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Wideband Circularly Polarized Vortex Surface Modes on Helically Grooved Metal Wires Volume 7, Number 6, December 2015 Hai-Zi Yao Shuncong Zhong

DOI: 10.1109/JPHOT.2015.2501165 1943-0655 Ó 2015 IEEE

IEEE Photonics Journal

Vortex Surface Modes on Grooved Metal Wires

Wideband Circularly Polarized Vortex Surface Modes on Helically Grooved Metal Wires Hai-Zi Yao1 and Shuncong Zhong1,2 1

Laboratory of Optics, Terahertz, and Non-Destructive Testing, School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China 2 Fujian Key Laboratory of Medical Instrument and Pharmaceutical Technology, Fuzhou 350108, China

DOI: 10.1109/JPHOT.2015.2501165 1943-0655 Ó 2015 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received October 14, 2015; revised November 4, 2015; accepted November 11, 2015. Date of current version November 25, 2015. This work was supported in part by the Fujian Provincial Excellent Young Scientist Fund under Grant 2014J07007, by the National Natural Science Foundation of China under Grant 51005077, by the Training Program of Fujian Excellent Talents in Universities, by the Specialized Research Fund for the Doctoral Program of Higher Education, the Chinese Ministry of Education under Grant 20133514110008, and by the Chinese Ministry of Health under Grant WKJ-FJ-27. Corresponding author: S. Zhong (e-mail: [email protected]).

Abstract: We report the characteristics of a right-handed helically grooved metal wire waveguide. For the helically grooved waveguide, the normal degenerate HE1 spoof surface plasmon polariton (SSPP) mode could be decomposed into two opposite circularly polarized modes, i.e., HE−1 and HE+1 SSPP modes, due to the chirality of helical grooves. The dispersion characteristics of the nondegenerate HE 1 SSPP modes were numerically obtained, and their spiral electromagnetic distributions were also presented. It was found that the HE 1 modes were circularly polarized; they were also vortex modes and possessed an orbit angular monument. In addition, the focusing characteristics of such waves near the waveguide end were investigated. The distinct advantages, such as a relatively long focusing length and the circular polarization of the chiral HE þ 1 SSPP modes, make the helically grooved metal wire waveguide a potential for near-field circular dichroism detection. Index Terms: Terahertz, spoof surface plasmon polaritons (SSPP), plasmonics.

1. Introduction The spoof surface plasmon polaritons (SSPP) wave, which mimics the real SPP on the flat metal surface in visible regime, is also the slow surface wave. The difference is that the SSPP wave is in the lower frequency regime, such as microwave and terahertz, and it is only supported by the corrugated metal surface [1], [2]. The terahertz (THz) SSPP wave is one of the hot research frontiers where confinement and enhancement of THz wave is needed for various engineering applications. The most promising one is to use the enhanced THz in biosensing field because many biomolecules have their unique vibrational frequency locating in the THz frequency region [3]–[6]. For improving the detecting limit and sensitivity of biosensing, more confined and enhanced THz radiation is better. The common strategy of simultaneously confining and enhancing THz wave is utilizing the SSPP metal waveguide. Several terahertz SSPP waveguide structures were proposed for achieving the goal, such as ultrathin planar plasmonic metamaterial [7], [8],

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metal surfaces textured by arrays of grooves or pillars [9]–[11], and so on. In addition to this plane structures, the cylindrical metal wire waveguide [12]–[14] supporting SSPP may be more useful in biosensing since it can be integrated into the apertureless terahertz near-field microscope [15]–[17] as the probe. However, all these waveguides above are concerning the linearly polarized wave. The characteristics of the linear polarization make these waveguides limited in some special applications, such as near-field terahertz circular dichroism detection. As we know, the spatial structures of many biomolecules such as enantiomer and DNA are chiral, and their chirality are directly related to their function. Therefore, it is very meaningful to use the THz spectrum technology to study the chirality of such chiral biomolecules. However, the chiral biomolecules only response differently to the circular polarizations of the excitation, i.e., chiral biomolecules have the different absorption to the left circularly polarized wave and the right circularly polarized wave that was called circular dichroism. Therefore, the highly circularly polarized THz wave is key to detecting the chirality and the related devices that can give rise to the circular polarized THz, especially the circularly polarized THz SSPP wave, is urgently needed. The motivation of the present work is to investigate a helical structure which possess the inherent chirality and to incorporate it with the cylindrical metal wire to realize an enhanced circularly polarized SSPP over a wide frequency band in THz spectrum. We first gave a brief theory about why the circular polarization is inherent of the normal SPP mode of cylindrical wire waveguide. Subsequently, we investigated the chiral characteristics of the proposed helically grooved metal wire waveguide [18], [19]. The degeneracy of the opposite circularly polarized SSPP modes on such waveguide were detailedly interpreted by analyzing their dispersion relations. Finally, the focusing characteristics of the circularly polarized SSPP wave leaving off the waveguide end was quantized to demonstrate its potential for near-field microscopy applications.

2. Theoretical Analysis It is well known that the normal SPP's wavefront of light on the metal cylinder moves parallel to the axis of the guide. Whereas, in fact, for the cylindrical metal wire waveguide, which is commonly treated in cylindrical coordinates, the so-called normal high mode such as HE1 mode is degenerated, and it is a superposition of two oppositely helical modes [20]. The helical modes are usually named as circularly polarized or helically polarized modes. Here, we call them as circularly polarized modes. For a cylindrical wire waveguide, due to the symmetry of geometry, there is no reason why one sense of circular polarization should be preferred to the other. Therefore, commonly, the two opposite circularly polarized wave, of the same frequency and having equal amplitudes, are traveling together in the same direction along the waveguide. Any one of the field components, whether for an E or H wave, can be written for the right-circularly polarized wave as [20] Sþ ¼ Kf ðr Þe jz e jm :

(1)

S ¼ Kf ðr Þe jz e jm

(2)

For the left-circularly polarized wave

where the choice of + or − sign depends on the values of the constant K , the radial function f , and the parity of m. Therefore, the composite wave Sþ þ S is S ¼ Kf ðr Þe jz ðejm ejm Þ

(3)

or S ¼ Kf ðr Þe


jz

cosðmÞ sinðmÞ

(4)

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Fig. 1. Right-handed helically grooved wire waveguide and its electromagnetic characteristics on the output plane. (a) The proposed waveguide is modeled by corrugating a cylindrical metal wire with a helix whose geometrical parameters are radius of cylinder, R ¼ 60 m radius of the circular section of helix, r ¼ 25 m, and pitch ¼ 100 m. An S-polarized (polarized perpendicular to the incident plane) Gaussian beam with frequency of f0 ¼ 1:3 THz is impinging on one end to excite the SSPP wave. (b)–(d) are the distribution on the output plane (10 m away from the end) of electric field Ez and phase of Ez and circular polarization degree C, respectively. The black circles in panel (c) indicate the cross section of the wire. Note that the figures are viewed against the propagation direction.

which is definitely the normal HE mode of the cylindrical waveguide found by the treatment in cylindrical coordinates. This clearly demonstrates the degeneracy of the normal HE modes on a cylindrical metal wire waveguide, i.e., each HE mode is a combination of two opposite circularlypolarized modes. For obtaining the circular polarization, only one constituent of such degenerated HE mode is needed. In the present work, we only discuss the first-order high mode, i.e., HE1 mode. To separate the co-existed helical modes, i.e., HE+1 and HE−1, we proposed a helically grooved metal wire as waveguide in which the azimuthal symmetry is broken. Noted that the terahertz helically grooved metal-wire waveguide was firstly proposed by Fernández-Domínguez's group [18], [19]. In the present work, we validated the vortical electromagnetic distribution of such chiral SPP waves on helically grooved metal wire and revealed that it possess an orbit angular momentum (OAM) by displaying its spiral phase distribution. Besides, we uncovered that the non-degenerate HE+1(HE−1) mode has intrinsic circular polarization and it can be supported in wide band. Moreover, we demonstrated its potential for the near-field circular dichroism detection by quantizing its relatively long focal length and small focal spot of the circular polarized HE+1 wave leading away from the end of the waveguide. The geometry of helically grooved metal wire waveguide is illustrated in Fig. 1(a). It consists of a metal wire of radius R, corrugated by a right-handed helix with a pitch and cross section radius r, forming the helical grooves on the surface of the metal wire. To demonstrate the coupling of SSPP modes, we used the finite-difference-time-domain (FDTD) method (using XFDTD 7.3.0 software, Remcom Inc.) to simulate the propagation of THz wave on such a waveguide. A linearly polarized monochromatic Gaussian beam, with a frequency of f0 ¼ 1:3 THz and a waist size equal to the diameter of the wire, was normally incident on one end of the helically grooved wire with beam focus at the central axis. The polarization direction of the incident is


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Fig. 2. Dispersion relation curves of the SSPP modes supported on the right-handed helically grooved wire waveguide. (Insets) Cross-sections of eigen modes for HE+1 mode and TM0 mode at ¼ 0:96=. The horizontal dashed lines are to denote the circular polarization band in which the circularly polarized HE+1 mode exists exclusively.

perpendicular to the incident plane. In the FDTD simulation, the parameters of R, r , and were set to 60 m, 25 m, and 100 m, respectively. The material of the geometry was modeled by perfect electric conductor. The waveguide surrounding is supposed to be cladded by the air. The grid cell were set to 5 m uniformly in the calculation domain and the perfectly matched layers (PML) were used to truncate the calculated domain.

3. Simulation Results and Discussions The instantaneous electric filed Ez at the output plane (10 m away from the output end) is displayed in Fig. 1(b). The counter-clockwise spiral distribution demonstrate that it is obviously a helical mode, HE+1. Note that the figures are viewed against the propagating direction. The reason for this phenomenon is that the break of azimuthal symmetry leads to the degeneracy of HE1 modes broken. As a result, the right-handed and the left-handed components are decomposed into two helical SSPP modes rotating in opposite directions. As shown in Fig. 2, the effect of symmetry-break is observed more clearly from the dispersion relation of eigen modes obtained by using RF module of COMSOL Multiphysics 5.0 software. It is obvious that the primary degenerated HE1 mode split into two separated curves denoted by HE−1 and HE+1 modes due to the introduced chirality of helical grooves; moreover, in contrast, a new degeneracy between HE−1 mode and fundamental TM0 mode emerges at the band edge. A further look shows that the divergence between the dispersion curves of HE−1 and HE+1 modes just generate a broad frequency band, within which the HE+1 circularly polarized mode can exists exclusively. This band is denoted by the horizontal dashed lines. As the chiral pattern, the term ejm (m ¼ 1 for the HE1 mode) in (1) implies that the HE+1 SSPP should has orbit angular momentum (OAM) [18]. The phase distribution of Ez is displayed in Fig. 1(c). It can be seen that the Ez phase accumulates from 0 to 2 along the circle around the axis, suggesting the non-degenerated HE+1 is indeed a vortex mode [21], [22]. This propagating vortex mode may be useful in optical spanner [23], [24]. To elucidate polarization of the HE+1 SSPP wave, we mapped the circular polarization degree C on the output plane shown in Fig. 1(d). The circular polarization degree C is defined as [25] C¼


2Ex Ey sinðx y Þ Ex2 þ Ey2 þ Ez2

(5)

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Fig. 3. Scattering distribution of the exiting THz wave near the end. (a) Z -directional time-averaged cross-section electromagnetic power flow of HE+1 mode at 1.3 THz, displayed in linear scale. (Inset) TM0 mode at 0.3 THz, shown in logarithmic scale. The overlaid graphs show the spatial distribution of the normalized electric field intensity along the horizontal centerline and the vertical line at the focus. (b) A whole view of Z -directional time-averaged power flow of HE+1 on the helically grooved waveguide displayed in logarithmic scale. Note that we applied independent intensity color scales to each of the graphs.

where Ex ðEy Þ; Ez are the transverse and longitudinal electric field components, respectively; and is the corresponding phase. It is clear that without the “entanglement” from the opposite mode, i.e., HE−1 mode, a good right-circular polarization is obtained for HE+1 wave even on the plane 10 m away from the waveguide end. The imperfect is due to the scattering at the irregular distal end. The circular polarization originates from the rotational properties of the HE+1 mode. Such purity of circular polarization is also because there is only HE+1 mode at 1.3 THz. It is worth stressing that the characteristics of circular polarization apply to the broad frequency band of ∼0.15 THz denoted by the dashed lines in Fig. 2 because in which the theoretical circularly-polarized HE+1 mode can exist exclusively. In other words, using the proposed device we could obtain a broadband circularly polarized THz wave. The bandwidth is mainly determined by the degree of the structure chirality, therefore it can be broadened by properly increasing the groove's depth and the helical lead angle. Note that if the working frequency is out the range of the circularpolarization band, the propagating wave will be mixed with other SSPP mode (e.g., TM mode or HE−1 mode), and thus, the pure circular polarization will get destroyed. Readers can find the details regarding the evolution of polarization for different frequencies wave propagating on such waveguide in [28]. For the practical application of such a structure as a scanning nearfield optical microscopy (SNOM) probe, the scattering of the propagating wave at the output end must be considered because it directly influence the interaction efficiency with the sample. For a clear show of the scattering characteristics, the Z -directional time-averaged power flow in the vicinity of output end was given in Fig. 3(a). It is surprising found that the exiting THz wave of HE+1 mode is not scattered off but focused after exiting the end. That contrasts with the behavior of fundamental TM0 mode in metal wire waveguide [26], [27] in which the exiting wave is scattered into conical shape by the edge of the end facet. The conical scattering of TM0 mode at 0.3 THz is also verified in our structure, shown as the inset in Fig. 3(a). Fig. 3(b) gives a whole view of Z -directional time-averaged power flow of HE+1 mode on the helically grooved waveguide. Note that the results in Fig. 3(a) are displayed in linear scale, whereas the inset and Fig. 3(b) are displayed in logarithmic scale.


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The overlaid graphs in Fig. 3(a) show the spatial distribution of the normalized intensity along the horizontal centerline and the vertical line at the focus. From the overlaid graphs, the measured focal diameter, described as the full width at half maximum (FWHM), is approximately 150 m; also, the longitudinal focusing length, defined as the distance over which the maximum intensity decay to 1=e, is about 625 m. These distinct advantages of relatively long focusing length and sub-wavelength focus make this structure potential for being applied in THz near-field microscopy. It is highlighted that the introduced chirality of helical grooves has a great effect on chirality of the supporting SSPP modes by breaking up the normal HE1 mode into two opposite circularlypolarized modes, HE+1 and HE−1 modes. More intuitively, the introduced chirality of the waveguide suppresses one intrinsic circularly-polarized mode with the opposite chirality. This suppressing effect is demonstrated in the affected dispersion relations that the opponent mode's dispersion curve is suppressed and eventually degenerates with the lower mode at the first Brillouin region boundary. Although all the mentioned figures are considering the HE+1 mode, it can be inferred that the opponent mode, i.e., HE−1 mode, has an opposite direction on rotation and polarization. It is mentioned that the excited HE−1 mode is always accompanied by the TM0 mode because the working frequency covers both dispersion curves of the two modes; thus, the distribution of the electromagnetic field and polarization degrees for the frequencies outside the circular polarization band behave complicated [28]. It is worth stressing that the desired frequency can be controlled by adjusting the geometry size of the structure. Moreover, according to reciprocal theory, we can also obtain an almost perfectly left-circularly polarized THz wave using a left-handed helically grooved metal wire waveguide in the same way. By integrating the time-averaged power flow on the output facet, the calculated power ratio between the output circular polarized wave and the input THz wave is approximately 1.1% for the case of 1.3 THz. Although the coupling efficiency is relatively low, it may be improved by optimizing the incident angle and illumination spot size. Besides, the surface geometry at the end of the waveguide can be tailored to optimize the focusing characteristics, e.g., a gradient helical grooves decorated on the conical metal wire can be used to generate a smaller focal spot in the vicinity of waveguide end [14]. A decorated helical-grooves structure with smooth transition into circular ring grooves at the waveguide end, may be helpful for obtaining a longer focusing length. We believe that modern nano-fabrication technique, such as direct laser writing [29], could put forward the proposed micron-sized 3-D helical structure into reality.

4. Conclusion In summary, we analyzed and characterized a right-handed helically grooved metal wire as a waveguide device at terahertz frequency region. Due to the symmetry break introduced by the helical grooves, the primal degenerated HE1 SSPP mode breaks up into a right-circularly polarized mode, HE+1, and a left-circularly polarized mode, HE−1. The divarication between dispersion curves of these two opposite modes generate a broad circular-polarization band. The distinct advantages of the chiral HE+1 mode include almost perfect circular polarization, the sub-wavelength focus, and the relatively long focusing length, making this the helically grooved metal wire potential in near-field circular dichroism detection, for instance, utilized as a point source of the circular polarized Terahertz wave.

Acknowledgment The authors thank Dr. Y. Shen (University of Liverpool, UK), L. Lin, J. Zhong, and Q. Zhang for useful discussions.

References [1] F. Garcia-Vidal, L. Martin-Moreno, and J. Pendry, “Surfaces with holes in them: New plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt., vol. 7, no. 2, pp. S97–S101, 2005. [2] J. Pendry, L. Martin-Moreno, and F. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science, vol. 305, no. 5685, pp. 847–848, Aug. 2004.


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[3] J.-H. Son, Terahertz Biomedical Science and Technology. Boca Raton, FL, USA: CRC, 2014. [4] E. Pickwell-MacPherson and V. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D, Appl. Phys., vol. 39, no. 17, Aug. 2006, Art. ID R301. [5] M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers, vol. 67, no. 4/5, pp. 310–313, 2002. [6] B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol., vol. 47, no. 21, pp. 3807–3814, Nov. 2002. [7] X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Nat. Acad. Sci., vol. 110, no. 1, pp. 40–45, Jan. 2013. [8] X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett., vol. 102, no. 21, May 2013, Art. ID 211909. [9] Z. Gao, L. Shen, J.-J. Wu, T.-J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun., vol. 285, no. 8, pp. 2076–2080, Apr. 2012. [10] A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” Appl. Phys. A, vol. 100, no. 2, pp. 375–378, Aug. 2010. [11] F. M. Zhu, Y. Y. Zhang, L. F. Shen, and Z. Gao, “Subwavelength guiding of terahertz radiation by shallowly corrugated metal surfaces,” J. Electromagn. Waves Appl., vol. 26, no. 1, pp. 120–129, 2012. [12] L. Shen, X. Chen, Y. Zhong, and K. Agarwal, “Effect of absorption on terahertz surface plasmon polaritons propagating along periodically corrugated metal wires,” Phys. Rev. B, vol. 77, no. 7, Feb. 2008, Art. ID 075408. [13] A. Fernández-Domínguez, L. Martín-Moreno, F. García-Vidal, S. R. Andrews, and S. Maier, “Spoof surface plasmon polariton modes propagating along periodically corrugated wires,” IEEE J. Sel. Topics Quantum Electron., vol. 14, no. 6, pp. 1515–1521, Nov./Dec. 2008. [14] S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., vol. 97, no. 17, Oct. 2006, Art. ID 176805. [15] R. Kersting, F. F. Buersgens, G. Acuna, and G. C. Cho, “Terahertz near-field microscopy,” Adv. Solid State Phys., vol. 47, pp. 203–222, 2008. [16] G. C. Cho, H.-T. Chen, S. Kraatz, N. Karpowicz, and R. Kersting, “Apertureless terahertz near-field microscopy,” Semicond. Sci. Technol., vol. 20, no. 7, 2005, Art. ID S286. [17] Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett., vol. 19, no. 3, pp. 159–161, Feb. 1994. [18] F. Rüting, A. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Subwavelength chiral surface plasmons that carry tuneable orbital angular momentum,” Phys. Rev. B, vol. 86, no. 7, Aug. 2012, Art. ID 075437. [19] A. I. Fernandez-Dominguez et al., “Terahertz surface plasmon polaritons on a helically grooved wire,” Appl. Phys. Lett., vol. 93, no. 14, Oct. 2008, Art. ID 141109. [20] R. Waldron, “A helical coordinate system and its applications in electromagnetic theory,” Quart. J. Mech. Appl. Math., vol. 11, no. 4, pp. 438–461, Jan. 1958. [21] D. L. Andrews, Structured Light and its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces. San Diego, CA, USA: Academic, 2011. [22] M. Soskin and M. Vasnetsov, “Singular optics,” Progr. Opt., vol. 42, no. 4, pp. 219–276, 2001. [23] M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon., vol. 5, no. 6, pp. 343–348, Jun. 2011. [24] N. Simpson, K. Dholakia, L. Allen, and M. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner,” Opt. Lett., vol. 22, no. 1, pp. 52–54, Jan. 1997. [25] P. Biagioni, J. S. Huang, L. Duo, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett., vol. 102, no. 25, Jun. 2009, Art. ID 256801. [26] S. Al-Bader and H. Jamid, “Diffraction of surface plasmon modes on abruptly terminated metallic nanowires,” Phys. Rev. B, vol. 76, no. 23, Dec. 2007, Art. ID 235410. [27] J. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” Proc. IEEE, vol. 95, no. 8, pp. 1624–1640, Aug. 2007. [28] H.-Z. Yao and S. Zhong, “Frequency-dependent circular-polarization of terahertz chiral spoof surface plasmon polariton on helically grooved metallic wire,” Opt. Commun., vol. 354, pp. 401–406, Nov. 2015. [29] J. K. Gansel et al., “Gold helix photonic metamaterial as broadband circular polarizer,” Science, vol. 325, no. 5947, pp. 1513–1515, Sep. 2009.


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