Abstract

Recently, effective surface plasmon polaritons (ESPPs) induced by structural dispersion in bounded waveguides were theoretically demonstrated and experimentally verified. Despite the theoretical and experimental efforts, whether ESPPs can mimic real SPPs in every aspect still remains an open question. In this work, we go one step further to study the hybridization of ESPPs in multilayer systems. We consider transverse electric (TE) modes in a conventional rectangular waveguide and a parallel-plate waveguide (PPW) and derive analytically the dispersion relations and asymptotic frequencies of the corresponding ESPPs modes in sandwiched structures consisting of alternating dielectrics of different permittivities. Our results show that the ESPPs can be categorized into odd and even parities (owing to the ‘plasmon’ hybridization) in a similar way as natural SPPs supported by the insulator/metal/insulator (IMI) and metal/insulator/metal (MIM) heterostructures in the optical regime. The similarities and differences between ESSPs and their optical counterparts are also discussed in details, which may provide valuable guidance for future application of ESPPs at the microwave and terahertz frequencies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Plasmonics offers a possible route to confine and manipulate electromagnetic waves at subwavelength scales [1–9]. As a result, light-matter interactions at metal-dielectric interfaces or in small metallic nanostructures can lead to huge near-field enhancement in the optical regime. Two ingredients of plasmonics, surface plasmon polaritons(SPPs) and localized surface plasmons(LSPs)have been developed throughout the 20th century, holding great promise for applications in miniaturization of photonic circuits, near-field optics, surface-enhanced spectroscopy, plasmonic antennas and photovoltaics, etc [1]. However, SPPs and LSPs only occur at metal/dielectric interface at optical frequencies and large dissipative losses impede the development of metal-based plasmonic devices at optical frequencies. In 2004, the concept of spoof surface plasmons at low frequencies(far infrared, terahertz or microwave) was proposed by Pendry to mimic real SPPs by engineering metal surfaces with periodic subwavelength grooves or holes [10]. Later on, in 2012, Garcia-Vidal et al. demonstrate that spoof localized surface plasmons (spoof-LSPs) can be supported by periodically textured perfect electric conducting particles [11]. A series of theoretical and experimental efforts have been made to realize low frequency plasmonics as well as its applications ever since [12–38]. However, all these work were in the same framework of spoof surface plasmons. In 2016, Engheta et al. provided an another route to realize a variety of plasmonic phenomena by exploiting structural dispersion of TE modes in bounded waveguides filled with materials of positive permittivity only [39]. Then, Li et al. gave a theoretical insight and experimental verification of this structural dispersion induced ESPPs in a rectangular waveguide and substrate integrated waveguide [40]. Later on, the transmission of ESPPs at a single interface in a parallel-plate waveguide was experimentally verified by Prudencio and associates [41].

Despite the theoretical and experimental attempts [39–41], whether ESPPs can mimic real SPPs in every aspect still remains an open question. So in this work, we go one step further to study the hybridization of ESPPs in multilayer systems. Specifically, we investigate the dispersion and transmission characteristics of ESPPs in multilayer systems in a conventional rectangular waveguide and a parallel-plate waveguide by engineering the TE modes. The dispersion relations of the odd and even ESPPs modes in two sandwiched structures consisting of alternating dielectrics of different relative permittivities are studied in detail. We find that these two sandwiched structures resemble nearly the same characteristics of the IMI and MIM heterostructures in the optical regime. Long-ranging ESPPs can be realized by decreasing the thickness of the air layer of the effective IMI structure. And negative group velocity can also be achieved by tuning the geometrical dimensions of each layer both for the effective IMI and MIM structures. In addition, the odd and even ELSPs modes in effective IMI/MIM structures are found to perfectly emulate the ultra-subwavelength confinement of SPPs in real IMI/MIM systems, which cannot be easily realized by conventional spoof LSPs [11,18,19,26] that a periodic array of grooves is needed with a depth on the order of one quarter of wavelength.

2. Theory

First, we consider a conventional rectangular waveguide with the cross section dimensions a×b in Fig. 1, which is filled with three layer isotropic and homogeneous dielectrics. For simplicity, it is assumed in this work that the dielectrics in Layer II (–b/2<y<-s) and Layer III (s<y<b/2) are the same (εr2=εr3 and μr2=μr3=1) and we only focus on two specific cases when εr2=εr3>εr1 and εr2=εr3<εr1, which are two triple-layer systems acting as effective IMI and effective MIM structures. As we know [40], the effective relative permittivity εe=εr(m/2a)2λ02 (λ0is the operating wavelength) of the dielectric filling in the rectangular waveguide corresponding to TEm0 mode can be tuned to be either positive, zero or negative by changing the operating frequency, lateral dimension of the waveguide and filling materials [39]. Then, the effective wave number ke would be ke=k0εe. Thus, it is anticipated that effective surface confined modes can be supported at Interface I (interface between Layer I and Layer II) and Interface II (interface between Layer I and Layer III) whenRe(εe1)Re(εe2)<0 and Re(εe1)Re(εe3)<0, in which εei=εri(m/2a)2λ02,i=1,2,3.

 figure: Fig. 1

Fig. 1 Effective SPPs in multilayer systems in a conventional rectangular waveguide filled with three-layered isotropic and homogeneous dielectrics with relative permittivities εr1, εr2 andεr3 and relative permeabilities μr1=μr2=μr3=1. Two interfaces (denoted as the two solid blue lines) are supposed to support coupled ESPPs modes transmitted along the z direction.

Download Full Size | PPT Slide | PDF

In order to derive the dispersion relations of the coupled ESPPs modes, we start by setting the magnetic vector potential for the effective coupled modes in Layer III in the form of A3=y^ψ3,ψ3=ejβz(B3ek3yy+C3ek3yy) with no variations in the x direction, in which B3 and C3 are the amplitudes of the decaying fields from Interface II to Layer III and the reflected fields bouncing back from the upper wall. k3y2=β2k3e2 is the wave number in the y direction with k3e=k0εe3 being the wave number in the effective dielectric of Layer III. Thus, from Maxwell's equations we can obtain all components of the electric and magnetic fields in Layer III as follows.

Hx3=jβμ0ejβz(B3ek3yy+C3ek3yy)Ey3=j1ωμ0ε0εe3(k32+k3y2)ejβz(B3ek3yy+C3ek3yy)Ez3=βk3yωμ0ε0εe3ejβz(B3ek3yy+C3ek3yy)
Similarly, we set the magnetic vector potentials in Layers I and II in the form of Ai=y^ψi,ψi=ejβz(Biekiyy+Ciekiyy),i=1,2, in which B1 and C1 are the amplitudes of the decaying fields from Interface II to Interface I and reflective fields from Interface I to Interface II, B2 and C2 are the amplitudes of the decaying fields from Interface I to Layer II and the reflected fields from the lower wall. kiy2=β2kie2,i=1,2 are the wave numbers in the -y direction with kie=k0εei being the wave numbers in the effective dielectrics of Layers I and II. So, the electric and magnetic fields in Layers I and II are derived as follows.
Hxi=jβμ0ejβz(Biekiyy+Ciekiyy)Eyi=j1ωμ0ε0εei(ki2+kiy2)ejβz(Biekiyy+Ciekiyy)Ezi=βkiyωμ0ε0εeiejβz(BiekiyyCiekiyy),i=1,2
By matching the following boundary conditions
y=s,HxIII=HxI;HzIII=HzI;EzIII=EzIy=s,HxII=HxI;HzII=HzI;EzII=EzIy=b/2,EzIII=0;y=b/2,EzII=0y=s,εe3EyIII=εe1EyI;y=s,εe2EyII=εe1EyI
we can get the dispersion relation for possible surface confined modes as
e4k1ys=(k1yεe1+k2yεe2tanh(k2yt))(k1yεe1k2yεe2tanh(k2yt))(k1yεe1+k3yεe3tanh(k3yt))(k1yεe1k3yεe3tanh(k3yt))
with kiy2=β2ki2+(mπa)2,i=1,2,3;m=1,2,3,....

As stated above, Layer II and Layer III has the same permittivity εr2=εr3(εe2=εe3) and thickness, and thus k2y=k3y. In this case, the dispersion relation (1) can be split into a pair of equations, namely

tanh(k1ys)=k2yεe1k1yεe2tanh(k2yt),
tanh(k1ys)=k1yεe2k2yεe1coth(k2yt).
It can be observed that Eq. (2) describes modes of odd vector parity(Ez is odd, Hxand Ey are even functions), while Eq. (3) describes modes of even vector parity(Ez is even, Hx and Ey are odd functions). If we consider an extreme case when the thickness of the two claddings becomes infinite that t(the rectangular waveguide becomes a parallel-plate waveguide with the separation a between the two plates), the two dispersion relations denoted by Eqs. (2) and (3) for the odd and even modes lead to
tanh(k1ys)=k2yεe1k1yεe2,
tanh(k1ys)=k1yεe2k2yεe1,
which are actually in the same form as those for the odd and even modes supported in sandwich structures in the optical regime [42] with only the replacement of εiεei(i=1,2).

3. Analysis and discussions

The dispersion relations [Eqs. (2) and (3)] and [Eqs. (4) and (5)] can now be applied to the effective IMI (εr2=εr3>εr1) and effective MIM (εr2=εr3<εr1) structures to investigate the properties of the coupled ESPPs modes in these two systems. In the following calculations and simulations, only TE1 mode is considered in a parallel-plate waveguide with the separation a=22.86mm and TE10mode (m = 1) in an X-band rectangular waveguide (a=22.86mm and b=10.16mm). The purple region is filled with a dielectric of relative permittivity εr2=4 and the blue region is filled with air of εr1=1. In the same manner as our previous work [40], we place a series of thin metallic wires with radius r=a/200 and period d=a/40 along the entire interface between the blue and purple regions. These thin metallic wires contribute to the suppression of TM modes and accumulation of electric charges to sustain the normal components of the electric field to face opposite to each other at the two interfaces. We remark that increasing the period d (such as a/10 or a/5) could affect the cutoff frequencies of the modes. However, the trend of the dispersion curves would not change. Thus, for better agreement with our analytical dispersion results, d is chosen as a/40 in this work.

We first consider an effective IMI structure in a parallel-plate waveguide with εr2=εr3=4;εr1=1 and calculate the dispersion curves for the odd and even modes using the analytical results in Eqs. (4) and (5) compared with the corresponding simulated dispersion curves using the commercial software CST STUDIO in Fig. 2. It can be observed that the simulations agree quite well with the analytical results. It is also quite interesting to note that the frequency of the odd modes are higher than the respective frequencies for a single interface ESPPs and the even modes. When the thickness of the air layer (Layer I) decreases, the odd modes also evolve into the TE1 mode supported in the dielectric filled parallel-plate waveguide and the confinement of the coupled ESPPs becomes weak. This implies that the propagation length of the ESPPs would drastically increased with negligible loss in the air, which is in analogous to the long-ranging SPPs in optical frequencies supported by IMI structures with decreasing metal film thickness [42]. The even ESPPs modes exhibit the opposite behavior—their confinement increases with decreasing air layer thickness, resulting in a reduction in propagation length. When the air layer thickness increases, the odd and even modes become increasingly decoupled and converge to the ESPPs at a single interface shown as the red solid line in Fig. 2. Different from the dispersion curves of real SPPs starting from zero frequency, all the dispersion curves of the odd and even modes start from the cutoff frequency of TE1 mode in the parallel-plate waveguide.

 figure: Fig. 2

Fig. 2 Dispersion relations of odd and even ESPPs modes in the effective IMI structure in a parallel-plate waveguide.

Download Full Size | PPT Slide | PDF

Accordingly, we can also study the effective MIM structure in a parallel-plate waveguide with εr2=εr3=1;εr1=4 and calculate the dispersion curves for the odd and even modes using the analytical results in Eqs. (4) and (5) compared with the corresponding simulated results in Fig. 3. Excellent agreement further demonstrate the validity of the above theory. It is also quite interesting to observe that the frequency of the even modes are higher than the respective frequencies for a single interface ESPPs and the odd modes. The even modes can exhibit negative group velocity with decreasing thickness 2s of the dielectric layer. The odd ESPPs modes, however, being the fundamental modes of the system, only have positive group velocity no matter how thick Layer I is. Fig. 4 further shows the dispersion relations of the fundamental odd mode for the effective MIM structure with the thickness of Layer I 2s = b and the dielectric in Layer I taken as lossy. We can observe that Re[β] does not go to infinity as the surface plasmon frequency is approached, but folds back, which is analogous to the real SPPs in silver/air/silver heterostructure [42]. With the increase of the dielectric loss, the dispersion curve folds back at a smaller value of Re[β].

 figure: Fig. 3

Fig. 3 Dispersion relations of odd and even ESPPs modes in the effective MIM structure in a parallel-plate waveguide.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4

Fig. 4 Dispersion relations of the fundamental odd ESPPs mode of an effective MIM structure for an dielectric core of size 10.16mm with different dielectric loss in the parallel-plate waveguide.

Download Full Size | PPT Slide | PDF

For comparison, we also plot the simulated and analytical dispersion relations [Eqs. (2) and (3)] of the odd and even ESPPs modes in the effective IMI and MIM structures in a rectangular waveguide shown in Figs. 5 and 6, respectively. Due to the imaging effect of the upper and lower walls of the rectangular waveguide, the dispersion relations show a bit difference, especially for the effective MIM structure shown in Fig. 6, in which the starting frequency of the even mode does not change no matter how thick the dielectric is. However, all these dispersion relations explicitly show the hybridization of the ESPPs modes in bounded waveguides and give us a route to design functional devices based on ESPPs by engineering the dispersion relations.

 figure: Fig. 5

Fig. 5 Dispersion relations of odd and even ESPPs modes in the effective IMI structure in a rectangular waveguide.

Download Full Size | PPT Slide | PDF

 figure: Fig. 6

Fig. 6 Dispersion relations of odd and even ESPPs modes in the effective MIM structure in a rectangular waveguide.

Download Full Size | PPT Slide | PDF

Then, we show in Figs. 7 and 8 how to excite coupled ESPPs modes in the effective IMI and MIM structures under wave port excitations in a standard X-band rectangular waveguide with the cross section dimension a×b=22.86×10.16mm2 and length L=10a.

 figure: Fig. 7

Fig. 7 Simulation of the odd ESPPs mode in effective IMI structure in a standard X-band rectangular waveguide, in which l3=6a and l1=l2=l4=l5=a (a) Structure of the interface (b) Distributions of electric lines of force on the yz plane (c) Distributions of Ey on the yz plane (d) Distributions of Ey on the xz plane (e) Odd ESPPs mode spectrum.

Download Full Size | PPT Slide | PDF

 figure: Fig. 8

Fig. 8 Simulation of the odd ESPPs mode in effective MIM structure in a standard X-band rectangular waveguide, in which l3=6a and l1=l2=l4=l5=a (a) Structure of the interface (b) Distributions of electric force of lines on the yz plane (c) Distributions of Ey on the yz plane (d) Distributions of Ey on the xz plane (e) Odd ESPPs mode spectrum.

Download Full Size | PPT Slide | PDF

For the effective IMI structure in Fig. 7(a), the middle region is of length l3=6a (with the air thickness 2s=0.2b) and the two side regions with length l2=l4=a are mode conversion ones with continuous variation of the air layer thickness from 0 to 2s. Considering that the wave port excitations(TE10 mode) is of odd mode form with respect to the symmetric plane at y = 0, the expected ESPPs are also odd mode with spectrum ranging from 3.28GHz to 4.62GHz according to the above theory. Simulations in CST STUDIO also demonstrate a passband between 3.2GHz and 4.62GHz in the S parameters spectrum from 2 to 6GHz shown in Fig. 7(e). At an arbitrary frequency point f0=4.5GHz, we calculate the effective relative permittivities of these three dielectrics as εe1=1.126 and εe2=εe3=1.874 and show in Figs. 7(b) to 7(d) the electric lines of force and Ey distributions in the yz(x = 0) and xz(y = b/2) planes. We can observe perfect conversion between the TE10 mode and the odd ESPPs mode. According to the dispersion relations in Fig. 5, the odd ESPPs mode exhibits both positive and negative group velocity when Layer II is thin enough. And with the increase of the working frequency f0, the wavelength of the ESPPs is dramatically shortened and the field confinement significantly enhances.

For the effective MIM structure in Fig. 8(a), the dielectric thickness is set as 2s=0.5b in the middle region and the two side regions are mode conversion ones with continuously decreasing dielectric thickness from b down to 2s. Due to the odd mode excitations(TE10), the expected ESPPs are also odd mode with spectrum ranging from 3.28GHz to 4.15GHz, theoretically. Excellent agreement can also be obtained by comparison with the simulated passband between 3.28GHz and 4.11GHz shown in Fig. 8(e). Figs. 8(b)-8(d) show the electric lines of force and Ey distributions in the yz(x = 0) and xz(y = b/2) planes at 3.9GHz.

In both effective IMI/MIM structures, fields are concentrated in the dielectrics, which is analogous to the fields concentrating in the air in the IMI/MIM structures at optical frequencies. Different from real SPPs, the cutoff and asymptotic frequencies of the ESPPs in multilayer systems in bounded waveguides can be flexibly controlled by the lateral dimension of the waveguide, dielectric parameters and mode number. Although we have limited our discussion of coupled ESPPs in three-layer structures in the parallel-plate waveguide and the rectangular waveguide to the fundamental bound modes of the system, it should be noted that the family of modes supported by this system is much richer than described above. The coupling between ESPPs at the two core/cladding interfaces changes dramatically when the permittivities of the sub- and superstrates are different.

4. Summary

In summary, the hybridization of the ESPPs in multilayer systems are studied in this work. Odd and even ESPPs modes in the effective IMI and MIM structures are investigated in detail by engineering the TE modes in a rectangular waveguide and a parallel-plate waveguide. We derive and analyze the dispersion relations and asymptotic frequencies of the odd and even ESPPs modes in these two sandwiched structure systems. Simulations demonstrate that the odd and even ESPPs modes in effective IMI and MIM structures resemble nearly the same characteristics of the odd and even SPPs in IMI and MIM heterostructures in the optical regime. Our results also show that different from SPPs in optical frequencies, the cutoff frequency and asymptotic frequency of the ESPPs in bounded waveguides can be flexibly tuned by the waveguide dimension, dielectric parameters and mode numbers. This work further demonstrate that ESPPs mimic real SPPs in an ultra-subwavelength confinement nature and can find potential applications in compact devices and circuits in the microwave and terahertz frequencies.

Funding

Natural Science Foundation of Jiangsu Province under Grant BK20151480; Fundamental Research Funds for the Central Universities under Grant NS2016039; Priority Academic Program Development of Jiangsu Higher Education Institutions; Singapore Ministry of Education Academic Research Fund TIER 1 under Grant RG72/15 and TIER 2 under Grant MOE2015-T2-1-145; National Natural Science Foundation of China (NSFC) (No.61701246); Natural Science Foundation of Jiangsu Higher Education Institutions of China (No.17KJB140014).

References and links

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]   [PubMed]  

2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef]   [PubMed]  

3. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]  

4. K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007). [CrossRef]   [PubMed]  

5. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef]   [PubMed]  

6. M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011). [CrossRef]   [PubMed]  

7. P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef]   [PubMed]  

8. W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009). [CrossRef]   [PubMed]  

9. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef]   [PubMed]  

10. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]   [PubMed]  

11. A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012). [CrossRef]   [PubMed]  

12. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef]   [PubMed]  

13. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005). [CrossRef]  

14. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006). [CrossRef]   [PubMed]  

15. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011). [CrossRef]  

16. X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013). [CrossRef]  

17. X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013). [CrossRef]  

18. Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014). [CrossRef]  

19. Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014). [CrossRef]  

20. Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015). [CrossRef]  

21. T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009). [CrossRef]  

22. X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009). [CrossRef]  

23. Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015). [CrossRef]   [PubMed]  

24. Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012). [CrossRef]  

25. S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012). [CrossRef]  

26. P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014). [CrossRef]  

27. B. J. Yang, Y. J. Zhou, and Q. X. Xiao, “Spoof localized surface plasmons in corrugated ring structures excited by microstrip line,” Opt. Express 23(16), 21434–21442 (2015). [CrossRef]   [PubMed]  

28. S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015). [CrossRef]  

29. L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015). [CrossRef]   [PubMed]  

30. L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015). [CrossRef]  

31. F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016). [CrossRef]   [PubMed]  

32. Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016). [CrossRef]   [PubMed]  

33. Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016). [CrossRef]   [PubMed]  

34. F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016). [CrossRef]  

35. Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016). [CrossRef]  

36. J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017). [CrossRef]  

37. L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017). [CrossRef]  

38. P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017). [CrossRef]  

39. C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016). [CrossRef]  

40. Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017). [CrossRef]  

41. F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017). [CrossRef]  

42. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

References

  • View by:
  • |
  • |
  • |

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
    [Crossref] [PubMed]
  3. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
    [Crossref]
  4. K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007).
    [Crossref] [PubMed]
  5. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
    [Crossref] [PubMed]
  6. M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
    [Crossref] [PubMed]
  7. P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
    [Crossref] [PubMed]
  8. W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
    [Crossref] [PubMed]
  9. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
    [Crossref] [PubMed]
  10. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
    [Crossref] [PubMed]
  11. A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
    [Crossref] [PubMed]
  12. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
    [Crossref] [PubMed]
  13. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
    [Crossref]
  14. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
    [Crossref] [PubMed]
  15. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
    [Crossref]
  16. X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
    [Crossref]
  17. X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013).
    [Crossref]
  18. Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
    [Crossref]
  19. Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
    [Crossref]
  20. Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
    [Crossref]
  21. T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
    [Crossref]
  22. X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
    [Crossref]
  23. Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
    [Crossref] [PubMed]
  24. Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
    [Crossref]
  25. S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
    [Crossref]
  26. P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
    [Crossref]
  27. B. J. Yang, Y. J. Zhou, and Q. X. Xiao, “Spoof localized surface plasmons in corrugated ring structures excited by microstrip line,” Opt. Express 23(16), 21434–21442 (2015).
    [Crossref] [PubMed]
  28. S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
    [Crossref]
  29. L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
    [Crossref] [PubMed]
  30. L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
    [Crossref]
  31. F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
    [Crossref] [PubMed]
  32. Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
    [Crossref] [PubMed]
  33. Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
    [Crossref] [PubMed]
  34. F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
    [Crossref]
  35. Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
    [Crossref]
  36. J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
    [Crossref]
  37. L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
    [Crossref]
  38. P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
    [Crossref]
  39. C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016).
    [Crossref]
  40. Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
    [Crossref]
  41. F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
    [Crossref]
  42. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

2017 (5)

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

2016 (6)

C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016).
[Crossref]

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

2015 (6)

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

B. J. Yang, Y. J. Zhou, and Q. X. Xiao, “Spoof localized surface plasmons in corrugated ring structures excited by microstrip line,” Opt. Express 23(16), 21434–21442 (2015).
[Crossref] [PubMed]

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

2014 (3)

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

2013 (2)

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013).
[Crossref]

2012 (3)

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

2011 (2)

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
[Crossref]

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

2009 (3)

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
[Crossref]

2008 (2)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

2007 (1)

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007).
[Crossref] [PubMed]

2006 (2)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

2005 (4)

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

2004 (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Berry, S. J.

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

Bozhevolnyi, S. I.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Camargo, P. H. C.

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

Campbell, T.

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

Chen, C.

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Chen, H.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Chen, H. S.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Chen, X.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Chen, X. L.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Chong, Y.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Costa, J. R.

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

Cuerda, J.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

Cui, T.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Cui, T. J.

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013).
[Crossref]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Eisler, H. J.

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Engheta, N.

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016).
[Crossref]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Fernandes, C. A.

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

Fernández-Domínguez, A. I.

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Gao, F.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Gao, X.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Gao, Z.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

Garcia-Vidal, F. J.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Giovampaola, C. D.

C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016).
[Crossref]

Gu, C.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Gu, C. Q.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Hao, R.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Hecht, B.

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Hess, W.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Hibbins, A. P.

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref] [PubMed]

Hooper, I. R.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

Huidobro, P. A.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

Jiang, Q.

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
[Crossref]

Jiang, T.

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

Jiang, W. X.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Joannopoulos, J. D.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Kato, J.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

Kawata, S.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

Kee, C.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Kim, J.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Kim, K.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Kim, S.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Li, E. P.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Li, L.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Li, W.

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

Li, Z.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Liao, Z.

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Lin, X.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Liu, L.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Liu, L. L.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Liu, Y.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

Lockyear, M. J.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

Lu, L.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Lu, X.

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

Luo, Y.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Ma, H. F.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Maier, S. A.

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Martin, O. J.

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Martin-Moreno, L.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
[Crossref]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Moreno, E.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

Mühlschlegel, P.

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Musa, M. Y.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Ning, P.

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Ning, P. P.

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Niu, Z.

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Oh, S.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Ozaki, M.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

Pan, B. C.

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Park, H.

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Pendry, J. B.

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Pors, A.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

Prudêncio, F. R.

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

Qin, P. F.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Qing, Q.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Ran, L.

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
[Crossref]

Sambles, J. R.

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref] [PubMed]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Shen, L.

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
[Crossref]

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

Shen, X.

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013).
[Crossref]

Shen, X. P.

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

Shi, J. H.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

Shi, X.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Shum, P.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Silveirinha, M. G.

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

Soljacic, M.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Sun, H.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Sun, H. Y.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

Sun, Y. H.

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007).
[Crossref] [PubMed]

Wang, Z. J.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Willets, K. A.

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007).
[Crossref] [PubMed]

Wu, J. J.

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

Xia, Y.

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

Xiao, Q. X.

Xu, B.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Xu, B. Z.

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Xu, H.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Xu, J.

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

Yan, J.

Yang, B. J.

Yang, T. J.

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

Yang, Y. H.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Yang, Z.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Yin, W. Y.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Zhang, B.

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Zhang, B. L.

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Zhang, J. J.

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Zhang, X.

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Zhao, J.

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Zhao, Y.

L. Liu, Z. Li, C. Gu, B. Xu, P. Ning, C. Chen, J. Yan, Z. Niu, and Y. Zhao, “Smooth bridge between guided waves and spoof surface plasmon polaritons,” Opt. Lett. 40(8), 1810–1813 (2015).
[Crossref] [PubMed]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Zheng, B.

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Zheng, X.

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

Zhou, Y.

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

Zhou, Y. J.

B. J. Yang, Y. J. Zhou, and Q. X. Xiao, “Spoof localized surface plasmons in corrugated ring structures excited by microstrip line,” Opt. Express 23(16), 21434–21442 (2015).
[Crossref] [PubMed]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
[Crossref]

ACS Photonics (2)

Z. Liao, X. Shen, B. C. Pan, J. Zhao, Y. Luo, and T. J. Cui, “Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions,” ACS Photonics 2(6), 738–743 (2015).
[Crossref]

Z. Liao, A. I. Fernández-Domínguez, J. J. Zhang, S. A. Maier, T. J. Cui, and Y. Luo, “Homogeneous metamaterial description of localized spoof plasmons in spiral geometries,” ACS Photonics 3(10), 1768–1775 (2016).
[Crossref]

Adv. Funct. Mater. (1)

F. Gao, Z. Gao, Y. Luo, and B. L. Zhang, “Invisibility Dips of Near-Field Energy Transport in a Spoof Plasmonic Metadimer,” Adv. Funct. Mater. 26(45), 8307–8312 (2016).
[Crossref]

Adv. Sci. (1)

P. F. Qin, Y. H. Yang, M. Y. Musa, B. Zheng, Z. J. Wang, R. Hao, W. Y. Yin, H. S. Chen, and E. P. Li, “Toroidal Localized Spoof Plasmons on Compact Metadisks,” Adv. Sci. 4, 1700487 (2017).
[Crossref]

Annu. Rev. Phys. Chem. (1)

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (7)

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011).
[Crossref]

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013).
[Crossref]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013).
[Crossref]

Z. Li, L. Liu, C. Gu, P. Ning, B. Xu, Z. Niu, and Y. Zhao, “Multi-band localized spoof plasmons with texturing closed surfaces,” Appl. Phys. Lett. 104(10), 101603 (2014).
[Crossref]

Z. Li, B. Xu, C. Gu, P. Ning, L. Liu, Z. Niu, and Y. Zhao, “Localized spoof plasmons in closed textured cavities,” Appl. Phys. Lett. 104(25), 251601 (2014).
[Crossref]

L. L. Liu, Z. Li, B. Z. Xu, P. P. Ning, C. Chen, J. Xu, X. L. Chen, and C. Q. Gu, “Dual-band trapping of spoof surface plasmon polaritons and negative group velocity realization through microstrip line with gradient holes,” Appl. Phys. Lett. 107(20), 201602 (2015).
[Crossref]

S. J. Berry, T. Campbell, A. P. Hibbins, and J. R. Sambles, “Surface wave resonances supported on a square array of square metallic pillars,” Appl. Phys. Lett. 100(10), 101107 (2012).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, and Y. Luo, “Ultra Low Loss High-Contrast Gratings based Spoof Surface Plasmonic Waveguide,” IEEE Trans. Microw. Theory Tech. 65(6), 2008–2018 (2017).
[Crossref]

J. Appl. Phys. (1)

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105(1), 013704 (2009).
[Crossref]

J. Opt. A (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7(2), S97–S101 (2005).
[Crossref]

Laser Photonics Rev. (1)

J. J. Zhang, Z. Liao, Y. Luo, X. P. Shen, S. A. Maier, and T. J. Cui, “Spoof Plasmon Hybridization,” Laser Photonics Rev. 11(1), 1600191 (2017).
[Crossref]

Nano Lett. (1)

W. Li, P. H. C. Camargo, X. Lu, and Y. Xia, “Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced raman scattering,” Nano Lett. 9(1), 485–490 (2009).
[Crossref] [PubMed]

Nat. Commun. (1)

F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, and B. Zhang, “Probing topological protection using a designer surface plasmon structure,” Nat. Commun. 7, 11619 (2016).
[Crossref] [PubMed]

Nat. Mater. (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

F. R. Prudêncio, J. R. Costa, C. A. Fernandes, N. Engheta, and M. G. Silveirinha, “Experimental verification of ‘waveguide’ plasmonics,” New J. Phys. 19(12), 123017 (2017).
[Crossref]

Opt. Commun. (1)

Z. Gao, L. Shen, J. J. Wu, T. J. Yang, and X. Zheng, “Terahertz surface plasmon polaritons in textured metal surfaces formed by square arrays of metallic pillars,” Opt. Commun. 285(8), 2076–2080 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Appl. (1)

Z. Li, L. L. Liu, H. Y. Sun, Y. H. Sun, C. Q. Gu, X. L. Chen, Y. Liu, and Y. Luo, “Effective surface plasmon polaritons induced by modal dispersion in a waveguide,” Phys. Rev. Appl. 7(4), 044028 (2017).
[Crossref]

Phys. Rev. B (2)

C. D. Giovampaola and N. Engheta, “Plasmonics without negative dielectrics,” Phys. Rev. B 93(19), 195152 (2016).
[Crossref]

S. Kim, S. Oh, K. Kim, J. Kim, H. Park, W. Hess, and C. Kee, “Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons,” Phys. Rev. B 91(3), 035116 (2015).
[Crossref]

Phys. Rev. Lett. (2)

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006).
[Crossref] [PubMed]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108(22), 223905 (2012).
[Crossref] [PubMed]

Phys. Rev. X (1)

P. A. Huidobro, X. P. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4(2), 021003 (2014).
[Crossref]

Phys. Today (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Prog. Electromagn. Res. M (1)

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagn. Res. M 8, 91–102 (2009).
[Crossref]

Sci. Rep. (3)

Z. Liao, Y. Luo, A. I. Fernández-Domínguez, X. Shen, S. A. Maier, and T. J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015).
[Crossref] [PubMed]

Z. Li, L. Liu, B. Xu, P. Ning, C. Chen, J. Xu, X. Chen, C. Gu, and Q. Qing, “High-Contrast Gratings based Spoof Surface Plasmons,” Sci. Rep. 6(1), 21199 (2016).
[Crossref] [PubMed]

Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations,” Sci. Rep. 6(1), 27158 (2016).
[Crossref] [PubMed]

Science (6)

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref] [PubMed]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Other (1)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Effective SPPs in multilayer systems in a conventional rectangular waveguide filled with three-layered isotropic and homogeneous dielectrics with relative permittivities ε r 1 , ε r 2 and ε r 3 and relative permeabilities μ r 1 = μ r 2 = μ r 3 = 1 . Two interfaces (denoted as the two solid blue lines) are supposed to support coupled ESPPs modes transmitted along the z direction.
Fig. 2
Fig. 2 Dispersion relations of odd and even ESPPs modes in the effective IMI structure in a parallel-plate waveguide.
Fig. 3
Fig. 3 Dispersion relations of odd and even ESPPs modes in the effective MIM structure in a parallel-plate waveguide.
Fig. 4
Fig. 4 Dispersion relations of the fundamental odd ESPPs mode of an effective MIM structure for an dielectric core of size 10.16mm with different dielectric loss in the parallel-plate waveguide.
Fig. 5
Fig. 5 Dispersion relations of odd and even ESPPs modes in the effective IMI structure in a rectangular waveguide.
Fig. 6
Fig. 6 Dispersion relations of odd and even ESPPs modes in the effective MIM structure in a rectangular waveguide.
Fig. 7
Fig. 7 Simulation of the odd ESPPs mode in effective IMI structure in a standard X-band rectangular waveguide, in which l 3 = 6 a and l 1 = l 2 = l 4 = l 5 = a (a) Structure of the interface (b) Distributions of electric lines of force on the yz plane (c) Distributions of Ey on the yz plane (d) Distributions of Ey on the xz plane (e) Odd ESPPs mode spectrum.
Fig. 8
Fig. 8 Simulation of the odd ESPPs mode in effective MIM structure in a standard X-band rectangular waveguide, in which l 3 = 6 a and l 1 = l 2 = l 4 = l 5 = a (a) Structure of the interface (b) Distributions of electric force of lines on the yz plane (c) Distributions of Ey on the yz plane (d) Distributions of Ey on the xz plane (e) Odd ESPPs mode spectrum.

Equations (8)

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

H x 3 = j β μ 0 e j β z ( B 3 e k 3 y y + C 3 e k 3 y y ) E y 3 = j 1 ω μ 0 ε 0 ε e 3 ( k 3 2 + k 3 y 2 ) e j β z ( B 3 e k 3 y y + C 3 e k 3 y y ) E z 3 = β k 3 y ω μ 0 ε 0 ε e 3 e j β z ( B 3 e k 3 y y + C 3 e k 3 y y )
H x i = j β μ 0 e j β z ( B i e k i y y + C i e k i y y ) E y i = j 1 ω μ 0 ε 0 ε e i ( k i 2 + k i y 2 ) e j β z ( B i e k i y y + C i e k i y y ) E z i = β k i y ω μ 0 ε 0 ε e i e j β z ( B i e k i y y C i e k i y y ) , i = 1 , 2
y = s , H x I I I = H x I ; H z I I I = H z I ; E z I I I = E z I y = s , H x I I = H x I ; H z I I = H z I ; E z I I = E z I y = b / 2 , E z I I I = 0 ; y = b / 2 , E z I I = 0 y = s , ε e 3 E y I I I = ε e 1 E y I ; y = s , ε e 2 E y I I = ε e 1 E y I
e 4 k 1 y s = ( k 1 y ε e 1 + k 2 y ε e 2 tan h ( k 2 y t ) ) ( k 1 y ε e 1 k 2 y ε e 2 tan h ( k 2 y t ) ) ( k 1 y ε e 1 + k 3 y ε e 3 tan h ( k 3 y t ) ) ( k 1 y ε e 1 k 3 y ε e 3 tan h ( k 3 y t ) )
tan h ( k 1 y s ) = k 2 y ε e 1 k 1 y ε e 2 tan h ( k 2 y t ) ,
tan h ( k 1 y s ) = k 1 y ε e 2 k 2 y ε e 1 coth ( k 2 y t ) .
tan h ( k 1 y s ) = k 2 y ε e 1 k 1 y ε e 2 ,
tan h ( k 1 y s ) = k 1 y ε e 2 k 2 y ε e 1 ,

Metrics