It is generally known that light transmission through a subwavelength aperture is very poor according to the diffraction theory [1]. This diffraction limits the manipulation and the applications of light at the subwavelength scale, such as the near-field optical scanning microscope, optical imaging and optical storage. In 1998, T. W. Ebbesen et al reported the enhanced transmission (ET) through subwavelength hole arrays [2]. By the periodic structure of hole arrays, the surface plasmon is resonant with the incident light, which leads to the ET at certain wavelengths. After then, ET through a single aperture was found if it was surrounded by period structures, such as dimples or grooves [3–5]. These findings attracted a lot of interests and many new results were reported about the ET. Some applications were designed according to these works and ET brought a lot of exciting results in other research fields. However, these structures are difficult to fabricate and this may be disadvantageous for the application of ET.

Recently, some works on H-shaped (or I-shaped) aperture [6–10] and bowtie aperture [11–14] reported higher near-field enhancement and smaller light spot than normal hole, which are very useful to enhance the near-field resolution and have been applied in near field imaging [15–17], nanolithography [18,19], and the vertical cavity surface emitting lasers [20,21]. These structured apertures may be easier to fabricate to obtain ET for many application purposes than the bull’s eye structure in Ref [5].

In this letter, we study the near-field enhancement of this structured aperture and focus our attention on their polarization properties. We design some structured circle holes in Ag film and employ the finite-difference time-domain (FDTD) method to simulate the near-field intensity transmitting through them. As shown in Fig. 1 , our samples are subwavelength holes with radius r = 100 nm and thickness h = 150 nm, which are set to default for comparison. We set a rod in the center of the hole (shortened as rod-hole) and two tooth-type structures on the side of the hole (shortened as tooth-hole). The length and the width of the rod and teeth are denoted as l_r and w_r, l_t and w_t respectively. The thicknesses of the rod or the teeth are set equal to the thickness of the silver film. In fact, some works have reported about the field enhancement by a scatter structure in the hole [22,23], partly similar to the rod-hole. And the tooth-hole refers to the H-hole. However, the main idea of our paper is focus on the polarization properties and for this purpose, both holes are set as circle shape to prevent the polarization influence of the hole.

 

Fig. 1 (a) A bare hole in silver film. Two structured holes (b) with a rod and (c) with two teeth.

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A home-made 3D FDTD code is used to simulate the fields transmitted through these structured holes. The simulation space is 1.2 × 1.2 × 0.3 μm³ and the constant space step is Δx = Δy = Δz = 2.5 nm. A plane incident pulse wave illuminates samples perpendicularly alone the z direction, with linear polarization. The detection plane is 50 nm away from the output surface of the film and parallel to the x-y plane sized as 0.4 × 0.4 μm² which is larger enough than the size of the hole to ensure main fields through out can be detected. We just try to simulate a practical case such as a near-filed imaging process or an optical storage process. So we use a detection plane with small distance from the output surface. The transmitted electromagnetic fields of all mesh points on the detection plane are recorded and Fourier transformed to frequency domain. Then the transmitted intensity on the detection can be calculated by the electromagnetic fields and integrated by all mesh points on the detection plane for every frequency. The normalized intensity spectrum can be obtained by normalizing the transmitted intensity by the incident intensity calculated by the same process. By using this method, we can obtain the spectrum information by only once simulation and it is not necessary to calculate the data wavelength by wavelength. The permittivity of Ag is given by the Lorentz-Drude model. The parameters can be obtained from Ref [24], which are coincident with the experimental data [25] well. By using the polarization vector, the Lorentz-Drude model can be transformed to time-domain and discretized [26].

The normalized intensity spectra of these two structured holes are shown in Fig. 2 . It is clear that there are strong enhancements peak when the polarization is along the longitudinal side of the rod and the teeth, i.e. x-polarization. However, for the incidence with y-polarization, there are only very week enhancements for the two types of the holes. The peaks are at 861 nm and 845 nm for the rod-hole and the tooth-hole respectively. If comparing with the results of a bare hole, the normalized intensities of the structured hole at peaks are 56.8 times and 38.9 times enhanced for the rod-hole and the tooth-hole respectively. The enhancement is not very high because the geometric parameters of the holes are not optimized. The rod-hole and tooth-hole used in Fig. 2 are just the typical ones but not the best ones. Among the simulations we have ever done, the best enhancement is about 705 times, which is obtained by a tooth-hole with h = 150 nm, r = 60 nm, l_t = 50 nm, and w_t = 20 nm. In fact, if the parameters are adjusted finely, stronger enhancement can be achieved.

 

Fig. 2 Normalized intensity spectra of the two structured holes for x- and y-polarization, and a bare hole without any structure. The geometric parameters are w_r = w_t = 40 nm, l_r = 120 nm, and l_t = 60 nm. These parameters are set as default.

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From the plots of the electric field distribution, we can see clearly the field enhancement, as shown in Fig. 3 . On the metal output surface, in Figs. 3(a) and 3(c), the fields are extraordinarily enhanced at the sharp edges of the rod and the teeth and show a very strong localized effect. However, if propagating a little distance away, the fields dump quickly and are diffracted to spots. This localized property is remarkable and we wonder if it is associated with the localized surface plasmon (LSP).

 

Fig. 3 |E| (a.u.) field distributions of the rod-hole and the tooth-hole. (a) and (c) are on the output surface, (b) and (d) are on the detection plane. The incidences are the peak wavelengths.

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As is well known, the nano-scaled metal particles can excite LSP on their surface, which leads to strong near-field enhancement. We think that it may be the same way to obtain the near-field enhancement through the structured holes. The enhancement peaks of the holes for x- and y-polarization are just attributed to the longitudinal and transverse plasmon resonances respectively. The two-tooth structure acts like two coupled nanorods [27], whose LSP resonance is very similar to an isolated nanorod. In Fig. 2(a), the spectra of the rod-hole and the tooth-hole are very similar and the peaks are almost at the same position. Actually, the LSP resonance peak is determined by the length of the nanorod along the polarization direction if other parameters are the same. As a coupled structure, we can consider the two teeth as one rod. So if 2l_t = l_r, the peaks of the rod-hole and the tooth-hole will be very close to each other. Furthermore, we simulated the normalized intensity spectra for different rod and teeth lengths, which are shown in Fig. 4 . And the peak wavelength as a function of the aspect ratio (defined by the length divided by the width) is shown in the inset of Fig. 4(a). The rule of these results is coincident with the LSP resonance of the metal nanorod well [28,29], which confirms our supposition of the origin of the near-field ET of these structured holes. In addition, the resonance wavelength tuned by the rod or teeth length maybe present more usefulness. Modifying the length of the rod or teeth, one can control or choose the resonance wavelength which can obtain strongest enhancement. Then a filter or a switch may be achieved.

 

Fig. 4 (a) Normalized intensity spectra of (a) the rod-hole and (b) the tooth-hole with different lengths. The inset in (a) is the peak wavelength as a function of the aspect ratio of the rod.

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As its own property, the excitation of the LSP is strongly dependent on the polarization of the incident light. Similarly, the excitation of the LSP resonance by the nanorod presents strong polarization dependence too [30,31]. It is easy to deduce that the structured holes should present a similar property of polarization dependence. We define the polarization angle θ by the polarization direction with respect to the x-axis. As shown in Fig. 5 , as the angle changes, one peak decreases even disappears and the other peak becomes strong. This is because that there are two LSP resonance modes (transverse mode and the longitudinal mode) when the polarization is parallel or perpendicular to the long side of the rod or teeth, which leads to two peaks at different wavelengths. The LSP resonance will change between the two modes when the polarization changes.

 

Fig. 5 Normalized intensity spectra of (a) the rod-hole and (b) the tooth-hole for different polarization angles.

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This polarization dependence of the near-field enhancement through the structured subwavelength holes may be very useful for some applications. We can use it to choose the incidence with certain polarization or choose the wavelength which can transmit through. However, if the polarization is not necessary, the polarization dependence may be a disadvantage for some applications, such as near-field imaging and optical storage. One must adjust the polarization angle to get the best effect. A design of structured hole with polarization independence may be very helpful for polarization independent devices.

At first, let us analyze the polarization dependence of the transmitted intensity by very elementary optical theory. According to the superposition principle, we know that two lights with perpendicular polarizations can be superposed simply if they have not phase difference. So we can treat an incidence with polarization angle θ as two waves with x-polarization and y-polarization respectively. Then the incident intensity can be expressed as

The transmittivity T_θ can be obtained

If we define the transmittivities of x- and y-polarization components as T_x and T_y, the output intensity components are$I_x^{out}=I_x^{in}{T}_x=I^{in}{T}_x{\cos }^2\theta$ and$I_y^{out}=I_y^{in}{T}_y=I^{in}{T}_y{\sin }^2\theta$. So we obtain the transmittivity of light with any polarization angle

As a linear system, the transmittivities T_x and T_y are invariable for any incident intensity. Thus if we know the transmittivities of a certain incident wavelength for the x- and y-polarization, we can obtain the transmittivity of any polarization angle by using Eq. (3). In Fig. 6(a) , we show the normalized intensity calculated by Eq. (3) and directly by FDTD simulation as a function of the polarization angle. The incident wavelengths are 861 nm for the rod-hole and 845 for the tooth-hole respectively. The figure shows clearly that the results by Eq. (3) and by FDTD are coincident very well. Especially, we calculate the spectra under polarization angle θ = 30° by Eq. (3) and FDTD as an example, which are shown in Fig. 6(b). We can see clearly that the spectra lines almost overlap with each other.

 

Fig. 6 (a) Normalized intensity as a function of polarization angle calculated by Eq. (3) and FDTD simulation at the peak wavelength. (b) Normalized intensity spectra calculated by Eq. (3) and FDTD simulation at θ = 30°.

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From Eq. (3), we can deduce that if T_x = T_y, then T_θ = T_x = T_y is independent of polarization angle θ. So if we design some structure in the hole which can realize the same transmittivity at x- and y-polarization, the transmittivity through this structured hole will be independent of the polarization and present an equal value. It is obvious that the fourfold rotational symmetric structure can realize this easily. Then we design two holes, a cross-hole and a four-tooth-hole, as show in the insets of Fig. 7 and we simulate their normalized intensity spectra under the incident waves with polarization angle θ = 0°, 30°, and 45° respectively. As shown in Fig. 7, we can see clearly that the three spectra for different polarization angles are almost the same. The only little difference is at the peak. We think that this may be attributed to the error of FDTD simulation. In spite of the little difference, the transmitted light through the cross-hole and the four-tooth-hole realize the polarization independence for the near-field enhancement. These structures and their original idea may be practical for some polarization independent devices.

 

Fig. 7 Normalized intensity spectra of (a) cross-hole and (b) four-tooth-hole for θ = 0°, 30°, and 45° respectively. The geometric parameters of the cross and the teeth are set equal to that of the rod and teeth in Fig. 2.

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As a conclusion, we present the near-field enhancement through structured subwavelength holes and their polarization properties by using of FDTD simulation. By setting some effective structures, a rod or two teeth in the holes, the near-field of the holes can be extraordinarily enhanced. We attribute this enhancement to the LSP excited by the rod and the teeth. The enhancement of the rod-hole and the tooth-hole exhibits very strong polarization dependence, which is determined by the property of the LSP directly. Starting from a basic optical theory, we find a simple way to design some polarization independent structures, i.e. cross-hole and four-tooth-hole. The intensity spectra of these two holes for different polarization angles almost overlap together and the polarization independence is realized. These results may be useful for some polarization dependence and independence applications.