The light transmission through a single subwavelength aperture surrounded by periodic grooves in layered films consisting of Ag and transparent dielectric is analyzed numerically by finite difference time domain (FDTD) method. Results show that the transmission through the aperture in the composite films is strongly enhanced by the modulation of grooves on the transparent dielectric. Two models are employed to explain the mechanisms of transmission enhancement.
©2005 Optical Society of America
As we know, light transmission through a small aperture whose size is compared with the wavelength of incident light on an opaque screen will be very poor and diffracted in all directions . A recent research by H. J. Lezec et al. gave us a new view on the transmission through a subwavelength aperture surrounded by periodic corrugation in a metal film . Enhanced light transmits through the structured metal film and propagates with a very small divergent angle. Thereafter, many experimental and theoretical studies have been published [3–20]. However, these studies almost only involved pure metal films. Some works [21–23] on enhanced transmission and beaming of light through dielectric photonic crystal waveguide were reported recently. Here we present some designs of new structures of layered films consisting of metal and dielectric.
In Fig. 1, we present three types of structures. Structure Dielectric-Ag (DA), as shown in Fig. 1(a), is a combination of Ag film and dielectric film with a slit through them and grooves parallel to the slit on their surfaces respectively. Structure Ag-Dielectric (AD), as shown in Fig. 1(b), is just the same as structure DA, but with opposite light incidence direction. Structure Dielectric-Ag-Dielectric (DAD), as shown in Fig. 1(c), is of sandwich type with an Ag film clamped by two dielectric films on both sides, and with grooves only on dielectric films. To compare, we use the same geometric parameters as followings in these three structures if not mentioned additionally: groove period p = 500 nm, groove and slit width w = 40 nm, number of the grooves on each side of the slit of either surface N = 5, thickness of Ag film hAg = 300 nm and depth of grooves on Ag surface dAg = 60 nm. Thickness of the dielectric film hdi and depth of the grooves on dielectric film ddi are variable, and we will study their relationships with transmission. The refractive index of dielectric is set to be n = 2.0, and is also assumed to be isotropic and nondispersive. The permittivity of Ag is given by Drude model. A TM mode plane wave with wavelength ranging 400 ~ 900 nm is incident perpendicularly on the structures and the zero-order transmission spectra are simulated by FDTD method.
The normalized-to-area (calculated by dividing the fraction of light transmitted by the fraction of surface area occupied by the apertures ) transmission spectra and the patterns of light emitting from AD and DAD structures at the wavelengths corresponding to transmission peaks are shown in Fig. 2. From these curves and patterns, it is seen clearly that our special structures of corrugated dielectric and Ag films also have the ability in enhancing the transmission through subwavelength aperture and beaming the output light. The beaming angles of the output light, i.e. full-width at half-maximum divergence, in Fig. 2(d) and (e) are ± 7.6° and ± 5.4° respectively.
Since transmission enhancement mainly depends on the properties of the incident surface [2, 5] and the output surface determines the distribution of the transmitted light [2, 4], we can analyze the DA structure first to understand the mechanism of transmission enhancement that is caused by dielectric film. To obtain a direct understanding on the enhancement by the grooves on dielectric film, we remove the grooves on the output surface i.e. Ag surface of DA structure in following simulations. Beaming light emission through AD structure will be discussed detailedly in a later work. In Fig. 2(a), there are two sharp transmission peaks in the spectrum of DA structure under the condition of hdi = ddi = 200 nm. The normalized-to-area transmissivities Tmax and the wavelengths λmax of the two peaks under different hdi (with ddi = hdi) of DA structure with grooves only on incident surface are given in Fig. 3. Results show that Tmax and λmax of peak one are relative to hdi regularly, but for peak two, they are almost independent of hdi and vary very little. This implies that the two peaks arise from different mechanisms. It will be verified that the mechanism of peak two is similar to that of pure metal films and the mechanism of peak one corresponds to a new mechanism that is determined by dielectric film and grooves on it.
The sketch maps of two models used to explain the two mechanisms are given in Fig. 4. In model one, as we see, a plane wave is incident on the DA structure and diffracted by the grooves on the incident surface. Then the diffracted light is reflected at the interface between dielectric and Ag, and reflected again on the other surface of dielectric film. The light propagating to the slit interferes with the light that is incident on the slit directly. The constructive interference light at selected wavelengths transmits through the slit and is modulated by the structures on the output side, forming an enhanced and beaming emission at last. In our simulation, there are no grooves on the output surface, so the transmitted light will be diffracted by the silt to a half cylinder uniformly. The optical path difference at the slit entrance is given by:
where n, p, hdi, and ddi is the refractive index, groove period, thickness, and depth of grooves on the dielectric film respectively. Δ' is the optical path difference caused by reflecting on metal surface, and it is dependent on the optical constants (n, k) of the metal and the angle of incident light. In the case of hdi = ddi, the Eq. (1) reduces to:
If Δ = mλ (m = 1, 2…), the light transmitted through the slit will be enhanced and lead to peaks to apear in the transmission spectrum at selected wavelengths. In addition, we haven’t taken into account the width w of grooves and slit because w is very small compared to p in our simulation. In fact, in Eq. (1) and (2), p is variable from (p - w) to (p + w), which causes spectrum broadening at the transmission peak. From Eq. (2), we can get the relations as followings: λmax ~ p, λmax ~ n, λmax ~ hdi. In Fig. 3(b), Fig. 5(b), and Fig. 6(b), approximate linear relations between λmax of peak one and hdi, p, n are shown clearly. These properties of peak one agree with model one well.
after reaching a maximum as hdi, p, and n increase. This is determined by the diffraction angle θ corresponding to peak one. In model one, light intensity diffracted by grooves distributes regularly as a function of θ. Light intensity decreases as θ increases. More power is concentrated at the area with small diffraction angle, so smaller θ, and more transmission. But the diffraction angle under which light can propagate to the slit is fixed by the geometry of the structure as:
where ddi = hdi. So θ will change as p and hdi vary. The angle of total reflection also affects the transmission. If the diffraction angle is smaller than the angle of total reflection, more light will propagate out the dielectric film but not be reflected. From all above, it is seen that as hdi increases, θ will decrease and Tmax will increase. But when θ decreases below the total reflection angle, Tmax will decrease rapidly. The case of p is just the opposite, and the case of n is also somewhat different. As n increases, angle of total reflection will decrease, and more light will be reflected and Tmax will increase. But as n increases, light will be diffracted more homogeneously by grooves at all θ, so Tmax will reduce on the contrary.
For peak two, it should be the same as the case of pure metal film studied previously. We employ the CDEW  model as model two, which matches our simulated result well. In the CDEW (composite diffracted evanescent wave) model, the transmission is modulated by interference of diffracted evanescent waves generated by subwavelength feathers at the surface, leading to transmission enhancement. Actually, the essential of model one and two is identical, and they all originate from constructive interference. So λmax corresponding to peak two as functions of n, p is similar to that of peak one, as shown in Fig. 5(b) and Fig. 6(b). However, Tmax of peak two as functions of n, p varies very little. Tmax and λmax vary little with hdi too, as shown in Fig. 3. The properties of the evanescent waves can explain this. The evanescent waves are waves trapped on the interface between metal and dielectric films, and their intensities decay exponentially from interface in the direction perpendicular to it. So the propagation and interference of the evanescent waves are irrespective of n, p and hdi, but modulated strongly by the depth of grooves. For the deeper grooves, more evanescent waves can be diffracted and more light will be transmitted. When the bottoms of the grooves expand to the interface, the modulated transmission will reach a maximum. In Fig. 7, as predicted, Tmax decreases rapidly as distance from interface to groove bottom (hdi - ddi) increases.
In conclusion, we have analyzed three new structures through which enhanced transmission is obtained. Two models are suggested to explain the properties of transmission. The new structures can lead to a great transmission enhancement. If the geometric parameters of dielectric film match, the transmission will be very high. A normalized-to-area transmission T = 16.6 in DAD structure is obtained. It seems that the structures on dielectric film are more efficient to enhance the transmission through subwavelength apertures and can be used in many optical devices such as optical data storage, photolithography, near-field microscopy and light emission. The experimental work is in progress.
This research is supported by the Preparatory Project of the National Key Fundamental Research Program (grant 2004CCA04400), and the Fok Ying Tung Education Foundation (grant 71008).
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