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Abstract
A voltage tunable filter based on a combined metal-insulator-metal nano-cavity waveguide of organic electro-optical material DAST is proposed by using the side-coupled method. The structure of this kind of filter consists of two Y-type cavities and a rectangular waveguide. The transmission spectra, the resonance wavelength, and the magnetic field distribution of the asymmetric Y-type cavity waveguide metal-insulator-metal structure filter has been calculated and analyzed by the finite element numerical simulation method. The results show that this filter has the features of a smooth transmission spectra, a flat passband with the maximum transmission of 0.97, a stopband with the minimum transmission of 0.001, and a wide bandwidth (full width at half maxima achieved 970 nm). The characteristics of the structure filter can be adjusted not only by changing the structural parameters, but also by applying a control voltage. Thus, the adjustability of the filter is increased, and the filter can realize the filtering function of channel selection of the three optical communication windows at the telecommunication regime. There will be great application prospect for this filter structure in high-density integrated circuits and nano-optics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritions (SPPs) are electromagnetic waves propagating along the interface between metals and dielectrics with an exponentially decaying field in a direction perpendicular to the interface, which are generated by the interaction of free electrons in metals and electromagnetic fields in dielectrics. As carriers of energy and information, it has the characteristics of overcome the diffraction limit of light in conventional optics and realize guiding and manipulating light at the sub-wavelength level, providing possibilities for fabricating nano-scale photonic components and optical devices [1,2]. Waveguide structures based on SPPs include metal-insulator-metal (MIM) and insulator-metal-insulator (IMI) structures, MIM waveguides are promising for the design of nanoscale all-optical devices with smaller size, high degree of confinement, and support for high group-speed propagation of sub-wavelength over a wide spectral range [3,4]. In recent years, a variety of nano-optics devices based on MIM structure have realized lots of achievements and breakthroughs in experimental and theoretical analysis, such as: electro-optical switches [5,6], filters [7,8], splitters [9,10], Y-shaped combiners [11], Mach-Zehnder interferometers [12], couplers [13,14], Bragg reflectors [15], Fano resonances [16,17] etc.
The filter is one of the main technologies in the field of optical communication, it is an important part of nano-integrated optics. According to the passband type, the MIM structure filters based on SPPs can be divided into narrow-band band-stop type, narrow-band band-pass type, flat-top band-pass type, and flat-bottom band-stop type. According to the coupling mode, it can be divided into direct-coupled [18,19], side-coupled [20–22] and aperture-coupled [23,24]. For the design and research of the filter, Hua Lu et al. [25] have proposed a filter with disk-shaped nano-cavities, which has the advantages of low stopband transmission and more stopband modes, but the passband is not flat enough and the transmission is not high enough, limiting the scope of its application. Iman Zand et al. [22] have proposed a filter with split-ring cavities, which overcomes the disadvantages of unflat and low transmission of passband, but the passband bandwidth is not wide enough and the stopband transmittance is not low enough.
In this paper, an MIM structure filter consisting of two Y-type cavities and a rectangular waveguide is proposed. The Y-type cavity consists of three rectangular cavities, it has the characteristics of simple structure, convenient manufacture and adjustability. The transmission characteristics of the filter are analyzed by the finite element method (FEM) numerical simulation method, which are optimized by analyzing the transmission spectra of the filter with different structural parameters. And the effect of the applied control voltage on the filter transmission characteristics is analyzed with the parameters unchanged. In the end, the optimized structure and simulation results are obtained by relationship between the transmission characteristics and the applied voltage, the structural parameters.
2. Structure design and simulation method
The schematic diagram of the asymmetric Y-type cavities MIM structure filter is shown in Fig. 1, which is composed of two Y-type cavities and an MIM waveguide through side-coupled. The width of the Y-type cavities is t, the height of the upper rectangle is ${h_1}$, the height and the offset distance of the lower rectangle are ${h_2}$ and g, the length of the middle rectangular cavity is D, the distance between the two Y-type cavities is d, and the distance between the input/output port and the Y-type cavity is L, and the width of the waveguide is W, where W, t, L are fixed to 50 nm, 35 nm, 150 nm. Because the width of the MIM waveguide is smaller than the wavelength of the incident light, only the transverse magnetic fundamental mode (TM) passes through the structure [26]. In this paper, the finite element simulation method with perfectly matched layer (PML) boundary condition is used to analyze and calculate the transmission characteristics of the Y-type cavity structures. The surface light source transmits from left to right, and the transmittance is defined as $T = {P_{0\textrm{ut}}}/{P_{\textrm{in}}}$, where ${P_{\textrm{in}}}$ and ${P_{0\textrm{ut}}}$ are the input power and the output power respectively.
Fig. 1. Schematic diagram of the asymmetric Y-type cavities MIM filter with structural parameters of ${h_1} = 100\;\textrm{nm}$, ${h_2} = 85\;\textrm{nm}$, $D = 135$ nm, $d = 390\;\textrm{nm}$, g $= 90$ nm, $t = 35$ nm, $w = 50$ nm, $L = 150$ nm.
The white part of the Fig. 1 represents air, the relative permittivity and the refractive index are ${\varepsilon _{\textrm{air}}} = n_{\textrm{air}}^2 = 1.0$. The blue part represents electro-optic (EO) material whose refractive index can be modulated with an applied electrical field. Here, 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) is chosen, it exhibits a large EO coefficient ($\kappa = dn/dE = 3.41\; \textrm{nm} \cdot {\textrm{V}^{ - 1}}$) compared with that of the standard inorganic EO materials such as $\textrm{LiNb}{\textrm{O}_3}\;({\kappa = dn/dE = 0.16\; \textrm{nm} \cdot {\textrm{V}^{ - 1}}} )$, because of a large delocalized π electron system [27]. At present, DAST is widely used in electro-optic switches, and the relationship between the refractive index of the EO material and the applied voltage as follows [5,6]:
where ${n_{\textrm{eo}}}(0 )$=2.2 is the refractive index for consideration, S is the thickness of the Y-type cavity in Fig. 2, here S is set to 50 nm. U is the applied control voltage. The voltage can range from 0 V to more than 10 V [28]. From Eq. (1), one can see that the applied control voltage will cause linearly the variation of the refractive index of the EO material.The gray part represents silver, the relative permittivity of silver is characterized by the Drude equation [29]:
When the SPPs wave propagates along the waveguide, parts of the wave will be trapped into the Y-type cavity to establish an oscillation. The phase change of the wave propagation in one cycle is expressed as $\Delta \varphi = 4{\pi}{n_{\textrm{eff}}}{L_{\textrm{eff}}}/\lambda + 2\varphi $. When $\Delta \varphi = 2m{\pi}\;({m = 1,2,3 \ldots } )$, a stable standing wave can be formed in the cavity. Therefore, the resonance wavelength of the SPPs is defined as [30,31]:
where ${L_{\textrm{eff}}}$ is the effective length of the cavity, $\varphi $ is the phase change caused by the reflection of SPPs at the metal-dielectric interface, ${n_{\textrm{eff}}}$ is the effective refractive index of the SPPs, which is defined as ${n_{\textrm{eff}}} = \beta /{k_0}$, $\beta $ is the propagation constant of SPPs in the waveguide, ${k_0} = 2\pi /\lambda $ is the wave number in free space, and the positive integer m is the antinodes number of the SPPs.3. Analysis of the transmission characteristics of Y-type cavity structures
The structural parameters are initialized: ${h_1}$, ${h_2}$, g, D and U are set to 100 nm, 85 nm, 90 nm, 135 nm and 0 V. The transmission spectrum of the single Y-type cavity structure, the symmetric Y-type cavities structure ($d = 0\;\textrm{nm}$) and the asymmetric Y-type cavities structure ($d = 390\;\textrm{nm}$) are shown in Fig. 3. From Fig. 3, it is clear that the transmission spectrum of three different MIM structures all have three resonance dips corresponding to Mode 1∼3 between the wavelengths of 800 nm and 2400 nm. And for the single Y-type cavity structure, the passband is flat and its transmittance is high, but the transmittance of the three resonance modes are not low enough (the minimum transmittance is 0.04). For the symmetric Y-type cavities structure, the transmittance of the three resonance modes are low enough (the minimum transmittance can reach 0.001), but the transmittance of the passband is significantly decreased, and the rising edge and the falling edge are not steep enough. The asymmetric Y-type cavities structure combines the advantages of the single Y-type cavity and the symmetrical Y-type cavities structure, which has a flatter passband than the symmetrical Y-type cavities structure, a wider passband bandwidth (Full width at half maxima (FWHM) can be achieved 970 nm) than the symmetrical Y-type cavities (FWHM is 740 nm). And the transmittance of its passband (0.97) is higher than that of the symmetrical Y-type cavities structure (0.93), the transmittance of the stopband (0.001) is lower than that of the single Y-type cavity structure (0.12), the rising and falling edges are steep enough. Thus, the characteristics of the asymmetrical Y-type cavities structure are better than many other structure filters [32–34].
Fig. 3. Comparison of transmission spectrum of the three different MIM structures: red line, blue line, black line represent a single Y-type cavity structure, a symmetric Y-type cavities structure and an asymmetric Y-type cavities structure, respectively.
In order to further explain the transmission characteristics of SPPs in these three structures in Fig. 3, the magnetic field ($|{H_\textrm{Z}^2} |$) distributions of the three structures with the parameters of initial value are numerically simulated, as shown in Fig. 4 and Fig. 5. The magnetic field distributions of the single Y-type cavity at the incident wave of the specific wavelength are shown in Figs. 4(a)–4(c). Due to the Y-type cavity is filled with DAST whose refractive index is higher than the refractive index of the air in the waveguide, so the Y-type cavity can be regarded as a “magnetic container”, which will “draw” the nearby magnetic field into the cavity [7,34]. Thus, when the SPPs wave from the beginning of the structure propagates along the waveguide and reaches the Y-type cavity, parts of the wave enters the Y-type cavity and rest still propagates along the waveguide. When the two parts of the wave become out-of-phase, destructive interfere will occur and a resonance dip will appear in the transmission spectra. And the interference between the corners of the Y-type cavity will cause a variety of resonance modes (Mode 1∼3) [22]. As shown in Figs. 4(a)–4(c), it is noticed that the magnetic field at the resonance wavelength is distributed in the Y-type cavity. Therefore, the power flow leaking into the waveguide is almost zero. The propagation of SPPs wave in the symmetric Y-type cavities structure is similar to that in the single Y-type cavity structure. But when the SPPs wave reaches the Y-type cavity, parts of the wave splits into two paths into the two Y-type cavities. After a certain propagation length, when the reflected wave of the two Y-type cavities and the transmission wave in the waveguide become out-of-phase, a dip will appear in the transmission spectra, as shown in Figs. 4(d)–4(f). It can be seen that the transmittance of the symmetric Y-type cavities structure is smaller than that of the single Y-type cavity structure at the same incident wavelength in Fig. 3, which effectively confirms the concept of “magnetic container”.
Fig. 4. Magnetic field distribution of the single Y-type cavity structure (a-c) and the symmetrical Y-type cavities structure (d-f) at different wavelengths: (a) $\lambda = 886\;\textrm{nm}$ (b) $\lambda = 1136\;\textrm{nm}$ (c) $\lambda = 2190\;\textrm{nm}$ (d) $\lambda = 892\;\textrm{nm}$ (e) $\lambda = 1144\;\textrm{nm}$ (f) $\lambda = 2190\;\textrm{nm}$.
Fig. 5. Magnetic field distributions of the asymmetrical Y-type cavities structure at different wavelengths: (a) $\lambda = 876\;\textrm{nm}$ (b) $\lambda = 1138\;\textrm{nm}$ (c) $\lambda = 2190\;\textrm{nm}$ (d) $\lambda = 1354\;\textrm{nm}$.
Figure 5 shows the magnetic field distributions of the asymmetrical Y-type cavities structure at the incident wave of the specific wavelength. The steady-state magnetic field distributions of the asymmetric Y-type cavities structure at wavelengths of 876 nm (Mode 3), 1138 nm (Mode 2), and 2190 nm (Mode 1) are shown in Figs. 5(a)–5(c), respectively. The transmittance at these three wavelengths can reach 0.001. Figure 5(d) shows the magnetic field distribution at the wavelength of 1354 nm and the transmittance is up to 0.97. The propagation of the SPPs wave in the asymmetric Y-type cavities structure is similar to that in the symmetric Y-type cavities structure. But when the SPPs wave reaches the first Y-type cavity, parts of the wave enters it and parts of the wave enters the second Y-type cavity after the transmission distance d. When two parts of the reflected wave and transmission wave in the waveguide become out-of-phase, interference destructive phenomenon will appear as shown in Figs. 5(a)–5(c), the interference between the corners of the Y-type cavity will cause a variety of resonance modes, different resonance modes have different resonance wavelengths, so the corresponding magnetic field distribution is also different. And a dip will appear in the transmission spectra as shown in Fig. 3. When two parts of the reflected wave and transmission wave become in-of-phase, interference constructive phenomenon will appear as shown in Fig. 5(d), and the transmission spectra at this time shows high transmittance. It can be seen from the magnetic field distributions that the asymmetric Y-type cavities proposed in this paper has reached the design expectation, combing the advantages of the single Y-type cavity and the symmetric Y-type cavities structure filters.
4. Influence of structural parameters on the asymmetric Y-type cavity structure filter
In order to explore the influence of structural parameters on the transmission characteristics of the asymmetric Y-type cavities structure filter, the control variable method is used to study it. The structural parameter ${h_1}$ is changed from 90 nm to 110 nm in steps of 5 nm, other structural parameters are kept as initial values (${h_2} = 85\;\textrm{nm}$, $D = 135$ nm, $d = 390$ nm, g $= 90\;\textrm{nm}$). From Fig. 6(a), it can be seen that with the increase of the parameter ${h_1}$, the transmission spectra of the asymmetric Y-type cavities structure filter occurs red shift, and the transmittance of the three modes remain basically unchanged. Here, the reason for the red shift of the transmission spectra is theoretically analyzed by using Eq. (3). The imaginary line in Fig. 1 is the transmission path of the SPPs in the Y-type cavity, and the effective length of the cavity is ${L_{\textrm{eff}}} = 2{h_1} + D + {h_2} + t$. The refractive index of the EO material DAST in the cavity remains unchanged as the applied voltage $U = 0\;\textrm{V}$, ${n_{\textrm{eff}}}$ is a fixed value. According to Eq. (3), ${L_{\textrm{eff}}}$ becomes larger as ${h_1}$ increases, so the resonance wavelength increases, the transmission spectra occurs red shift. In order to better explain this phenomenon, the resonance wavelengths of different structural parameters ${h_1}$ are studied and analyzed. From Fig. 6(b), it can be seen that there is a positive linear relationship between resonance wavelength and parameter ${h_1}.$ It is calculated that $\Delta {\lambda _{\textrm{Mode}\; 1}}/\Delta {h_1} \approx 12$, $\Delta {\lambda _{\textrm{Mode}\; 2}}/\Delta {h_1}\; \approx 5.2$, $\Delta {\lambda _{\textrm{Mode}\; 3}}/\Delta {h_1} \approx 3.2$, so the resonance wavelength is negatively correlated with the number of mode. The theoretical analysis and simulation results can be mutually confirmed.
Fig. 6. Transmission characteristics of the asymmetrical Y-type cavities filter at different structural parameter ${h_1}$: (a) transmission spectrum, (b) resonance wavelength.
When the other structural parameters are kept as initial values (${h_1} = 100\;\textrm{nm}$, $D = 135\;\textrm{nm}$, $d = 390\;\textrm{nm}$, g $= 90\;\textrm{nm}$), the structural parameter ${h_2}$ is changed from 65 nm to 105 nm in steps of 10 nm. From Fig. 7(a), with the increase of ${h_2}$, the transmission spectra of the asymmetric Y-type cavities structure filter is red-shifted, the transmittance of Mode 1 tends to increase, the transmittance of Mode 2 tends to decrease, and the transmittance of Mode 3 remains unchanged. According to Eq. (3), when the applied voltage $U = 0\;\textrm{V}$, ${n_{\textrm{eff}}}$ is constant. And the increase of ${h_2}$ causes ${L_{\textrm{eff}}}$ to increase. Therefore, the resonance wavelength increases. It can be seen from Fig. 7(b) that the resonance wavelength and ${h_2}$ are positively correlated, which is consistent with the theoretical analysis results.
Fig. 7. Transmission characteristics of the asymmetrical Y-type cavities filter at different structural parameter ${h_2}$: (a) transmission spectrum, (b) resonance wavelength.
When the structural parameter D is changed from 110 nm to 130 nm in steps of 5 nm, the other structural parameters are kept as initial values (${h_1} = 100\;\textrm{nm}$, ${h_2} = 85\;\textrm{nm}$, $d = 390\;\textrm{nm}$, g $= 90\;\textrm{nm}$). As shown in Fig. 8(a), the transmission spectra occurs red shift, the transmittance of Mode 1 tends to increase, the transmittance of Mode 2 tends to decrease, and the transmittance Mode 3 remains substantially static. The resonance wavelength increase as D increases according to Eq. (3). The positive linear correlation between D and resonance wavelength agrees well with the simulation results shown in Fig. 8(b).
Fig. 8. Transmission characteristics of the asymmetrical Y-type cavities filter at different structural parameter D: (a) transmission spectrum, (b) resonance wavelength.
As shown in Fig. 9(a), when the other structural parameters are kept as initial values (${h_1} = 100\;\textrm{nm}$, ${h_2} = 85\;\textrm{nm}$, $D = 135\;\textrm{nm}$, g $= 90$ nm), the structural parameter d is increased from 350 nm to 390 nm in steps of 10 nm, the transmission spectra of the structural filter is immobile, and the three resonance modes remain unchanged. Due to ${L_{\textrm{eff}}} = 2{h_1} + D + {h_2} + t$, and the distance between the two Y-type cavities d has little influence on ${L_{\textrm{eff}}}$. Thus, ${L_{\textrm{eff}}}$ is constant with the increase of d, and the resonance wavelength is fixed. The relationship between the resonance wavelength and d is shown in Fig. 9(b), It is calculated that $\Delta {\lambda _{\textrm{Mode}\; 1}}/\Delta d = \Delta {\lambda _{\textrm{Mode}\; 2}}/\Delta d = \,\; \Delta {\lambda _{\textrm{Mode}\; 3}}/\Delta d \approx 0$, the resonance wavelengths of the three modes are constant.
Fig. 9. Transmission characteristics of the asymmetrical Y-type cavities filter at different structural parameter d: (a) transmission spectrum, (b) resonance wavelength.
5. Influence of applied voltage U on the asymmetric Y-type cavity structure filter
Structural parameters are all set to initial values: (${h_1} = 100\;\textrm{nm}$, ${h_2} = 85\;\textrm{nm}$, $D = 135\;\textrm{nm}$, $d = 390\;\textrm{nm}$, g $= 90\;\textrm{nm}$), the applied voltage is changed from 0 $\textrm{V}$ to 2.0 $\textrm{V}$ and the step size is 0.5 $\textrm{V}$. It can be seen from Fig. 10(a) that with the increase of the applied control voltage, the transmission spectra occurs red shift. This phenomenon can be analyzed by using Eq. (3). When the structural parameters of the asymmetric Y-type cavities structure filter are kept as initial value, ${L_{\textrm{eff}}}$ is a constant. The refractive index of the Y-type cavity filled with the EO material DAST increases as the applied voltage increases, which causes the increase of ${n_{\textrm{eff}}}$. And according to Eq. (3), the resonance wavelength is positively correlated with … Thus, the increase of the applied voltage leads to the increase of the resonance wavelength and causes the red shift of the transmission spectra. Figure 10(b) shows the positive linear relationship between the resonance wavelengths of the three resonance modes and the applied voltage. It is calculated that $\Delta {\lambda _{\textrm{Mode}\; 1}}/\Delta U \approx 108\; \textrm{nm} \cdot {\textrm{V}^{ - 1}}$, $\Delta {\lambda _{\textrm{Mode}\; 2}}/\Delta U \approx 56\; \textrm{nm} \cdot {\textrm{V}^{ - 1}}$, $\Delta {\lambda _{\textrm{Mode}\; 3}}/\Delta U \approx 40\; \textrm{nm} \cdot {\textrm{V}^{ - 1}}$. Obviously, there is a negative correlation between the resonance wavelength and number of mode, which is consistent with the theoretical analysis results. Therefore, the proposed filter can achieve the adjustment of its transmission spectra and filter the specific wavelength or wave band not only by changing the structural parameters, but also by changing the applied voltage.
Fig. 10. Transmission characteristics of the asymmetrical Y-type cavities filter by changing applied voltage U: (a) transmission spectrum, (b) resonance wavelength.
6. Optimization based on the asymmetric Y-type cavity structure filter
The transmission spectra of the asymmetric Y-type cavities structure filter can be optimized by studying the influence of structural parameters and applied voltage on the transmission characteristics of the filter, so that the filter can be applied to the three communication windows (850 nm, 1310 nm and 1550 nm) of the optical communication band, especially the second and the third windows. The optimized structural parameters, applied voltage and transmission spectra are shown in Fig. 11. When the structural parameters and the applied voltage are set to ${h_1} = 60\;\textrm{nm}$, ${h_2} = 55\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 2.7\;\textrm{V}$, the first window of the optical communication band is located in the stopband of the transmission spectra, the second and the third windows are located in the passband, as shown by the red line in Fig. 11. When ${h_1} = 50\;\textrm{nm}$, ${h_2} = 45\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 0\;\textrm{V}$, the second window of the optical communication band is located in the stopband of the transmission spectra, the first and the third windows are located in the passband, as shown by the blue line in Fig. 11. When ${h_1} = 60\;\textrm{nm}$, ${h_2} = 55\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 2\;\textrm{V}$, the third window in the optical communication band is located in the stopband of the transmission spectra, the second and the third windows are located in the passband, as shown by the purple line in Fig. 11. The transmission spectra of the three optimized structures have the flat passband whose transmittance is high, the narrow bandwidth of the stopband, the steep rising and falling edges. Therefore, selective control of the on and off of the transmission of the three communication windows in the optical communication band can be achieved.
Fig. 11. Transmission spectra of the optimized asymmetrical Y-type cavities filters: red line (${h_1} = 60\;\textrm{nm}$, ${h_2} = 55\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 2.7\;\textrm{V}$), blue line (${h_1} = 50\;\textrm{nm}$, ${h_2} = 55\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 0\;\textrm{V}$), purple line (${h_1} = 60\;\textrm{nm}$, ${h_2} = 55\;\textrm{nm}$, $D = 80\;\textrm{nm}$, $U = 2\;\textrm{V}$).
7. Conclusion
In this paper, a voltage tunable asymmetric Y-type cavities MIM structure filter based on side coupled is proposed, the transmission characteristics of the filter are simulated by finite element method. The simulation results show that the filter can not only adjust the transmission characteristics of the filter by changing the structural parameters, but also can realize the movement (red shift or blue shift) of the transmission spectra of the filter by adjusting the applied voltage without changing the structural parameters, and the resonance wavelength has a linear relationship with the applied voltage. And the transmittance of the passband of the filter is as high as 0.97, the transmittance of the stopband is as low as 0.001, and the FWHM can reach 970 nm. Then three optimized filters proposed can realize the filtering function of channel selection for three communication windows (850 nm, 1310 nm, 1550 nm) of optical communication band. In summary, the proposed filters have the characteristics of a small structure size, a flat passband with high transmittance, a wide FWHM, steep rising edge and falling edge as well as voltage adjustability, the filters may be have a number of engineering application value in high density integrated optical circuit design and nano-optical research.
Funding
Foundation for Innovative Research Groups of the National Natural Science Foundation of China (61631007); Fundamental Research Funds for the Central Universities (lzujbky-2018-K11).
Acknowledgments
System numerical simulation was provided by COMSOL, Inc.
Disclosures
The authors declare no conflicts of interest.
References
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]
2. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005). [CrossRef]
3. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007). [CrossRef]
4. B. Yun, G. Hu, and Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D: Appl. Phys. 43(38), 385102 (2010). [CrossRef]
5. X. Mei, X. G. Huang, and T. Jin, “A sub-wavelength electro-optic switch based on plasmonic T-shaped waveguide,” Plasmonics 6(4), 613–618 (2011). [CrossRef]
6. J. H. Zhu, X. G. Huang, and X. Mei, “Plasmonic electro-optical switches operating at telecom wavelengths,” Plasmonics 6(3), 605–612 (2011). [CrossRef]
7. Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, and X. Luo, “Characteristics of plasmonic filters with a notch located along rectangular resonators,” Plasmonics 8(2), 167–171 (2013). [CrossRef]
8. H. Lu, X. Liu, Y. Gong, D. Mao, and L. Wang, “Enhancement of transmission efficiency of nanoplasmonic wavelength demultiplexer based on channel drop filters and reflection nanocavities,” Opt. Express 19(14), 12885–12890 (2011). [CrossRef]
9. F. Afshinmanesh, W. Cai, and M. L. Brongersma, “A submicron plasmonic dichroic splitter,” Nat. Commun. 2(1), 525–526 (2011). [CrossRef]
10. X. Zhu, W. Yan, N. A. Mortensen, and S. Xiao, “Bends and splitters in graphene nanoribbon waveguides,” Opt. Express 21(3), 3486–3491 (2013). [CrossRef]
11. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef]
12. J. Y. Laluet and T. W. Ebbesen, “Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef]
13. H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Phys. E 40(10), 3025–3029 (2008). [CrossRef]
14. S. J. Im, Y. H. Han, and K. S. Ho, “Nanoscale optical directional coupler,” Plasmonics 12(6), 1741–1747 (2017). [CrossRef]
15. Z. Han and E. Forsberg, “Surface plasmon bragg gratings formed in metal-insulator-metal wave-guides,” IEEE Photonics Technol. Lett. 19(2), 91–93 (2007). [CrossRef]
16. Z. Li, K. Wen, L. Chen, and L. Lei, “Control of multiple Fano resonances based on a subwavelength MIM coupled cavities system,” IEEE Access 7, 59369–59375 (2019). [CrossRef]
17. Y. Fang, K. Wen, Z. Li, B. Wu, L. Chen, J. Zhou, and D. Zhou, “Multiple Fano resonances based on end-coupled semi-ring rectangular resonator,” IEEE Photonics J. 11(4), 1–8 (2019). [CrossRef]
18. B. Yun, G. Hu, and Y. Cui, “A nanometric plasmonic waveguide filter based on Fabry-Perot resonator,” Opt. Commun. 284(1), 485–489 (2011). [CrossRef]
19. C. P. Yin and H. Z. Wang, “The transmission characteristics of surface plas-mon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef]
20. Q. Zhang and X. P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express 17(9), 7533–7539 (2009). [CrossRef]
21. J. Tao and X. G. Huang, “All-optical plasmonic switches based on coupled nano-disk cavity structures containing nonlinear material,” Plasmonics 6(4), 753–759 (2011). [CrossRef]
22. I. Zand, A. Mahigir, T. Pakizeh, and M. S. Abrishamian, “Selective-mode optical nanofilters based on plasmonic complementary split-ring resonators,” Opt. Express 20(7), 7516–7525 (2012). [CrossRef]
23. Z. Han, V. Van and W, and N. Herman, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef]
24. X. Peng, H. Li, C. Wu, G. Cao, and Z. Liu, “Research on transmission characteristics of aperture-coupled square-ring resonator based filter,” Opt. Commun. 294(5), 368–371 (2013). [CrossRef]
25. H. Lu, X. Liu, Y. Gong, L. Wang, and D. Mao, “Multi-channel plasmonic waveguide filters with disk-shaped nanocavities,” Opt. Commun. 284(10-11), 2613–2616 (2011). [CrossRef]
26. C. Y. Xue and S. B. Yan, “Electro-magnetically induced transparency and refractive index sensing for a plasmonic waveguide with a stub coupled ring resonator,” Plasmonics 12(4), 1007–1013 (2017). [CrossRef]
27. D. R. Calawa and T. M. Lyszczarz, “Fabrication of crystalline organic waveguides with an exceptionally large electro-optic coefficient,” Appl. Phys. Lett. 84(19), 3729–3731 (2004). [CrossRef]
28. Y. J. Zhu, X. G. Huang, and X. Mei, “A surface plasmon polariton electro-optic switch based on a metal-insulator-metal structure with a strip waveguide and two side-coupled cavities,” Chin. Phys. Lett. 29(6), 064214 (2012). [CrossRef]
29. N. Hu, G. Zhang, H. An, Y. Shi, and M. Gu, “Design and optimization of the multifunctional rectangular cavity band-pass filter based on the surface plasmon polariton,” Plasmonics 12(5), 1457–1462 (2017). [CrossRef]
30. K. Wen, Y. Hu, L. Chen, J. Zhou, L. Lei, and Z. Meng, “Single/dual fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016). [CrossRef]
31. J. Chen, C. Sun, and Q. Gong, “Fano resonances in a single defect nanocavity coupled with a plasmonic waveguide,” Opt. Lett. 39(1), 52–55 (2014). [CrossRef]
32. B. Yun, G. Hu, and Y. Cui, “Resonant mode analysis of the nanoscale surface plasmon polariton waveguide filter with rectangle cavity,” Plasmonics 8(2), 267–275 (2013). [CrossRef]
33. G. Zheng, W. Su, Y. Chen, C. Zhang, M. Lai, and Y. Liu, “Band-stop filters based on a coupled circular ring metal-insulator-metal resonator containing nonlinear material,” J. Opt. 14(5), 055001 (2012). [CrossRef]
34. V. F. Nezhad, S. Abaslou, and M. S. Abrishamian, “Plasmonic band-stop filter with asymmetric rec-tangular ring for WDM networks,” J. Opt. 15(5), 055007 (2013). [CrossRef]
