1. Introduction

Confining light in subwavelength volumes is important for the development of future nano-photonic devices with miniaturization and high integration, which has attracted wide research interest in recent years [1–3]. Many techniques have been proposed to realize this goal, including V-shaped metallic nanostructures [4], aperiodic metal/dielectric waveguides [5] and near field plates [6, 7]. Very recently, a new concept for confining and enhancing light was proposed by using the light funneling effect in a metal film with deep subwavelength apertures. G. Subramania et al. presented a new paradigm structure which demonstrated efficient ultrabroadband funneling of optical power confined in an area as small as ~(λ/500)² with non-resonant mechanism in 2011 [8]. During the same year, Patrick Bouchon et al. theoretically and experimentally demonstrated a total funneling effect of light in high aspect ratio gold gratings, which was explained by a resonant mechanism involving the magneto electric interference [9, 10]. A study of enhanced light funneling through a subwavelength aperture with realistic epsilon-near-zero (ENZ) materials [11] was presented by D.C. Adams et al. recently. However, realization of these structures usually involves thick noble metals and deep nano-grooves, such as gold films with thickness and groove depth more than 1 μm [10], which limits the realistic applications of this kind of structure. Besides, the wide bandwidth of the reflection spectrum of the light funneling in the thick metal film does not satisfy the requirement of highly sensitive infrared detection and sensing. On the other hand, metal/dielectric multilayer film metamaterials with special hyperbolic dispersion possess many unique optical properties after being engineered with nano-patterns [12, 13]. The funneling effect in metal/dielectric multilayer structure may exhibit some different properties because of the resonant cavity between films and coupling of waves, which have not been discussed yet.

In this paper, we demonstrate a highly efficient light funneling effect in metal/dielectric multilayer films with subwavelength grooves by numerical simulations and experiments. A dip to nearly zero in the simulated reflection spectrum at a resonant wavelength can be produced. All of the light power at the resonance can be funneled into the subwavelength groove from the top metal slit and is enhanced in the thin dielectric layers sandwiched by the metal films. The simulated result shows a much narrower resonance dip than previously reported funneling effects in thick metal films and the total thickness of multilayer films is thinner than the metal film for producing a resonance at the same wavelength. Another advantage is that a narrow groove width is not essential for the multilayer metal/dielectric structure, which makes the fabrication easier. Further analyses show that grooves with different widths correspond to different resonant wavelengths with high absorption and the reflection spectrum is affected by the numbers of metal/dielectric pairs and the profile of the grooves according to the simulations. The coupling effect between two grooves with different distance is analyzed. These results extend the light funneling effect to multilayer plasmonic structures and can be more favorable in the applications of infrared detectors and biological sensing.

2. Structure and results

Figure 1(a) shows the proposed structure which consists of two pairs of Au/MgF₂ films, periodic nano-grooves and a continuous Au film on the substrate of silicon. The structure can be fabricated by e-beam evaporation and focused ion beam (FIB). The simulated reflection spectra for the designed multilayer structure and a thick Au film with nano-grooves are shown in Fig. 1(b). Structures of Au films with deep grooves are commonly used for previous studies of light funneling and plotted here for a comparison. The incident light is TM polarized (electrical field is perpendicular to the gratings). The numerical simulations are done by COMSOL Multiphysics 3.5a. Refractive index of Au comes from Ref. 14 and the value of refractive index of MgF₂ is 1.37.

 

Fig. 1 (a) Schematic of designed Au/MgF₂ multilayer structure with nano-grooves. The thicknesses of Au/MgF₂ films are 80 nm and 110 nm, respectively and 80 nm for the bottom Au layer. The total depth h is 380 nm. The periodΛof the grating is 800 nm and the width w of the groove is 100 nm. (b) Comparison of the reflection spectra of the designed Au/MgF₂ multilayer structure and Au films with groove depth h = 380 nm and h = 500 nm, respectively.

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A narrow band reflection dip with almost zero reflecion can be seen at the wavelength of 2.8 μm for the multilayer structure. There is no transmissive light because of the thick Au layer at bottom. It means almost 100% of the light at 2.8 μm can be funneled into the multilayer structure through a narrow groove which covers an area of only 12.5% of the surface within one period. As a comparison, a deeper groove depth of 500 nm is required to generate a similar resonance near 2.8 μm for the single Au film and the bandwidth is much wider than that of the structure with Au/MgF₂ multilayer films. The absorption at the resonance is only 50% for the Au film with groove depth of 500 nm and high absorption can typically be achieved through deeper grooves, like 2000 nm demonstrated in Ref. 10 or reducing the groove width to near 50 nm [9], both of which make the fabrication challenging.

To understand the mechanism of the above phenomenon, we analyze the distribution of the Poynting vector in the Au/MgF₂ multilayer structures with subwavelength grooves because it represents the propagation direction of the light. Figures 2(a) , 2(b) and 2(c) illustrate the mechanism of light funneling effect in the multilayer structure, which can be identified as the electro-magnetic interference (EMI) of the incident wave and evanescent field. The Poynting vector can be expressed as the sum of decomposited terms at the resonant wavelength without considering the reflected component [9]:

 

Fig. 2 Schematic of streamlines of the different Poynting vector components at the resonant wavelength in the Au/ MgF₂ multilayer structure with a subwavelength groove: (a) Incident wave S_i (b) EMI S_ei (c) Total Poynting vector S (d) Simulated magnetic field (color bar) and power flow (white arrows) by COMSOL at the resonance in the designed structure. The parameters of the structure are the same as Fig. 1(a).

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The process can be explained by two mechanisms: the top Au slit works like a funnel, making all the light over a wide range squeeze into the groove; the slits form a F-P resonant cavity and absorb the light at a resonant wavelength. The dip position of the reflection spectrum corresponds to the resonant wavelength λ_m and can determined by the equation:

The bandwidth BW of the resonance is determined by the Q factor as BW = f₀/Q, where f₀ is the resonant frequency. The comparatively higher Q factor for the metal-dielectric multilayer structure than the single metal film originates from the scattering and coupling of electromagnetic waves [17, 18].

The simulated magnetic field and the power flow (indicated by the arrow) at the resonant wavelength are shown in Fig. 2(d). We can see that the power flow of the light is funneled into the grooves from a wide range of outer space and then kept in the thin MgF₂ layers. The magnetic fields show the enhanced light power in the MgF₂ layers.

3. Discussion

The reflection spectrum of the metal/dielectric multilayer grating structure is influenced by many factors,such as the width, depth, period and profile of grooves. Figure 3 shows the influences of the numbers of pairs, groove width and period.

 

Fig. 3 Simulated reflection spectra (a) multilayer grating structures with different Au/MgF₂ pair numbers and the thicknesses of Au/MgF₂ are 80 nm/110 nm; (b) multilayer structure with 3 pairs of Au/MgF₂ (50 nm/80 nm) and the total thickness is 390 nm; (c) structures with different groove widths and the same period of 800 nm; (d) structures with different periods and the same groove depth of 100 nm. The pairs of Au/MgF₂ are two in all the structures in (c) and (d).

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Supposing the thicknesses of Au/MgF2 (80 nm/110 nm) are kept the same, different pair numbers of metal/dielectric films lead to differences in groove depth and resonance cavities. It shows in Fig. 3(a) that one pair of Au/MgF₂ films cannot form an efficient resonant cavity with high Q factor and the absorption of light at resonant wavelength is only about 40%. However, too many pairs of films will also destroy the perfect narrowband absorption, such as three pairs in Fig. 3(a). High order Fabry-Perot-like resonance appears because of the deeper groove depth and wave coupling between the three dielectric layers [19]. However, if the total thickness of the multilayer film is kept almost the same as the case of two pairs in Fig. 3(a), but the number of pairs is increased to three by reducing the individual layer thickness, there will be still only one reflection dip, as shown in Fig. 3(b). This means it is the total groove depth that determines the order of the resonance. Its position will be slightly shifted to longer wavelengths because the effective index n_eff of the guided mode inside the metal/dielectric structure becomes larger when the layer thickness is reduced. The resonance wavelength λ_m will be increased according to Eq. (2).

When the materials and pair numbers are fixed, the corresponding resonant wavelength will be influenced by the groove depth and period. As shown in Fig. 3(c) and 3(d), the resonance dips red shift when the groove width reduces from 250 nm to 50 nm or the period increases from 700 nm to 900 nm. By taking into account both influences of periods and groove widths, we can find that the resonance wavelength is mainly determined by the width W_m/d of metal/dielectric ribbons, which is calculated by W_m/d = Λ-w (period minus groove width). Reducing the groove width or increasing the period both produce a result of longer W_m/d, and therefore the reflection dip moves to a longer wavelength. Their relation can be estimated by $W_{m/d}\approx \frac{1}{4}{\lambda }_m$. This property makes it suitable for the applications over various wavelength ranges.

Next, we consider the influence of the profile of the grooves. The sidewall of the groove commonly becomes tilted during the fabrication process of etching or FIB. The schematic and simulated reflection spectra of the multilayer structure with different top slit width w are plotted in Fig. 4(a) and 4(b). The resonance wavelength shifts to short wavelengths as w increases and the bandwidth of the resonance becomes wider. The wider bandwidth is caused by the trapezoid profile of groove, which has many slight different widths along the vertical direction of the sidewall. Each groove width corresponds to one respective resonance wavelength and therefore the reflection spectrum is a composition of several adjacent reflection dips, making the final spectrum a little wider. The perfect broadband absorption cannot be achieved here because of its very limited film layer numbers.

 

Fig. 4 (a) Schematic of the Au/MgF₂ multilayer structure with tilted sidewalls. The width of top slit is w. (b) Simulated reflection spectra of the structure with different w.

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One more interesting phenomenon we found is the antisymmetric field distributions in the Au/MgF₂ multilayer structure with double period grooves, which means keeping the large period 2Λ = 1.6 μm unchanged and reducing the distance L between the two grooves from 800 nm to 700 nm, as shown in Fig. 5(a) . Other parameters are the same as the structure in Fig. 1(a). Figure 5(b) shows that the previous single resonance splits into three different resonance dips. These multiple resonances are caused by the asymmetry of the grooves' positions. The incident light is funneled into nano-grooves and propagates in the dielectric layers of the multilayer films. There will be phase difference for the propagating waves because the lengths of the dielectric layers between the two grooves are different, and therefore constructive and destructive interferences may happen when the phase conditions are fulfilled. Simulated magnetic field and electrical field distributions from COMSOL3.5a further demonstrate this phenomenon, as shown in Fig. 5(c) and 5(d). We can see that enhanced magnetic field and electrical field are only confined in the first MgF₂ layer between the two grooves at short wavelength 2 μm. Then they move to the second MgF₂ layer between the two grooves, which are equally distributed in the both MgF₂ layer at 2.33 μm and totally in the second MgF₂ layer at 2.4 μm. Later they continue to move to the longer dielectric part outside the two grooves as the increasing of the incident wavelength. They repeat the previous process again from the first MgF₂ layer to the second layer from 2.7 μm to 3.4 μm.

 

Fig. 5 (a) Schematic of the Au/MgF₂ multilayer structure with double period grooves and L = 700 nm. (b) Reflection spectrum of the structure in (a). (c) Magnetic fields at different wavelengths in the multilayer structure. (d) Electrical fields at different wavelengths in the multilayer structure

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Light absorbers or detectors with high performance usually require excellent incident angle-insensitive property [20]. We further numerically analyzed the angle dependence of incident light for the structure with parameters described in Fig. 1(a). The simulated result of the reflection spectra as a function of wavelength and incident angles is shown in Fig. 6 . Absorption of the structures can be calculated by 1-R, where R is the reflection. High narrow band absorption is maintained until incident angle θ is larger than 80 degree for the Au/MgF₂ multilayer structure with narrow grooves.

 

Fig. 6 Simulated reflection spectrum of the Au/MgF₂ multilayer structure with the narrow grooves

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One sample with the structure parameters in Fig. 1(a) was fabricated for experimental demonstration. The multilayer films are deposited by e-beam evaporation using the tool SJ-26 evaporator and the narrow grooves are fabricated by FIB (FEI Nova 200 Nano-lab). A scanning electron microscope (SEM) image of the cross section drilled by FIB is shown in Fig. 7(a) . The experiment result is measured by an infrared polarizer and a Fourier transform infrared spectroscopy (FTIR) spectrometer and is ploted in Fig. 7(b) compared with the simulation result. The resonance positon of the experimental result matches the simulation well while the bandwidth is a much wider than the simulated one, which is mainly caused by fabrication imperfections, such as tilted sidewalls and surface roughness during the fabrication of FIB.

 

Fig. 7 (a) Angled SEM image of the cross section of the fabricated sample. The cross section is also cut by FIB. (b) Experimental and simulated reflection spectra of the fabricated sample.

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5. Conclusion

We comprehensively studied the light funneling effect in the Au/ MgF₂ multilayer structures with subwavelength grooves mainly by numerical simulations and experiment. The mechanism of light funneling in metal/dielectric multilayer is demonstrated from the perspective of electro-magnetic interference and resonant cavity. The reflection spectrum of the structure with vertical grooves shows narrow band resonance and the resonant wavelength is dependent on the groove width and Au/ MgF₂ pair numbers. Further analyses illustrate that the sawtoothed profile of grooves will increase the bandwidth and shift the position of the resonance. Antisymmetric field distributions are generated by slightly changing the distance between the two grooves. The above structures also exhibit good incident angle insensitive property. These results give better understanding of light funneling effect and can have promising applications for infrared sensors and detectors.