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Nearly perfect resonant absorption of TE-polarized light at metal surfaces coated with arrayed dielectric stripes Zhijun Sun,* Wei Chen, and Ling Guo Department of Physics, Xiamen University, Xiamen 361005, China *Corresponding author: [email protected] Received February 25, 2014; revised March 27, 2014; accepted March 29, 2014; posted April 1, 2014 (Doc. ID 207051); published April 22, 2014 A quasi-transverse electric (TE) surface wave mode exists at a metal surface coated with an ultrathin high-index dielectric layer. As the coating is in dielectric stripe arrays, nearly perfect absorption of TE-polarized incidence light is observed in simulations, due to resonances of the quasi-surface waves at each segment of the dielectric-coated metal surfaces. In analysis, the Fabry–Perot-like nature of the resonances is clarified, and effects of symmetry on different behaviors of the odd- and even-order resonance modes are discussed. While the absorption peak is tunable, perfect absorption appears near cut-off wavelength of the surface mode. © 2014 Optical Society of America OCIS codes: (240.6690) Surface waves; (050.6624) Subwavelength structures; (260.5740) Resonance; (260.3910) Metal optics. http://dx.doi.org/10.1364/OL.39.002637
Confinement and manipulation of light in the subwavelength scale are usually implemented with metallic microstructures/nanostructures via excitation of surface plasmons (SPs). Anomalous spectral properties in transmission, reflection, and absorption [1–6], arising from near-field SP behaviors, can thus be designed, which has attracted much attention for applications in biosensing [7,8], photovoltaics [9], nanolensing [10,11], light emitting [12,13], etc. As SPs are excited at metal surfaces with only the transverse-magnetic (TM) component of the light, the transverse-electric (TE) component of the light is usually excluded in subwavelength optical interactions. To overcome this limitation, we propose building a quasi-TE surface wave mode by introducing an ultrathin high-index dielectric (HID) layer on the metal surface, such that TE-polarized light also becomes capable of interacting with metallic microstructures/ nanostructures at the mesoscopic level [14]. Previously, nearly null reflection (or enhanced absorption) of light on metal surfaces with dielectricinterspaced metal nanostructures has been reported and widely studied [15–19]. The phenomenon is generally explained due to resonances of SPs confined within each unit of the metallic nanostructures. In this Letter, we show that resonances of the confined quasi-TE surface waves at each segment of the HID-coated metal surfaces can also result in nearly perfect absorption of TE-polarized light. Compared to some literature reports on absorption of TE-polarized light in metallic gratings [20], our absorption mechanism is based on resonances of the quasi-TE surface wave, instead of the resonant cavity modes of guided waves in wide and deep grating grooves. Figure 1(a) schematically illustrates the structure under investigation. The incidence light is TE polarized with its electric field parallel to the direction of the HID stripes. In this case, no SP waves can be excited, and the incidence light is usually highly reflected, without diffractions in the subwavelength regime (p < λ). Using numerical simulations based on the finite-difference time-domain method, we show in Fig. 1(b) the reflection 0146-9592/14/092637-04$15.00/0
spectrum of such a metal (Ag) surface, with HID stripes of index nd 4, thickness td 20 nm, period p 400 nm, and stripe width w 340 nm, under normal incidence of TE-polarized light. Strikingly among its unusual characteristics in the spectrum, a dip with extremely low reflectance (R 5 × 10−5 ) is observed at λ 477.7 nm, indicating a perfect absorption (A 1 − R) of the incidence light, besides two other dips locating at λ 612 and 363.3 nm. In the following analysis, the three reflection minima are ascribed to the zeroth-, second-, and fourth-order horizontally oscillating resonances of the quasi-TE surface waves along individual segments of the HID stripes on the metal surface. For comparison, the reflection spectrum of the metal surface with a continuous HID layer is also plotted in Fig. 1(b),
Fig. 1. (a) Schematic illustration of the metal surface coated with arrayed dielectric stripes upon incidence of TE-polarized light. (b) Reflection spectrum of the structure (nd 4, td 20 nm, p 400 nm, w 340 nm), in comparison with that of the metal surface with the dielectric layer being continuous. © 2014 Optical Society of America
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showing a minimum at λ 642 nm. In this case, only multiple interferences in the vertical direction exist in the HID layer, and Fabry–Perot resonances take place at the minimum. Considering proximity of the minima at λ 612 nm and λ 642 nm for the two curves in Fig. 1(b), they are of the same nature, as horizontal confinement of the zeroth-order resonance in the stripe regions is very weak; the HID stripe layer can be considered an effective dielectric layer in the subwavelength regime. In analysis, we first give a brief introduction of the quasi-TE surface wave. It is known that TE waveguiding modes may exist in a dielectric layer on a metal surface [21], i.e., a metal–dielectric–air (MDA) structure. And cut-off thicknesses exist, even for the lowest order waveguide mode. Usually, for relatively low index dielectrics, the dielectric layer has to be thick enough, and distributions of the mode field spread like those in a conventional dielectric waveguide. However, if the dielectric layer has a high index, its thickness can be largely reduced to a nanoscale. Thus the fundamental TE mode (TE0) comes to have a quasi-evanescent transverse distribution of the transverse electric field (E y ), as shown in Fig. 2(a). This is similar to the distribution of TM field (H y ) of a TMpolarized SP mode. As such, we consider it a quasisurface-wave, locating at a HID coated metasurface of metal. Also, the quasi-TE quasi-surface wave is shown to be magnetic, as pseudo surface polarization currents are induced, accompanied with discontinuity of the tangential magnetic field across the metasurface [14]. In Fig. 2(b), normalized complex propagation constants β∕k0 ; k0 2π∕λ0 , or effective indices (N eff β∕k0 ), of the quasi-TE surface wave mode, calculated with the dispersion relation in Ref. [14], are plotted as functions of the wavelength for nd 4 of the HID layer, in comparison with those for a lower index of nd 2. For a given set of nd ; td , a cut-off wavelength is clearly indicated, e.g., at around λ 630 nm for nd 4 and td 20 nm; i.e., the quasi-surface wave exists only below
Fig. 2. (a) Illustration of the formation of the quasi-TE surface wave at a MDA surface. The bottom graph is plotted for nd 4, td 20 nm at λ 500 nm. (b) Real (solid line) and imaginary (dashed line) parts of the normalized propagation constants of the quasi-surface waves at MDA surfaces. (c)–(e) Dependences of the cut-off wavelength of the TE0 and TE1 modes in MDA waveguides (c), mode field width (d), and (absorption coefficient (e) on the dielectric thickness for nd 4 and 2 and at wavelengths of λ 500 and 600 nm.
the cut-off wavelength, beyond which the field cannot be effectively confined near the metal surface, but extends deeply into the air region. In Fig. 2(c), cut-off wavelengths of the two lowest order waveguiding modes (TE0 and TE1) are shown with their dependences on the dielectric layer thickness for nd 4 and 2. A regime between cut-off wavelengths of the TE0 and TE1 modes, is thus defined for designing of the quasi-surface waves. Further, as shown in Figs. 2(d) and 2(e), we calculated the mode field width, MFW td 1∕γ a 1∕γ m , and absorption coefficient, α 4π∕λ · ImN eff , of the TE0 mode with their dependences on the dielectric thickness at λ 500 and 600 nm for nd 4 and 2, where γ a and γ m are, respectively, the imaginary parts of complex transverse propagation constants in the air and metal regions. From Figs. 2(d) and 2(e), cut-off widths of the TE0 modes are also indicated, below which the MFW becomes extremely large, and, meanwhile, α approaches zero. Here, large td is not of our interest. Only when td is small and near the cut-off thickness, where the absorption is near the maximum, can the field be most strongly confined in the evanescent region. This is the condition at which the TE0 mode is suitably considered a quasisurface wave mode. These results also suggest that a medium of higher index is preferred for the dielectric, which allows a thinner HID layer and the existence of the quasi-surface mode in a wider Vis–NIR spectrum range. To identify the resonance modes in Fig. 1(b), we simulated field distributions at the reflection dips λ 363.3, 477.7, and 612 nm. As shown in Figs. 3(a), 3(b), and 3(c), the quasi-surface waves distribute as standing waves at the HID-stripe regions, respectively with 4, 2, and 0 zerofield nodes (dynamically invariant, not shown here). Since the quasi-TE surface wave exists only at the MDA metasurface but not at a bare metal surface, it can be only confined within the HID-stripe region, as illustrated in Fig. 3(d). Therefore, the resonances are Fabry– Perot-like in nature, instead of Bloch-wave resonances. It is known that, for Bloch-wave resonances, the field at the middle position of each periodic segment is either a maximum or zero [22]; here none of the cases appear in
Fig. 3. (a)–(c) Distributions of the TE field (E y ) at the reflection minima in Fig. 1(b). The dielectric layer is too thin to show in the plots (but implied), and the HID stripes locate symmetrically in the middle on metal surfaces, whose width is labeled with w. (d) Schematic model describing resonant interactions of light at the metal surface.
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the bare metal surface region. The Fabry–Perot-like nature of the resonances is also supported by the results, to be shown later, that the resonance positions are effectively determined by the HID stripe width instead of the structure period, a critical characteristic to distinguish the two types of resonance modes. As a Fabry–Perot-like resonance mode, horizontal confinement of the quasisurface waves is realized by scattering at both side ends of the MDA stripe regions, which are also the scattering channel for excitation of the quasi-surface wave mode. The Fabry–Perot-like resonances can be described with the following equation: 2ksw · w φA φB 2mπ
m 0; 1; 2; …;
(1)
where ksw ReN eff · 2π∕λ is the real part of the wavevector of the quasi-TE surface wave, φA and φB are scattering reflection phase shifts at two side-ends of the MDA stripe regions, and m is the resonance order. Under normal incidence, φA φB , and only symmetric even orders of the resonance modes can be excited due to symmetry of the coupling configuration. Thus in Fig. 1(b) we observed resonance effects of only the zeroth-, second-, and fourth-orders, identified with their number of the zero-field nodes [Fig. 3]. It is to be shown that, under oblique incidences, effects of the odd-order resonances will come to appear in the reflection spectra due to asymmetry of the coupling. Here, it is noted that, for the zeroth-order resonance at λ 612 nm, N eff of the quasi-surface wave approaches one near cutoff; and the horizontal confinement is effectively rather weak. Thus the resonance is due mainly to vertical confinement of the field in the HID layer, and the reflection minimum is in proximity to that of the metal surface coated with a continuous HID layer, shown in Fig. 1(b). The resonance reflection (or absorption) properties can further be understood by investigating the effects of structure dimensions. In Fig. 4(a), calculated refection spectra for structures of various periods are plotted; the
Fig. 4. Dependences of the reflection spectra on (a) structure parameters of period, (b) HID stripe width, and (d) thickness. (c) indicates stripe-width dependences of the second-order resonance position shown in (b), together with modeled optical path (N eff · w) and end phase shift of the Fabry–Perot resonance.
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HID layers have nd 4 and td 20 nm, and the stripe widths are fixed at 300 nm. In the spectra, three groups of reflection dips are shown locating at around λ 600, 455, and 342 nm, corresponding to zeroth-, second-, and fourth-order resonances of the quasi-surface waves. It is observed that the resonance positions are not much shifted within each group of the reflection dips, even as the period is largely varied from 350 to 600 nm. It is noted that diffraction effects of the grating-like structure appear as small kinks in the reflection spectra locating at λ ≈ p (observable even for smaller p if magnified). It is also found that, as the period is larger than the resonance wavelength, the first-order resonance minimum, e.g., at λ 575 nm for p 600 nm, appears due to a break of the original symmetry by the diffraction effect. Figure 4(b) shows dependence of the reflection on the HID stripe width, in which the period is fixed at 400 nm. It observed that all three resonance reflection minima show redshifts with increase of the stripe width. In Fig. 4(c), reflection minimum positions of the second-order resonance are plotted as a function of the stripe width, demonstrating a roughly linear relation. By substituting the N eff calculated in Fig. 2(b) and the resonance wavelength λres into Eq. (1), reflection phase shifts at the ends (φA φB ) can be derived. The phase shift is a function of wavelength, and shown to be negative. Here, we are also interested in the dependence of the reflectance value at resonance positions on the stripe width in Fig. 4(b). Generally, it is observed in our investigations that the lowest reflection dip appears at the resonance position corresponding to the maximum of ImN eff as shown in Fig. 2(b), where the quasi-surface wave is most lossy. Usually maximal ImN eff appears right below the cut-off wavelength. For a given HID medium, with increase of the HID layer thickness, cut-off wavelength of the quasi-surface wave increases, while the real effective index decreases. As such, thickness of the HID layer can be used to shift the positions of the resonance reflection dips, as shown in Fig. 4(d). We further studied dependence of the reflection on incidence angles. Figure 5(a) shows the reflection spectra of the structure studied in Fig. 1(b) for various incidence angles. It is notably observed that, as symmetry in coupling of incidence light is broken under oblique incidence conditions, new groups of reflection dips come to appear, and become even deeper with increase of the incidence angle. They are verified due to odd-order Fabry–Perot resonances of the quasi-surface waves along each segment of the HID stripes, e.g., for m 1 and 3. It is also interestingly observed that, with increase of the incidence angle, the reflection dips shift in opposite directions for the even- and odd-order resonance modes; e.g., the even-order resonance positions blueshift, but the odd-order ones redshift. In Figs. 5(b)–5(e), field distributions at the resonance positions (m 1, 2, 3, 4) for an incidence angle of 10° are demonstrated. Dynamic evolution of the fields showed that, besides resonant oscillation of the fields, there is a net power flow of the quasi-surface waves along the metal surfaces. Notably, the net power flow is in the forward direction for the even-order resonances, but in the backward direction for the odd-order resonances, as indicated in the figures. The observation triggers us to relate it to the
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quasi-surface waves at a MDA metasurface, and further to devise novel microphotonic/nanophotonic devices. The authors acknowledge financial support from the NSFC (No. 61275063), the National Key Scientific Program (No. 2012CB933503), the Natural Science Foundation of Fujian Province of China (No. 2011J06002), and the Fundamental Research Funds for the Central Universities (No. 2012121009).
Fig. 5. (a) Dependence of the reflection spectra on incidence angles (θ). (b)–(e) Field distributions (E y ) at resonance positions λ 526, 472.1, 392.1, and 361.3 nm (corresponding to m 1, 2, 3, 4) for θ 10° in (a). The grating ridges locate symmetrically in the middle on metal surfaces. The arrows indicate directions of the incidence plane wave and observed net power flow along the metal surface.
opposite shifts of reflection dips for even- and odd-order resonance modes as mentioned above. The phenomenon is thought to be due to asymmetric excitation and reflection of the quasi-surface waves at two side-ends of each MDA stripe region under oblique incidence; i.e., under the oblique incidence conditions shown in Fig. 5, coupling of incidence light energy into the resonance “cavity” is more efficient at the left end of the MDA stripe regions than the right end for the even-order resonances, and it is more efficient at the right end of the MDA stripe regions than the left end for the odd-order resonances. Meanwhile, the reflection phase shifts at both ends of the stripe regions will also be unequal, φA ≠ φB , under oblique incidence conditions. In summary, we demonstrated nearly perfect absorption of TE-polarized light at metal surfaces coated with arrayed high-index dielectric stripes, resulting from Fabry–Perot-type resonances of the TE quasi-surface waves along each segment of the HID stripes of the MDA surface. The work suggests a way to mesoscopically activate the metal surfaces or microstructures/ nanostructures for TE-polarized light by designing TE
References 1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998). 2. Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003). 3. S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010). 4. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011). 5. A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013). 6. T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005). 7. A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004). 8. Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006). 9. M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012). 10. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. MartinMoreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002). 11. Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004). 12. S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006). 13. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009). 14. Z. Sun, X. Zuo, T. Guan, and W. Chen, Opt. Express 22, 4714 (2014). 15. Z. Sun and X. Zuo, Plasmonics 6, 83 (2011). 16. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010). 17. B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. Khoo, S. Chen, and T. J. Huang, Opt. Express 19, 15221 (2011). 18. J. Hendrickson, J. Guo, B. Zhang, W. Buchwald, and R. Soref, Opt. Lett. 37, 371 (2012). 19. A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012). 20. N. Bonod, G. Tayeb, D. Maystre, S. Enoch, and E. Popov, Opt. Express 16, 15431 (2008). 21. I. P. Kaminow, W. L. Mammal, and H. P. Weber, Appl. Opt. 13, 396 (1974). 22. J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
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Nearly perfect resonant absorption of TE-polarized light at metal surfaces coated with arrayed dielectric stripes Zhijun Sun,* Wei Chen, and Ling Guo Department of Physics, Xiamen University, Xiamen 361005, China *Corresponding author: [email protected] Received February 25, 2014; revised March 27, 2014; accepted March 29, 2014; posted April 1, 2014 (Doc. ID 207051); published April 22, 2014 A quasi-transverse electric (TE) surface wave mode exists at a metal surface coated with an ultrathin high-index dielectric layer. As the coating is in dielectric stripe arrays, nearly perfect absorption of TE-polarized incidence light is observed in simulations, due to resonances of the quasi-surface waves at each segment of the dielectric-coated metal surfaces. In analysis, the Fabry–Perot-like nature of the resonances is clarified, and effects of symmetry on different behaviors of the odd- and even-order resonance modes are discussed. While the absorption peak is tunable, perfect absorption appears near cut-off wavelength of the surface mode. © 2014 Optical Society of America OCIS codes: (240.6690) Surface waves; (050.6624) Subwavelength structures; (260.5740) Resonance; (260.3910) Metal optics. http://dx.doi.org/10.1364/OL.39.002637
Confinement and manipulation of light in the subwavelength scale are usually implemented with metallic microstructures/nanostructures via excitation of surface plasmons (SPs). Anomalous spectral properties in transmission, reflection, and absorption [1–6], arising from near-field SP behaviors, can thus be designed, which has attracted much attention for applications in biosensing [7,8], photovoltaics [9], nanolensing [10,11], light emitting [12,13], etc. As SPs are excited at metal surfaces with only the transverse-magnetic (TM) component of the light, the transverse-electric (TE) component of the light is usually excluded in subwavelength optical interactions. To overcome this limitation, we propose building a quasi-TE surface wave mode by introducing an ultrathin high-index dielectric (HID) layer on the metal surface, such that TE-polarized light also becomes capable of interacting with metallic microstructures/ nanostructures at the mesoscopic level [14]. Previously, nearly null reflection (or enhanced absorption) of light on metal surfaces with dielectricinterspaced metal nanostructures has been reported and widely studied [15–19]. The phenomenon is generally explained due to resonances of SPs confined within each unit of the metallic nanostructures. In this Letter, we show that resonances of the confined quasi-TE surface waves at each segment of the HID-coated metal surfaces can also result in nearly perfect absorption of TE-polarized light. Compared to some literature reports on absorption of TE-polarized light in metallic gratings [20], our absorption mechanism is based on resonances of the quasi-TE surface wave, instead of the resonant cavity modes of guided waves in wide and deep grating grooves. Figure 1(a) schematically illustrates the structure under investigation. The incidence light is TE polarized with its electric field parallel to the direction of the HID stripes. In this case, no SP waves can be excited, and the incidence light is usually highly reflected, without diffractions in the subwavelength regime (p < λ). Using numerical simulations based on the finite-difference time-domain method, we show in Fig. 1(b) the reflection 0146-9592/14/092637-04$15.00/0
spectrum of such a metal (Ag) surface, with HID stripes of index nd 4, thickness td 20 nm, period p 400 nm, and stripe width w 340 nm, under normal incidence of TE-polarized light. Strikingly among its unusual characteristics in the spectrum, a dip with extremely low reflectance (R 5 × 10−5 ) is observed at λ 477.7 nm, indicating a perfect absorption (A 1 − R) of the incidence light, besides two other dips locating at λ 612 and 363.3 nm. In the following analysis, the three reflection minima are ascribed to the zeroth-, second-, and fourth-order horizontally oscillating resonances of the quasi-TE surface waves along individual segments of the HID stripes on the metal surface. For comparison, the reflection spectrum of the metal surface with a continuous HID layer is also plotted in Fig. 1(b),
Fig. 1. (a) Schematic illustration of the metal surface coated with arrayed dielectric stripes upon incidence of TE-polarized light. (b) Reflection spectrum of the structure (nd 4, td 20 nm, p 400 nm, w 340 nm), in comparison with that of the metal surface with the dielectric layer being continuous. © 2014 Optical Society of America
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showing a minimum at λ 642 nm. In this case, only multiple interferences in the vertical direction exist in the HID layer, and Fabry–Perot resonances take place at the minimum. Considering proximity of the minima at λ 612 nm and λ 642 nm for the two curves in Fig. 1(b), they are of the same nature, as horizontal confinement of the zeroth-order resonance in the stripe regions is very weak; the HID stripe layer can be considered an effective dielectric layer in the subwavelength regime. In analysis, we first give a brief introduction of the quasi-TE surface wave. It is known that TE waveguiding modes may exist in a dielectric layer on a metal surface [21], i.e., a metal–dielectric–air (MDA) structure. And cut-off thicknesses exist, even for the lowest order waveguide mode. Usually, for relatively low index dielectrics, the dielectric layer has to be thick enough, and distributions of the mode field spread like those in a conventional dielectric waveguide. However, if the dielectric layer has a high index, its thickness can be largely reduced to a nanoscale. Thus the fundamental TE mode (TE0) comes to have a quasi-evanescent transverse distribution of the transverse electric field (E y ), as shown in Fig. 2(a). This is similar to the distribution of TM field (H y ) of a TMpolarized SP mode. As such, we consider it a quasisurface-wave, locating at a HID coated metasurface of metal. Also, the quasi-TE quasi-surface wave is shown to be magnetic, as pseudo surface polarization currents are induced, accompanied with discontinuity of the tangential magnetic field across the metasurface [14]. In Fig. 2(b), normalized complex propagation constants β∕k0 ; k0 2π∕λ0 , or effective indices (N eff β∕k0 ), of the quasi-TE surface wave mode, calculated with the dispersion relation in Ref. [14], are plotted as functions of the wavelength for nd 4 of the HID layer, in comparison with those for a lower index of nd 2. For a given set of nd ; td , a cut-off wavelength is clearly indicated, e.g., at around λ 630 nm for nd 4 and td 20 nm; i.e., the quasi-surface wave exists only below
Fig. 2. (a) Illustration of the formation of the quasi-TE surface wave at a MDA surface. The bottom graph is plotted for nd 4, td 20 nm at λ 500 nm. (b) Real (solid line) and imaginary (dashed line) parts of the normalized propagation constants of the quasi-surface waves at MDA surfaces. (c)–(e) Dependences of the cut-off wavelength of the TE0 and TE1 modes in MDA waveguides (c), mode field width (d), and (absorption coefficient (e) on the dielectric thickness for nd 4 and 2 and at wavelengths of λ 500 and 600 nm.
the cut-off wavelength, beyond which the field cannot be effectively confined near the metal surface, but extends deeply into the air region. In Fig. 2(c), cut-off wavelengths of the two lowest order waveguiding modes (TE0 and TE1) are shown with their dependences on the dielectric layer thickness for nd 4 and 2. A regime between cut-off wavelengths of the TE0 and TE1 modes, is thus defined for designing of the quasi-surface waves. Further, as shown in Figs. 2(d) and 2(e), we calculated the mode field width, MFW td 1∕γ a 1∕γ m , and absorption coefficient, α 4π∕λ · ImN eff , of the TE0 mode with their dependences on the dielectric thickness at λ 500 and 600 nm for nd 4 and 2, where γ a and γ m are, respectively, the imaginary parts of complex transverse propagation constants in the air and metal regions. From Figs. 2(d) and 2(e), cut-off widths of the TE0 modes are also indicated, below which the MFW becomes extremely large, and, meanwhile, α approaches zero. Here, large td is not of our interest. Only when td is small and near the cut-off thickness, where the absorption is near the maximum, can the field be most strongly confined in the evanescent region. This is the condition at which the TE0 mode is suitably considered a quasisurface wave mode. These results also suggest that a medium of higher index is preferred for the dielectric, which allows a thinner HID layer and the existence of the quasi-surface mode in a wider Vis–NIR spectrum range. To identify the resonance modes in Fig. 1(b), we simulated field distributions at the reflection dips λ 363.3, 477.7, and 612 nm. As shown in Figs. 3(a), 3(b), and 3(c), the quasi-surface waves distribute as standing waves at the HID-stripe regions, respectively with 4, 2, and 0 zerofield nodes (dynamically invariant, not shown here). Since the quasi-TE surface wave exists only at the MDA metasurface but not at a bare metal surface, it can be only confined within the HID-stripe region, as illustrated in Fig. 3(d). Therefore, the resonances are Fabry– Perot-like in nature, instead of Bloch-wave resonances. It is known that, for Bloch-wave resonances, the field at the middle position of each periodic segment is either a maximum or zero [22]; here none of the cases appear in
Fig. 3. (a)–(c) Distributions of the TE field (E y ) at the reflection minima in Fig. 1(b). The dielectric layer is too thin to show in the plots (but implied), and the HID stripes locate symmetrically in the middle on metal surfaces, whose width is labeled with w. (d) Schematic model describing resonant interactions of light at the metal surface.
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the bare metal surface region. The Fabry–Perot-like nature of the resonances is also supported by the results, to be shown later, that the resonance positions are effectively determined by the HID stripe width instead of the structure period, a critical characteristic to distinguish the two types of resonance modes. As a Fabry–Perot-like resonance mode, horizontal confinement of the quasisurface waves is realized by scattering at both side ends of the MDA stripe regions, which are also the scattering channel for excitation of the quasi-surface wave mode. The Fabry–Perot-like resonances can be described with the following equation: 2ksw · w φA φB 2mπ
m 0; 1; 2; …;
(1)
where ksw ReN eff · 2π∕λ is the real part of the wavevector of the quasi-TE surface wave, φA and φB are scattering reflection phase shifts at two side-ends of the MDA stripe regions, and m is the resonance order. Under normal incidence, φA φB , and only symmetric even orders of the resonance modes can be excited due to symmetry of the coupling configuration. Thus in Fig. 1(b) we observed resonance effects of only the zeroth-, second-, and fourth-orders, identified with their number of the zero-field nodes [Fig. 3]. It is to be shown that, under oblique incidences, effects of the odd-order resonances will come to appear in the reflection spectra due to asymmetry of the coupling. Here, it is noted that, for the zeroth-order resonance at λ 612 nm, N eff of the quasi-surface wave approaches one near cutoff; and the horizontal confinement is effectively rather weak. Thus the resonance is due mainly to vertical confinement of the field in the HID layer, and the reflection minimum is in proximity to that of the metal surface coated with a continuous HID layer, shown in Fig. 1(b). The resonance reflection (or absorption) properties can further be understood by investigating the effects of structure dimensions. In Fig. 4(a), calculated refection spectra for structures of various periods are plotted; the
Fig. 4. Dependences of the reflection spectra on (a) structure parameters of period, (b) HID stripe width, and (d) thickness. (c) indicates stripe-width dependences of the second-order resonance position shown in (b), together with modeled optical path (N eff · w) and end phase shift of the Fabry–Perot resonance.
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HID layers have nd 4 and td 20 nm, and the stripe widths are fixed at 300 nm. In the spectra, three groups of reflection dips are shown locating at around λ 600, 455, and 342 nm, corresponding to zeroth-, second-, and fourth-order resonances of the quasi-surface waves. It is observed that the resonance positions are not much shifted within each group of the reflection dips, even as the period is largely varied from 350 to 600 nm. It is noted that diffraction effects of the grating-like structure appear as small kinks in the reflection spectra locating at λ ≈ p (observable even for smaller p if magnified). It is also found that, as the period is larger than the resonance wavelength, the first-order resonance minimum, e.g., at λ 575 nm for p 600 nm, appears due to a break of the original symmetry by the diffraction effect. Figure 4(b) shows dependence of the reflection on the HID stripe width, in which the period is fixed at 400 nm. It observed that all three resonance reflection minima show redshifts with increase of the stripe width. In Fig. 4(c), reflection minimum positions of the second-order resonance are plotted as a function of the stripe width, demonstrating a roughly linear relation. By substituting the N eff calculated in Fig. 2(b) and the resonance wavelength λres into Eq. (1), reflection phase shifts at the ends (φA φB ) can be derived. The phase shift is a function of wavelength, and shown to be negative. Here, we are also interested in the dependence of the reflectance value at resonance positions on the stripe width in Fig. 4(b). Generally, it is observed in our investigations that the lowest reflection dip appears at the resonance position corresponding to the maximum of ImN eff as shown in Fig. 2(b), where the quasi-surface wave is most lossy. Usually maximal ImN eff appears right below the cut-off wavelength. For a given HID medium, with increase of the HID layer thickness, cut-off wavelength of the quasi-surface wave increases, while the real effective index decreases. As such, thickness of the HID layer can be used to shift the positions of the resonance reflection dips, as shown in Fig. 4(d). We further studied dependence of the reflection on incidence angles. Figure 5(a) shows the reflection spectra of the structure studied in Fig. 1(b) for various incidence angles. It is notably observed that, as symmetry in coupling of incidence light is broken under oblique incidence conditions, new groups of reflection dips come to appear, and become even deeper with increase of the incidence angle. They are verified due to odd-order Fabry–Perot resonances of the quasi-surface waves along each segment of the HID stripes, e.g., for m 1 and 3. It is also interestingly observed that, with increase of the incidence angle, the reflection dips shift in opposite directions for the even- and odd-order resonance modes; e.g., the even-order resonance positions blueshift, but the odd-order ones redshift. In Figs. 5(b)–5(e), field distributions at the resonance positions (m 1, 2, 3, 4) for an incidence angle of 10° are demonstrated. Dynamic evolution of the fields showed that, besides resonant oscillation of the fields, there is a net power flow of the quasi-surface waves along the metal surfaces. Notably, the net power flow is in the forward direction for the even-order resonances, but in the backward direction for the odd-order resonances, as indicated in the figures. The observation triggers us to relate it to the
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OPTICS LETTERS / Vol. 39, No. 9 / May 1, 2014
quasi-surface waves at a MDA metasurface, and further to devise novel microphotonic/nanophotonic devices. The authors acknowledge financial support from the NSFC (No. 61275063), the National Key Scientific Program (No. 2012CB933503), the Natural Science Foundation of Fujian Province of China (No. 2011J06002), and the Fundamental Research Funds for the Central Universities (No. 2012121009).
Fig. 5. (a) Dependence of the reflection spectra on incidence angles (θ). (b)–(e) Field distributions (E y ) at resonance positions λ 526, 472.1, 392.1, and 361.3 nm (corresponding to m 1, 2, 3, 4) for θ 10° in (a). The grating ridges locate symmetrically in the middle on metal surfaces. The arrows indicate directions of the incidence plane wave and observed net power flow along the metal surface.
opposite shifts of reflection dips for even- and odd-order resonance modes as mentioned above. The phenomenon is thought to be due to asymmetric excitation and reflection of the quasi-surface waves at two side-ends of each MDA stripe region under oblique incidence; i.e., under the oblique incidence conditions shown in Fig. 5, coupling of incidence light energy into the resonance “cavity” is more efficient at the left end of the MDA stripe regions than the right end for the even-order resonances, and it is more efficient at the right end of the MDA stripe regions than the left end for the odd-order resonances. Meanwhile, the reflection phase shifts at both ends of the stripe regions will also be unequal, φA ≠ φB , under oblique incidence conditions. In summary, we demonstrated nearly perfect absorption of TE-polarized light at metal surfaces coated with arrayed high-index dielectric stripes, resulting from Fabry–Perot-type resonances of the TE quasi-surface waves along each segment of the HID stripes of the MDA surface. The work suggests a way to mesoscopically activate the metal surfaces or microstructures/ nanostructures for TE-polarized light by designing TE
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