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 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”.

 

Fig. 1 (a, b) Schematic boundary conditions for TM- and TE-polarization fields at a metal surface. (c) Tangential magnetic field (H_z) 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) Quasi-evanescent distributions of the ASW fields (H_z and E_y) at a MDA surface

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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 ${\sigma }_e={\epsilon }_0\left(E_{2n}-E_{1n}\right)$ 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 ${\alpha }_m=0$; thus there is no existence of a magnetic surface wave mode.

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 ${\sigma }_e={\alpha }_m=0$, 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 (${{\alpha }^{\prime }}_m\ne 0$) [Fig. 1(b)], there will be a discontinuity of the tangential magnetic field (H_t or H_z) at the meta-surface with opposite sign [Fig. 1(c)], i.e., ${{\alpha }^{\prime }}_m=H_{2t}-H_{1t}$; and vice versa. Then existence of a magnetic surface wave mode becomes possible. It’s known in electromagnetics that bound current density $J_b=\nabla \times M+\partial P/\partial t$. As the magnetization field $M=0$ for nonmagnetic media, an ultra-thin dielectric layer can be introduced at the metal surface, in which $\partial P/\partial t\ne 0$ for a time-varying polarization field, to bring in a pseudo surface polarization current,

Based on EM theory, dispersion relation of the TE-mode artificial surface wave can be solved, as described with the transcendental equation:

In Fig. 2(a), real parts of the normalized propagation constants (β) of the artificial surface waves at MDA surfaces of various n_d and t_d are plotted as functions of the wavelength, which are usually also defined as effective index of a guided mode (N_eff = β/k₀, k₀ = 2π/λ₀). Among our observations, it is distinctly shown that there exists a transition wavelength (λ_trans); above it, N_eff→1 with negligible imaginary part. In fact, as λ₀>λ_trans, the fields extend largely into the air region and is not well confined in vicinity of the MDA surface region. The situation does not coincide with our common definition of a surface mode. It is an extended TE surface wave, like the TM “spoof surface plasmons” that can be excited at structured perfect conductor surfaces, usually in the microwave or terahertz regime [20,21]. Figure 2(b) shows dependences of the transition wavelength and the wavelength corresponding to a half-wavelength confinement of the surface waves on thickness of the HID layer. Close spacing of the two curves implies that, in the regime below the transition wavelength, the surface waves are generally well confined in the subwavelength scale. The results in Figs. 2(a) and 2(b) also suggest that a medium of higher index is a superior choice for the HID layer, so that that the artificial surface waves can be better confined and exist in a broader band, extending to the long-wavelength infrared range, while keeping an extremely small thickness of the HID layer for incorporation into subwavelength metal structures.

 

Fig. 2 (a) Real-part normalized propagation constants of the ASWs at various MDA surfaces as functions of the wavelength. (b) Dependences of the transition wavelength (λ_trans) and the wavelength characterizing confinement (W_1/e) of the ASWs on the HID thickness. (c, d) Field distributions (E_y) of the propagating ASWs excited at MDA surfaces (n_d = 4, t_d = 20 nm) with three equal-spaced grooves. The panel on right side of (c) shows corresponding H_z field in the boxed region in (c).

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We then performed two-dimensional (2D) finite-difference time-domain (FDTD) simulations to validate excitation and propagation of the artificial surface waves at a MDA surface. As indicated in Figs. 2(c) and 2(d), three equal-spaced grooves are introduced on the MDA surfaces (n_d = 4, t_d = 20 nm) as couplers for excitation of the artificial surface waves. It was verified that, upon normal incidence of TE-polarized input beams, only when distances (center-to-center) between the grooves d_c = N_eff∙λ₀, satisfying the phase matching condition, there is an efficient coupling of the surface wave; otherwise, there appears an effect of interferences between multiple surface waves generated at individual grooves. In Fig. 2(c), λ₀ = 500 nm, well below the transition wavelength, N_eff = 1.4212 and d_c = 711 nm, the surface wave fields are highly confined at the MDA surface. And the tangential magnetic fields (H_z) on both sides of the HID layer are in opposite phase as expected in previous discussion. In Fig. 2(d), λ₀ = 610 nm, just around the transition wavelength, N_eff = 1.0027 and d_c = 612 nm, the coupled surface wave field extend largely into the air region. Note that, for the artificial surface waves, a contradiction exists between the loss and the field confinement in designing of the MDA surface, similar to that of SPs. Comparing the two types of surface modes, the TE artificial surface waves at a MDA surface generally have slightly higher loss than the TM SP waves at the corresponding MA surface; but in a small range closer to the transition wavelength, the TE artificial surface wave turns to be less lossy.

3. Properties of the artificial surface waves interacting with metallic nanostructures

In this section, we demonstrate propagation and resonance properties of the artificial surface waves in several HID-modified basic metal structures that have been widely studied in plasmonics. As only TE-polarization modes are concerned, 2D structures are used in analyses for simplicity and clarity.

3.1 Waveguiding in a metallic narrow gap

Firstly, we study TE waveguide mode of the artificial surface wave in a metallic (Ag) narrow gap whose sidewalls are modified with HID layers, forming a metal-dielectric-air-dielectric-metal (MDADM) structure. Figure 3(a) shows transverse field distribution of the gap mode in a MDADM waveguide. Maxima of the field locate at the MDA meta-surface boundaries, and the field in the gap is like a superposition of two evanescent waves, resulting in a minimum at the gap center. The field profile is similar to that of SPs in a metal gap waveguide. Figures 3(b) and 3(c) show dependences of effective index of the waveguide mode, whose real part decreases with increase of the wavelength and increases with decrease of the gap width, same as that of a SP gap mode [3]. However there exists a cutoff wavelength here, corresponding to Re(β/k₀) = 1 in definition. When Re(β/k₀)<1 [the shaded region in Fig. 3(b)], it becomes a metallic leaky mode; the power is strongly attenuated like it propagates in a bulk metal. Figure 3(d) demonstrates that compact bending of the waveguide can be realized without degradation of the mode characteristics, similar to the SP gap waveguides. But due to limitation of the cutoff wavelength and relatively higher loss in the visible range, such waveguides may not be appropriate for use in integrated photonics, but can be adopted as a basic element in designing metamaterial structures for interaction with TE-polarized light, utilizing other properties of the artificial surface waves.

 

Fig. 3 (a) Transverse field distribution of the ASW mode in a MDADM waveguide (n_d = 4, t_d = 20 nm) with gap width s = 80 nm at λ₀ = 500 nm. (b) Normalized propagation constant as a function of wavelength for s = 80 nm. (c) Dependence of the normalized propagation constant on the gap width at λ₀ = 500 nm. (d) Field distribution of the wave propagating through a round bend, in which s = 100 nm, λ₀ = 500 nm, and the bend radius is 500 nm.

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Here one may think that the MDADM waveguide does not provide subwavelength confinement of the field taking into account the index of the HID layers. This is in fact a matter of definition on “subwavelength”, for the dimension of s only or s + 2t_d of the gap. Nevertheless more important is that, by introducing the HID layers, an originally metallic subwavelength gap comes to allow a waveguiding mode for TE-polarized light in a form of the artificial surface waves. And, in many circumstances, introduction of the ultra-thin HID layers at surfaces of a metallic subwavelength structure is more feasible (e.g. using chemical vapor deposition processes) and functional, compared to filling the metallic gaps fully with a high index dielectric medium.

3.2 Enhancing the transmission of TE-polarized light through metallic nanoslit arrays

Enhanced optical transmission of nano-apertured thick metal film is a typical plasmonic phenomenon [22]. For 2D metallic narrow slit arrays, high transmission is permitted only for TM-polarized light due to excitation of SPs [23,24]; for TE-polarized light, the transmission is negligible. Here we modify the structure by covering its metal surfaces with thin HID layers of uniform thickness, as illustrated in Fig. 4(a). For such a structure with HID layers of n_d = 4 and t_d = 20 nm, period p = 400 nm, metal (Ag) thickness h = 200 nm, and gap width s = 60 nm, we calculated its transmission spectrum for normal incidence of TE-polarized light using FDTD simulation. As shown in Fig. 4(b), several pass-bands (or peaks) appear in the spectrum demonstrating prominent transmission, similar to that of SP-enhanced transmission for TM-polarized light. In comparison, if all segments of the HID layers are removed from it, transmission of the TE-polarized light in the full spectrum range is shown to be negligible as expected. Further, if the sidewall HID layers in the slits are removed leaving only the top and bottom surface HID layers, the transmission is strongly suppressed showing only two lower peaks. On the contrary, if the sidewall HID layers in the slits remains only, there is still a significant transmission in a wide band. The results tell that the sidewall HID layers in the slits are critical for transmission of TE-polarized light; addition of the top and bottom HID layers assists the transmission, but may also suppress it at particular wavelengths (e.g., at the transmission dip λ₀ = 514 nm). Additionally, since cutoff exists for the artificial surface waves in the MDADM slits, the transmission is forbidden in the long wavelength range.

 

Fig. 4 (a) Schematic illustration of a HID-modified metal (Ag) slit array. (b) Transmission spectra of the metal slit array (n_d = 4, t_d = 20 nm, s = 60 nm, p = 400 nm, h = 200 nm), compared with that without all the HID layers, and those with remaining HID layers only at the top and bottom metal surfaces (curve 1) or on sidewalls of the slits (curve 2). The inset is a magnification for display of curves 1 and 2. (c) Spectrum of field intensity in the resonant slit cavity. (d-h) Distributions of the steady state field magnitude (|E_y|) within a period of the structure at resonance wavelengths indicated with arrows in (b). Note the light is normally incident from the bottom side.

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In explanation of the transmission spectrum, we identified resonance modes in the slits by analyzing the impulse response of inside field intensity, referring to the transmission mechanisms for TM-polarized light [23,25]. As shown in Fig. 4(c), four resonance peaks are identified locating at λ₀ = 413, 489, 545 and 605 nm, in close proximity to the transmission peaks in Fig. 4(b) at λ₀ = 413, 488, 554 and 595 nm. Another resonance mode was also identified from analyses of the steady state field distributions, which is at the null transmission dip λ₀ = 514 nm, demonstrating in-plane resonance of the artificial surface wave at the bottom MDA surface [Fig. 4(d)]. Its negative role in transmission is same as that of in-plane SP resonances for TM-polarized light [24,26]. It is verified that the resonance position can be roughly estimated with λ_res = Re(N_eff)∙p, the 1st-order phase matching condition. Using the calculated data in Fig. 2(a), a match is found at λ_res = 519 nm, where Re(N_eff) = 1.297. In fact, the transmission dip is quite broad; a precise determination needs to consider the effects of narrow slits and periodicity of the structure to account for Bloch wave nature of the resonance [27,28]. Field distributions in Figs. 4(e)–4(h) clearly demonstrate Fabry-Pérot-like resonances of artificial surface waves in slits, corresponding to resonance orders of m = 1, 2, 3, 4 respectively, determined with the number of zero-field node(s) in slits. Note that proximity and interference of the 1st- and 2nd-order resonances cause the field at the node position of the 1st-order resonance [Fig. 4(f)] to be not exactly zero.

Here a few literature reports should be mentioned [29–32], in which dielectric layers are also introduced in apertured metallic structures to enhance the transmission of s-polarized light (i.e., TE-polarized here). But in those works, the dielectric layers all have relatively low indices and large thicknesses; thus conventional waveguide modes are considered, instead of the artificial surface wave mode treated here. Note that for the conventional TE waveguide mode in a metal-dielectric-metal structure, the dielectric gap has to be wide enough, characterized with a cut-off width, below which extremely high loss prohibits existence of a propagating mode in the waveguide. As such, to achieve a prominent transmission in those reports, the dielectric media usually fill the apertured fully, the apertured metal films are rather thin, and the slits are wide relative to the wavelength of the light. Therefore, characteristics and mechanisms of the enhanced transmission in our work are different from those in literature reports, while mimicking that of SP-enhanced transmission due to comparative nature of the surface waves induced in the metallic structures.

3.3 Resonances in a 2D metallic nanoparticle

We further studied resonances of the artificial surface waves in a HID-modified 2D “nanoparticle” ― a 100-nm-thick Ag cylinder coated with a HID layer of n_d = 4 and t_d = 20 nm. Figure 5(a) shows the spectra of integrated electric and magnetic field energy densities in the metal region upon normal incidence of TE-polarized plane-wave light, normalized with those in the same region with only an air background. In fact, the spectrum of electric field energy density is also a reflection of the absorption in the structure, as both are proportional to the square of electric field. In the spectra, three distinct peaks are observed locating at λ₀ = 562, 404 and 316 nm. Steady state distributions of the fields at the peak wavelengths are then simulated, shown in Figs. 5(b)–5(d). It can be identified that the three peaks correspond to respectively the dipolar, quadrupole and sextupole resonances of the artificial surface waves. The results are analogous to SP resonances in single metal nanoparticles [33]. Considering that electric and magnetic field magnitudes of the incidence light are 1, the electric fields are slightly enhanced; but the magnetic fields are strongly enhanced, particularly in the HID region, though all the media are nonmagnetic. The enhancement factor is shown to be comparable to that of the SP electric field at a location a few nanometers distant from the surface of a metal nanosphere when nonlocal effects of SP charges are taken into account [34].

 

Fig. 5 (a) Spectra of the relative integrated electric and magnetic field energy densities in a HID-modified metal cylinder (Ag core diameter D = 100 nm, n_d = 4, t_d = 20 nm) upon normal incidence of TE-polarized light. (b-d) Distributions of the steady state electric field magnitudes (|E_y|) and square of the magnetic field (|H|²) at the dipolar, quadrupole and sextupole resonance positions of λ₀ = 562, 404 and 316 nm. Note that light is incident from the bottom side.

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It was verified in Fig. 6 that, for a Ag cylinder without the HID layer, no distinct resonances or enhancements of the magnetic fields exist for both TE- and TM-polarized incidence light; there are only resonances and enhancement of the electric field for TM-polarized incidence light. Additionally, for the Ag cylinder without the HID layer, even in the SP resonance condition under incidence of TM-polarized light, the magnetic energy density shows a much weaker peak, compared to that of the Ag cylinder with a HID coating. Thus, the near-field magnetic field at resonance positions is strongly enhanced by introducing a HID layer even without using any magnetic media. This is in line with the point in some recent work of Miroshnichenko et al. [35], i.e., to have optical magnetism in dielectrics; but we do here by utilizing the artificial TE surface waves.

 

Fig. 6 Spectra of the relative integrated magnetic (a) and electric energy densities (b) in a Ag metal cylinder (D = 100 nm) with or without modification of a HID layer (n_d = 4, t_d = 20 nm). “MDA” and “MA” refer to respectively the structures with and without the HID layer. Comparison is made for both TE and TM polarized incidence light.

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4. Conclusion

In conclusion, we proposed the artificial TE-mode surface waves at a HID-modified meta-surface of metal, an analogy of SP waves at metal surfaces, which behave like SP waves in various aspects. Properties of the artificial surface waves are demonstrated in some typical metallic nanostructures. From these examples, we expect that a variety of other plasmonic metal structures can also be modified as such for interactions with TE-polarized light, while still possessing their plasmonic properties. Besides, near-field properties of the artificial surface waves allow enhancement and control of magnetic dipole transitions in optical materials [36,37] and optical interactions in active magnetic materials [38].