Professor Hung-chun Chang

Graduate Institute of Photonics and Optoelectronics, National Taiwan University

臺灣大學光電所 張宏鈞教授

The phenomenon of extraordinary transmission through periodically arranged sub-wavelength holes in metal films has attracted considerable interest during past decades. The main mechanisms responsible for this phenomenon have been widely believed to be the excitation of surface plasmon polaritons (SPPs), or the surface electromagnetic (EM) modes, and Wood’s anomalies (WAs) set up by periodically arranged holes. In addition, it has been shown that the shape of the aperture, resulting in shape resonances (SRs), has a strong effect on the transmission spectra. In this work, we study the optical properties of differently shaped apertures composed of one to three horizontal slits, named x-arm slits, and one vertical slit, named y-arm slit. Figure 1(a) shows the geometry of a unit cell of one sub-wavelength metallic structure example we study. The metal (silver) film with thickness 75 nm is coated on a silicon substrate. An in-house developed 3D finite-difference time-domain (FDTD) method numerical model is used to simulate the EM field distributions and transmission spectra under normal incidence of light. Periodic boundary conditions are applied to the xz and yz planes to simulate a square periodic array of apertures. The SR wavelength might dominantly depend on the slit length. But for more complex-shaped apertures, the SR paths may have some ambiguities to be estimated by the modified cutoff wavelengths of the rectangular waveguide (i.e., λ_res = 2n_effL_res/m, where is the effective refractive index, L_res is the resonant length, and m is an integer) due to the slight difference of the L_res between those possible contours. We have found that analyzing the near-field features is helpful in distinguishing the SR modes. For example, the modulus of the electric field, |E|, defined by , contours clear geometry of the resonant length. Within the SR paths, the distribution of the phase component parallel to the polarization of the incident light (e.g., φ_Ex under x-polarized light) is quite homogeneous and the phase component along the propagation direction, φ_Ez, exhibits a 180^。jump at the center of the slit width. By focusing on the anti-phase property of φ_Ez along the SR contours and the symmetry requirement preserved for certain polarization state of light, those SR paths that cannot meet the above two criteria together are obviated and the possible right ones are left. In order to testify the validity of such principles in determining the SR paths, we design a set of apertures with onefold or twofold mirror symmetry, composed of x-arm slits and one y-arm slit, as shown in Fig. 1(b). We find the FDTD-obtained field-profile predictions agree well with the real SR modes, which are validated by the near-field analyses. Moreover, we discuss how the separation distance between slit elements in the apertures affects the SR wavelength under specific incident-wave polarization, showing how the coupling between adjacent slits would play a role in the variation of the spectra, as shown in Fig. 1(c). By delicately studying the properties of such factors and how they interact, we could manipulate the spectra with an additional degree of freedom, which could be important to structures with multi-holes or multi-slits in one unit cell. (Hui-Hsin Hsiao and Hung-chun Chang, in META’13 Abstracts, pp. 161–162, March 18–22, 2013.)

(a)	(b)	(c)
Figure 1. (a) The unit cell and the near-field plane cut in our simulation. (b) Top view and structural parameters of samples 1–5. (c) Transmission spectra with an y-polarized light under normal incidence. The inset shows two adjacent unit cells with separation distances between the x-arm slits, s1 and s2, specified.

 

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