Abstract: Transmission enhanced dual-wavelength light beaming is realized by a dielectric-metal-dielectric structure. Guided-mode resonance theory is used on the dielectric grating flanked single nanoslit in an optically thick metal to predict the original structure parameters for transmission enhanced dual-wavelength (442 nm and 633 nm) light beaming. Finite-difference time-domain numerical simulations confirm the theoretical prediction and demonstrate that the normalized-to-area transmittance of 10.8 and 14.7 and beaming angle of 2.40° and 2.65° for 442 nm and 633 nm, respectively, are achieved with a single structure, suggesting the potential applications of such structures in optical data storage, nanoscale wavelength multiplexing, directional light sources and emitters.
©2009 Optical Society of America
The phenomenon dealing with extraordinary transmission  and directional beaming of light  has stimulated much interest over the last years. Based on the surface plasmon polariton (SPP) propagation on the metallic surface, a series of novel applications such as nanofocusing [3–5], nanoguiding of light [6,7] has been demonstrated. A metallic nanoslit flanked by periodic metallic corrugations [2,8–10], dielectric gratings [11,12], and surrounded by metal heterostructures  can be used for enhanced transmission or directional beaming of light. Huygens’s principle [4,9,10], rigorous coupled wave theory  and guided mode resonance theory  are used to design the structures and interpret the physics behind the extraordinary transmission as well as directional beaming phenomenon. Recently, dual-wavelength enhanced transmission of light is realized by a periodic metallic corrugations flanked metal nanoslit, of which two wavelengths are enhanced by the left and right corrugations separately , but this method is not proper for dual-wavelength directional beaming because of the cross effect of the left and right corrugations. We previously proposed a dielectric gratings flanked metal nanoslit for directional beaming of dual-wavelength light , which is particularly interesting in optical data storage (one for writing and the other for reading). However, the transmission efficiency of such beaming light is limited. In this paper, we go on designing a single nanoslit in an optically thick metal film flanked with dielectric gratings in both input and output surfaces for enhanced dual-wavelength light beaming.
2. Theoretical design
Figure 1 illustrates the proposed structure, where a nanoslit with a width of w = 100 nm is introduced in the center of a metal Ag film with a thickness of hm = 200 nm. The input surface is covered by a dielectric grating with thickness hi and period Λi = ai + bi, while the output surface is covered by the other one with thickness ho and period Λo = ao + bo, where ai (ao) and bi (bo) are the widths of the dielectric films (with dielectric constant εd) and air gaps (ε0) of the input (output) gratings, respectively. When a TM-polarized (magnetic field parallel to the y direction) plane electromagnetic wave with wavelength λ is incident from the input grating at an angle θ, it couples into surface modes (SPPs) and propagation modes on the input metallic surface firstly, and then into the SPPs in the metal nanoslit and surface modes and propagation modes on the output metallic surface, and finally couples out to propagation modes in the air by the diffraction of the output dielectric grating at an angle θ' [13,14,16].
The input and output gratings can be designed separately, since the input and output gratings are responsible for the transmission enhancement and directional beaming of light independently [2,9,10,12]. If normal incidence (θ = 0) and directional beaming [θ' = 0, Fig. 1] are assumed, the coupling in and coupling out are inverse processes, which means the input and output gratings share the same structure parameters (Λi = Λo, ai = ao, bi = bo, hi = ho). The coupling between propagation modes in the air at an angle of ϕ (stands for θ or θ') and the modes on the input and output metallic surface for two different wavelengths λ1 and λ2 is governed by the grating Eq. (8),14]14,17]18] of the grating layer, ƒ( = a/Λ, approaching 1) is the filling factor of the grating. To get a feasible result, the guided mode resonance approximation (ƒ approaching 1) should be satisfied, meaning that the air gap with a narrower width bi (bo) is the limitation of the model we used in this Letter [14,17].
If the filling factor ƒ = 0.93 and the dielectric constants of the Ag film and the dielectric layer (Si3N4) are used as εm1 = −6.6086 + i0.1947, εd1 = 4.2243 at λ1 (442 nm) and εm2 = −18.3132 + i0.4981 and εd2 = 4.0828 at λ2 (633 nm), respectively [19,20], a solution of Eq. (2) at hi = 192 nm is obtained as βrλ1 = βrλ2 = βr = 2.169 × 107 m−1 with TM1(λ1) and TM0(λ2) modes in the structure. TMm(λn) denotes the m-th order TM mode for wavelengths λn (n = 1, 2). Then we get grating period Λi = 2π/βr = 290 nm from Eq. (1) for θ = θ' = 0 with ai = 270 nm and bi = 20 nm. The above analysis provides the theoretically predicted structure parameters (TPSPs: ai = ao = 270 nm, bi = bo = 20 nm, hi = ho = 192 nm) for enhanced directional beaming of dual-wavelength light simultaneously.
3. Numerical simulation and analysis
In the following, we use finite-difference time-domain (FDTD) numerical simulation to demonstrate the above prediction. The number of grating period is set to be 19 for both input and output gratings while optimized structure parameters for the output gratings (OSPs: ao = 275 nm, bo = 20 nm and ho = 195 nm) are slightly different from the TPSPs determined by the previous method . For the input gratings, the OSPs (ai = 255 nm, bi = 20 nm and hi = 220 nm) are determined by the method which we will discuss below.
Figure 2(a) illustrates the FDTD simulated dependence of normalized-to-area transmittance (defined as transmittance normalized to the incident flux in the direction normal to the metal surfaces and to the slit area) on wavelength for different structures. For a structure only with output gratings (dash-dotted black curve), we see that these is no transmission peak, confirming that the output surface shows little effect on the transmittance compared to the input surface [9,10,12]. For a structure with TPSPs at input and output gratings (dashed blue curve), there are two transmission peaks at 439 nm (Peak 1) and 650 nm (Peak 2) appeared. For the structure with OSPs at input and output gratings (solid red curve), peaks 1 and 2 shift to 442 nm and 633 nm, respectively. Figures 2(b) and 2(c) show the FDTD simulated wavelength dependence of peak 1 around 442 nm (Lines L1, L3) and peak 2 around 633 nm (Lines L2, L4) on the input grating thickness hi [Fig. 2(b)] and period Λi [Fig. 2(c)] while the other parameters are at OSPs (ai = 255 nm, bi = 20 nm, ao = 275 nm, bo = 20 nm and ho = 195 nm) and (bi = 20 nm, hi = 220 nm, ao = 275 nm, bo = 20 nm and ho = 195 nm), respectively. The slopes of Lines L1, L2, L3 and L4 shown in Figs. 2(b) and 2(c) are 0.36, 0.11, 0.65 and 1.57. Since peak 1 is sensitive to both hi and Λi (see Lines L1 and L3), but peak 2 only sensitive to Λi (Lines L2 and L4), we shift peak 2 from 650 to 633 nm by reducing Λi and then shift peak 1 to 442 nm by increasing hi in TPSPs [see Fig. 2(a)]. Figure 2(d) shows the transmittance of the beaming light on the error δ of grating structure parameters ai and hi [see Fig. 1] for λ1 = 442 nm (Curve C1 for ai and Curve C3 for hi) and λ2 = 633 nm (Curve C2 for ai and Curve C4 for hi), where ai and hi corresponds to the designed 255 nm and 220 nm, respectively. From Fig. 2(d) we see that the peak transmittance shows a reduction with the increased error δ. This is due to the broken of the transmission enhancement condition Eq. (1) by deviation of the grating period Λi( = ai + bi) (Curve C1 and Curve C2) or βr determined by the grating thickness hi (Curve C3 and Curve C4). The transmittance is sensitive to ai (Curve C1 and Curve C2) as the transmission enhancement condition Eq. (1) is sensitive to Λi( = ai + bi). Since βr of the surface mode TM0(λ2) is not sensitive to hi when hi >150 nm [13,14], the transmittance changes slower for TM0(λ2) around hi (Curve C4) than TM0(λ2) around ai (Curve C2). From the above analysis we can see that the OSPs for input gratings (ai = 255 nm, bi = 20 nm, hi = 220 nm) could be obtained by fine adjustment of TPSPs, at which normalized-to-area transmissions of 10.8 for λ1 and 14.7 for λ2 are achieved.
Figure 3(a) presents the FDTD simulated dependence of HAHMs (half angles at half-maximum) and DEs (defined as the total energy confined in the full width at half maximum of the central beam divided by light energy radiated into the free space) of emitted central beams on wavelength deviation Δλ from λ1 = 442 nm (Curve C5 and Curve C7) and λ2 = 633 nm (Curve C6 and Curve C8) with OSPs at both input and output grating, respectively. The data are obtained along the x axis on a line z = 60 μm away from the output gratings. From Curve C5 we see that HAHM of the beaming light around λ1 decreases to about 3° as Δλ is increased from −12 nm to −4 nm and keeps steady as Δλ is increasing to 10 nm, and then rise up as Δλ is further increased, while Curve C7 shows the opposite properties. This can be understood by calculating the diffraction angle θ' of the emitted light through submitting βr of TM1 [inset of Fig. 3(a)] into Eq. (1). The θ' decreases from positive [βr>2.169 × 107 m−1, spreading] to zero [βr = 2.169 × 107 m−1, directional beaming] and then to negative [βr<2.169 × 107 m−1, focusing] as Δλ changes from −12 nm to 12 nm. The two beams emitted from the left and right half of the output gratings overlapped , which results in a relatively flat range of Curve C5 and Curve C7, as Δλ increasing from −4 nm to 5 nm. For wavelength around λ2, the slope of the dispersion curve of TM0 is smaller than that of TM1 [Fig. 3(a), inset], which would result in a relatively flat range of Curve C6 and Curve C8 in an even larger range of Δλ from −12 nm to 12 nm. Note from Fig. 3(a) that the HAHMs are 2.40° and 2.65°, while the DEs are 0.43 and 0.39 at λ1 and λ2 respectively, implying that the enhanced directional beaming of dual-wavelength light λ1 and λ2 are achieved simultaneously.
Figure 3(b) shows the dependence of the normalized transmittance and HAHMs of emitted central beams on the incident angle |θ| for λ1 = 442 nm (Curve C9 and Curve C11) and λ2 = 633 nm (Curve C10 and Curve C12) with OSPs at both input and output gratings, respectively. From Curve C9 (C10) we see that the normalized transmittance of the beaming light decreases to about 1 (3) for λ1 (λ2) as |θ| is increased from 0° to 5° (7°) and keeps steady as |θ| is increasing to 20°, while Curve C11 (C12) keeps steady as |θ| is increased from 0° to 5° (7°) and then rise up rapidly. The grating equation Eq. (1) is broken as |θ| is increased for the structure with OSPs at the input grating, which results in a decreasing coupling efficiency from the incident light to SPPs on the input metallic surface, and then the decreasing transmittance (Curve C9 and Curve C10). With the increase of |θ|, the near field distribution of light in the central slit is changed, which results in a field redistribution in the far field and then a broadening of the HAHMs. From the above analysis we can see that the enhanced directional beaming of dual-wavelength light λ1 and λ2 can be realized with |θ|≤5°, respectively.
In summary, we have designed a dielectric-metal-dielectric structure to realize the transmission enhanced dual-wavelength light beaming based on guided-mode resonance theory. A single nanoslit in an optically thick metal film flanked by dielectric gratings on both input and output surfaces of the slit can realize transmission enhanced directional beaming of two wavelength lights (442 nm and 633 nm) simultaneously. FDTD simulations well demonstrate the theoretical prediction. The proposed structures would be interesting in high density optical data storage, spatial and spectral multiplexing, nanoscale directional light sources and emitters, biosensors, near-field optics and spectroscopy, etc.
This work is financially supported by the National Basic Research Program (Grant No. 2007CB935300) and NSFC (Grant Nos. 10774116 and 60736041).
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