Abstract

We have proposed a simple metal-dielectric-metal (MDM) waveguide system side-coupled with single-mode and multimode resonators. This proposed structure can achieve a typical dual plasmon-induced transparency (PIT) effect in the transmission spectra. The two PIT peaks exhibit opposite evolution tendencies with the increase in the depth of stubs. A multimode-coupled mode theory (M-CMT), confirmed by simulated results, is originally introduced to investigate the coupling effects of the proposed structure. Compared to the previous reported multichannel filters, the proposed structure includes obvious advantages, such as structural simplicity and ease of fabrication. In addition, the sensing characteristics of the proposed structure based on PIT effects are discussed numerically. The results demonstrate that the proposed structure is suitable for applications in multichannel filters, optical switches, and sensors.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The remarkable capability of surface plasmon polaritons (SPPs) for light manipulation on a sub-wavelength scale beyond the diffraction limit [1] has prompted extensive theoretical and experimental research on highly integrated photonic systems [2–10]. SPPs can be excited on the surface of metals [11–13] and various metal-like materials [14–16]. Among the various plasmonic structures, the metal-dielectric-metal (MDM) waveguide has been recognized as a good integrated photonic device owing to the advantages including the support for SPPs propagation at the metal-dielectric boundary, light manipulation at a sub-wavelength scale, etc [17]. Due to these potential features, simple structure, ease of construction, and industrial fabrication, the MDM waveguide structure has been extensively investigated for designing optical filters [12,18,19], switches [20–22], sensors [23–25], and slow-light devices [26,27].

Matsuzaki et al. originally proposed a stub(or stub pair)-coupled MDM waveguide for wavelength-selective filtering [2]. When a single stub(or stub pair) is extended to a periodic stub, due to the bandgap structure of the transmission spectrum after multiple filtering [12,28–32], the periodic-stub-coupled MDM waveguide structure supports broad stopband/passband filtering function and a sub-wavelength broadband slow-light guided mode [33]. When a single-set-periodic-stub-coupled MDM waveguide is expanded to a two-set-periodic-stub-coupled structure with two different stub depths, a narrow-passband filter function is achieved due to the overlap of the bandgap edges of the two periodic structures under appropriate parameters [18,34], i.e., the heterostructured waveguide can achieve single plasmon-induced transparency (PIT) effects. However, when heterostructures are used for achieving multiple PIT effects, the waveguide becomes more complicated. Moreover, when N single-mode stub resonators with graded depths are side-coupled to an MDM waveguide, N-1 PIT peaks will appear in the transmission spectrum due to the phase-coupled effect between two adjacent stubs with detuned resonant wavelengths, achieving a multichannel filtering function [7,35]. Besides, a bright-dark-dark waveguide system can achieve dual PIT spectral response due to the destructive interference between two adjacent resonator modes [20,36,37]. Nevertheless, among the above waveguide structures, it is necessary to couple N resonators to generate N-1 PIT peaks due to the phase coupling effect [7,35,38] or destructive interference [20,36,37] between the adjacent single-mode resonators, and three resonators result in dual PIT peaks. However, a simpler structure is preferred. To the best of our knowledge, there are few reports on the realization of dual PIT effects with two stub-coupled MDM waveguides.

In this work, based on the basic coupled mode theory (CMT) [26], we introduce the multimode-coupled mode theory (M-CMT) to understand the coupling effects and analyze the spectral responses in an MDM waveguide structure side-coupled with a single-mode stub and a multimode stub. Moreover, the structure can achieve double PIT peaks by suitably adjusting these structural parameters. Compared to the previous waveguide structures with the same functions [20,35,38], the simplicity of our proposed structure is a significant advantage, and it can achieve more PIT peaks compared to a similar structure [26]. The theoretical calculation results are consistent with the simulation results, and this study provides basic analysis ideas for single-mode and multimode resonator-coupled systems. Because of the simple structure and ease of fabrication, the proposed system has great potential for applications in multichannel filters, sensors, and switches.

2. Structural model and theoretical analysis

The proposed MDM waveguide system, which includes a single-mode stub and a multimode stub, is shown in Fig. 1. For simplicity, the left stub is marked as stub1, while the right stub is marked as stub2. The structural parameters include the width w of the main waveguide, width w1 and depth d1 of stub1, width w2 and depth d2 of stub2, and the coupling distance L12 between stub1 and stub2. Besides, L is the distance between the light source and the monitor. In the simulation, we respectively select air and silver as the insulator and metal of the system. The dielectric constant of silver, which is regulated by the frequency of the light wave, is expressed by the Drude mode [39]: εm(ω) = ε-ωp/(ω2 + iωγp), where ω, ωp(1.37 × 1016 rad/s), ε(3.7), and γp(4.08 × 1013 rad/s) are the angular frequency, plasma frequency, relative dielectric constant at infinite frequency, and damping rate of the incident wave, respectively.

 

Fig. 1 Two-dimensional schematic of the MDM waveguide side-coupled with a single-mode stub and a multimode stub.

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The spectral response features of the system are qualitatively analyzed by two-dimensional finite-difference time-domain(FDTD) simulation, where the boundary conditions are set as perfectly matched layers with a mesh grid (Δx = Δy = 2 nm and t = Δx/2c, c is the speed of light in vacuum). When a Gaussian beam is input to the left of the main waveguide, SPPs, which propagate along the surface, are generated at the dielectric-metal interface, coupling part of the energy into the stubs and exciting the resonant modes.

In the simulations, the parameters are set as follows: d1 = 250 nm, d2 = 355 nm, L = 680 nm, L12 = 200 nm, w = w1 = 60 nm, and w2 = 80 nm. Figure 2(a) displays the transmission spectra of the system coupled with only one stub: stub1(or stub2). For stub1, a transmission dip is formed at wavelength of 527 nm, as indicated by the black curve. Conversely, for stub2, two transmission dips are formed at wavelengths of 430 nm and 654 nm, respectively, as indicated by the blue curve, and there is a relatively wide transmission window between the two dips. It can be seen that the incident wave excites a resonant mode in stub1 and stimulates two resonant modes in stub2. The resonator, where the incident wave excites only one resonant mode, is called single-mode resonator. The resonator, where the incident wave stimulates two or more resonant modes, is called multimode resonator. Hence, stub1 and stub2 correspond to single-mode and multimode resonators, respectively. Two typical PIT peaks can be observed in the transmission spectrum of the two stub-coupled system, as displayed in Fig. 2(b). To explore the formation mechanism of the dual PIT shapes, the magnetic field distributions of the single stub-coupled structure at the three resonant dips are exhibited in Figs. 2(c)–2(e), respectively. TMmn indicates the resonant modes, where m and n are non-negative integers representing the number of standing-wave nodes along the x-direction and y-direction, respectively. The resonant mode of stub1 corresponds to TM01 (λ = 527 nm), while those of stub2 correspond to TM01 (λ = 654 nm) and TM02 (λ = 430 nm), respectively. When the two stubs are coupled to the main waveguide simultaneously, direct and indirect couplings occur between the stub resonators [26]. Physically, the coupling effects occur between the resonant modes, rather than between the stubs, i.e., the resonant mode of the single-mode stub interacts with each resonant mode of the multimode stub, respectively. Furthermore, direct coupling occurs between any two resonant modes of the multimode-stub resonator [40]. Thus, the transmission window of stub2 is split into two transmission windows, exhibiting a special spectral response with double PIT peaks, as depicted in Fig. 2(b). And the two peaks are recorded as P12 (λ = 467 nm) and P11 (λ = 564 nm), respectively. So, based on the coupling of TM01 and TM02 of stub2, the interaction between the TM01 modes of the two stubs produces P11, and the coupling between TM01 of stub1 and TM02 of stub2 produces P12. The above conclusion is further confirmed by the magnetic field distributions of the PIT peaks displayed in Figs. 2(f) and 2(g).

 

Fig. 2 (a) and (b) Transmission spectra of the MDM waveguide side-coupled with a single-mode stub (stub1, black curve), multimode stub (stub2, blue curve), and single-mode and multimode stubs (stub1 and stub2, red curve) with w = 60 nm, w1 = 60 nm, w2 = 80 nm, L12 = 200 nm, d1 = 250 nm, and d2 = 380 nm. (c)–(e) Magnetic field distributions of the individual single-mode and multimode stub-coupled structure at the resonant dips. (f) and (g) Magnetic field distributions of the coupled structure at the two PIT peaks.

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Next, in order to explore the coupling effects in the single-mode and multimode resonator-coupled system, and study the spectral response behaviors of the system in detail, based on the direct coupling among the resonant modes of the multimode resonator [40,41], considering the direct and indirect couplings between the resonant modes of different stubs, we introduce an extended M-CMT. In Fig. 1, S±,in(N)(N=1,2) and S±,out(N)(N=1,2) represent the incoming and outgoing waves in the main waveguide, respectively. The subscript ± indicates the propagating directions of the waveguide modes, and an (n = 1, 2, 3) is the energy amplitude of the nth resonant mode. Thus, the extended M-CMT can be expressed as follows:

da1dt=(jω11τo11τi1)a1+S+,in(1)1τo1+S,in(1)1τo1jμ12a2jμ13a3,
da2dt=(jω21τo21τi2)a2+S+,in(2)1τo2+S,in(2)1τo2jμ21a1jμ23a3,
da3dt=(jω31τo31τi3)a3+S+,in(2)1τo3+S,in(2)1τo3jμ32a2jμ31a1,
Where ωn (n = 1, 2, 3) is the resonant angular frequency of the nth resonant mode. 1/τon = ωn/(2Qon) and 1/τin = ωn/(2Qin) are the decay rate due to the energy coupled into the main waveguide and the intrinsic loss of the nth resonant mode, respectively. μmn = ωn/(2Qcn) (mn) is the direct coupling coefficient between the mth and nth resonant modes. Here, the quality factors (Q-factors) corresponding to these three losses are Qin, Qon, and Qcn, respectively. For the nth resonant mode, the total Q-factor is expressed as Qtn = λ/Δλ (λ and Δλ are the resonant wavelength and full width of half maximum (FWHM), respectively). The internal quality factor Qin can be calculated with the definition from [14]. And these quality factors satisfy the relationship, 1/Qtn = 1/Qin + 1/Qon.

When a wave beam propagates between the two stubs, it causes a phase shift,φ=Re(βspp)L12=ωRe(neff)L12/c, where L12, βSPP, and neff are the coupling distance, propagation constant, and effective refractive index of the SPPs [42], respectively. Based on the principle of conservation of energy, the following relationships can be obtained:

S,in(1)=S,out(2)ejφ,S+,in(2)=S+,out(1)ejφ,
S±,out(1)=S±,in(1)1τo1a1,S±,out(2)=S±,in(2)(1τo2a2+1τo3a3),

Theoretically, combining the boundary condition of Sin(2)=0 with Eqs. (1)–(5), the amplitude transmittance of the proposed system can be deduced as follows:

t=S+,out(2)S+,in(1)=ejφ(1+1γ3τo3)+(1τo1ejφ+1τo3x31γ3)(FD+EB)+(1τo2+1τo3x32γ3)(FA+EC)ABCD,
Where
A=γ1x23+x21x13,B=γ2γ3x23x32,C=γ3x21+x31x23,D=x12x23+γ2x13,
E=1τo1x231τo2x13ejφ,F=(1τo2γ3+1τo3x23)ejφ,
x23=jμ23,x32=jμ32,
xmn=1τomτonejφ+jμmn(m=1,n=2,3;m=2,n=1;m=3,n=1).
Where γn=j(ωωn)1/τon1/τin(n=1,2,3), and the transmission is expressed as .

3. Results and discussion

Figures 3(a) and 3(b) show the FDTD simulated and M-CMT calculated transmission spectra of the proposed system for different d2 values, and the other parameter values are same as in Fig. 2. The PIT peaks are recorded as P11 or P12 near d2 = 355 nm, and P12 or P13 near d2 = 555 nm. The simulation results are consistent with the calculated ones, not only proving the correctness of the theoretical model but also providing a basic idea for further researches. Figures 3(c)–3(e) depict respectively the wavelengths, transmission, and Q-factors of the PIT peaks for different d2 values. Figure 3 displays three interesting results: (i) When d2 = 355 nm (or 555 nm), the transmission spectrum exhibits substantially symmetric double PIT peaks; (ii) As d2 increases, both PIT peaks exhibit a significant red shift as shown in Figs. 3(a)–3(c); (iii) As d2 increases, the transmission of the right PIT peak slowly increases and its bandwidth widens, becoming a wide transmission window with low Q-factors, while the left PIT peak changes in the opposite direction and eventually disappears near d2 = 471 nm as shown in Figs. 3(d) and 3(e). The above phenomena can be ascribed to the red shift of the resonant modes with the gradual increase in d2.

 

Fig. 3 (a) and (b) Transmission spectra of the numerical and theoretical calculations, respectively, for various d2 values. (c) Wavelengths, (d) transmission, and (e) Q-factors of the PIT peaks, respectively.

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Figure 4(a) displays the simulated transmission spectra of the system coupled only with the multimode stub for different d2 values, and the other parameters are same as in Fig. 2. As d2 increases, the transmission spectra undergo a red-shift and more dips appear, i.e., more resonant modes are stimulated in the multimode stub. When d2 increases to 475 nm, three resonant modes are excited in the wavelength range of 400−1100 nm. The transmission valleys are recorded as dip1, dip2, and dip3, respectively. Figures 4(c)–4(e) display the magnetic field distributions of dip1, dip2, and dip3, corresponding to TM01, TM02, and TM03, respectively. Figure 4(b) depicts the linear relationship between the resonant wavelengths and d2. When d2 = 471 nm, the resonant wavelength of TM02 is equal to that of TM01 of stub1 with d1 = 250 nm. When d2 < 471 nm, the resonant wavelength of the stub1 is between those of TM01 and TM02 of stub2. Hence, based on the direct coupling between the modes of stub2, TM01 of stub1 couples with TM01 and TM02 of stub2, respectively, producing two PIT peaks recorded as P11 and P12, respectively. As d2 increases, the wavelength detuning between the TM01 modes of stub1 and stub2 increases, resulting in an increase for the transmission and FWHM of P11, as shown in Figs. 3(a), 3(b), and 3(d), thereby decreasing the Q-factor of P11, as illustrated in Fig. 3(e). However, the wavelength detuning between TM01 of stub1 and TM02 of stub2 reduces continuously, resulting in a decrease in the transmission and FWHM for P12, as illustrated in Figs. 3(a), 3(b), and 3(d), and continuously increasing in Q-factor, as illustrated in Fig. 3(e); then P12 completely disappears at d2 = 471 nm, as depicted in Fig. 3(d). When d2 > 471 nm, TM03 is excited in the short wavelength band, and the resonant wavelength of TM01 of stub1 is between those of TM02 and TM03 of stub2, as shown in Fig. 4(b), resulting in a large wavelength detuning between the two TM01 modes of stub1 and stub2. So, the coupling between them shows a wide transmission window, which is not considered in the work. Next, we only consider the coupling effects that TM01 of stub1 interacts with TM02 and TM03 of stub2, respectively. Similarly, as d2 increases, the detuning of the resonant wavelength between TM01 and TM02 increases, resulting in enlarging for the transmission and FWHM of P12. Whereas the detuning of the resonant wavelength between TM01 and TM03 exhibits an opposite trend with the increase in d2, reducing the transmission and FWHM of P13.

 

Fig. 4 (a) Transmission spectra of the MDM waveguide side-coupled with the multimode stub for various d2 values. (b) Resonant wavelengths of dip1, dip2, and dip3 for various d2 values. (c)−(e) Magnetic field distributions of the MDM waveguide side-coupled with the multimode stub at these resonant dips.

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According to the above analysis, as d2 increases, P11 slowly evolves into a broad transmission window, while P12 undergoes a special evolution process of gradual narrowing, disappearing, and gradual widening, before becoming a broad transmission window, as depicted in Figs. 3(a), 3(b), and 3(d). If d2 increases continuously, P13 will also undergo the same evolution process, and a new PIT peak will appear in the transmission spectra in the short-wavelength band.

In the above, the modulation effect of d2 on the two PIT peaks has been analyzed. Besides, other structural parameters, such as the depth of the single-mode stub and coupling distance, can well regulate the transmission features of the system. Next, we briefly discuss the regulation characteristics of d1 on PIT peaks. In the case of d2 = 355 nm and d1 = 250 nm, the resonant wavelength of stub1 is between the ones of stub2, and the transmission spectrum exhibits substantially symmetric dual PIT peaks, as shown in Fig. 2(b). As d1 increases, the resonant wavelength of TM01 of stub1 has a red-shift while the resonant wavelengths of TM01 and TM02 of stub2 remain constants. So, the wavelength detuning between the TM01 modes of stub1 and stub2 decreases with an increase in d1, resulting in a decrease for the transmission and FWHM of P11. However, the wavelength detuning between TM01 of stub1 and TM02 of stub2 increases continuously, leading to an increase in the transmission and FWHM of P12. Thus, the two PIT peaks exhibit opposite evolution trends with the change in d1, where the tendencies are completely opposite to those with the increase in d2. In addition, it should be noted that multiple modes will be excited when the depth of stub1 is too large, so the depth of stub1 cannot be too large.

Finally, we investigate the sensing features because of the sensitivity of the optical transmission characteristics to the environment, and the application potential in sensors. Figure 5(a) illustrates the simulated spectra of the proposed system for various refractive indexes n, and the other parameters are same as in Fig. 2. In Fig. 5(a), with the increase of n, the transmission spectra show significant red-shift, maintaining nearly the same spectral shape. Figure 5(b) exhibits the relationship between the wavelengths of the PIT peaks (or dips) and the refractive index. The sensitivity is defined as S = Δλmn [43], where Δn and Δλm are the changes in the refractive index and the corresponding wavelength shift of the PIT peaks (or dips), respectively. Because Fig. 5(b) shows good linear relationships, the sensitivities are equal to the slopes of the lines. By linear fitting, we obtain the corresponding slopes, and the slopes (sensitivities) of dip1, P11, dip2, P12 and dip3 are 625.51 nm/RIU, 526.77 nm/RIU, 476.91 nm/RIU, 413.34 nm/RIU, and 359.94 nm/RIU, respectively. These good linear relationships may be attributable to the relationship between the neff and the refractive index. The neff of the SPPs in an MDM waveguide with width w is expressed as follows [44,45]:

 

Fig. 5 (a) Transmission spectra for various refractive indices n, when d1 = 250 nm and d2 = 355 nm. (b) Wavelengths of the dips and peaks with respect to refractive indices n. (c)Relationship between Re(neff) and the wavelength, for n = 1.00, 1.03, and 1.06, respectively. (d) Relationship between Re(neff) and n, for λ = 430 nm, 527 nm, and 654 nm, respectively.

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neffεd+2εdεdεmk0w(εm),

Where εd and εm are the relative dielectric constants of the dielectric and metal, respectively, and k0 is the wave vector in vacuum. When n = 1, 1.03, 1.06, and w = 60 nm, Fig. 5(c) depicts the relationship between the real part of the effective index Re(neff) of the SPPs and the wavelength of TM mode. When λ = 430 nm, 527 nm, and 654 nm, Fig. 5(d) displays obvious linear relations between Re(neff) and refractive indexes. These linear relationships are also satisfied for other wavelengths. In addition, because the resonant wavelength is proportional to Re(neff) of the SPPs, the resonant wavelengths and the wavelengths of PIT peaks are necessarily proportional to the refractive index of the medium, as revealed in Fig. 5(b). Thus the proposed structure can be utilized as a sensor for monitoring the refractive index of the environment, the environmental temperature, and liquid concentration.

4. Conclusions

In this study, a simple MDM waveguide structure side-coupled with a single-mode stub and a multimode stub at different positions have been presented. This system can achieve dual PIT peaks and can be used as a dual-channel filter. Moreover, its spectral responses are numerically and theoretically investigated. In order to comprehend the coupling effects of the proposed system, we have originally introduced an extended M-CMT, which considers not only the coupling effect between the modes in the multimode resonator but also the coupling effects between the modes from different resonators. Besides, our proposed structure is simpler than the previous structures with the same function. Furthermore, we have studied the sensing features of the proposed system by analyzing the relationships between the wavelengths of the dips (or peaks) and the refractive index, established that a very good linear relationship exists between them. This excellent linear relationship can serve as the foundation for sensor design.

Funding

National Natural Science Foundation of China (NSFC) (61275174); Fundamental Research Funds for the Central Universities of Central South University (2018zzts105); Scientific Research Fund of Hunan Provincial Education Department (16C0294).

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36. H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018). [CrossRef]  

37. Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018). [CrossRef]   [PubMed]  

38. H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012). [CrossRef]  

39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]  

40. Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016). [CrossRef]   [PubMed]  

41. Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016). [CrossRef]  

42. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]  

43. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef]   [PubMed]  

44. S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008). [CrossRef]   [PubMed]  

45. S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014). [CrossRef]  

References

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  5. Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
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  7. X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
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  16. Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
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  17. Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
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    [Crossref] [PubMed]
  21. G. Wang, H. Lu, X. Liu, and Y. Gong, “Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating,” Nanotechnology 23(44), 444009 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  24. T. Wu, Y. Liu, Z. Yu, Y. Peng, C. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
    [Crossref] [PubMed]
  25. Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
    [Crossref] [PubMed]
  26. G. Cao, H. Li, S. Zhan, Z. He, Z. Guo, X. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39(2), 216–219 (2014).
    [Crossref] [PubMed]
  27. X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
    [Crossref]
  28. X. Lin and X. Huang, “Numerical modeling of a teeth-shaped nanoplasmonic waveguide filter,” J. Opt. Soc. Am. B 26(7), 1263–1268 (2009).
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  29. J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Surface plasmon reflector based on serial stub structure,” Opt. Express 17(22), 20134–20139 (2009).
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  30. A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18(6), 6191–6204 (2010).
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  31. Y. Huang, C. Min, and G. Veronis, “Subwavelength slow-light waveguides based on a plasmonic analogue of electromagnetically induced transparency,” Appl. Phys. Lett. 99(14), 143117 (2011).
    [Crossref]
  32. A. N. Taheri and H. Kaatuzian, “Numerical investigation of a nano-scale electro-plasmonic switch based on metal-insulator-metal stub filter,” Opt. Quantum Electron. 47(2), 159–168 (2015).
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  33. L. Yang, C. Min, and G. Veronis, “Guided subwavelength slow-light mode supported by a plasmonic waveguide system,” Opt. Lett. 35(24), 4184–4186 (2010).
    [Crossref] [PubMed]
  34. H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
    [Crossref]
  35. J. Chen, C. Wang, R. Zhang, and J. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37(24), 5133–5135 (2012).
    [Crossref] [PubMed]
  36. H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018).
    [Crossref]
  37. Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
    [Crossref] [PubMed]
  38. H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012).
    [Crossref]
  39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  40. Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
    [Crossref] [PubMed]
  41. Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
    [Crossref]
  42. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
    [Crossref]
  43. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
    [Crossref] [PubMed]
  44. S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008).
    [Crossref] [PubMed]
  45. S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
    [Crossref]

2019 (1)

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref] [PubMed]

2018 (4)

H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018).
[Crossref]

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

M. Dowran, A. Kumar, B. Lawrie, R. Pooser, and A. Marino, “Quantum-enhanced plasmonic sensing,” Optica 5(5), 628 (2018).
[Crossref]

Q. Hong, F. Xiong, W. Xu, Z. Zhu, K. Liu, X. Yuan, J. Zhang, and S. Qin, “Towards high performance hybrid two-dimensional material plasmonic devices: strong and highly anisotropic plasmonic resonances in nanostructured graphene-black phosphorus bilayer,” Opt. Express 26(17), 22528–22535 (2018).
[Crossref] [PubMed]

2017 (3)

Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
[Crossref] [PubMed]

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

X. Yang, X. Hu, H. Yang, and Q. Gong, “Ultracompact all-optical logic gates based on nonlinear plasmonic nanocavities,” Nanophotonics 6(1), 365–376 (2017).
[Crossref]

2016 (10)

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref] [PubMed]

H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
[Crossref] [PubMed]

Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
[Crossref] [PubMed]

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

P. Dastmalchi and G. Veronis, “Plasmonic switches based on subwavelength cavity resonators,” J. Opt. Soc. Am. B 33(12), 2486–2492 (2016).
[Crossref]

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
[Crossref] [PubMed]

Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
[Crossref]

2015 (4)

Z. He, H. Li, S. Zhan, B. Li, Z. Chen, and H. Xu, “Tunable multi-switching in plasmonic waveguide with kerr nonlinear resonator,” Sci. Rep. 5(1), 15837 (2015).
[Crossref] [PubMed]

X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
[Crossref]

A. N. Taheri and H. Kaatuzian, “Numerical investigation of a nano-scale electro-plasmonic switch based on metal-insulator-metal stub filter,” Opt. Quantum Electron. 47(2), 159–168 (2015).
[Crossref]

S. Zhan, H. Li, Z. He, B. Li, Z. Chen, and H. Xu, “Sensing analysis based on plasmon induced transparency in nanocavity-coupled waveguide,” Opt. Express 23(16), 20313–20320 (2015).
[Crossref] [PubMed]

2014 (5)

X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
[Crossref]

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104(23), 231114 (2014).
[Crossref]

T. Wu, Y. Liu, Z. Yu, Y. Peng, C. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
[Crossref] [PubMed]

G. Cao, H. Li, S. Zhan, Z. He, Z. Guo, X. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39(2), 216–219 (2014).
[Crossref] [PubMed]

S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

2012 (4)

J. Chen, C. Wang, R. Zhang, and J. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37(24), 5133–5135 (2012).
[Crossref] [PubMed]

G. Wang, H. Lu, X. Liu, and Y. Gong, “Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating,” Nanotechnology 23(44), 444009 (2012).
[Crossref] [PubMed]

H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012).
[Crossref] [PubMed]

H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012).
[Crossref]

2011 (3)

Z. Han and S. I. Bozhevolnyi, “Plasmon-induced transparency with detuned ultracompact Fabry-Perot resonators in integrated plasmonic devices,” Opt. Express 19(4), 3251–3257 (2011).
[Crossref] [PubMed]

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

Y. Huang, C. Min, and G. Veronis, “Subwavelength slow-light waveguides based on a plasmonic analogue of electromagnetically induced transparency,” Appl. Phys. Lett. 99(14), 143117 (2011).
[Crossref]

2010 (4)

2009 (3)

2008 (2)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[Crossref]

Agrawal, G. P.

Bai, W.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

Bi, K.

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

Cai, L.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

Cao, G.

G. Cao, H. Li, S. Zhan, Z. He, Z. Guo, X. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39(2), 216–219 (2014).
[Crossref] [PubMed]

S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

Chai, Z.

X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
[Crossref]

Chang, S.

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

Chen, D.

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
[Crossref] [PubMed]

Chen, H.

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104(23), 231114 (2014).
[Crossref]

Chen, J.

Chen, Y.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref] [PubMed]

Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
[Crossref] [PubMed]

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
[Crossref] [PubMed]

S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref] [PubMed]

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

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S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
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Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
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Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
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Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
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Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
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Z. He, H. Li, S. Zhan, B. Li, Z. Chen, and H. Xu, “Tunable multi-switching in plasmonic waveguide with kerr nonlinear resonator,” Sci. Rep. 5(1), 15837 (2015).
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S. Zhan, H. Li, Z. He, B. Li, Z. Chen, and H. Xu, “Sensing analysis based on plasmon induced transparency in nanocavity-coupled waveguide,” Opt. Express 23(16), 20313–20320 (2015).
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Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
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X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
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Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
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X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
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Liu, K.

Liu, N.

Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
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Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
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Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
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S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
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G. Wang, H. Lu, X. Liu, and Y. Gong, “Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating,” Nanotechnology 23(44), 444009 (2012).
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H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012).
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Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
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Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
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Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
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Song, G.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
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A. N. Taheri and H. Kaatuzian, “Numerical investigation of a nano-scale electro-plasmonic switch based on metal-insulator-metal stub filter,” Opt. Quantum Electron. 47(2), 159–168 (2015).
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X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
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H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012).
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H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
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X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
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Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
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H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
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Xiong, F.

Xu, H.

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
[Crossref]

Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
[Crossref] [PubMed]

Z. He, H. Li, S. Zhan, B. Li, Z. Chen, and H. Xu, “Tunable multi-switching in plasmonic waveguide with kerr nonlinear resonator,” Sci. Rep. 5(1), 15837 (2015).
[Crossref] [PubMed]

S. Zhan, H. Li, Z. He, B. Li, Z. Chen, and H. Xu, “Sensing analysis based on plasmon induced transparency in nanocavity-coupled waveguide,” Opt. Express 23(16), 20313–20320 (2015).
[Crossref] [PubMed]

Xu, S.

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

Xu, W.

Xu, X.

Xu, Y.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

Yan, P.

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

Yang, H.

X. Yang, X. Hu, H. Yang, and Q. Gong, “Ultracompact all-optical logic gates based on nonlinear plasmonic nanocavities,” Nanophotonics 6(1), 365–376 (2017).
[Crossref]

X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
[Crossref]

G. Cao, H. Li, S. Zhan, Z. He, Z. Guo, X. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39(2), 216–219 (2014).
[Crossref] [PubMed]

S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

Yang, J.

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
[Crossref] [PubMed]

Yang, L.

Yang, X.

X. Yang, X. Hu, H. Yang, and Q. Gong, “Ultracompact all-optical logic gates based on nonlinear plasmonic nanocavities,” Nanophotonics 6(1), 365–376 (2017).
[Crossref]

X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
[Crossref]

Ye, H.

Yu, Z.

Yuan, X.

Yue, Z.

H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018).
[Crossref]

Zhan, S.

Z. He, H. Li, S. Zhan, B. Li, Z. Chen, and H. Xu, “Tunable multi-switching in plasmonic waveguide with kerr nonlinear resonator,” Sci. Rep. 5(1), 15837 (2015).
[Crossref] [PubMed]

S. Zhan, H. Li, Z. He, B. Li, Z. Chen, and H. Xu, “Sensing analysis based on plasmon induced transparency in nanocavity-coupled waveguide,” Opt. Express 23(16), 20313–20320 (2015).
[Crossref] [PubMed]

G. Cao, H. Li, S. Zhan, Z. He, Z. Guo, X. Xu, and H. Yang, “Uniform theoretical description of plasmon-induced transparency in plasmonic stub waveguide,” Opt. Lett. 39(2), 216–219 (2014).
[Crossref] [PubMed]

S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

Zhang, G.

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

Zhang, J.

Q. Hong, F. Xiong, W. Xu, Z. Zhu, K. Liu, X. Yuan, J. Zhang, and S. Qin, “Towards high performance hybrid two-dimensional material plasmonic devices: strong and highly anisotropic plasmonic resonances in nanostructured graphene-black phosphorus bilayer,” Opt. Express 26(17), 22528–22535 (2018).
[Crossref] [PubMed]

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

H. Wang, J. Yang, J. Zhang, J. Huang, W. Wu, D. Chen, and G. Xiao, “Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure,” Opt. Lett. 41(6), 1233–1236 (2016).
[Crossref] [PubMed]

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

Zhang, L.

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104(23), 231114 (2014).
[Crossref]

Zhang, Q.

Zhang, R.

Zhang, S.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref] [PubMed]

S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref] [PubMed]

Zhang, Y.

Zhang, Z.

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104(23), 231114 (2014).
[Crossref]

Zhao, H.

Zhao, J.

H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018).
[Crossref]

Zhao, M.

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

Zheng, M.

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
[Crossref] [PubMed]

Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
[Crossref]

Zhou, Y.

Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
[Crossref] [PubMed]

Zhu, X.

S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref] [PubMed]

Zhu, Z.

ACS Nano (2)

Y. Chen, K. Bi, Q. Wang, M. Zheng, Q. Liu, Y. Han, J. Yang, S. Chang, G. Zhang, and H. Duan, “Rapid focused Ion beam milling based fabrication of plasmonic nanoparticles and assemblies via “sketch and peel” strategy,” ACS Nano 10(12), 11228–11236 (2016).
[Crossref] [PubMed]

S. Zhang, G. C. Li, Y. Chen, X. Zhu, S.-D. Liu, D. Y. Lei, and H. Duan, “Pronounced fano resonance in single gold split nanodisks with 15-nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref] [PubMed]

Appl. Phys. Express (3)

Z. Chen, H. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Multiple plasmon-induced transparency effects in a multimode-cavity-coupled metal–dielectric–metal waveguide,” Appl. Phys. Express 10(9), 092201 (2017).
[Crossref]

Z. Chen, H. Li, B. Li, Z. He, H. Xu, M. Zheng, and M. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

Z. He, Y. Peng, B. Li, Z. Chen, H. Xu, M. Zheng, and H. Li, “Aspect ratio control and sensing applications for a slot waveguide with a multimode stub,” Appl. Phys. Express 9(7), 072002 (2016).
[Crossref]

Appl. Phys. Lett. (4)

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).
[Crossref]

X. Yang, X. Hu, Z. Chai, C. Lu, H. Yang, and Q. Gong, “Tunable ultracompact chip-integrated multichannel filter based on plasmon-induced transparencies,” Appl. Phys. Lett. 104(22), 221114 (2014).
[Crossref]

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104(23), 231114 (2014).
[Crossref]

Y. Huang, C. Min, and G. Veronis, “Subwavelength slow-light waveguides based on a plasmonic analogue of electromagnetically induced transparency,” Appl. Phys. Lett. 99(14), 143117 (2011).
[Crossref]

IEEE Photonic. Tech. L. (1)

H. Wang, J. Yang, W. Wu, J. Huang, J. Zhang, P. Yan, D. Chen, and G. Xiao, “The transmission characteristics of asymmetrical multi-teeth-shaped plasmonic waveguide structure,” IEEE Photonic. Tech. L. 28(21), 2467–2470 (2016).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. D Appl. Phys. (2)

X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Dynamically tunable slow light based on plasmon induced transparency in disk resonators coupled MDM waveguide system,” J. Phys. D Appl. Phys. 48(23), 235102 (2015).
[Crossref]

S. Zhan, H. Li, G. Cao, Z. He, B. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

Materials (Basel) (1)

Z. Zhang, J. Yang, X. He, Y. Han, J. Zhang, J. Huang, D. Chen, and S. Xu, “Active enhancement of slow light based on plasmon-induced transparency with gain materials,” Materials (Basel) 11(6), 941 (2018).
[Crossref] [PubMed]

Nano Lett. (3)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. 17(9), 5555–5560 (2017).
[Crossref] [PubMed]

Y. Chen, Q. Xiang, Z. Li, Y. Wang, Y. Meng, and H. Duan, ““Sketch and peel” lithography for high-resolution multiscale patterning,” Nano Lett. 16(5), 3253–3259 (2016).
[Crossref] [PubMed]

Nanophotonics (1)

X. Yang, X. Hu, H. Yang, and Q. Gong, “Ultracompact all-optical logic gates based on nonlinear plasmonic nanocavities,” Nanophotonics 6(1), 365–376 (2017).
[Crossref]

Nanoscale (1)

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

Nanotechnology (2)

G. Wang, H. Lu, X. Liu, and Y. Gong, “Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating,” Nanotechnology 23(44), 444009 (2012).
[Crossref] [PubMed]

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref] [PubMed]

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Opt. Commun. (1)

H. Lu, Z. Yue, and J. Zhao, “Multiple plasmonically induced transparency for chip-scale bandpass filters in metallic nanowaveguides,” Opt. Commun. 414, 16–21 (2018).
[Crossref]

Opt. Express (9)

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Surface plasmon reflector based on serial stub structure,” Opt. Express 17(22), 20134–20139 (2009).
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A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18(6), 6191–6204 (2010).
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T. Wu, Y. Liu, Z. Yu, Y. Peng, C. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
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Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16(21), 16314–16325 (2008).
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Z. Han and S. I. Bozhevolnyi, “Plasmon-induced transparency with detuned ultracompact Fabry-Perot resonators in integrated plasmonic devices,” Opt. Express 19(4), 3251–3257 (2011).
[Crossref] [PubMed]

Q. Hong, F. Xiong, W. Xu, Z. Zhu, K. Liu, X. Yuan, J. Zhang, and S. Qin, “Towards high performance hybrid two-dimensional material plasmonic devices: strong and highly anisotropic plasmonic resonances in nanostructured graphene-black phosphorus bilayer,” Opt. Express 26(17), 22528–22535 (2018).
[Crossref] [PubMed]

S. Zhan, H. Li, Z. He, B. Li, Z. Chen, and H. Xu, “Sensing analysis based on plasmon induced transparency in nanocavity-coupled waveguide,” Opt. Express 23(16), 20313–20320 (2015).
[Crossref] [PubMed]

J. Tao, X. G. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17(16), 13989–13994 (2009).
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S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008).
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Opt. Quantum Electron. (1)

A. N. Taheri and H. Kaatuzian, “Numerical investigation of a nano-scale electro-plasmonic switch based on metal-insulator-metal stub filter,” Opt. Quantum Electron. 47(2), 159–168 (2015).
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H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012).
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Z. He, H. Li, S. Zhan, B. Li, Z. Chen, and H. Xu, “Tunable multi-switching in plasmonic waveguide with kerr nonlinear resonator,” Sci. Rep. 5(1), 15837 (2015).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Two-dimensional schematic of the MDM waveguide side-coupled with a single-mode stub and a multimode stub.
Fig. 2
Fig. 2 (a) and (b) Transmission spectra of the MDM waveguide side-coupled with a single-mode stub (stub1, black curve), multimode stub (stub2, blue curve), and single-mode and multimode stubs (stub1 and stub2, red curve) with w = 60 nm, w1 = 60 nm, w2 = 80 nm, L12 = 200 nm, d1 = 250 nm, and d2 = 380 nm. (c)–(e) Magnetic field distributions of the individual single-mode and multimode stub-coupled structure at the resonant dips. (f) and (g) Magnetic field distributions of the coupled structure at the two PIT peaks.
Fig. 3
Fig. 3 (a) and (b) Transmission spectra of the numerical and theoretical calculations, respectively, for various d2 values. (c) Wavelengths, (d) transmission, and (e) Q-factors of the PIT peaks, respectively.
Fig. 4
Fig. 4 (a) Transmission spectra of the MDM waveguide side-coupled with the multimode stub for various d2 values. (b) Resonant wavelengths of dip1, dip2, and dip3 for various d2 values. (c)−(e) Magnetic field distributions of the MDM waveguide side-coupled with the multimode stub at these resonant dips.
Fig. 5
Fig. 5 (a) Transmission spectra for various refractive indices n, when d1 = 250 nm and d2 = 355 nm. (b) Wavelengths of the dips and peaks with respect to refractive indices n. (c)Relationship between Re(neff) and the wavelength, for n = 1.00, 1.03, and 1.06, respectively. (d) Relationship between Re(neff) and n, for λ = 430 nm, 527 nm, and 654 nm, respectively.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

d a 1 d t = ( j ω 1 1 τ o 1 1 τ i 1 ) a 1 + S + , in ( 1 ) 1 τ o 1 + S , in ( 1 ) 1 τ o 1 j μ 12 a 2 j μ 13 a 3 ,
d a 2 d t = ( j ω 2 1 τ o 2 1 τ i 2 ) a 2 + S + , in ( 2 ) 1 τ o 2 + S , in ( 2 ) 1 τ o 2 j μ 21 a 1 j μ 23 a 3 ,
d a 3 d t = ( j ω 3 1 τ o 3 1 τ i 3 ) a 3 + S + , in ( 2 ) 1 τ o 3 + S , in ( 2 ) 1 τ o 3 j μ 32 a 2 j μ 31 a 1 ,
S , i n ( 1 ) = S , o u t ( 2 ) e j φ , S + , i n ( 2 ) = S + , o u t ( 1 ) e j φ ,
S ± , o u t ( 1 ) = S ± , i n ( 1 ) 1 τ o 1 a 1 , S ± , o u t ( 2 ) = S ± , i n ( 2 ) ( 1 τ o 2 a 2 + 1 τ o3 a 3 ) ,
t = S + , o u t ( 2 ) S + , i n ( 1 ) = e j φ ( 1 + 1 γ 3 τ o 3 ) + ( 1 τ o 1 e j φ + 1 τ o 3 x 31 γ 3 ) ( F D + E B ) + ( 1 τ o 2 + 1 τ o 3 x 32 γ 3 ) ( F A + E C ) A B C D ,
A = γ 1 x 23 + x 21 x 13 , B = γ 2 γ 3 x 23 x 32 , C = γ 3 x 21 + x 31 x 23 , D = x 12 x 23 + γ 2 x 13 ,
E = 1 τ o 1 x 23 1 τ o 2 x 13 e j φ , F = ( 1 τ o 2 γ 3 + 1 τ o 3 x 23 ) e j φ ,
x 23 = j μ 23 , x 32 = j μ 32 ,
x m n = 1 τ o m τ o n e j φ + j μ m n ( m = 1 , n = 2 , 3 ; m = 2 , n = 1 ; m = 3 , n = 1 ) .
n e f f ε d + 2 ε d ε d ε m k 0 w ( ε m ) ,

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