because the first resonance is quite broad, leading to the positioning of the second resonance still within the first one. A similar behavior was experimentally observed in plasmonic nanorods [17]. For different groove heights, it is seen that when H increases, both resonances not only shift to the left, but also become narrower. This is due to the tighter modal confinement for a larger groove depth, as shown by the dispersion curves in Fig. 1(c).
Fig. 2. (a) Normalized SCS. (b) Average FE for the terahertz antenna with groove number N 3 and different groove height (solid lines). The dashed lines in (a) are for a bare dipole antenna with loss considered. (c), (d) H z distributions for the two resonances when groove height is P.
June 1, 2015 / Vol. 40, No. 11 / OPTICS LETTERS
These resonances in the SCS curves are due to the excitation and propagation of the SSP modes, similar to those supported by the nanostripe antennas working in optical frequencies [16,18]. Propagating SSPs back and forth along the corrugated metallic stripe will have reflections at both terminations, and the constructive interference of the SSP waves can be achieved when the following phase condition is fulfilled [16]: kSSP L Φ mπwhere m 1; 2; 3…;
(2)
where kSSP is the wavevector of the SSP mode, L is the length of stripe antenna, m is an positive integer indicating the resonance order, and Φ is the reflection phase at both terminations due to the partial scattering of the SSP modes into free space. Figures 2(c) and 2(d) illustrate the distributions of the magnetic field (H z ) in this stripe antenna at the two resonances when the antenna groove height H is equal to P. One can easily see that the order m of the two resonances is 1 and 3. The first resonance has a mode profile quite resembling a regular dipole mode, resulting from a small deviation of the SSP wavevector to that of the light at this frequency. The SSP mode at the second resonance is more confined within the grooves, due to this frequency being closer to an asymptotic frequency. The resonance with the even order of m 2 is not excited at the normal incidence, due to symmetry reasons. One of the most remarkable properties of optical nanoantennas is the FE at the resonant frequencies. To illuminate this property of the proposed SSP-based antennas, the electric field in the simulated structure is alsoR characterized. An average FE factor, defined by FE jEjdl∕L∕jE 0 j, where jEj is the amplitude of the electric field and jE 0 j is that for the incident light, is used to eliminate the influence of the corner effect. The integration is performed along the upper surface of the antenna, and the results are shown for different groove heights in Fig. 2(b). It is seen that at the first resonance, where a broad, normalized SCS is shown, the average FE does not exhibit any resonant behavior, probably because its mode profile resembles that of a dipole resonance. Notably, at the second resonance, the FE increases for a larger groove height, and FEs up to 12 and 22 are achieved, respectively, for groove heights of P and 1.5 P. Then, the local electric field intensity is enhanced by two orders of magnitude compared to the incident plane wave. In the above calculations, the metal is assumed to be a PEC for simplicity. To make sure our results have more guidance for real applications, a stripe antenna that is composed of copper to take into account the Ohmic loss has also been investigated. The permittivity of copper is characterized by a Drude model εω 1 − ωp ∕ ω2 iωγ, where ω is the angular frequency, ωp 1.123 × 1016 Hz is the plasma frequency, and γ 1.379 × 1013 Hz is the collision frequency [19]. Although the metal loss is expected to deteriorate the properties of the antennas, the results for the antenna made from copper with a groove height of P shown as the dotted lines in Figs. 2(a) and 2(b) demonstrate that the characteristics of both the SCS and FE remain almost unchanged for the first resonance, while for the second resonance, both
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results are decreased only by a few percents. Actually, the average FE at the second resonance due to the excitation of SSP mode is still up to 10.5 times. To highlight the properties of the proposed antennas, the normalized SCS for a regular dipole antenna made of copper (with the absorption loss being considered) is shown as the dashed line in Figs. 2(a) and 2(b) for comparison. It is evident that only a single resonance with a broad bandwidth at around 0.1 f 0 is present. At this frequency, the dipole works as a half-wave antenna. The almost flat FE is due to an average of the field, although it is known that at the resonance, the dipole antenna has some local FE. Even higher orders of resonances can also be found when more grooves are used in the antenna design. The normalized SCS and FE for the antennas with the groove numbers of 5 and 7 are presented in Figs. 3(a) and 3(b), respectively. Here, the groove height is fixed to be H P. It is evident that the higher orders appear as m 1, 3, and 5 for N 5 and m 1, 3, 5, and 7 for N 7. For a specific antenna, the SCS resonance is sharper, and the FE is stronger for higher orders of resonances. It is worth noting that the highest FE also happens when the resonance number is equal to the number of grooves. We attribute this phenomenon to the hybridization of the antenna resonance, with the individual groove resonance formed by the standing TEM mode supported by individual grooves. It is seen that the position of this (sharpest) resonance, while being dependent on the groove depth, is practically independent on the number of grooves (cf. Figs. 2 and 3). The structure given in Fig. 1(b) is a two-dimensional case, which is easier to use to demonstrate the principal of the proposed antenna. In practice, it corresponds to a groove array with a much longer dimension in the z direction. To facilitate the use of the proposed antenna structure in real applications, the three-dimensional planar structure schematically shown as the inset in Fig. 4 is used. Actually, the use of this structure has been used for the propagation of SSP modes [20]. In our simulation, the thickness of the metal stripe h is assumed as 0.2 P, and the other parameters are same as those in the two-dimensional situation. A linearly polarized plane wave with the electric field along the x direction is used for excitation. As is shown in Fig. 4, a similar FE resonance achieved at the top surface of the antenna can be obtained from this finite, thick-stripe antenna, and surprisingly, the FE factor is even higher than that its two-dimensional counterpart, with the average FE factor of the second resonance as high as 50. This implies that the local electric field
Fig. 3. (a) Normalized SCS. (b) Average FE for the terahertz antennas with groove numbers N 5 and 7.
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OPTICS LETTERS / Vol. 40, No. 11 / June 1, 2015
have a significant impact on the applied research in the terahertz or microwave regimes.
Fig. 4.
Average FE, with a thickness of h 0.2 P.
intensity can be enhanced by three orders of magnitude. The ease of fabrication, together with the ultra-high FE, makes this stripe antenna an ideal platform for highsensitivity sensing applications in the terahertz and microwave regimes. Sharp resonances supported by SSP-based stripe antennas imply enhanced field-matter interactions and, thereby, new possibilities for improving environmental sensitivity and single-molecule detection in the terahertz regime. That is to say, the proposed SSP-based antennas with extreme FEs hold high potential in applications such as surface-enhanced terahertz absorption spectroscopy. Both the application scope and sensitivity of the conventional technique of terahertz time-domain spectroscopy will be improved substantially. In conclusion, we have shown that a corrugated metallic stripe with a few grooves can be utilized to realize novel SSP-based antennas that work in the terahertz regime. Resonances based on the retardation effect of the propagating SSP modes exhibit sharp, normalized scattering cross sections and enhanced average electric fields. Extremely sharp (high-order) SSP resonances associated with strongly confined and enhanced local fields, which have been identified and exploited in this work, provide new design perspectives for terahertzoriented metamaterials and sensing configurations. As a result, we believe that the proposed novel antennas will
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