Abstract

Surface plasmon polariton reflector (SPPR) based on metal-insulator-metal (MIM) Bragg grating waveguide is numerically studied. A quasi-chirped technique is applied to the engraved grooves in the surface of the MIM waveguide, and a new kind of broad-bandgap SPPR is achieved. Meanwhile, by optimizing the profile of gap width between the metal and dielectric, the spectral sidelobe of SPPR is effectively suppressed and thus the performance of the SPPR is further improved.

©2009 Optical Society of America

1. Introduction

In response to the needs of realization of highly integrated optical devices and circuits, surface plasmon polaritons (SPPs) are considered as one of the most promising ways for overcoming the diffraction limit and manipulating light at a subwavelength scale [1]. The SPPs are electromagnetic modes coupled to the oscillations of conduction electrons propagating along the interface between dielectric and metallic materials. The electromagnetic field associated with the SPPs is bounded along the interface and decreases exponentially in the direction perpendicular to the interface, which can thereby result in a subwavelength confinement of the electromagnetic mode [2]. One of the most attractive aspects of SPPs is the way they help us concentrate and channel light using subwavelength structures. Some photonic devices based on SPPs-assisted light control, such as lenses [3], modulators [4], sensors [5], filters [6, 7], waveguides [811], splitters [12], resonators [13, 14], interferometers [15,16], and cavities [17], have been theoretically proposed and experimentally demonstrated.

For SPPs-based photonic devices, the insulator-metal-insulator (IMI) waveguide [11, 15, 1826] and the metal-insulator-metal (MIM) waveguide [2730] are two types of fundamental and basic structures. The IMI-type waveguide has less loss and longer propagation length, but suffers from its poor ability of confining light into subwavelength scale, and is not suitable for the purpose of high integration. The MIM-type waveguide has been shown to be efficient for subwavelength manipulation of light with an acceptable propagation length [31], thus has recently attracted more and more attention. Wang et al. reported a planar heterowaveguide constructed by alternately stacking two kinds of MIM waveguides [32], which can improve the efficiency of energy transfer at the range of subwavelength because it provides spatial light confinement with lateral dimensions of less than the free-space wavelength. However, their MIM waveguides have big ohmic losses by introducing a lossy material such as aluminum. To deal with this problem, low-loss MIM SPP Bragg reflectors have been realized based on periodically changing the dielectric materials between the MIM waveguide [33, 34]. S-shaped Bragg cells to suppress sidelobe of the MIM SPP reflectors are also discussed [35]. Quite recently, Liu et al. has investigated a MIM SPP wide bandgap reflector [36], because photonic element with a wide bandgap is very important in applications [37, 38]. This reflector with relatively wide bandgap is realized by modulating the MIM waveguide width and inserting the dielectric materials. However, since the contrasts of the waveguide width and the dielectric constant in different layers cannot be sufficiently large in their design, the contrast of the effective refractive index is actually not large enough. Thereby, the bandgap of their reflector can not be as wide as expected.

It is well know that chirp technique can increase the photonic bandwidth in Bragg gratings [20, 39]. In this paper, by means of a quasi-chirped technique, the Bragg-grating-based MIM surface plasmon polariton reflector (SPPR) with a broad bandgap is successfully obtained. To ensure reflectors with nice filtering characters, we should guarantee them to have near-zero transmission in the band and small sidelobe out the band [40, 41]. Therefore, the MIM SPP waveguide to suppress spectral sidelobe is also investigated by the apodization technique. This paper is organized as follows. In Section 2, the model of the MIM SPP waveguide is presented and its optical properties are studied. Section 3 describes the quasi-chirped technique to realize broad bandgap MIM SPPR. In section 4, the SPP waveguides with apodized and micro-cavity structure are both demonstrated. Finally, conclusion and discussion are made in section 5.

2. Fundamental properties of the MIM SPP waveguide

The MIM SPP waveguide consists of a dielectric core with a width w surrounded by two semi-infinite metallic claddings, as shown in Fig.1 (a). There are two possible plasmonic modes in the MIM waveguide, i.e., the anti-symmetric mode and the symmetric mode. The symmetric mode in MIM waveguide exhibits cut-off when the width decreases to a cut-off thickness which is about hundreds of nanometers. Since the gap width w in our structure is bellow the cut-off thickness, the anti-symmetric mode is considered here. When a light is injected to the MIM waveguide, it will be transformed into the coupled SPPs on the metal interface and propagate along the waveguide with a complex propagation constant βspp. According to the Maxwell equations and boundary conditions, the dispersion relation of the SPPs can be obtained as:

kdεmtanh(kdw2)+εdkm=0,
kd,m=βspp2εd,mk02,
neff=βsppk0,

where kd and km are transverse propagation constants of the dielectric and metal, respectively. k0=2π/λ is the propagation constant in vacuum, neff is the effective refractive index of SPP mode, εd and εm are the dielectric constant of metal cladding and dielectric core, respectively. In the MIM waveguide, we assume that the metal to be silver and whose permittivity can be described by Drude formula [32]

εm=1wp2w02+iw0γ,

where w0, wp and γ are the frequency of incident light, buck plasmon and electron collision, respectively. For sliver, the value of above parameters can be chosen as: wp=1.37×1016 Hz, and γ=0.15×1013 Hz [42].

 figure: Fig. 1.

Fig. 1. (a) Scheme of the MIM SPP waveguide. (b) Magnetic field distribution of |Hy|2 inside the MIM waveguide (Media 1). (c) Real part of the effective refractive index versus gap width w and wavelength λ in the Ag-SiO2-Ag (nd=1.46) and the Ag-PSiO2-Ag (nd=1.23) MIM waveguide, respectively.

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The light propagation along the MIM waveguide is modeled by the two-dimensional finite-difference-time-domain (FDTD) method [43]. In the MIM waveguide, the metal is dispersive and determined by the Drude formula, so electric filed E for FDTD update equation in the metal can be obtained as:

En+1=EnΔtε0Jn+12Δtε0Δ×Hn+12,
Jn+12=1γΔt21+γΔt2Jn12+ε0wp2Δt1+γΔt2En.

The magnetic filed H for FDTD update equation in the metal is the same as that in the dielectric and is determined by

Hn+12=Hn12Δtμ0Δ×En·

In the FDTD simulation, the source is S=sin(w0t), the gap width w=20 nm, spatial and temporal cell size are set as Δxy=5nm and Δtx/(2c), respectively, where c is the velocity of light in vacuum, and t is the time step. Meanwhile, the perfectly matched layer (PML) is used as absorbing boundary condition [43]. The calculated magnetic filed distribution |Hy|2 in the MIM structure is depicted in Fig. 1(b), as shown the light is highly localized along the two metal surfaces and propagating along the dielectric. In Fig. 1(c), the effective refractive index variations with gap width w, wavelength λ, and dielectric constant εd are displayed. It can be obtained that the light propagation of the SPPs through the MIM waveguide shows little wavelength dispersion, and is mainly controlled by the gap width w and the dielectric constant εd. A smaller w and a larger εd tend to generate a larger effective refractive index. Therefore, by periodically changing the dielectric material and gap width, periodical effective refractive index can be formed. This personality provides us with an effective tool to design Bragg-grating-based MIM SPP devices in analogous to conventional Bragg grating to deal with classical optics.

3. Broad bandgap SPPR based on a quasi-chirped technique

In this section, a new structure to obtain broad bandgap MIM SPPR is proposed as shown in Fig. 2 (a), where grooves are periodically engraved on the two metal surfaces and different dielectrics are filled in the gap. In Fig. 2(b), the n-th period of the proposed structure containing a layer An and a layer Bn is depicted. Here, LAn and LBn are the length of the layer An and the layer Bn, WAn and WBn are the gap width of the layer An and the layer Bn, respectively. In the Bragg gratings, the photonic bandwidth can be effectively increased by the chirp technique [20, 37]. Here, we applied the quasi-chirped technique to the MIM structure to enlarge the bandgap of the SPPR. In the proposed quasi-chirped MIM structure, there are k segments. Each segment consists of periodically stacking the layer An and the layer Bn with constant length LAn and LBn, i.e., each segment is uniform. But in different segment, the length LAn and LBn are different and determined by

Segment 1, LAn=λB 1/(4×n Aeff 1), LBn=λB 1/(4×nBeff 1), n=1,2…,n 1,

Segment 2, LAn=λB 2/(4×n Aeff 2), LBn=λB 2/(4×nBeff 2), n=1,2…,n 2,

……

Segment k, LAn=λBk/(4×nAeffk), LBn=λBk/(4×nBeffk), n=1,2…,nk.

Here, λBk is the desired central wavelength of the k-th bandgap. nAeffk and nBeffk are the effective refractive index in the dielectric A and B at the wavelength λB k, and are obtained by Eqs. (1)(3) and demonstrated in Fig. 2(c). The total numbers of the periods along the MIM structure are N=n1+n2…+nk.

 figure: Fig.2.

Fig.2. (a) Scheme of the quasi-chirped MIM SPP waveguide. (b) The n-th period of the proposed MIM structure in (a). (c) The effective refractive index of the SPP mode in the dielectric An and Bn, respectively. In the design, it is assumed that the dielectrics of layer An (n=1, 2…,N) and Bn are Sio2 (nA=1.46) and air (nB=1.0), and the width WAn and WBn are 80 nm and 120 nm, respectively.

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Before analyzing the quasi-chirped MIM SPP structure, uniform MIM SPPR (we label it as uniform-design-1) is presented. It contains one segment (S2) with 40 uniform periods. The used parameters are shown in Table 1. The wavelength λB 2 is 1550 nm, the effective refractive index nAeff and nBeff are 1.8263 and 1.1715, thus the length LAn and LBs (n=1,2…40) is 212 nm and 330 nm, respectively. The transmission spectrum of the uniform-design-1 is shown in Fig. 3, with a bandgap centering at λB 2 (1550 nm) and ranging from about 1360 nm to 1790 nm. In above analysis, the transmission spectrum is achieved by the transfer matrix method [44] which is effective to study the spectral properties of the Bragg-grating-based MIM SPP waveguide [32, 33]. Uniform-design-1 has uniform periods and is the same as the structure proposed in [36]. In order to show the feasibility of the proposed quasi-chirped technique to widen the bandgap, two quasi-chirped MIM SPPRs are designed. The first quasi-chirped SPPR (quasi-chirped-design-2) contains two segments. The first segment includes 20 periods, λB 1 is 1200 nm, so the length LAn and LBn in each period are 163 nm and 255 nm, respectively. The second segment also includes 20 periods, but λB2 is 1550 nm, so the LAn and LBn are 212 nm and 330 nm, respectively. The transmission spectrum of this reflector is shown in Fig. (3), as shown that the bandgap is effectively widened from about 1050 nm to 1790 nm comparing with the situation of uniform-design-1. The quasi-chirped MIM SPPR with three segments (quasi-chirped-design-3) is also designed. The three segments are all containing 15 periods, LAn and LBn for each segment are 163 nm and 255 nm, 212 nm and 330 nm, 260 nm 405 nm, respectively. The transmission spectrum is also plotted in Fig. (3), from which it can be obtained that the reflector’s bandgap is further enlarged.

From the Fig. 3 and the Table 1, it can be clearly noted that the quasi-chirped technique is effective to achieve MIM SPPR with a broad bandgap. The reason for the quasi-chirped technique to widen the bandgap can be understood intuitively by the band structure [45]. In the uniform-design-1, the MIM SPPR contains one segment, and its band structure is shown with red solid line in Fig. 4, where the Bloch wave number versus angular frequency is exhibited. In the quasi-chirped-design-2, the MIM SPPR contains two segments (S1 and S2), whose corresponding bands are centering at λB 1 (1200 nm) and λB2 (1550 nm), respectively. When the two segments are combing together in quasi-chirped-design-2, their bandgap will be incorporated as depicted in Fig. 4, therefore, the bandgap of quasi-chirped-design-2 is wider than that of uniform-design-1. Bearing this in mind, it is not strange that quasi-chirped-design-3 has a broader bandgap.

Tables Icon

Table 1. Parameters for the three designed Bragg-grating-based MIM SPPRs.

Notes: λBk is central wavelength of the k-th segment, nAeffk and nBeffk are the effective refractive index in the dielectric A and B at the wavelength λBk, LAn and LBn are the length of layer An and layer Bn, respectively. nk is the numbers of periods in the k-th segment, and N is the total numbers of the periods in the MIM SPPR. S1, S2, and S3 represent segment 1, segment 2, and segment 3, respectively.

 figure: Fig. 3.

Fig. 3. Transmission spectrum of the three designed MIM SPPRs. The reflector of uniform-design-1 contains one uniform segment, the quasi-chirped-design-2 and the quasi-chirped-design-3 contain two and three segments, respectively. The used parameters in these designed reflectors are shown in the Table 1 in detail.

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 figure: Fig. 4.

Fig. 4. Band structure for the segment related in the Table 1. Here, ω B is angular frequency corresponding to the wavelength of 1550 nm, Λ is the period length, and K is the Bloch wave number.

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4. Apodized MIM SPPR with small sidelobe

In this section, the apdization technique to suppress the sidelobe of the SPPR is investigated. The apodization profile is applied to the effective refractive index having a form of:

nAeff(n)=n0+n0nA0f(n)
nBeff(n)=n0n0nB0f(n)
f(n)=exp[nF]2

where n is the integer from -(N-1)/2 to (N-1)/2, N is the numbers of period, n 0=nA 0+nB 0, f(n) is the apodization function with a Gaussian profile, nA 0 and nB 0 are the effective refractive index of SPP mode in the dielectric A and B at wavelength λB, respectively. In our simulation, N=21, λB=1550 nm, nA=1.46 and nB=1.0, thus nA 0=1.8263, nB 0=1.1715, LAnB/(4nA 0)=212 nm, and LBnB/(4nB 0)=330 nm. The apodized effective refractive-index nAeff and nBff are shown in Fig. 5(a), from which the associated MIM SPP widths WAn and WBn are optimized and shown in Fig. 5(b). The transmission of the apodized SPPR is plotted in Fig. 5(c), as shown that that sidelobe of apodized reflector is effectively suppressed in contrast to the non-apodized reflector. In addition, the sidelobe can be further suppressed by decreasing F in Eq. (10), whereas at the cost of slightly narrowing the bandgap.

In [33, 36], photonic nanocavities in uniform MIM structure are studied. Here, nanocavity in apodizd MIM structure is demonstrated. In the apodized MIM SPP waveguide, by introducing a defect at the center, i.e., by repeating the B11 layer in the 11-th period, the SPP nanocavity is formed. The transmission spectrum is depicted in the Fig. 6. It displays a sharp peak inside the bandgap and suggests the existence of the SPP defect mode, which can find important applications such as ultra-narrow threshold lasers and light-emitting diodes [46].

 figure: Fig. 5.

Fig. 5. (a) The Gaussian apodized effective refractive index nAeff and nBeff. (b) The optimized variations of width WAn and WBn (n=1,2,..N) along the MIM SPP waveguide. (c) Spectral reflectivity of the apodized and non-apodized MIM SPPR.

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 figure: Fig. 6.

Fig. 6. Transmission spectrum of nanocavity structure formed by introducing a defect at the center of the apodized MIM SPP waveguide.

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5. Discussion and conclusion

In conclusion, utilizing the FDTD method and the dispersion relation, we have numerically investigated Bragg-grating-based MIM SPP waveguide, and find that the propagation of the SPPs through the MIM waveguide is highly confined in the metal surfaces and is controlled by the gap width and dielectric. By introducing a finite array of periodic grooves on the two metal surfaces and applying the quasi-chirped technique to them, a broad bandgap SPPR is obtained successfully. The underlying physical mechanism for the quasi-chirped technique to enlarge photonic bandgap is explained by the transfer matrix method and the theory of band structure. The MIM SPP waveguide to suppress the spectral sidelobe of SPPR is also presented by optimally varying the gap width. At last, we demonstrate that by introducing a defect at the centre of the apodized MIM SPP waveguide, a SPP nanocavity can be formed. These designed reflectors have good filtering characteristics such as broadband, near-zero transmission in the band and small sidelobe out the band, and are expected to have important potential applications in the highly integrated SPP-based photonic networks.

Acknowledgments

This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grant 10874239 and 10604066.

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “surface plasmon subwavelength optics,” Nature. 424, 824–830 (2003).
    [Crossref] [PubMed]
  2. H. Rather, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  3. K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
    [Crossref] [PubMed]
  4. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
    [Crossref]
  5. K. Donghyun, “Effect of the azimuthal orientation on the performance of grating-coupled surface-plasmon resonance biosensors,” Appl. Opt. 44, 3218–3223 (2005).
    [Crossref]
  6. A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
    [Crossref] [PubMed]
  7. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
    [Crossref]
  8. S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
    [Crossref]
  9. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
    [Crossref]
  10. Kazuo Tanaka, Masahiro Tanaka, and Tatsuhiko Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express. 13, 256–266 (2005)
    [Crossref] [PubMed]
  11. P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express. 14, 13030–13042 (2006).
    [Crossref] [PubMed]
  12. S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
    [Crossref] [PubMed]
  13. M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express. 16, 20227–20240 (2008)
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  14. Z. Zheng, Y. Wan, X. Zhao, and J. Zhu, “Spectral interferometric measurement of wavelength-dependent phase response for surface plasmon resonance sensors,” Appl. Opt. 48, 2491–2495 (2009).
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  15. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
    [Crossref] [PubMed]
  16. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
    [Crossref]
  17. J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
    [Crossref] [PubMed]
  18. P. Berin, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B. 61, 10484–10503 (2000).
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  19. R. Charbonneau, P. Berini, E. Berolo, and E. L. Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000).
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  20. S. Jetté-Charbonneau, “A study of Bragg gratings based on plasmon-polariton waveguides,” M.A.Sc. thesis, University of Ottawa, Ottawa, Canada, 2003.
  21. S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
    [Crossref]
  22. S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006).
    [Crossref]
  23. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
    [Crossref]
  24. P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
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  25. J. Mu and W. Huang, “Low-Loss Insulator-Metal-Insulator SPPs Bragg Reflector,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper JMB41
  26. P. Berini, R. Charbonnneau, and N. Lahoud, “Long-Range Surface Plasmons Along Membrane-Supported Metal Stripes,” IEEE J. Quantum Electron. 14, 1479–1495 (2008)
    [Crossref]
  27. R Selker, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A. 21, 2442–2446 (2004).
    [Crossref]
  28. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
    [Crossref]
  29. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express. 16, 413–425 (2008).
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  30. G. Veronis, Z. Yu, S. Kocabas, D.M. Miller, S. Brongersma, and Fan, “Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale,” Chin. Opt. Lett. 7, 302–308 (2009).
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  31. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B. 73, 035407–035415 (2006).
    [Crossref]
  32. B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107–013109 (2005).
    [Crossref]
  33. A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express. 14, 11318–11323 (2006).
    [Crossref]
  34. A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express. 16, 1475–1480 (2008).
    [Crossref] [PubMed]
  35. Z. H. Han, E. Forsberg, and S. L. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
    [Crossref]
  36. J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
    [Crossref] [PubMed]
  37. L. Frandsen, A. Harpoth, P. Borel, M. Kristensen, J. Jensen, and O. Sigmund, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express 12, 5916–5921 (2004).
    [Crossref] [PubMed]
  38. K. A. Suneet, M. Usha, and P. O. Sant, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B. 23, 2566–2571 (2006).
    [Crossref]
  39. T. Erdogan, “Fiber grating spectrum,” J. Lightw. Technol. 15, 1277–1293 (1997).
    [Crossref]
  40. K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998).
    [Crossref]
  41. S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006)
    [Crossref]
  42. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B. 6, 4370–4379 (1972).
    [Crossref]
  43. A. Taflove and S. C. Hagness, “Computational Electrodynamics. The Finite-Difference Time-Domain Method,” 2nd ed.2000 (Artech House, Boston.).
  44. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
    [Crossref] [PubMed]
  45. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–437 (1977).
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  46. P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
    [Crossref]

2009 (2)

2008 (7)

A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express. 16, 1475–1480 (2008).
[Crossref] [PubMed]

J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
[Crossref] [PubMed]

P. Berini, R. Charbonnneau, and N. Lahoud, “Long-Range Surface Plasmons Along Membrane-Supported Metal Stripes,” IEEE J. Quantum Electron. 14, 1479–1495 (2008)
[Crossref]

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[Crossref]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express. 16, 413–425 (2008).
[Crossref] [PubMed]

S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
[Crossref] [PubMed]

M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express. 16, 20227–20240 (2008)
[Crossref] [PubMed]

2007 (3)

J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
[Crossref] [PubMed]

P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
[Crossref]

Z. H. Han, E. Forsberg, and S. L. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[Crossref]

2006 (10)

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B. 73, 035407–035415 (2006).
[Crossref]

K. A. Suneet, M. Usha, and P. O. Sant, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B. 23, 2566–2571 (2006).
[Crossref]

S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006).
[Crossref]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
[Crossref] [PubMed]

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[Crossref]

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express. 14, 13030–13042 (2006).
[Crossref] [PubMed]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
[Crossref]

A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express. 14, 11318–11323 (2006).
[Crossref]

S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006)
[Crossref]

2005 (8)

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
[Crossref]

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[Crossref]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
[Crossref]

Kazuo Tanaka, Masahiro Tanaka, and Tatsuhiko Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express. 13, 256–266 (2005)
[Crossref] [PubMed]

K. Donghyun, “Effect of the azimuthal orientation on the performance of grating-coupled surface-plasmon resonance biosensors,” Appl. Opt. 44, 3218–3223 (2005).
[Crossref]

A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
[Crossref]

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107–013109 (2005).
[Crossref]

2004 (3)

L. Frandsen, A. Harpoth, P. Borel, M. Kristensen, J. Jensen, and O. Sigmund, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express 12, 5916–5921 (2004).
[Crossref] [PubMed]

R Selker, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A. 21, 2442–2446 (2004).
[Crossref]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
[Crossref]

2003 (2)

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

K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

2000 (2)

P. Berin, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B. 61, 10484–10503 (2000).
[Crossref]

R. Charbonneau, P. Berini, E. Berolo, and E. L. Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000).
[Crossref]

1998 (1)

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998).
[Crossref]

1997 (1)

T. Erdogan, “Fiber grating spectrum,” J. Lightw. Technol. 15, 1277–1293 (1997).
[Crossref]

1987 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

1977 (1)

1972 (1)

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

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B. 73, 035407–035415 (2006).
[Crossref]

Barclay, P. E.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[Crossref]

Barnes, W. L.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
[Crossref]

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

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
[Crossref] [PubMed]

Berin, P.

P. Berin, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B. 61, 10484–10503 (2000).
[Crossref]

Berini, P.

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[Crossref]

P. Berini, R. Charbonnneau, and N. Lahoud, “Long-Range Surface Plasmons Along Membrane-Supported Metal Stripes,” IEEE J. Quantum Electron. 14, 1479–1495 (2008)
[Crossref]

P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
[Crossref]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
[Crossref]

S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006)
[Crossref]

S. Jetté-Charbonneau and P. Berini, “Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides,” J. Opt. Soc. Am. A. 23, 1757–1767 (2006).
[Crossref]

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express. 14, 13030–13042 (2006).
[Crossref] [PubMed]

S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
[Crossref]

R. Charbonneau, P. Berini, E. Berolo, and E. L. Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000).
[Crossref]

Berolo, E.

Boltasseva, A.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
[Crossref]

A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
[Crossref]

Borel, P.

Bouhelier, A.

J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
[Crossref] [PubMed]

Bozhevolnyi, S.

A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
[Crossref]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
[Crossref]

Breukelaar, I.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
[Crossref]

Brongersma, M. L.

R Selker, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A. 21, 2442–2446 (2004).
[Crossref]

Brongersma, S.

Catrysse, P. B.

R Selker, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A. 21, 2442–2446 (2004).
[Crossref]

Charbonneau, R.

P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
[Crossref]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
[Crossref]

R. Charbonneau, P. Berini, E. Berolo, and E. L. Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000).
[Crossref]

Charbonnneau, R.

P. Berini, R. Charbonnneau, and N. Lahoud, “Long-Range Surface Plasmons Along Membrane-Supported Metal Stripes,” IEEE J. Quantum Electron. 14, 1479–1495 (2008)
[Crossref]

S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
[Crossref]

Chichkov, B.

S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
[Crossref] [PubMed]

Christy, R. W.

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

Dereux, A.

J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
[Crossref] [PubMed]

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

Des, F. G.

J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
[Crossref] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
[Crossref] [PubMed]

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J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B. 73, 035407–035415 (2006).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
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Friedman, M. D.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
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J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
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P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
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J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
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S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
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P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
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K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998).
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A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
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A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
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A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
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T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
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K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
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J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
[Crossref] [PubMed]

Liu, L.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[Crossref]

Maier, S. A.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
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J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
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A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express. 16, 1475–1480 (2008).
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A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express. 14, 11318–11323 (2006).
[Crossref]

Mattiussi, G.

P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
[Crossref]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
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S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
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Mu, J.

J. Mu and W. Huang, “Low-Loss Insulator-Metal-Insulator SPPs Bragg Reflector,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper JMB41

Nejati, H.

A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express. 16, 1475–1480 (2008).
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M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express. 16, 20227–20240 (2008)
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A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightw. Technol. 24, 912–918 (2006).
[Crossref]

A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 23, 413–422 (2005).
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T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
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S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
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S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
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J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express. 16, 413–425 (2008).
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S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
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P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
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K. A. Suneet, M. Usha, and P. O. Sant, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B. 23, 2566–2571 (2006).
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R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightw. Technol. 24, 477–494(2006).
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S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
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Sigmund, O.

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A. Boltasseva, S. Bozhevolnyi, T. Sondergaard, T. Nikolajsen, and K. Leosson, “Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons,” Opt. Express. 13, 4237–4243 (2005).
[Crossref] [PubMed]

Stepanov, A.

S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express. 16, 14369–14379 (2008)
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K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. 91, 227402 (2003).
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K. A. Suneet, M. Usha, and P. O. Sant, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B. 23, 2566–2571 (2006).
[Crossref]

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M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

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J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B. 73, 035407–035415 (2006).
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A. Taflove and S. C. Hagness, “Computational Electrodynamics. The Finite-Difference Time-Domain Method,” 2nd ed.2000 (Artech House, Boston.).

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Kazuo Tanaka, Masahiro Tanaka, and Tatsuhiko Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express. 13, 256–266 (2005)
[Crossref] [PubMed]

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M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express. 16, 20227–20240 (2008)
[Crossref] [PubMed]

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K. A. Suneet, M. Usha, and P. O. Sant, “Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material,” J. Opt. Soc. Am. B. 23, 2566–2571 (2006).
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Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.Y. Laluet, and T.W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature. 440, 508–511 (2006).
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J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
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B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107–013109 (2005).
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J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
[Crossref] [PubMed]

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P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
[Crossref]

Wedge, S.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
[Crossref]

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J. C. Weeber, A. Bouhelier, F. G. Des, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett. 7, 1352–1359 (2007).
[Crossref] [PubMed]

Wen, S.C.

J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
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Yariv, A.

Yeh, P.

Yu, Z.

Zervas, M. N.

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998).
[Crossref]

Zhao, X.

Zheng, Z.

Zhu, J.

Zou, B. S.

J. Q. Liu, L.L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S.C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express. 16, 4888–4894 (2008).
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Adv. Mater. (1)

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393–1396 (2005).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface Plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833 (2004).
[Crossref]

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experiemental demonstration of fiber-accessible metal nanoparticle plasmon waveguide for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[Crossref]

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107–013109 (2005).
[Crossref]

Chin. Opt. Lett. (1)

IEEE J. Quantum Electron. (3)

S. Jetté-Charbonneau, R. Charbonnneau, N. Lahoud, G. A. Mattiussu, and P. Berini. “Bragg Gratings Based on Long-Range Surface Plasmon-Polariton Waveguides: Comparison of Theory and Experiment.” IEEE J. Quantum Electron. 41, 1480–1491 (2005)
[Crossref]

P. Berini, R. Charbonnneau, and N. Lahoud, “Long-Range Surface Plasmons Along Membrane-Supported Metal Stripes,” IEEE J. Quantum Electron. 14, 1479–1495 (2008)
[Crossref]

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Z. H. Han, E. Forsberg, and S. L. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[Crossref]

J. Appl. Phys. (1)

P. Berini, R. Charbonneau, S. Jetté-Charbonneau, N. Lahound, and G. Mattiussi., “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 103, 113114 (2007)
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Supplementary Material (1)

» Media 1: MOV (1098 KB)     

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Figures (6)

Fig. 1.
Fig. 1. (a) Scheme of the MIM SPP waveguide. (b) Magnetic field distribution of |Hy|2 inside the MIM waveguide (Media 1). (c) Real part of the effective refractive index versus gap width w and wavelength λ in the Ag-SiO2-Ag (nd =1.46) and the Ag-PSiO2-Ag (nd =1.23) MIM waveguide, respectively.
Fig.2.
Fig.2. (a) Scheme of the quasi-chirped MIM SPP waveguide. (b) The n-th period of the proposed MIM structure in (a). (c) The effective refractive index of the SPP mode in the dielectric An and Bn , respectively. In the design, it is assumed that the dielectrics of layer An (n=1, 2…,N) and Bn are Sio2 (nA =1.46) and air (nB =1.0), and the width WAn and WBn are 80 nm and 120 nm, respectively.
Fig. 3.
Fig. 3. Transmission spectrum of the three designed MIM SPPRs. The reflector of uniform-design-1 contains one uniform segment, the quasi-chirped-design-2 and the quasi-chirped-design-3 contain two and three segments, respectively. The used parameters in these designed reflectors are shown in the Table 1 in detail.
Fig. 4.
Fig. 4. Band structure for the segment related in the Table 1. Here, ω B is angular frequency corresponding to the wavelength of 1550 nm, Λ is the period length, and K is the Bloch wave number.
Fig. 5.
Fig. 5. (a) The Gaussian apodized effective refractive index nAeff and nBeff . (b) The optimized variations of width WAn and WBn (n=1,2,..N) along the MIM SPP waveguide. (c) Spectral reflectivity of the apodized and non-apodized MIM SPPR.
Fig. 6.
Fig. 6. Transmission spectrum of nanocavity structure formed by introducing a defect at the center of the apodized MIM SPP waveguide.

Tables (1)

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Table 1. Parameters for the three designed Bragg-grating-based MIM SPPRs.

Equations (10)

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kdεmtanh(kdw2)+εdkm=0,
kd,m=βspp2εd,mk02,
neff=βsppk0,
εm=1wp2w02+iw0γ,
En+1=EnΔtε0Jn+12Δtε0Δ×Hn+12,
Jn+12=1γΔt21+γΔt2Jn12+ε0wp2Δt1+γΔt2En.
Hn+12=Hn12Δtμ0Δ×En·
nAeff(n)=n0+n0nA0f(n)
nBeff(n)=n0n0nB0f(n)
f(n)=exp[nF]2

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