1. Introduction

Extraordinary transmission by subwavelength hole arrays [1] as well as a single hole surrounded by surface corrugations [2–5] has attracted a great amount of interest and offers promising applications. The transmission processes of this kind of trench-surrounded metallic aperture can be separated into three independent steps: coupling in, transmission through and coupling out from the aperture [6]. Although surface corrugations at the entrance plane can be optimized to enhance the transmission as shown in Ref. [2–4] for instance by tailoring the width and depth of the periodic trench structures for a given transmission wavelength, the transmission is still too low for practical applications.

In current research about the transmission enhancement, the structures surrounding the nano slit are mostly trench structures. A nano trench can effectively excite the surface waves but is incapable of confining them, so that parts of the excited surface wave energies are leak away without being coupled into the aperture. In this paper, we attempt to recycle the surface wave by using a pair of bumps bordering the conventional trench-surrounded slit to confine the excited surface waves for further enhancing the transmission through the metallic slit.

It is worth to mention that bumps, trenches or discontinuities of the dielectric constant on the surface can be seen as surface defects and at the arrival to the surface defect the incident surface plasmon polariton (SPP) is partially reflected, transmitted and scattered into the free space above the metal structure. Sanchez-Gil et al obtained the scattering equations for the SPP from a one-dimensional surface defect using the local impedance boundary condition [7–8]. The SPP reflection, transmission and scattering coefficients were computed. The SPP maximum reflection of <8% is achieved for either protuberance or indentation (plasmon mirrors) of the width a<λ/10 and height h<λ/5. A Bragg SPP mirror, consisting of several periodic ridges of height 60 nm for a wavelength of 800 nm, was integrated experimentally in the SPP waveguide for SPP routing [9]. A Bragg SPP mirror with a reflectivity of 65% was obtained by using a grating of ten ridges [9].

We show in this paper by the finite-difference time-domain (FDTD) simulation that when the height of the bump is larger than the depth of penetration on air side of the surface waves, the bump can serve as a perfect surface wave reflector (SWR). We demonstrate that the transmission through a conventional trench-surrounded nano slit can be enhanced by 1.75 times through recycling the escaping energy by a pair of bumps. Moreover, the sideband of the transmission spectrum is not affected when the peak transmission value is enhanced by the application of the pair of SWRs.

2. Enhancing transmission with surrounded trenches

We use the FDTD method to investigate the transmission of a nanoscale slit, which is surrounded by two sets of periodic trenches and bordered by two bumps, as shown in Fig. 1(d). In the FDTD, the grid scale is set to 5nm to capture the fine geometric features. The perfectly-matched-layer conditions were used to absorb parasitic reflections at the boundaries of the computation window. A TM-polarization (H field perpendicular to the x-z plane) beam of size 13μm and wavelength λ ₀ =670nm is incident to the slit along the z-axis. The structure is of real metal silver with the wavelength dependent permittivity ε_m= ε’_m + ε“_m =-18+1.16i at λ ₀ according to Ref. [10].

 

Fig. 1. Schematic of the analyzed structures, (a) single slit, (b) periodic set of trenches, (c) trench-surrounded slit and (d) trench-surrounded slit bordering by a pair of bumps.

Download Full Size | PDF

The transmission of a bare slit of width a_s=50nm, as shown in Fig. 1(a), is computed by the FDTD as about 1%. The thickness of the slit h_s=400nm is designed to satisfy the Fabry-Perot (FP) resonance condition [11–12] for a high transmission. The transmission coefficient is defined as the transmitted power flux normalized by the total power of an input beam of the total width of 13μm, in order to compare the computed results for the different structures shown in Figs. 1(a)–1(d). The transmission flux is calculated by integrating the time-averaged Poynting vector through a semi-circular “detector” with a radius of 3μm as shown on Fig. 1(a).

We then consider a structure of a single slit with two sets of periodic trenches on both sides of the slit, as shown in the Fig. 1(c). Each set consists of N=10 trenches of width a_T=325nm, depth h_T =50nm and fixed period 620nm. The set of periodic trenches provides momentum to the free space incident beam and excites the surface waves. The surface wave energy flux is calculated by integrating the time-averaged Poynting vector through a line “detector” normal to the metallic surface with a height of 1μm and a distance of L=6μm from the periodic trenches, as shown on Fig. 1(b). The period of 620nm is optimized by the FDTD for maximizing the surface wave energy

The SPPs excited by the sets of trenches are propagated on the structure surface towards the slit. The distance d from the most inner trench to the center of the slit determines the phase of the SPP, which will be coupled into the slit and interfered with the input beam impinging on the slit [13]. The simulation shows that the slit maximum energy transmission occurs when d=325nm is close to 0.5λ₀/n_spp, where the SPP effective index $n_{spp}=\sqrt{{\epsilon }_d{\epsilon }_m^{\text{'}}/({\epsilon }_d+{\epsilon }_m^{\text{'}})}=1.029$ with ε´_m=-18 for Ag. In addition, when a plane wave is incident on the trenches, the excited surface waves would have an initial phase shift of π [5]. Thus, there is constructive interference between the SPP and the incident beam at the entrance the slit, which enhances the slit transmission.

The trenches are designed in such a way that the transmission of the SPP over the trenches is maximal and the scattering loss of the SPP into the free space by the trenches is minimal. Sanchez-Gil et al. showed that the transmission and scattering of the SPP exhibit oscillatory behavior with increasing trench width [7]. The oscillation period and the defect width that correspond to the minimum scattering depend on the trench depth. We find out that when the trench width a_T=325nm=λ_spi/2 the trench yields the minimum scattering and the maximum SPP transmission with trench depth h_T=50nm.

The transmission spectra through a slit surrounded by N=0, 2, 6 and 10 pairs of trenches are shown in Fig. 2, respectively. The spectra present the transmission maxima at wavelength of 670nm. More trenches lead to higher transmission. The maximum transmission is and 28.2% for N=2, 6 and 10, respectively. As the transmission through the bare slit on a silver film is 1%, it is clear that the transmission power of the slit surrounded by 10 pairs of trenches is enhanced by 28 times.

 

Fig. 2. Transmission spectra of a slit of width 50nm, thickness 400nm, bordered by two sets of N trenches of width 325nm, depth 50nm and period 620nm. The distance from the first trench to the slit center d=325nm.

Download Full Size | PDF

3. Enhancing transmission through a trench-surrounded slit using metallic bumps

Figure 3(a) shows the distribution of H_y ² for the optimized 10-trench-surrounded slit. Parts of the surface waves excited by the trenches are coupled into and transmitted through the slit. In Fig. 3(a) one can also observe an evident drawback of the trench-surrounded structure: parts of the surface waves on the metallic surface are transmitted through the most outer trenches and leak. In our simulation, about 30% of the total incident power leaks out and is lost. To further enhance the transmission, we propose using surface wave reflectors (SWRs) to recycle the leaking surface waves.

 

Fig. 3. H_y ² distribution for a plane wave of beam size 13μm normally incident on a nano slit, (a) bordered by 10 pairs of trenches, (b) bordered by 10 pairs of trenches and the SWR pair. In all cases, a_s=50nm, h_s=400nm, d=325nm, a_T=325nm and h_T=50nm. The size of the rectangular metallic bump is height × width = 1μm × 1μm.

Download Full Size | PDF

When the surface wave encounters a surface defect, such as a trench or a bump, it is partially reflected, transmitted and scattered. The surface defect as a SPP mirror has typically low reflectivity (<8%), which can reach a maximum when the width of the defect is about 0.1λ [7]. According to Sancher-Gil et al, this reflectivity is independent of the defect height H, as long as the height does not exceed the range (H<0.2λ), where the theory based on the local impedance boundary condition is valid [7].

With the FDTD we can study the bumps of any height and width. Figure 4(a) shows the reflectivity of a bump on an Ag film as a surface waves reflector as a function of bump height H and width W. In order to compute the surface wave reflectivity of the bump with the FDTD, we define a line “detector” at x=0μm. The bump is placed at x=5μm. The surface wave impinges from x=-5μm forward to the bump. The detector “measures” $H_{y^{SUM}}=H_{y^{+}}+H_{y^{-}}$ , in which the forward surface wave $H_{y^{+}}$ can be separately measured at the flat Ag/air interface without the bump, so that the reflected backward surface wave $H_{y^{-}}$ is obtained. The reflectivity of the bump is computed by:

where L=5μm and the absorption coefficient of the SPP at the Ag/Air interface α =2^*Im(k_spp) =0.0365μm ^-1, $H_{y^{+}}{|}_{x=5\mu m}$ is measured by the line detector at the front surface of the bump. We found that the reflectivity of the metallic bump increases with increasing of the bump height, H. For a fixed width of W=0.5μm, the reflectivity increases from 7% to 95% for height, H from 0.05μm to 1μm. When H is shorter than the effective depth of penetration of the SPP on the air side, (λ/2π)((ε_m + ε_d)/ε² _d)^1/2 =0.44μm for Ag/Air interface at the wavelength of 670nm, part of the surface wave climbs over the bump, resulting in a reduced reflectivity.

The H_y ² distributions for a surface wave encountering a metallic bump of different dimensions are shown in Figs. 4(b)–4(e). It can be seen in Fig. 4(b) that when the bump height H=0.1 μm, parts of surface wave overpass the bump. One can see in Fig. 4(d) the interference fringes of the surface waves on the hill of the bump of small height. The higher the bump as a surface wave mirror, the higher reflectivity, as shown in Figs. 4(c)–4(e). Most surface waves are reflected by the bump and form standing waves with the input surface wave, as shown in Fig. 4(e). We use two rectangular bumps of size H×W = 1μm×1μm of the same metal Ag as a SWR pair, bordering the optimized 10-trench-surrounded slit, as shown in Fig. 1(d). The SWR pair themselves are not illuminated by the input beam.

 

Fig. 4. (a). Surface wave reflectivity of a metallic bump as functions of the height (H) and width (W) of the bump. H_y ² distribution of a surface wave impinges a bump with different width and height, (b) W=0.5μm H=0.1μm, (c) W=0.5μm H=0.4μm, (d) W=1.0μm H=0.2μm, (e) W=1.0μm H=0.8μm. In all cases, λ₀ = 670nm, and ε^Ag=-18+1.16i.

Download Full Size | PDF

The transmission through the nano slit remains the same for bumps with widths varying from 0.05μm to 1.00μm, as shown in Fig. 5. Bumps with a series of different heights for a chosen width of 1.00μm are also simulated. The slit transmission increases exponentially with the height of the bump, as shown in Fig. 5. It is saturated when the bump height (>0.5μm) exceeds the effective depth of penetration of the SPP in the air.

 

Fig. 5. Transmission of a 10-trench-surrounded slit as a function of the height (square) and the width (triangle) of the SWR. In all cases, a_s=50nm, h_s=400nm, d=325nm, a_T=325nm, h_T=50nm and λ ₀=670nm.

Download Full Size | PDF

The H_y ² distribution of the 10-trench-surrounded slit bordered by the SWRs is shown in Fig. 4(e). It can be seen that most of the surface waves are confined in the cavity formed by the pair of SWRs. Over 95% of the surface waves are reflected, therefore, no more surface waves leak from the edge of the metallic film. Nevertheless, not all of the reflected surface waves can transmit through the slit, because surface waves propagating back to the slit suffer from propagation loss, such as absorption by the metal, scattering by the trenches and the coupling loss at the trenches. The slit transmission, whether enhanced or suppressed, depends on the distance between the SWR pair and oscillates periodically as the position of the SWR varies. This reveals effect of the interference between the forward and backward surface waves within in the cavity formed by the pair of SWRs. As a result, the slit transmission is maximal at λ=670nm when the SWR pair are positioned 8.32μm from the slit center on the both sides.

The transmission spectra through a trench-surrounded slit bordered by a pair of SWRs are shown in Fig. 6. The red, green and blue curves represent the spectra of a slit respectively bordered by 2, 6, and 10 pairs of trenches and bordered by a pair of SWRs. The transmission peaks of the red, green and blue curves are 8.54%, 28.5% and 49.3%, respectively. More trenches results in higher transmission. As a reference, the maximum transmission of a bare slit is 1%, as shown by the black curve in Fig. 2 and the maximum transmission of the optimized 10-trench-surrounded slit is 28.2%. Therefore, the pair of bumps, as the SWRs, enhances the slit transmission by 1.75 fold.

 

Fig. 6. Transmission spectra of a nano-scaled slit bordered by N pairs of trenches and one pair of SWRs, where N=2, 6, and 10. The black line shows the spectrum of a bare slit for reference. In all cases, a_s=50nm, h_s=400nm, d=325nm, a_T=325nm, h_T=50nm. The size of the rectangular metallic bump is height × width = 1μm × 1μm.

Download Full Size | PDF

5. Conclusion

To summarize, a large transmission of light through a nano metallic slit, which is surrounded by nano trenches and bordered by bumps, is obtained by the FDTD calculation. Two sets of trenches surrounding the nano slit excite the surface waves. A nano metallic bump of 1μm height and 1μm width showed a reflectivity larger than 95%. Therefore, pair of bumps bordering the trenches can enhance the slit transmission by 1.75 fold when bordered, such that the overall transmission efficiency of the proposed structure reaches 50%. In addition, the sideband of the transmission spectrum is not affected although the peak transmission value is enhanced by the SWRs. Analog the SWR into a bull eye structure, this device thus holds potential for the applications where both high throughput and high resolution are required.

Metallic nanospheres could also be used as SWRs for recycling the surface waves although the recycling ratio needs to be further investigated. The fabrication with the metallic nanospheres is better suited for applications: the nanospheres can be aligned at an appropriate position by self-assembling or manipulating by scanning probe microscope. In the near future, this type of a high transmission device might be fabricated by a combination of focused ion beam milling and self-assembling techniques.