Artificial TE-mode surface waves at metal surfaces mimicking surface plasmons Zhijun Sun,* Xiaoliu Zuo, Tengpeng Guan, and Wei Chen Department of Physics, Xiamen University, Xiamen, Fujian 361005, China * [email protected]
Abstract: Manipulation of light in subwavelength scale can be realized with metallic nanostructures for TM-polarization components due to excitation of surface plasmons. TE-polarization components of light are usually excluded in subwavelength metal structures for mesoscopic optical interactions. Here we show that, by introducing very thin high index dielectric layers on structured metal surfaces, pseudo surface polarization currents can be induced near metal surfaces, which bring to excitation of artificial TE-mode surface waves at the composite meta-surfaces. This provides us a way to manipulate TE-polarized light in subwavelength scale. Typical properties of the artificial surface waves are further demonstrate for their excitation, propagation, optical transmission, and enhancement and resonances of the localized fields, mimicking those of surface plasmon waves. ©2014 Optical Society of America OCIS codes: (240.6690) Surface waves; (050.6624) Subwavelength structures; (260.3910) Metal optics; (260.5430) Polarization.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824– 830 (2003). H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer, 1988). S. I. Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford, 2009). D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). M. T. Flanagan and R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20(23), 968–970 (1984). R. J. Green, R. A. Frazier, K. M. Shakesheff, M. C. Davies, C. J. Roberts, and S. J. Tendler, “Surface plasmon resonance analysis of dynamic biological interactions with biomaterials,” Biomaterials 21(18), 1823–1835 (2000). S. Kawata, ed., Near Field Optics and Surface Plasmon Polaritons (Springer, 2001). N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U. S. A. 100(23), 13549–13554 (2003). R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277(1), 61–64 (2000). B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). F. García de Abajo and J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005). R. Sainidou and F. J. Garcia de Abajo, “Plasmon guided modes in nanoparticle metamaterials,” Opt. Express 16(7), 4499–4506 (2008). I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974). A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14(4), 1347–1361 (1976). C. Ciracì, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for plasmonics: a macroscopic approach to a microscopic problem,” ChemPhysChem 14(6), 1109–1116 (2013).
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4714
19. C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B 26(12), 7008–7011 (1982). 20. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). 21. N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010). 22. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). 23. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999). 24. Z. Sun, Y. S. Jung, and H. K. Kim, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83(15), 3021–3023 (2003). 25. Z. Sun and X. Zuo, “Tuning resonant optical transmission of metallic nanoslit arrays with embedded microcavities,” Opt. Lett. 34(9), 1411–1413 (2009). 26. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002). 27. Y. J. Chen, E. S. Koteles, R. J. Seymour, G. J. Sonek, and J. M. Ballantyne, “Surface plasmon on gratings: coupling in the minigap regions,” Solid State Commun. 46(2), 95–99 (1983). 28. D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987). 29. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmonics: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006). 30. M. Guillaumée, A. Y. Nikitin, M. J. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. GarcíaVidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010). 31. I. Schwarz, N. Livneh, and R. Rapaport, “General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations,” Opt. Express 20(1), 426–439 (2012). 32. K. C. Balram and D. A. B. Miller, “Self-aligned silicon fins in metallic slits as a platform for planar wavelengthselective nanoscale resonant photodetectors,” Opt. Express 20(20), 22735–22742 (2012). 33. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1976). 34. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072– 1074 (2012). 35. A. E. Miroshnichenko, W. Liu, D. Neshev, Y. S. Kivshar, A. I. Kuznetsov, Y. H. Fu, and B. Luk’yanchuk, “Magnetic light: optical magnetism of dielectric nanoparticles,” Opt. Photonics News 23(12), 35 (2012). 36. N. Noginova, Y. Barnakov, H. Li, and M. A. Noginov, “Effect of metallic surface on electric dipole and magnetic dipole emission transitions in Eu3+ doped polymeric film,” Opt. Express 17(13), 10767–10772 (2009). 37. S. Karaveli and R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). 38. S. Peng, C. Lei, Y. Ren, R. E. Cook, and Y. Sun, “Plasmonic/magnetic bifunctional nanoparticles,” Angew. Chem. Int. Ed. Engl. 50(14), 3158–3163 (2011).
1. Introduction Metallic nanostructures can be used to manipulate light in the subwavelength scale due to excitation of surface plasmons (SPs) [1], a surface wave associated with collective oscillation of free electrons in metals [2]. This opens an avenue to developing plasmonic devices for ultra-compact photonic integration [3] and artificial metamaterials possessing optical properties unavailable from natural materials [4,5]. Besides, intrinsic near-field properties of SPs bring a variety of applications in diagnosis bio-sensing [6,7], super-resolution imaging [8,9] and photodynamic cancer cell treatment [10], etc.. SP waves are TM waves, i.e., the magnetic field is always perpendicular to the wave propagation direction, and can be optically excited in metallic nanostructures with only TM-polarization component of the incidence light, which is usually defined with respect to the structure and can be considered as that magnetic fields of the incidence light and excited SP waves are in parallel. Generally, a surface mode with evanescent distribution of its field in the transverse direction is essential for a wave to be confined in a subwavelength scale to propagate and oscillate. But for TE-polarization components, orthogonal to the TM-polarization components, of the incidence waves, no surface wave mode exists in nanostructures composed of ordinary metal and dielectric materials. Though metamaterials with negative magnetic permeability may be designed to support artificial TE-mode surface waves [11–15], realization is difficult especially in the optical regime. In this paper, we propose a simple way to modify the surface of metal structures such that TE-polarized incidence light can excite SP-like artificial surface
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4715
waves to propagate at metal surfaces, thus TE-polarized light can also be manipulated in metallic nanostructures. The concept is schematically illustrated in Fig. 1. The modification is to introduce a very thin high-index dielectric (HID) layer on the metal surface to form a metal-dielectric-air (MDA) composite “meta-surface”. 2. Construction of the TE-mode artificial surface waves In comparison, it is known that, for TM-polarization fields at a metal surface [Fig. 1(a)], there is a discontinuity of the electric fields in the surface normal direction on both sides. Hence surface polarization charges of density σ e = ε 0 ( E2 n − E1n ) are induced to support electric SPs. While the magnetic field is only in the y-direction in the case and continuous at the interface for nonmagnetic media, surface polarization current density α m = 0 ; thus there is no existence of a magnetic surface wave mode.
Fig. 1. (a, b) Schematic boundary conditions for TM- and TE-polarization fields at a metal surface. (c) Tangential magnetic field (Hz) at a meta-surface of metal with surface polarization currents. (d, e) Illustrations of the fields and polarization charges or currents for SPs at a MA surface (d) and the artificial ASWs at a MDA surface (e). (f) Dispersion curve of the artificial ASWs at a MDA surface, in comparison with that of the SPs at a MA surface. (g, h) Quasievanescent distributions of the ASW fields (Hz and Ey) at a MDA surface
For TE-polarization fields at a metal surface, usually the electric field is null in the surface normal direction, and the tangential magnetic fields are continuous. Therefore σ e = α m = 0 , neither type of the electromagnetic (EM) surface wave modes can exist. But if we can introduce a meta-surface of the metal such that surface polarization currents are induced ( α m′ ≠ 0 ) [Fig. 1(b)], there will be a discontinuity of the tangential magnetic field (Ht or Hz) at the meta-surface with opposite sign [Fig. 1(c)], i.e., α m′ = H 2 t − H1t ; and vice versa. Then existence of a magnetic surface wave mode becomes possible. It’s known in electromagnetics that bound current density J b = ∇ × M + ∂P ∂t . As the magnetization field M = 0 for nonmagnetic media, an ultra-thin dielectric layer can be introduced at the metal surface, in which ∂P ∂t ≠ 0 for a time-varying polarization field, to bring in a pseudo surface polarization current, ∂P α m′ = ΔH t′ = y td (1) ∂t
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4716
where Py is the mean transverse polarization field, Py = ε 0 ( ε d − 1) E y , in the dielectric layer of relative permittivity ε d and thickness td. As the pseudo surface polarization currents oscillate harmonically with the fields in time and space, an artificial surface wave (ASW) mode is thus formed at the MDA meta-surface, which is schematically illustrated in Fig. 1(e), similar to oscillations of the surface charges and fields of SP waves at a MA surface [Fig. 1(d)]. Here it is shown that, only for dielectric materials of high indices (large ε d ), we can have td
Abstract: Manipulation of light in subwavelength scale can be realized with metallic nanostructures for TM-polarization components due to excitation of surface plasmons. TE-polarization components of light are usually excluded in subwavelength metal structures for mesoscopic optical interactions. Here we show that, by introducing very thin high index dielectric layers on structured metal surfaces, pseudo surface polarization currents can be induced near metal surfaces, which bring to excitation of artificial TE-mode surface waves at the composite meta-surfaces. This provides us a way to manipulate TE-polarized light in subwavelength scale. Typical properties of the artificial surface waves are further demonstrate for their excitation, propagation, optical transmission, and enhancement and resonances of the localized fields, mimicking those of surface plasmon waves. ©2014 Optical Society of America OCIS codes: (240.6690) Surface waves; (050.6624) Subwavelength structures; (260.3910) Metal optics; (260.5430) Polarization.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824– 830 (2003). H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer, 1988). S. I. Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford, 2009). D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). M. T. Flanagan and R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20(23), 968–970 (1984). R. J. Green, R. A. Frazier, K. M. Shakesheff, M. C. Davies, C. J. Roberts, and S. J. Tendler, “Surface plasmon resonance analysis of dynamic biological interactions with biomaterials,” Biomaterials 21(18), 1823–1835 (2000). S. Kawata, ed., Near Field Optics and Surface Plasmon Polaritons (Springer, 2001). N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U. S. A. 100(23), 13549–13554 (2003). R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277(1), 61–64 (2000). B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). F. García de Abajo and J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005). R. Sainidou and F. J. Garcia de Abajo, “Plasmon guided modes in nanoparticle metamaterials,” Opt. Express 16(7), 4499–4506 (2008). I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974). A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14(4), 1347–1361 (1976). C. Ciracì, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for plasmonics: a macroscopic approach to a microscopic problem,” ChemPhysChem 14(6), 1109–1116 (2013).
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4714
19. C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B 26(12), 7008–7011 (1982). 20. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). 21. N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010). 22. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). 23. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999). 24. Z. Sun, Y. S. Jung, and H. K. Kim, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83(15), 3021–3023 (2003). 25. Z. Sun and X. Zuo, “Tuning resonant optical transmission of metallic nanoslit arrays with embedded microcavities,” Opt. Lett. 34(9), 1411–1413 (2009). 26. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002). 27. Y. J. Chen, E. S. Koteles, R. J. Seymour, G. J. Sonek, and J. M. Ballantyne, “Surface plasmon on gratings: coupling in the minigap regions,” Solid State Commun. 46(2), 95–99 (1983). 28. D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987). 29. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmonics: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006). 30. M. Guillaumée, A. Y. Nikitin, M. J. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. GarcíaVidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010). 31. I. Schwarz, N. Livneh, and R. Rapaport, “General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations,” Opt. Express 20(1), 426–439 (2012). 32. K. C. Balram and D. A. B. Miller, “Self-aligned silicon fins in metallic slits as a platform for planar wavelengthselective nanoscale resonant photodetectors,” Opt. Express 20(20), 22735–22742 (2012). 33. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1976). 34. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072– 1074 (2012). 35. A. E. Miroshnichenko, W. Liu, D. Neshev, Y. S. Kivshar, A. I. Kuznetsov, Y. H. Fu, and B. Luk’yanchuk, “Magnetic light: optical magnetism of dielectric nanoparticles,” Opt. Photonics News 23(12), 35 (2012). 36. N. Noginova, Y. Barnakov, H. Li, and M. A. Noginov, “Effect of metallic surface on electric dipole and magnetic dipole emission transitions in Eu3+ doped polymeric film,” Opt. Express 17(13), 10767–10772 (2009). 37. S. Karaveli and R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). 38. S. Peng, C. Lei, Y. Ren, R. E. Cook, and Y. Sun, “Plasmonic/magnetic bifunctional nanoparticles,” Angew. Chem. Int. Ed. Engl. 50(14), 3158–3163 (2011).
1. Introduction Metallic nanostructures can be used to manipulate light in the subwavelength scale due to excitation of surface plasmons (SPs) [1], a surface wave associated with collective oscillation of free electrons in metals [2]. This opens an avenue to developing plasmonic devices for ultra-compact photonic integration [3] and artificial metamaterials possessing optical properties unavailable from natural materials [4,5]. Besides, intrinsic near-field properties of SPs bring a variety of applications in diagnosis bio-sensing [6,7], super-resolution imaging [8,9] and photodynamic cancer cell treatment [10], etc.. SP waves are TM waves, i.e., the magnetic field is always perpendicular to the wave propagation direction, and can be optically excited in metallic nanostructures with only TM-polarization component of the incidence light, which is usually defined with respect to the structure and can be considered as that magnetic fields of the incidence light and excited SP waves are in parallel. Generally, a surface mode with evanescent distribution of its field in the transverse direction is essential for a wave to be confined in a subwavelength scale to propagate and oscillate. But for TE-polarization components, orthogonal to the TM-polarization components, of the incidence waves, no surface wave mode exists in nanostructures composed of ordinary metal and dielectric materials. Though metamaterials with negative magnetic permeability may be designed to support artificial TE-mode surface waves [11–15], realization is difficult especially in the optical regime. In this paper, we propose a simple way to modify the surface of metal structures such that TE-polarized incidence light can excite SP-like artificial surface
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4715
waves to propagate at metal surfaces, thus TE-polarized light can also be manipulated in metallic nanostructures. The concept is schematically illustrated in Fig. 1. The modification is to introduce a very thin high-index dielectric (HID) layer on the metal surface to form a metal-dielectric-air (MDA) composite “meta-surface”. 2. Construction of the TE-mode artificial surface waves In comparison, it is known that, for TM-polarization fields at a metal surface [Fig. 1(a)], there is a discontinuity of the electric fields in the surface normal direction on both sides. Hence surface polarization charges of density σ e = ε 0 ( E2 n − E1n ) are induced to support electric SPs. While the magnetic field is only in the y-direction in the case and continuous at the interface for nonmagnetic media, surface polarization current density α m = 0 ; thus there is no existence of a magnetic surface wave mode.
Fig. 1. (a, b) Schematic boundary conditions for TM- and TE-polarization fields at a metal surface. (c) Tangential magnetic field (Hz) at a meta-surface of metal with surface polarization currents. (d, e) Illustrations of the fields and polarization charges or currents for SPs at a MA surface (d) and the artificial ASWs at a MDA surface (e). (f) Dispersion curve of the artificial ASWs at a MDA surface, in comparison with that of the SPs at a MA surface. (g, h) Quasievanescent distributions of the ASW fields (Hz and Ey) at a MDA surface
For TE-polarization fields at a metal surface, usually the electric field is null in the surface normal direction, and the tangential magnetic fields are continuous. Therefore σ e = α m = 0 , neither type of the electromagnetic (EM) surface wave modes can exist. But if we can introduce a meta-surface of the metal such that surface polarization currents are induced ( α m′ ≠ 0 ) [Fig. 1(b)], there will be a discontinuity of the tangential magnetic field (Ht or Hz) at the meta-surface with opposite sign [Fig. 1(c)], i.e., α m′ = H 2 t − H1t ; and vice versa. Then existence of a magnetic surface wave mode becomes possible. It’s known in electromagnetics that bound current density J b = ∇ × M + ∂P ∂t . As the magnetization field M = 0 for nonmagnetic media, an ultra-thin dielectric layer can be introduced at the metal surface, in which ∂P ∂t ≠ 0 for a time-varying polarization field, to bring in a pseudo surface polarization current, ∂P α m′ = ΔH t′ = y td (1) ∂t
#199364 - $15.00 USD (C) 2014 OSA
Received 14 Oct 2013; revised 14 Feb 2014; accepted 16 Feb 2014; published 21 Feb 2014 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004714 | OPTICS EXPRESS 4716
where Py is the mean transverse polarization field, Py = ε 0 ( ε d − 1) E y , in the dielectric layer of relative permittivity ε d and thickness td. As the pseudo surface polarization currents oscillate harmonically with the fields in time and space, an artificial surface wave (ASW) mode is thus formed at the MDA meta-surface, which is schematically illustrated in Fig. 1(e), similar to oscillations of the surface charges and fields of SP waves at a MA surface [Fig. 1(d)]. Here it is shown that, only for dielectric materials of high indices (large ε d ), we can have td
