Effect of Paired Apertures in a Periodic Hole Array on Higher Order Plasmon Modes

From the SelectedWorks of Fang-Tzu Chuang Winter November, 2012 Effect of Paired Apertures in a Periodic Hole Array on Higher Order Plasmon Modes Fang-Tzu Chuang, National Taiwan University Available at: https://works.bepress.com/ft_chuang/12/

2052 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 22, NOVEMBER 15, 2012 Effect of Paired Apertures in a Periodic Hole Array on Higher Order Plasmon Modes Yu-Cheng Chen, Hui-Hsin Hsiao, Chun-Ti Lu, Yi-Tsung Chang, Hung-Hsin Chen, Fang-Tzu Chuang, Shao-Yu Huang, Chih-Wei Yu, Hung-Chun Chang, and Si-Chen Lee, Fellow, IEEE Abstract We demonstrate that the transmission of higherorder surface plasmon modes in the mid-infrared range can be enhanced through rectangular hole array on the basis of paired apertures. Experiments prove that enhanced high-order transmission can be generated by either identical shapes or combinations of different hole shapes in pairs. The structure factor is adopted to explain the observed intensity of enhanced transmission. Numerical simulations of the enhanced secondorder mode verify a significant field enhancement in a unit cell of pairs. It is clarified that the separation between the paired apertures and the paired resonance is the key to determine certain higher-order plasmon modes to be enhanced. Index Terms Higher order, paired apertures, surface plasmon. (a) (c) (b) I. INTRODUCTION HOLES with different shapes have been investigated in extraordinary transmission (EOT) since the first observation by Ebbesen et al. [1], [2]. Applications based on this phenomenon that was attributed to the generation of surface plasmon (SP) [1] have been proposed in second harmonic generation (SHG) as well [3], [4]. It has been long believed that the enhancement of transmission spectrum strongly depend on the hole sizes, shapes [5], and periods. Much effort have been dedicated to these properties in fundamental modes, however, few explore the possible generation of higher order modes [6], [7] due to its weak intensity. Recently, the possible second order harmonic generation of radiation by periodic hole arrays aroused great interest [3], [4]. Unlike bowtie structures with two oppositely pointed triangles [7], it is the purpose of this letter to demonstrate that the paired apertures with identical or combination of different shapes or sizes can also enhance the transmission of higher order SP Manuscript received July 10, 2012; revised September 6, 2012; accepted September 10, 2012. Date of publication October 10, 2012; date of current version October 31, 2012. This work was supported by the National Science Council of China under Contract NSC 100-2120-M-002. Y.-C. Chen, H.-H. Hsiao, C.-T. Lu, H.-C. Chang, and S.-C. Lee are with the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan (e-mail: r99941037@ntu.edu.tw; d96941018@ntu.edu.tw; ck_1218@hotmail.com; hcchang@cc.ee.ntu.edu.tw; sclee@cc.ee.ntu.edu.tw). Y.-T. Chang is with the Department of Electrical Engineering, National Sun-Yet Sen University, Kaohsiung 804, Taiwan (e-mail: ytchang@mail.ee.nsysu.edu.tw). H.-H. Chen, F.-T. Chuang, S.-Y. Huang, and C.-W. Yu are with the Graduate Institute of Electronics Engineering, National Taiwan University, Taipei 10617, Taiwan (e-mail: d97943018@ntu.edu.tw; d98943024@ntu.edu.tw; r98943077@ntu.edu.tw; zoojohnny@gmail.com). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2012.2219303 (d) 1041 1135/$31.00 2012 IEEE Fig. 1. (a) Schematic diagrams showing the top and side view of the paired aperture structure in rectangular lattice. (b) Measurement setup. (c) SEM photos of the paired holes with identical shapes, i.e., squares (Group A), circles (Group B), and triangles (Group C). (d) SEM photos of Group D and E. modes. Studies examining paired apertures and the influence of basis on the transmission value have been proposed. [8] However, here it is found and demonstrated that the concept of structure factor in constructing the reciprocal lattice of a crystal [9] can be adopted to explain the observed intensity of higher order modes. This provides an innovative method to design the basis structure to specifically enhance a certain higher order SP mode for effective applications. II. EXPERIMENTAL SETUP AND THEORY In this letter, the 75 nm thick gold film was deposited on double polished silicon substrate by thermal evaporation and perforated with hole arrays in rectangular lattice. The reason for using rectangular lattice in this letter is because one can observe specific higher order plasmon modes more accurately in single X direction by eliminating the interference from similar plasmon modes in Y directions. The paired holes on

CHEN et al.: EFFECT OF PAIRED APERTURES IN A PERIODIC HOLE ARRAY 2053 TABLE I STRUCTURAL PARAMETERS OF GROUP A, B, C, D, AND ESAMPLES Group A Group B Group C Group D Group E A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 D1 D2 D3 E1 E2 E3 Px (μm) 7.0 7.0 7.0 7.0 7.0 Py (μm) 4.5 4.5 4.5 4.5 4.5 w(μm) 1.3 1.3 1.7 2.0 w 1 μm) 2.0 w 2 (μm) 1.3 1.3 1.7 S (μm) 2.3 2.8 3.3 3.6 2.3 2.8 3.3 3.6 2.7 3.2 3.6 3.6 3.6 R 0.32 0.4 0.47 0.51 0.32 0.4 0.47 0.51 0.38 0.46 0.51 0.51 0.51 S: the separation between the two center points of the paired apertures; R: the ratio of separation S to the period in x direction Px. each lattice point have identical shape (square in Fig. 1(a)). Here Fig. 1(a) shows the schematic top and side views of the sample. Fig. 1(b) shows the experimental setup and the sample lies in the xy plane with light incident in z direction while the polarization of light was along y direction. A Bruker IFS 66 v/s FTIR system was used to measure transmission spectra. The main reason using rectangular lattice is because that one can observe specific higher order plasmon modes more accurately in single x-direction by eliminating the interference generated by different higher order plasmon modes in the y-direction. In the first set, symmetric paired apertures at each lattice point have identical shape, i.e., squares (Group A), circles (Group B), and triangles (Group C). The structural parameters are listed in Table I which include the x-direction period (Px), y-direction period (Py), the aperture size (w), and the separation between the paired apertures (S). All x-period (P x ) and y-period (P y ) of the rectangular lattice were fixed at Px = 7 μm, Py = 4.5 μm. The separation (S) between the center points of apertures is varied to study its effects on the transmission. The ratio of separation S to x-period P x is defined as separation ratio (R). Fig. 1(c) shows the SEM photos of the paired apertures with identical shapes, i.e., square (Group A), circle (Group B), and triangle (Group C), respectively. For the second set, the asymmetric paired apertures at each lattice point have either different shape (Group D),or identical shape but different size (Group E). The SEM photos of Group D and E samples are displayed in Fig. 1(d). The detailed structural parameters of Group D and E samples are also listed in Table I. The theoretical model used to calculate the transmission intensities is based on the concept of structure factor (S G ). It has been shown that the enhanced transmission in perfect conductor perforated with hole arrays has its origin in the resonance-induced field enhancement arising from the periodic structure factor. [10] The structure factor is defined as the Fourier integral over a unit cell, representing the scattering amplitude for a crystal by Fourier analysis. The structure factor S G for electric field scattering is given by S G = dv E(r)e j (G r). (1) cell Here E(r) is the electric field intensity in the position r and G is the reciprocal lattice vector. When the periodic structure is reduced to merely a thin film and the aperture is placed at the position where z = 0, the structure factor may be transformed Fig. 2. Transmission spectra of samples with different separations measured by FTIR. (a) Group A. (b) Group B. (c) Group C. (d) Dispersion relation of sample A4 from 0 to 50. to the form like 2D periodic aperture arrays. It is assumed that the electric field in the z-direction is constant zero and the conditions approximately fit Fraunhofer Diffraction [11] in thin films. The equivalent equation for two dimensions may be written as S G = da E(x, y)e j2π(f xx+ f y y) (2) area where E(x, y) represents the spatial distribution of electric field passing through different apertures in a unit cell with varied geometry [12]. Here f x, f y symbolizes the spatial frequencies (f x = n x /Px, f y = n y /Py ) along x, y directions, while n x and n y are the SPP mode numbers in integers. The structure factor can be represented in different forms based on the three types of aperture shape when integrating over the aperture. III. RESULTS AND DISCUSSION The normal transmission spectra of Groups A, B, and C samples are shown in Fig. 2(a), 2(b), and 2(c), respectively. In order to investigate the separation effect, the separation S between the paired apertures is increased from 2.3 μm (Group A and B samples) or 2.7 μm (Group C) to 3.6 μm. The dispersion relation of A4 along x-direction is shown in Fig. 2(d).

2054 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 22, NOVEMBER 15, 2012 The dispersion of of A4 along y-direction are similar to those of ordinary periodic hole array without paired aperture. For the free-space wavelength of surface plasmon polaritons (SPPs), the peak positions can be calculated using the simplified formula given by equation [12] Px 2 λ = + P2 y i 2 + j 2 ε rd (3) where Px, Py is the x, y period of the hole array, ε rd is the relative dielectric constant of Si (εrd = 11.9 for Si) and i, j integers stand for the order of SPP modes in x and y-direction, respectively. Experimental results clearly show that the higher order SPP modes dominate the spectra instead of fundamental one in all three groups of sample in Fig. 2. For instance, the transmittance of Au/Si (2,0), (3,0), and (4,0) modes at 12 μm, 8 μm, and 6 μm are much stronger than the Au/Si (1,0) mode at 24 μm for all. This phenomenon contradicts to the fact that fundamental mode is always the strongest one in the spectra. It can be seen that the Au/Si (3,0) modes are enhanced when the two apertures are very close, i.e., sample A1, B1 and C1. Fig. 3(a) and (b) shows the FDTD simulated transmission spectra for isolated paired squares of A1, A2, and A4 under Ex and Ey polarization, respectively Based on the results, isolated pairs have relatively higher transmittance especially at the shorter wavelengths (6 12 μm) where (4,0), (2,1), and (2,0) modes exist. This localized resonance effect may give rise to larger field enhancement for higher order modes and also help explain why the fundamental modes have comparatively weak transmittance. The transmittance of the fundamental mode Au/Si (1,0) and Au/Si (3,0) modes (black, green) decays gradually when the separation increases. In addition, it is observed that the Au/Si (2,0) and Au/Si (4,0) modes (blue, red) are enhanced significantly while the separation ratio approaches 1/2. However, the Au/Si (2,0) mode at 0.51 ratio may overlap with the Au/Si (1,0) mode of the periodic structure with a period of Px/2. Therefore, asymmetric paired apertures are examined in the following section. In fact, it is observed that Au/Si (2,1) modes are the strongest modes in Fig. 2(a), 2(b), and 2(c), this is the result of strong coupling between the 2 nd order of x polarization and the fundamental mode Au/Si (0,1) of y polarization. This result demonstrates that hole shape is not the only key factor to enhance the higher order modes, since paired circles can also enhance the second order SPP modes. Similar effects were discovered in bowtie structures as well, where it was attributed to the narrow tips and noncentrosymmetric shape between periodic elements that provided field enhancement [7]. However, it is confirmed now that other shapes in pairs could also achieve enhancement of higher order modes while parameters are fixed and even without sharp tips. Based on the results shown above, it is important to find out the complete mechanism and key factors that determine which higher order modes could be enhanced. Despite resonance from single apertures, here the SG is proposed to explain as well. Theoretical calculations of structure factor intensity square S G 2 using Eq. (2) as a function of separation ratio (a) Fig. 3. FDTD-simulated transmission spectra of isolated paired apertures for samples A1, A2, and A4 under (a) Ex polarization and (b) Ey polarization. Fig. 4. Comparison of experimental transmittance (dots) with theoretical structure factor (solid lines) as a function of separation ratios for samples. (a) Group A. (b) Group B. (c) Group C. R are shown in Fig. 4(a), 4(b), and 4(c) for Group A, B and C samples, respectively. The calculated structure factor shown on the right axis for different modes is presented in arbitrary units. Here the S G 2 of each mode is normalized by setting the origin of each curve to match the first dot of the measured transmittance, respectively. The calculated structure factor (solid lines) is used to show the relative trend for each mode while the separation ratio is varied from 0.32 to 0.51. The measured transmittances (colored dots) on the left axis are used to compare with. In Fig. 4(a), it is noted that the theoretical SG curve fits quite well with the measured transmittance (dots), especially for higher order SPP modes. In order to further understand the connection between separation ratio and high order SPP modes, the experiment was extended to asymmetric paired apertures with different shapes in one unit (Group D) or identical shapes but different hole sizes in one unit (Group E), respectively. All the parameters were fixed to investigate the influence of hole geometry on higher order SP modes. Fig. 5(a) depicts the transmission spectra of samples D1, D2, and D3. Experimental results suggest that asymmetric paired apertures (i.e., triangle/circle, triangle/square, circle/square) fixed at same periods can also excite higher order modes. Here the Au/Si (2,0) mode surpasses the fundamental mode Au/Si (1,0) evidently. The 3 rd and 4 th order modes are no longer obvious when compared to the previous result of symmetric paired apertures. Fig. 5(b) shows the dispersion diagram of sample D2 which exhibits the strongest Au/Si (2,0) transmittance of all. This demonstrates that the 2 nd order SP mode can be effectively enhanced even using asymmetric pairs. Fig. 5(c) displays the transmission spectra of samples E1, E2, and E3 which are asymmetric (b)

CHEN et al.: EFFECT OF PAIRED APERTURES IN A PERIODIC HOLE ARRAY 2055 12 μm between the two apertures, which is responsible for enhancing the 2 nd order SP mode. The red colors indicate that the field enhancement mostly concentrates at the straight sides of hole instead of sharp tips like bowties. This FDTD results provides good qualitative agreement between the simulated field enhancements and the measured higher order modes. Fig. 5. (a) Transmission spectra of Group D samples. (b) Dispersion relation of sample D2. (c) Transmission spectra of Group E samples. (d) Dispersion relation of sample E1. All the x periods, y periods, and separations are fixed. Fig. 6. Electric field distribution of asymmetric paired sample D2 under x-polarized incident light by FDTD simulations at a wavelength of (a) 12 μm and (b) 24 μm. apertures with the same shape but different sizes. Obviously, the transmission of Au/Si (2,0) mode is well enhanced in three different geometries. Again, the dispersion relation of E1 is shown in Fig. 5(d). The results demonstrate that it is possible to enhance higher order SP modes using asymmetric paired apertures, especially the second order transmission mode. In other words, the second order SP mode can be significantly enhanced without oppositely pointing narrow tips. Therefore, it is elucidated that the separation of two paired holes is the predominant factor for generation and determination of enhanced higher order modes. The finite-difference time-domain (FDTD) simulations of asymmetric paired hole structures is performed to investigate the influence of hole shape on the local electric field intensity. Here sample D2 is taken as an example. Fig. 6(a) and 6(b) display the FDTD calculated electric field in x-polarization (Ex) 5nm above the Au/Si interface of sample D2 at a wavelength of 12 μm and 24 μm, respectively. Since the x-period is fixed at 7 μm, the electric field of Au/Si (1,0) fundamental mode at 24 μm should be the strongest under normal conditions. However, the electric field of the 2 nd order mode Au/Si (2,0) at 12 μm is much stronger than that at 24 μm. The maximum electric field intensity increases three times at IV. CONCLUSION In conclusion, the enhanced extraordinary transmission of high order SP modes through rectangular hole array with a basis constructed of paired apertures of identical shapes (i.e., squares, circles, and triangles) and a combination of different shape or identical shape but different size were investigated. It was demonstrated that the higher order SP modes can be generated by periodic hole array with various paired apertures as the basis both experimentally and numerically. Despite the resonance effect from unit pairs, the separation ratio of the two paired holes is also a key factor for the generation and determination of enhanced higher order SP modes. 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