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Abstract
Integrated dielectric metamaterials with plasmonic structures can cause drastic optical resonances and strengthen the capacity of light absorption. Here, we describe the optical properties of silicon nanoarrays on a thin silver film for extreme light confinement at subwavelength nanoscales. We attain the nearly total absorption in silicon nanostrips, which support magnetic quadruple Mie-type resonances in the visible regions. The Mie resonant field of the dielectric nanostrip engages the screening response of the silver film, resulting in plasmon resonance configuration and thus achieving perfect light absorption in the dielectric nanostrip. Moreover, we can attain similar results in other nanostructures, such as silicon cylinder and rhombus column arrays. Because it can sustain hybridized plasmon modes and magnetic modes, the combined system will benefit the application of solar energy accumulation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The advantages of surface plasmon polaritons (SPPs) have brought remarkable interests, due to their behavior of the electron coherent oscillations interacting with electromagnetic waves. Localized surface plasmon resonances (LSPRs) can control and modulate electromagnetic waves at the subwavelength dimension [1–8], confining the electrons within the interfaces of metals. Especially, metallic nanoparticles acting as antennas can modulate light-matter interactions by the collective plasmonic resonances, thereby strongly absorbing and confining light [9–11]. Multifarious plasmonic applications based on nanoresonators hence have been investigated, such as fluorescence [12], nonlinear optical responses [13,14], sensing [15,16], color printing [17,18] and scattering and absorption enhancement [19–21]. In addition, the unique Mie resonators own a few admirable features including the directional characteristic scattering through the generation of intricate multipole modes and high magnetic field intensity [22]. The field of the Mie resonance in dielectric nanoparticles engages the screening response of the semiconductor substrate, resulting in directional emission patterns [23]. Most prominently, high-index dielectric nanoparticles support both electric and magnetic resonant modes, whose relative spectral position can be tailored by tuning the geometrical dimensions of particles [24–27]. Due to the properties of light localization below the diffraction limit [28,29], metamaterials [30–32] have been extensively investigated based on dielectric and metal nanostructures [33–38] at subwavelength scale. However, the metals have the features of inevitable losses and dispersive refractive index while the dielectrics are low-loss. Considering the synthetical properties of two materials, a rational design to combine the dielectrics with metals to attain the total absorption enhancement in dielectric nanostructures can be adopted. The combined optical and electronic properties of this configuration benefit from the adjacent plasmonic resonance in metals, which is an especially notable mechanism and more significant to expand the utilization of SPPs.
Here, we construct arrays of the dielectric nanostrip on optically plasmonic film in the visible regions. We demonstrate strongly enhanced field distribution on the dielectrics which support the magnetic resonances. We apply versatile coupled-mode theory (CMT) and finite-difference time-domain (FDTD) simulations to investigate the interaction between dielectric nanostrip and plasmonic structure, which attains nearly total absorption. This is particularly interesting for accumulation energy and contributes to the application of energy storage. The absorption intensity remains relatively high strength by selecting the polarization and oblique angle of incident light, which affords a new horizon of freedom for the modulation of the resonances. Moreover, our scheme does not rely on a fixed refractive index and, thus, it can be stretched to wide scope applied devices for accumulation energy.
2. Structure and theory
Figure 1 displays the schematic illustration of dielectric (silicon) nanostrips on a metal (silver) film. For our simulations, the parameters of the structure are l = 200 nm, w = 100 nm, h = 150 nm, and t = 70 nm, respectively. The period of the unit cell is set to be p = 300 nm, which isshorter than the wavelengths to reduce higher order diffractions. The permittivity of silver is taken as the Drude model [28]: where ε∞ = 3.7 is the dielectric constant at infinite angular frequency, ωp = 9.1 eV is the bulk plasma frequency that corresponds to the oscillating frequency of freedom conduction electrons, γ = 0.018 eV is the damping constant, and ω is the incident light angular frequency. Furthermore, the refractive index of silicon is 3.45. Our numerical calculations is performed by the FDTD method where the grid sizes in the x and y and z directions are chosen to be Δx = Δy = Δz = 1 nm and Δt = Δx/2c, here, c is the velocity of light in a vacuum. In addition, the periodical boundary conditions are applied in the x- and y-axis and the perfectly matched layer is employed in the z-axis.
Fig. 1 (a) Schematic representation of dielectric nanostrip arrays, which defines the resonant mode of the dielectric nanostrip and plasmonic film. The system is illuminated by a y-polarized incident TM light with an incidence angle of φ. (b) Vertical view of the structure with different parametric definitions. The polarization angle θ is defined with respect to the x-axis.
When the incident electromagnetic wave normally irradiates the system with polarization direction along y axis, we calculate and simulate the electric field image and absorption spectra of the structure. Note that the light can be absorbed by the structures at given wavelengths, resulting from constructive interference and taking into account the material characteristics, geometrical parameters, as well as the properties of optical source. By tuning permeability (μ) and permittivity (ε) quantitative values of resonances, it can attain the condition of ε = μ, where the effective impedance is same as that in free space. Total absorption is possible in theory when the effective impedance of the silver nanostrip matches very well with that of the free space [39]. It brings about significant response of incident electric field being absolutely absorption by the structure. Because of the generation of SPPs at the metal surface, nanostructures could enhance electronic and magnetic fields through confining light to subwavelength ranges. The versatile CMT [26,27] can be utilized to eclucidate the intrinsic nature of this formation as follows
where S1 and S2 depict the light amplitudes of incident electric field input and output passing the nanostrip, respectively. The a represents the normalized amplitude of the SPP resonance. Without the input waves, the external leakage rate η characterize the amplitude change with time in the LSPRs, whose resonant frequency is ω0. When the extremely small lossy silicon nanostrip is placed on the silver film, there is a pimping intrinsic loss rate σ of SPP resonance based on the introduced dissipative losses. Finally, i is the imaginary unit and ω represents the incident frequency of light. Based on the time reversal symmetry relationship and energy conservation mechanism [40], the entire system satisfies with the Eqs. (1) and (2). Through solving Eqs. (1) and (2) numerically with the frequency range e+iωt, the reflecance of this nanosystem could be represented as R in Eq. (3). Because the ultra-thickness metal film can block all trasnmission, the absorption of the system can be elucidated by A = 1 - R. As can be seen from the Eq. (4), the versatile CMT has three main parameters (σ, η, and ω). We solve the Eq. (4) and can obtain a nearly perfect absorption phenomenon at the critical coupling condition where external leakage rate is equal to intrinsic loss rates (σ = η), when the SPP resonance satisfies ω = ω0. When the electromagnetic field is all localized within the dielectric, the nanosystem can realize the perfect absorption.In addition, the experimental implementation of our structure is feasible based on the state-of-the-art technology. The proposed dielectric-metal structure was fabricated by using electron beam lithography [41]. A 150 nm thick silicon film was deposited on a 70 nm thick silver film by chemical vapor deposition. Moreover, a collimated (<0.3° divergence) halogen lamp source and a USB-2000 fiber spectrometer (Ocean Optics) [42] are used for measuring the reflectance of the system, thereby obtaining the absorption spectrum.
3. Results and analysis
Figure 2(a) shows the FDTD-simulated (lines) and CMT-calculated (dotted line) absorption spectra of the structure. The coupled structure attain perfect absorption peak at λ0 = 493 nm. The corresponding electromagnetic field diagram at the resonant wavelength λ0 is exhibited in Fig. 2(b), which describes a vertical section of the electric field and the magnetic field (arrows). When the proposed structure satisfies the dispersion conditions shown in Eq. (5) [43] and Eq. (6) [42], the dielectric nanostrips can realize perfect absorption of the incident light due to the excitation of resonant modes.
Where β and k0 represent the wave vector constant of the SPPs and the light in free space, ε0, εd, and εm denote permittivity of the air, dielectric, and metal, respectively. The effective index (neff) is given by Re (β/k0). As well, the phase shift is ξ and mode constant is represented by m in Eq. (6). In our calculation, Fig. 2(b) describes the electric field and the magnetic field corresponding to the m = 2 when the width (w) and effective index (neff) of dielectric remains constant at the resonant wavelength λ0.Fig. 2 (a) Fitted and simulated absorption spectra for the design with single silicon nanostrip (black line), single silver film (blue line), and the coupled system (cyan and red line). (b) Electric field image of this proposed structure at the resonant wavelength of λ0 = 493 nm on the x-z plane. The relevant poles are described by + and − signs. Arrows show the magnetic field. Ez distribution on the z = 50 nm as shown in (c) and z = −100 nm (d) planes for λ0 = 493 nm.
Therefore, the absorption peak ascribes the magnetic quadrupole of dielectric, which is excited by the LSPRs from the metal as depicted in Fig. 2(b). Overall, we obtain remarkably good agreement between the CMT (with fitting parameters η = σ = 3.727 × 1013 Hz) and the results of numerical simulations. The corresponding electric field distributions on the x-y plane at resonant wavelength are depicted. Figure 2(c) demonstrates that the silicon nanostrip is treated as a dipole mode from the top view. In addition, Fig. 2(d) elucidates the light transfer into energy field enhancement through the influence of plasmonic to excite the magnetic modes of the dielectric.
Next, we investigate the absorption spectra at different polarization angles θ between the excitation of the longitudinal or transverse LSPRs. The polarization angle θ varies interval for 30° begin from the x axis (short axis of the silicon nanostrip). From the absorption spectra shown in Figs. 3(a)-3(c), the longitudinal and transverse LSPRs absorption apparent response are underneath different polarization angle θ. Note that the absorption peaks almost gradually increase when incident polarization angle increases. There are still strong absorptions for different polarization angles. And two Fano resonances with certain extent modulation depth arise in the spectra due to the influence of period. Especially, until up to 90°, we note that the resonant absorption intensity attains the maximum value. Considering the polarization independence effect for the absorption in the silicon nanostrip, almost perfect absorption is achieved. Therefore, a simple surface plasmon resonance application for accumulation energy can be designed, utilizing freedom selective of the polarization. It is realizable to switch between the transverse and longitudinal LSPRs under different polarization angles. Through the transformation of convertible incident polarization, one can attain the corresponding energy accumulation devices.
Fig. 3 (a) Absorption spectra of the nanostructure for different electric polarization angles θ from 0 to 90°, taking 30° as a step. (b) Absorption spectra as a function of the polarization angle of incident light wave and the wavelength. (c) The intensity of absorption as a function of θ.
To further demonstrate absorption features of the designed structure, we immediately obtain the spectra diagram of different incident oblique angles φ, as shown in Figs. 4(a)-4(c). Under normal incidence, the absorption peak is of the maximum value resulting from the impact of plasmons to generate the magnetic quadrupole modes of the dielectric. That is to say, the variation of resonant absorption peak can be explained from the magnetic quadrupole of Mie resonance through the interaction of LSPRs. Moreover, with the increase of the incident angle, one can easily find the absorption intensity of the resonant peak decreases. Furthermore, the corresponding FWHM (full width at half maximum) of the resonance and the maximum absorption decrease with the increase of angle. The oblique incident light can excite parallel and perpendicular electric dipole mode of structure. However, there is only parallel magnetic dipole mode for the structure and no perpendicular magnetic dipole mode at the oblique incidence [36,44]. It is corresponding that the silicon dark modes cannot be generated directly by the incident light. Additionally, as the oblique angle of the incident electric field becomes relative larger, the component perpendicular to the horizontal plane becomes gradually decrease, which causes weak interference for the characteristic resonant absorption in the spectra. Moreover, the value of absorption is still larger than 55% at the resonant wavelength even though the incident oblique angle up to 60°. The corresponding absorption spectra do not signally rely on the incident polarization angle, thereby enabling the good absorption stability and then leading to more facilitate and feasible in applied devices.
Fig. 4 (a) Absorption spectra of nanostructure at different incident oblique angles φ from 0 to 60°, taking 15° as a step. (b) Absorption spectra as a function of the incident oblique angle φ and wavelength. (c) The intensity of absorption as a function of φ.
Figure 5(a) demonstrates the absorption spectra at various lengths of silicon nanostrip, because the generation of the absorption resonance depends on the dielectric nanostrip. We find that the absorption intensity almost remains unchanged, which can be attributed to the direction of length along the polarization direction. Our results manifest that the absorption resonance can be associated with the parameters of silicon nanostrip and the setting of polarization direction.
Fig. 5 (a) Dependence of absorption spectra on the silicon length l. (b) Simulated absorption spectra at varied refractive indices n of the dielectric nanostrips.
Additionally, the transform for circumstance around the nanostrips impacts the resonant modes. Following the conditions, the perfect absorption resonant wavelength is sensitive to the change refractive index constants of dielectric nanostrip. The absorption spectra are shown in Fig. 5(b) where the dielectric parameters of refractive index are set from 3.3 to 3.6 with an increment of 0.05. We note an evident interaction between the refractive index of dielectric nanostrips and absorption response. The wavelength of the absorption peak tends to exhibit a redshift with the increase of the refractive index. It is mainly because that with refractive index n increase, the effective optical path increases, thereby enabling the redshift of the resonance wavelength. Therefore, the absorption resonant wavelength can be tuned through modulating the refractive index constant of dielectric nanostrip. It is good for a wide range of applications with varied refractive index for accumulation energy.
Furthermore, we investigate dielectric (silicon) cylinder and rhombus column arrays on a metal (silver) film. The radius (a0) of the cylinder is 40 nm and the side length (b0) of the rhombic is 80 nm. The other parameters are same as those in Fig. 1. It is worth noting that the presented mechanism of Mie resonances by the influence of LSPRs can attain similar results in silicon cylinder and rhombus column arrays whose corresponding simulated absorption spectra are displayed in Figs. 6(a)-6(d). Compared with the absorption spectra of silicon nanostrip arrays, there are still absorption peaks owing to the impact of LSPRs in the silverfilm. We notice the appearance of strong absorption at wavelengths of 528 and 509 nm for dielectric cylinder and rhombus arrays. In addition, two resonances with certain extent modulation depth arise in the spectra due to the influence of period. Moreover, the magnetic resonant mode of dielectric nanostructures can be directly excited in a dielectric interfering with metallic system. Therefore, the coupling between Mie resonances and LSPRs is a general method to excite the total absorption in dielectric.
Fig. 6 Schematic representation of dielectric cylinder (a) and rhombus (b) column arrays, respectively. Corresponding simulated absorption spectra for the dielectric cylinder (c) and rhombus (d) column arrays.
4. Conclusions
We have shown that the plasmonic excitation processes that are related to perfect light absorption with strong interfacial character involve the plasmonic coupling and the Mie resonance. The resonant mechanism and the interactions between the dielectric and metal are revealed in detail. Otherwise, surface enhanced processes at the dielectric-metal interface often invoke their generation and energy distributions, realizing the perfect absorption in the visible light wavelength. Moreover, we find that the energy of the photon is absorbed and transferred in the silicon nanostrip by the screening response of the silver film. Further progress in understanding how electrons interact with light depicts the energy of light into the silicon nanostrip through altering the corresponding parameters. In addition, the design nanostructure creates a path for realizing full energy absorption of dielectric, which is of high application for energy accumulation device in solar energy.
Funding
National Natural Science Foundation of China (NSFC) (61505052, 61176116, 11074069, 61775055).
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