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Tunable Resonances in the Plasmonic Split-Ring Resonator Volume 6, Number 3, June 2014 Jing Chen Yudong Li Zongqiang Chen Jingyang Peng Jun Qian Jingjun Xu Qian Sun

DOI: 10.1109/JPHOT.2014.2323294 1943-0655 Ó 2014 IEEE

IEEE Photonics Journal

Resonances in Plasmonic Split-Ring Resonator

Tunable Resonances in the Plasmonic Split-Ring Resonator Jing Chen, Yudong Li, Zongqiang Chen, Jingyang Peng, Jun Qian, Jingjun Xu, and Qian Sun MOE Key Laboratory of Weak Light Nonlinear Photonics, Tianjin Key Laboratory of Photonics and Technology of Information Science, School of Physics, Nankai University, Tianjin 300071, China DOI: 10.1109/JPHOT.2014.2323294 1943-0655 Ó 2014 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received March 21, 2014; revised May 5, 2014; accepted May 7, 2014. Date of publication May 13, 2014; date of current version May 23, 2014. This work was supported by the National Natural Science Foundation of China under Grants 61178004 and 11304164, by the Research Fund for the Doctoral Program of Higher Education of China under Grants 20110031120005 and 20130031120006, by the Tianjin Natural Science Foundation under Grant 13JCQNJC01700, and by the Program for Changjiang Scholars and Innovative Research Team in Nankai University. Corresponding author: Q. Sun (e-mail: [email protected]).

Abstract: A nanoscale resonator composed of two metal–insulator–metal (MIM) waveguides and a split ring is investigated numerically. The multipolar plasmonic resonance modes can be excited, weakened, or even cut off by adjusting the split angle. These novel phenomena are due to the electric polarization in the split area. Odd modes exhibit when the electric field is polarized perpendicular to the split. The resonator acts as a LC circuit for the electric field polarized parallel to the split, in which even modes are excited. The capacitance diminished when the split depth is increased, and the resonance wavelengths of even modes exhibit blue shift. Our results imply an extensive potential for tunable multichannel filters and biosensor devices in integrated nano-optics. Index Terms: Surface plasmons, optical resonators, integrated optics devices.

1. Introduction Metallic structures in nanoscale exhibit a wide variety of optical phenomena which made them to be a topic of nano-optics [1]. These structures overcome diffraction limit due to their surface plasmon resonances, which are highly sensitive to the structure geometries and surrounding medium. Metalinsulator-metal (MIM) structures and insulator-metal-insulator (IMI) structures are two common kinds of plasmonic structures. MIM/IMI structures can be used to guide, enhance and modify optical fields in nanoscale, such as filters [2], [3], couplers [4], sensors [5], [6], logic gates [7], and so on. To date, MIM/IMI ring shaped structures have gained great interest for their promising properties due to the local surface plasmon resonances. These structures are promising building blocks for the integrated photonic components, such as modulator, filter, and sensor, etc. Lithography, etching and template methods make it possible to fabricate metallic ring structures [8]–[12]. One or several types of resonances with odd modes appear when light passing through the ring resonator, which can be used to design narrow band-pass filters [13]–[15]. The resonance frequencies are highly tunable by adjusting the geometric parameters of the ring [8], [13], [15], [16]. Recent theoretical and experimental work has demonstrated that split-ring resonators rather than perfect rings can support multipolar plasmonic resonances [17]–[20]. Multichannel filters can be achieved by taking advantage of multipolar resonances. Most of these researches are concentrated

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Fig. 1. The split-ring resonator is composed of two MIM waveguides and a split-ring waveguide.

on IMI split-ring structures under normal illumination. Resonances in these symmetric breaking structures can be described by LC-resonance method [17], [19]. When the polarization of incident electric field is parallel to the split of the ring, plasmonic resonances with odd modes can be obtained. Whereas even resonance modes are excited if the polarization of the incident electric field is perpendicular to the split. The reinterpretation of the resonances in the split structures is reported in Ref. [21]. All the resonances can be understood as plasmonic resonances with different orders. The LC-resonance corresponds to the fundamental plasmonic mode. The MIM split-ring structures have a strong confinement of light comparing with the IMI structures, which are suitable for high optical integration. MIM split-ring resonators can be studied by using Babinet’s principle [22]. The polarization condition for odd/even resonance modes is contrary to the one in IMI structure. In this paper, a novel split-ring resonator with two MIM waveguides is proposed and numerically investigated. Comparing with the ring resonator, a silver strip is positioned within the MIM ring, resulting in a split-ring resonator. Multiploar resonances are achieved due to different polarizations of the electric filed in the split area. The resonances can be excited, weakened or even cut-off by adjusting the split angle, which are easily modified to the visible and near-infrared ranges. This modulation method is more convenient than the one, which is via changing the geometric parameters of the whole ring or the partial ring [13], [15]. The transmission peaks of even resonance modes exhibit blue shift as increasing the depth of the split.

2. Structure and Numerical Simulation The sketch of the split-ring resonator is shown in Fig. 1. The white and gray areas denote air and Ag, respectively. The two MIM waveguides and ring have the same width W ¼ 50 nm. The coupling distance between MIM waveguide and ring is d ¼ 10 nm. The outer radius of the ring resonator is R ¼ 200 nm, while the inner radius is r ¼ 150 nm. A silver strip is positioned in the MIM resonator to split the ring, which width is w ¼ 50 nm and depth is h ¼ 10 nm. The position of the split is defined as split angle . In this paper, the resonances of the structure are investigated with the split angle rotating from ¼ 0 to ¼ 90 . The resonance spectra are calculated by using finite-difference time-domain (FDTD) method. The frequency-dependent complex relative permittivity of silver is characterized by the Drude model: "m ð!Þ ¼ "1 !2p =!ð! þ iÞ. Here, !p ¼ 9:1 eV is the bulk plasma frequency; ¼ 0:018 eV is the damping frequency of the oscillations; ! is the angular frequency of the incident electromagnetic radiation; and "1 ¼ 3:7 is the dielectric constant at infinite angular frequency [23]. The refractive index of air is n ¼ 1. To avoid reflection from the output end of the structure, the perfectly matched layer is employed, which can reduce the numerical reflection effectively. A plane wave is emitted into the left MIM waveguide to excite surface plasmon resonances. The incident light is TM polarized and the incident direction is along the þz axis.

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Fig. 2. The transmission spectra of the split-ring resonator with different split angles.

Fig. 3. The normalized field distributions of jHy j at different split angels with mode number M: (a)–(e) M ¼ 1, (f)–(j) M ¼ 2, (k)–(o) M ¼ 3 and (p)–(t) M ¼ 4, respectively.

3. Simulation Results and Analysis The transmission property of the perfect ring resonator is simulated firstly, as shown in Fig. 2. There are two transmission peaks at the incident wavelengths ¼ 1617 nm and ¼ 820 nm, respectively. Field distributions of jHy j for the perfect ring resonator are shown in Fig. 3(a) and (k). Two nodes ðN ¼ 2Þ can be observed in the magnetic field distribution at wavelength ¼ 1617 nm, which is identified as mode 1 ðM ¼ N 1 ¼ 1Þ. Similarly, mode 3 ðM ¼ 3Þ appears at ¼ 820 nm with four distinct nodes ðN ¼ 4Þ. Transmission spectra of the split-ring resonator with different split angles are plotted in Fig. 2. The split angles are 0 , 15 , 30 , 45 , 60 , 75 , 90 , respectively. For mode 1 ðM ¼ 1Þ, the transmission peaks become weaker as the split angle increasing from ¼ 0 to ¼ 90 , shown in Fig. 2. The resonance wavelengths exhibit slight blue shift. Two distinct nodes ðN ¼ 2Þ can be observed at the incident wavelength 1617 nm, seen in Fig. 3(a)–(e). The transmission light wears off as the split angle increasing. When the split angle ¼ 90 , the two distinct nodes disappear, as shown in Fig. 3(e). For mode 3, increasing the split angle from ¼ 0 to

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Fig. 4. The field distributions of E? and E== at different split angles with mode number M: (a) M ¼ 1 and M ¼ 3; (b) M ¼ 2 and M ¼ 4.

¼ 45 results in weakened the transmission peaks. The transmission peak values enhance if the split angle increased from ¼ 45 to ¼ 90 , as shown in Fig. 2. Four nodes ðN ¼ 4Þ exhibit at the incident wavelength 820 nm, seen in Fig. 3(k)–(o). When the split angle is ¼ 45 , mode 3 with four nodes almost disappears. In Fig. 2, transmission peaks at the incident wavelength 1188 nm and 725 nm generate at proper splitting angles, respectively. These are corresponding to mode 2 ðM ¼ 2Þ with three nodes ðN ¼ 3Þ and mode 4 ðM ¼ 4Þ with five nodes ðN ¼ 5Þ in the magnetic field, as shown in Fig. 3(f)–(j) and (p)–(t). The varieties of the transmission peaks in mode 2 and mode 4 are more complicated. For mode 2, the transmission peak values are all most the same at the split angle ¼ 15 ; 30 ; 60 . While mode 2 disappears when the split angle is ¼ 0 or ¼ 45 . The transmission peak value becomes larger at split angle ¼ 75 , the maximum value is at ¼ 90 . For mode 4, the transmission peak values enhance from ¼ 15 to ¼ 45 . The peaks degenerate from ¼ 45 to ¼ 75 . The peak value becomes larger at ¼ 90 . Mode 4 is cut-off at split angle ¼ 0 . In conclusion, the resonance of the split-ring resonator with split angle ¼ 0 acts as a perfect ring. The Ag strip does not split the ring effectively. Only odd modes (mode 1 and mode 3) can be obtained. When the split angle is ¼ 45 , mode 1 and mode 4 are excited, while mode 2 and mode 3 are cut-off. When the split angle is ¼ 90 , mode 2 and mode 3 are excited, while mode 1 and mode 4 are cut-off. Modes 1-4 are coexistence at other angles from ¼ 0 to ¼ 90 . Here, we will discuss the novel phenomena mentioned above. Both odd modes and even modes can be obtained in the MIM split-ring resonator with proper polarization of the excited electric filed. The polarization directions of the electric field in the split area are defined as shown in Fig. 1. That means the polarization direction of excited electric field E== is parallel to the Ag split, while the polarization direction of E? is perpendicular to the split. The polarized conditions for exciting odd/even resonance modes in MIM resonator are contrary to the IMI ones according to Babinet’s principle [17], [22]. In the MIM structure, if the polarization of the excited electric field is parallel to the split, even modes can be excited. The resonator can be treated in terms of a LC circuit. If the polarization of the excited electric field is perpendicular to the split, odd modes generate. As mentioned above, odd modes are modulated by E? , while even modes are modulated by E== . Odd modes are excited at the wavelengths 1617 nm and 820 nm. Even modes are excited at 1188 nm and 725 nm. Now we discuss the contribution of the excited electric filed with the split angle rotating. The amplitudes of electric fields E? and E== with different split angles are plotted in Fig. 4. When a split is positioned in the ring, electric field in the split area is effectively considered while others are neglected, for the surface plasmon can be only excited at the surface of the Ag strip and the depth of split is extremely small. In Fig. 4(a), E? of mode 1 is decreasing when the split angle increased from ¼ 0 to ¼ 90 . So the transmission peaks of mode1 are diminishing to zero, as shown in Fig. 2. For mode 3, the electric field is decreasing as the split angle rotating from

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Fig. 5. The transmission spectra of the split-ring resonator with different split depths. The split angle is ¼ 90 .

¼ 0 to ¼ 45 , and it is increasing as the angle rotating from ¼ 45 to ¼ 90 . In this condition, mode 3 is weakened firstly and then strengthened, which turning point is at ¼ 45 , as shown in Figs. 2 and 3. In Fig. 4(b), curves of E== versus split angle for mode 2 and mode 4 are plotted, which denote the variety properties of mode 2 and mode 4. The variation curves of E== meet the transmission spectra quite well. In summary, at the split angel ¼ 0 , the excited electric fields E? of mode 1 and mode 3 possess maximum amplitudes. The amplitudes of E== of mode 2 and mode 4 are zero. Therefore, the maximum transmission peak values of mode 1 and mode 3 are achieved, while mode 2 and mode 4 are cut-off. For the depth of the split is extremely small, absorption loss can be neglected. The resonance status of the split-ring with ¼ 0 acts as a perfect ring, only odd modes exhibit. The Ag strip does not split the ring effectively. At other split angles rotating from 0 to 90 , the Ag strip has significant effect on E? and E== . Both odd and even modes can be modulated by adjusting the split angle. Finally, the influence of the split depth h on the resonance transmission is studied. To simplify the discussion, the split-ring with angle ¼ 90 is investigated. Fig. 5 shows the resonance spectra with different split depths h. The resonance peaks of mode 2 are blue shift as Ag split depth increasing. As mentioned above, mode 2 can be seen as a result of LC circuit resonance. The air area in the splitring acts as a capacitor, and the silver area in the split-ring acts as an inductance [17]. The capacitor in our MIM structure is arc shaped, which is difficult to calculate. So we employ the IMI split-ring structure equivalently according to Babinet’s principle [24]. The total electric field of single IMI splitring eigenmode must resemble the total magnetic field of the MIM split-ring eigenmode. The electric polarization condition for odd/even modes is interchanged in these two structures. The transmission peaks for IMI/MIM split-ring are approximately at the same wavelengths. So it is advisable to study the split depth of IMI structure instead of the one in MIM structure. Our structure contains two MIM waveguides. These will choose some eigenmodes of the ones in single split-ring. The transmission peaks are not influenced by these waveguides. In the IMI structure, eigenfrequency !LC of a LC oscillator can be written as: !LC ¼ ðLCÞ1=2 [17]. The increasing depth of the split led to a decrease of capacitor and an increase of eigenfrequency !LC . Equivalently, the transmission peaks exhibit blue shift in MIM structure when the split depth is increasing. The electric field increases due to the lower losing as the split depth increasing. Mode 4 exhibits at 666 nm, which becomes more pronounced the larger the split becomes. That is due to lower energy losing in the split-ring resonator. The transmission peaks of mode 4 are also blue shift as the split depth increasing. However, the resonance wavelengths of mode 3 exhibit a slight blue shift when the split depth increasing. The predictive simulations suggest a potential use for nanosensors.

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4. Conclusion In conclusion, we have investigated a nanoscale resonator based on two MIM waveguides and a split-ring. The resonances with different split angles are simulated by FDTD method. Both odd and even modes can be excited, weakened or even cut-off by adjusting split angle. These novel phenomena are due to the polarization of the electric field in the split area. When the split angle is at ¼ 0 , the split doesn’t work effectively. The split-ring can be treated as the perfect ring resonator. When the splitting angle is at ¼ 45 , mode 1 and mode 4 exhibit. While the angle rotating to ¼ 90 , mode 2 and mode 3 can be observed. And with other angles from 0 to 90 , modes 1–4 are coexistence. The resonance wavelengths can be conveniently modified to the visible and nearinfrared ranges. Furthermore, mode 3 and mode 4 are suitable for sensing applications within the biological window (700–900 nm). Transmission peaks of even modes are blue shift as the split depth increasing. The results imply that our structures have extensive potential for tunable multichannel filters and biosensor devices in integrated nano-optics.

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