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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7516–7525
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Selective-mode optical nanofilters based on plasmonic complementary split-ring resonators

Iman Zand, Amirreza Mahigir, Tavakol Pakizeh, and Mohammad S. Abrishamian  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7516-7525 (2012)
http://dx.doi.org/10.1364/OE.20.007516


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Abstract

A nanoplasmonic optical filtering technique based on a complementary split-ring resonator structure is proposed. The basic and modal properties of the square-nanoring are studied using the group theory. Degeneracy and non-degeneracy of the possible TM odd- and even-modes are characterized based on the symmetry elements of the ring structure. Distinctively, the proposed technique allows selecting and exciting the proper plasmonic modes of the nanoring in the side-coupled arrangement. It is found that the non-integer modes can be excited due to the presence of a metallic nano-wall. These modes are highly sensitive to the nano-wall dimensions, in contrast to the regular integer modes. Moreover, the transmission-line theory is used to derive the resonance condition of the modes. The results show the optical transmission spectrum of the investigated filter can be efficiently modified and tuned either by manipulation of the position or by variation of the width of the employed nano-wall inside the ring. The numerical results support the theoretical analysis.

© 2012 OSA

1. Introduction

Outstanding properties of plasmonic components such as their ability to highly confine optical waves below the diffraction limit and low bending-loss have made these structures a prime candidate for miniaturized photonic integrated circuits [1

1. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

, 2

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

]. Great potential of plasmonic guiding nanostructures for high integration have motivated significant activities to explore their characteristics. Among those structures, the MIM configuration has attracted much interest due to its unique characteristics such as strong localization and ease of fabrication [3

3. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” Opt. Express 16, 2129–2140 (2008). [CrossRef] [PubMed]

7

7. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

]. Different optical components such as Y-shaped combiners [8

8. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef] [PubMed]

], Mach-Zehnder interferometers [9

9. 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(7083), 508–511 (2006). [CrossRef] [PubMed]

], and couplers [10

10. H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

] have been designed and demonstrated.

In recent years, plasmonic resonators have been subject of numerous studies. In this regard, the plasmonic stubs [11

11. Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16(21), 16314–16325 (2008). [CrossRef] [PubMed]

13

13. J. Tao, X. G. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17(16), 13989–13994 (2009). [CrossRef] [PubMed]

], nano-capillary resonators [14

14. J. Tao, X. G. Huang, and J. H. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18(11), 11111–11116 (2010). [CrossRef] [PubMed]

], side-coupled Fabry–Perot [15

15. A. Noual, A. Akjouj, Y. Pennec, J.-N. Gillet, and B. Djafari-Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys. 11(10), 103020 (2009). [CrossRef]

, 16

16. X. Mei, X. Huang, J. Tao, J. Zhu, Y. Zhu, and X. Jin, “A wavelength demultiplexing structure based on plasmonic MDM side-coupled cavities,” J. Opt. Soc. Am. B 27(12), 2707–2713 (2010). [CrossRef]

], and slot cavities [17

17. G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19(4), 3513–3518 (2011). [CrossRef] [PubMed]

19

19. F. Hu, H. Yi, and Z. Zhou, “Wavelength demultiplexing structure based on arrayed plasmonic slot cavities,” Opt. Lett. 36(8), 1500–1502 (2011). [CrossRef] [PubMed]

] have been investigated. These structures which generally are used for manipulating optical waves have been successfully employed as the efficient components to achieve key optical devices such as wavelength demultiplexing structures [14

14. J. Tao, X. G. Huang, and J. H. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18(11), 11111–11116 (2010). [CrossRef] [PubMed]

17

17. G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19(4), 3513–3518 (2011). [CrossRef] [PubMed]

, 19

19. F. Hu, H. Yi, and Z. Zhou, “Wavelength demultiplexing structure based on arrayed plasmonic slot cavities,” Opt. Lett. 36(8), 1500–1502 (2011). [CrossRef] [PubMed]

], band-stop and band-pas filters [11

11. Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16(21), 16314–16325 (2008). [CrossRef] [PubMed]

13

13. J. Tao, X. G. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17(16), 13989–13994 (2009). [CrossRef] [PubMed]

, 18

18. H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18(17), 17922–17927 (2010). [CrossRef] [PubMed]

]. One type of plasmonic resonators is ring resonator structure which generally possesses circular or rectangular geometries. Plasmonic band-stop filters based on the circular and rectangular ring resonators have been introduced in [20

20. S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14(7), 2932–2937 (2006). [CrossRef] [PubMed]

] and [21

21. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

], respectively. Consequently, the band-stop [22

22. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded plasmonic waveguide-ring resonators,” Opt. Express 17(4), 2968–2975 (2009). [CrossRef] [PubMed]

, 23

23. Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]

] and band-pass [24

24. T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef] [PubMed]

, 25

25. B. Yun, G. Hu, and Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D Appl. Phys. 43(38), 385102 (2010). [CrossRef]

] filters have been proposed based on the end-coupled and side-coupled arrangements. In addition, an optical add-drop coupler based on the square ring has been suggested [26

26. J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]

].

2. Modeling and theoretical analysis

Figure 1
Fig. 1 Schematic of the proposed 2D plasmonic filter based on the CSRR structure including a metallic nano-wall placed in the position of (a) P1, (b) P2, and (c) P3.
shows the schematic of the proposed structure. The rectangular ring is surrounded by the metal (Ag) region. This ring is excited by a plasmonic channel waveguide, so-called bus-waveguide, in the side-coupled arrangement as shown in Fig. 1(a-c). The waveguide confines the exciting optical power in the insulator (air) region. Splitting the MIM square ring by adding a metallic nano-wall makes the structure a complement to the metallic SRR. In this study, the wall is placed in three positions, denoted by P1 (Fig. 1(a)), P2 (Fig. 1(b)), and P3 (Fig. 1(c)). The main structural parameters of the filter are the width of the MIM waveguide (d), gap size between the bus-waveguide and the ring (s), side length of the ring (L), wave-guiding length in the ring (Leff), and width of the nano-wall (w). To calculate transmittance of the filter (T=Pout/Pin) incident power of Pinand transmitted power of Pout are monitored at positions of S and T, respectively. The insulator is assumed to be air (εi=1), and the complex relative permittivity of silver εm(ω) is characterized by the Drude model: εm(ω)=εωp2/(ω2+iγω), where ε=3.7, ωp=9.1eV, and γ=0.018eV [34

34. Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007). [CrossRef]

]. The width of the MIM waveguides (d) is set to be 50 nm to ensure that only the fundamental TM mode is supported. The complex propagation constant β of this waveguide mode can be obtained from solving the eigenvalue equation [7

7. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

]:
tanh(γid2)=εiγmεmγi
(1)
where γi and γm, the wave attenuation constants in the transverse direction, defined as γi=β2εik02 and γm=β2εmk02; and εi, εm, k0, and βare the dielectric constants of the insulator and the metal, wave number in free-space, and the propagation constant of the guided mode, respectively. In the simulations, the structure in the z direction is considered to be infinite (2D), schematically shown in Fig. 1(a). We note, however, for on-chip optical components, the structures should be made finite [3

3. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” Opt. Express 16, 2129–2140 (2008). [CrossRef] [PubMed]

5

5. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]

].

2.1 Square ring resonator

The resonance modes of a rectangular ring are often compared with the modes of a circular ring. In the side-coupled arrangement, it is expected that a rectangular ring couples more efficiently to a bus-waveguide, compared to a circular ring. Another feature is that in contrast to a circular ring, a rectangular ring may exhibit new resonance modes because of its certain geometrical symmetry. Generally speaking, the possible differences in their transmission spectra are mainly attributed to the role of the corners of a rectangular ring structure [21

21. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

, 26

26. J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]

]. In this section, we investigate the effects of the corners on the resonance modes of the square ring in more details using the group theory and the principle of perturbation. Hence, physical origins of the effects are discussed. This enables us to theoretically study the modes of the CSRRs.

Unlike the end-coupled square ring [25

25. B. Yun, G. Hu, and Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D Appl. Phys. 43(38), 385102 (2010). [CrossRef]

], all corner- and face-modes of the square ring can be excited in the side-coupled arrangement. For an isolated square ring the two odd resonant (TMn) modes are degenerate, exhibiting a single resonance. However, the bus-waveguide breaks the symmetry of the structure, and as a result the degeneracy is lifted. Hence, the degenerate modes coupled to each other, and the modes split to two modes. One mode (TMns) is symmetric with respect to the symmetry plane of the whole structure, and the other mode (TMna) is asymmetric. These modes cannot be distinguished in the transmission spectrum of a side-coupled square ring because of the weak splitting of the modes and the relatively low Q-factor of the plasmonic resonators. Thus, it is expected that the odd modes have wider bandwidth in comparison with the even modes. Moreover, the traveling-wave (TW) characteristic of the odd resonances reported in [26

26. J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]

] is possibly due to the excitation of the standing-wave TMns and TMna modes which are out-of-phase. It should be emphasized that theTMnsand TMna modes become degenerate by removing the bus-waveguide.

2.2 Complementary SRR: CSRR

According to the above discussion, by placing a metallic nano-wall on the symmetry planes of the square ring one can manipulate only one of the TMmc or TMmf mode classes and thereby can modify the transmission spectrum of the filter. For this purpose, in here three proper positions for the wall are considered which are located in the corner and middle of the square faces of the ring, as shown in Fig. 1(a)-1(c). Since the minima of the electric field occur on the both sides of the metallic wall, a resonance mode may be drastically manipulated, depending on weather the wall is placed in the antinodes of magnetic fields (nodes of electric fields) or not. In fact, for the resonance modes, an antinode of the magnetic field (or node of the electric field) can be treated as an equivalent electrical short-circuit. Thus, by placing the nano-wall in the defined position P1 or P2, the TMmc modes are suppressed, but for the wall placed in the position P3, the TMmf modes are suppressed. Moreover, the metallic nano-wall placed in the position P1 or P2 suppresses one of theTMna and TMnsmodes, respectively. Although, for the position P3, a new mode (TM1(P3)) can be created which is neither TMna mode nor TMns mode. The antinode of the magnetic field of this mode is located on the symmetry plane of the ring.

Comparing structures of the proposed plasmonic CSRR and MIM cavity [16

16. X. Mei, X. Huang, J. Tao, J. Zhu, Y. Zhu, and X. Jin, “A wavelength demultiplexing structure based on plasmonic MDM side-coupled cavities,” J. Opt. Soc. Am. B 27(12), 2707–2713 (2010). [CrossRef]

] indicates that the CSRR can be considered as a closed straight cavity which is bent, and its ends are separated by the wall. Based on this analogy the CSRR can support both the integer modes (including even number of antinodes) and the non-integer modes (including odd number of antinodes). The square ring, in contrary, only supports the integer modes [21

21. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

, 25

25. B. Yun, G. Hu, and Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D Appl. Phys. 43(38), 385102 (2010). [CrossRef]

, 26

26. J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]

]. In the CSRR, there are two possible arrangements for the magnetic fields on the sides of the wall. They can be either with the same (integer modes) or opposite (non-integer modes) polarities on the sides of the wall. There is an important phenomenon which brings about a special characteristic for the non-integer modes in comparison with the integers modes. This phenomenon can be understood by comparing the polarities of the magnetic fields on the sides of the wall for the both types of modes. Particularly, in the non-integer modes opposite polarity of the magnetic fields on the sides of the wall indicates flow of co-directional electrical currents in the wall. On the other side, for the integer modes, two contra-directional current excited in the wall cancel each other out. Based on this behavior it can be concluded that, for the non-integer modes, the metallic nano-wall acts like a nanoinductor. Thus, the non-integer modes become highly sensitive to dimensions of the wall. Moreover, based on the symmetry arguments, the anti-nodes of the non-integer modes can be altered by changing position of the nano-wall.

The resonance condition of the CSRR structure can be obtained by employing the transmission line theory. The schematic of the transmission line resonator model of the integer and non-integer modes of the CSRR is shown in Fig. 2(b)
Fig. 2 (a) Schematics of the isolated CSRRs with their symmetry plane (AA') for the nano-wall placed in the middle of the face and corner. (b) The transmission-line model of the CSRR.
. Symmetry plane (AA') of the resonator is also plotted for the clarity. The input impedance seen from the left (ZL) and right (ZR) side of the symmetry plane can be simply expressed by [36

36. D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).

]:
ZL=ZR=Z02Zwall+iZ0tan(βLeff/2)Z0+i2Zwalltan(βLeff/2)
(3)
where Leff is the wave-guiding length in the ring as shown in Fig. 1, and Zwall is the impedance of the nano-wall. Due to the inductance behavior of the nano-wall its equivalent impedance can be expressed by Zwall=iωd/(ω2εm(ω)w), where w and d are the width and length of the inductance, respectively [37

37. A. Alu, M. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77(14), 144107 (2008). [CrossRef]

]; and εm(ω) is the permittivity of the wall made of the silver. The characteristic impedance of the MIM waveguide in each section is denoted by Z0, shown in Fig. 2(b), and it can be expressed by Z0=βd/ωε0 [6

6. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]

]. The values of β can be obtained by solving Eq. (1). Since the resonator is symmetrical, at the midpoint of the line, the resonance condition required that ZR=ZL*=ZL, or simplyIm{ZL}=0. By employing this condition, the resonance wavelengths of the modes can be obtained. It should be pointed that the mentioned condition is true when the metal loss is ignored and hence β is real. For the complex β (lossy metals) minimums of Im{ZL} should be found. In the case of the integer modes, the nano-wall is placed where the equivalent short-circuit of these modes exist. Moreover, as mentioned earlier, the integer modes do not support co-directional flow of the currents in the wall. Hence, by applying Zwall0 the resonance condition of the integer modes can be obtained. In special case in which β is real, the resonance condition would be ‘tan(βLeff/2)=0’ (or βLeff=2Nπ) where N, an integer, is the mode number of an integer mode. The described condition is similar to the resonance condition of the rectangular ring proposed in [21

21. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

]. The only difference is the effective length of the resonator which is decreased by the width of the wall. Therefore, it is expected that resonance wavelengths of the integer modes of the CSRR to be similar to the corresponding modes of the regular ring. However, the position and width of the wall should be properly considered.

3. Simulation results and discussions

3.1 Integer and non-integer modes

3.2 Effects of the position of the nano-wall

Manipulating the transmission spectra of the CSRRs by exciting or suppressing the TM2c or TM2f modes of the regular ring is one of the features of incorporating the nano-wall inside the ring. According to Fig. 3, for the cases that the wall is placed in the positions P1 and P2, TM2c is severely suppressed. However, the TM2f mode is suppressed if the wall is placed in P3. Comparing the resonance wavelengths and the field profiles of the TM2c and TM2f modes with the TM2c(P3) and TM2f(P1-P2) modes shows that unaffected even modes are almost the same as their counterpart modes in the regular ring structure. This behavior is in accordance with the theoretical descriptions presented in Sec. 2. In contrast, the first resonance of the ring TM1(Pi) is not suppressed for all of P1, P2, and P3 positions. For the case with the wall placed in P1 (P2), the TM1a (TM1s) mode is suppressed, and the TM1s (TM1a) mode remains unaffected. By positioning the wall in P3, a resonance mode (TM1(P3)) which possesses the antinodes of the magnetic field in the corners is excited. In this case, the optical power guided by the bus-waveguide can couple to the ring from the corners.

3.3 Tunability of the resonances: Effects of the width of the nano-wall

4. Conclusion

In summary, a 2D plasmonic nanofilter designed based on the CSRR structure is proposed. The theoretical analysis and the numerical calculations demonstrate the mode-selectivity and the filtering tunability of the proposed structure. Interestingly, incorporating a metallic nano-wall within the MIM nanoring structure led to excitation of the non-integer modes. The results show these modes are highly tunable by manipulating the width of the nano-wall. The basic electromagnetic modes of the plasmonic CSRR are elaborated using the group theory. Moreover, the transmission-line theory is used to estimate the resonance wavelengths of the proposed structure. The band shift of ~120 nm is achieved for the fundamental mode of the CSRR upon a gradual variation of the width of the wall from 10 to 50 nm. The findings suggest the potential of our design for a tunable and compact optical nanofilter in integrated optical circuits and for nanophotonics applications.

References and links

1.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

2.

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

3.

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” Opt. Express 16, 2129–2140 (2008). [CrossRef] [PubMed]

4.

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. (Deerfield Beach Fla.) 22(45), 5120–5124 (2010). [CrossRef] [PubMed]

5.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]

6.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]

7.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

8.

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef] [PubMed]

9.

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(7083), 508–511 (2006). [CrossRef] [PubMed]

10.

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

11.

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16(21), 16314–16325 (2008). [CrossRef] [PubMed]

12.

X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef] [PubMed]

13.

J. Tao, X. G. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17(16), 13989–13994 (2009). [CrossRef] [PubMed]

14.

J. Tao, X. G. Huang, and J. H. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18(11), 11111–11116 (2010). [CrossRef] [PubMed]

15.

A. Noual, A. Akjouj, Y. Pennec, J.-N. Gillet, and B. Djafari-Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys. 11(10), 103020 (2009). [CrossRef]

16.

X. Mei, X. Huang, J. Tao, J. Zhu, Y. Zhu, and X. Jin, “A wavelength demultiplexing structure based on plasmonic MDM side-coupled cavities,” J. Opt. Soc. Am. B 27(12), 2707–2713 (2010). [CrossRef]

17.

G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19(4), 3513–3518 (2011). [CrossRef] [PubMed]

18.

H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18(17), 17922–17927 (2010). [CrossRef] [PubMed]

19.

F. Hu, H. Yi, and Z. Zhou, “Wavelength demultiplexing structure based on arrayed plasmonic slot cavities,” Opt. Lett. 36(8), 1500–1502 (2011). [CrossRef] [PubMed]

20.

S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14(7), 2932–2937 (2006). [CrossRef] [PubMed]

21.

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

22.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded plasmonic waveguide-ring resonators,” Opt. Express 17(4), 2968–2975 (2009). [CrossRef] [PubMed]

23.

Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]

24.

T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef] [PubMed]

25.

B. Yun, G. Hu, and Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D Appl. Phys. 43(38), 385102 (2010). [CrossRef]

26.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]

27.

T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008). [CrossRef] [PubMed]

28.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16(3), 2080–2090 (2008). [CrossRef] [PubMed]

29.

M. Navarro-Cía, M. Aznabet, M. Beruete, F. Falcone, O. El Mrabet, M. Sorolla, and M. Essaaidi, “Stacked complementary metasurfaces for ultraslow microwave metamaterials,” Appl. Phys. Lett. 96(16), 164103 (2010). [CrossRef]

30.

Y. Dong and T. Itoh, “Substrate Integrated Waveguide Loaded by Complementary Split-Ring Resonators for Miniaturized Diplexer Design,” IEEE Microw.Wireless Compon. Lett. 21(1), 10–12 (2011). [CrossRef]

31.

G. Kumar, A. Cui, S. Pandey, and A. Nahata, “Planar terahertz waveguides based on complementary split ring resonators,” Opt. Express 19(2), 1072–1080 (2011). [CrossRef] [PubMed]

32.

S. F. A. Kettle, Symmetry and Structure: Readable Group Theory for Chemists, 3rd ed. (Wiley, 2007).

33.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2005).

34.

Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007). [CrossRef]

35.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE Press, 2001).

36.

D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).

37.

A. Alu, M. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77(14), 144107 (2008). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7400) Optical devices : Waveguides, slab
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: January 4, 2012
Revised Manuscript: March 4, 2012
Manuscript Accepted: March 4, 2012
Published: March 19, 2012

Citation
Iman Zand, Amirreza Mahigir, Tavakol Pakizeh, and Mohammad S. Abrishamian, "Selective-mode optical nanofilters based on plasmonic complementary split-ring resonators," Opt. Express 20, 7516-7525 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7516


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References

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  23. Z. Han, V. Van, W. N. Herman, P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]
  24. T. B. Wang, X. W. Wen, C. P. Yin, H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef] [PubMed]
  25. B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metal-insulator-metal waveguide,” J. Phys. D Appl. Phys. 43(38), 385102 (2010). [CrossRef]
  26. J. Liu, G. Fang, H. Zhao, Y. Zhang, S. Liu, “Plasmon flow control at gap waveguide junctions using square ring resonators,” J. Phys. D Appl. Phys. 43(5), 055103 (2010). [CrossRef]
  27. T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008). [CrossRef] [PubMed]
  28. C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16(3), 2080–2090 (2008). [CrossRef] [PubMed]
  29. M. Navarro-Cía, M. Aznabet, M. Beruete, F. Falcone, O. El Mrabet, M. Sorolla, M. Essaaidi, “Stacked complementary metasurfaces for ultraslow microwave metamaterials,” Appl. Phys. Lett. 96(16), 164103 (2010). [CrossRef]
  30. Y. Dong, T. Itoh, “Substrate Integrated Waveguide Loaded by Complementary Split-Ring Resonators for Miniaturized Diplexer Design,” IEEE Microw.Wireless Compon. Lett. 21(1), 10–12 (2011). [CrossRef]
  31. G. Kumar, A. Cui, S. Pandey, A. Nahata, “Planar terahertz waveguides based on complementary split ring resonators,” Opt. Express 19(2), 1072–1080 (2011). [CrossRef] [PubMed]
  32. S. F. A. Kettle, Symmetry and Structure: Readable Group Theory for Chemists, 3rd ed. (Wiley, 2007).
  33. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2005).
  34. Z. H. Han, E. Forsberg, S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19(2), 91–93 (2007). [CrossRef]
  35. R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE Press, 2001).
  36. D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).
  37. A. Alu, M. Young, N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77(14), 144107 (2008). [CrossRef]

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