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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 4 — Feb. 19, 2007
  • pp: 1755–1761
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Propagation characteristics of the supermode based on two coupled semi-infinite rib plasmonic waveguides

Sheng Hsiung Chang, Tsen Chieh Chiu, and Chao-Yi Tai  »View Author Affiliations


Optics Express, Vol. 15, Issue 4, pp. 1755-1761 (2007)
http://dx.doi.org/10.1364/OE.15.001755


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Abstract

We report on the propagation characteristics of a plasmonic waveguide structure based on two coupled rectangular wedges. Dispersion, propagation loss, and field distributions are investigated by three-dimensional finite-difference time-domain method. The considered structure supports only one supermode over 30THz bandwidth, and the calculated propagation loss at λ=1.55μm is 0.0257dB/μm, which is lower than the existing report by 1.7 times while keeping comparable field localizations. The all-planar structure in conjunction with the linearly dispersive characteristic over a wide operational bandwidth signifies its great potential for optical signal transporting in nanophotonic circuits.

© 2007 Optical Society of America

1. Introduction

Photonic components are superior to electronic ones in terms of the large operational bandwidth, fast switching speed, and low cross-talk, enabling all-optical signal processing and system on chip (SOC) applications. With the growing demand of miniaturized photonic devices and high density optical integrated circuits (OICs), plasmonic waveguides (PWs) have re-grab people’s attention for the great capability of overcoming diffraction limit [1–5

1. J. R. Krenn, “Nanoparticle waveguide: watching energy transfer,” Nature Materials 2,210 (2003). [CrossRef] [PubMed]

] by transporting lightwave in form of surface waves along the interface between metal and dielectrics. In contrast to conventional optical waveguides operated based on total internal reflection (TIR), PWs first turn the incident light into surface plasmon polaritons (SPPs) [6

6. B. E. Sernelius, Surface modes in physics, 1st ed. (Wiley-VCH, Berlin, 2001).

] and later transport SPPs along the metal-dielectric interface due to boundary condition constraints. As a consequence, the electromagnetic field maintains its maximum at the interface while evanescently decays into both-side surroundings. In order to compromise the enhanced field localization and the propagation length, a variety of PW structures such as rectangular metallic stripes [7

7. J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60,663 (2002). [CrossRef]

], metallic rods [8

8. C. A. Pfeiffer, E. N. Economou, and K. L Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B 10,3038 (1974). [CrossRef]

], metallic nanochains [9

9. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the Optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82,2590 (1999). [CrossRef]

], metallic gaps [10

10. K. Tananka, M. Tanaka, and T. Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express 13,256 (2005). [CrossRef]

,11

11. L. Chen, Ja. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31,2133 (2006). [CrossRef] [PubMed]

], and trapezium-like nanowedges [12

12. T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79,4583 (2001). [CrossRef]

] etc have been proposed and widely investigated. Up to now, only channel plasmon polaritons (CPPs) [13–15

13. I. V. Novikov and A. A. Marardudin, “Channel polaritons,” Phys. Rev. B 66,035403 (2002). [CrossRef]

] in metallic V-grooves have been demonstrated to satisfy simultaneously low propagation loss and strong localization [16

16. S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, and W. Ebbesen, “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005). [CrossRef] [PubMed]

]. In addition, theoretical simulation predicts that CPPs can be guided through sharp bends with nearly zero propagation loss [17

17. D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30,1186 (2005). [CrossRef] [PubMed]

] and high tolerance to structural imperfections [16

16. S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, and W. Ebbesen, “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005). [CrossRef] [PubMed]

], pushing a step further toward to the construction of compact nanophotonic circuits.

Fig. 1 The structure of the coupled semi-infinite rib plasmonic waveguide.

2. Simulation methodology

A three-dimensional finite-difference time-domain (3D FDTD) algorithm is developed for analyzing the propagation properties of the PWs. The development of the 3D-FDTD code is based on the standard Yee cell [22

22. K. S. Yee, “Numerical solution of initial boundary value problem involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14,302 (1966). [CrossRef]

]. For modeling the interaction of light with metal, the recursive algorithm [23

23. R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, “A frequency-dependent finite difference time domain formulation for dispersive materials,” IEEE Trans. Electromag. Comp. 32,222 (1990). [CrossRef]

] is included into the FDTD framework in order to update the calculated electromagnetic fields. Specifically, the metal is modeled via the classical Drude’s model [24

24. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr. L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, W,” Appl. Opt. 24,4493 (1985). [CrossRef] [PubMed]

] in which the time dependent relative permittivity is parameterized as ε(t) = ε {1 + ω 2 P[1 - exp(-vct)] /vc}, where ε is the background relative permittivity of the metal, ωP is the angular plasma frequency, and vc is the collision frequency. The mesh layout, boundaries and excitation conditions for the calculation are depicted in Fig. 2(a) and 2(b). As shown in Fig. 2, finite computational domain is realized by imposing 10-cell perfectly matched layer (PML) [25

25. G. X. Fan and Q. H. Liu, “An FDTD algorithm with perfectly matched layers for general dispersive media,” IEEE Trans. Antennas Propagat. 48,637 (2000). [CrossRef]

] to absorb the outgoing electromagnetic waves without producing significant reflections back into the simulation domain. The cell size and the time step used to discretize the space domain and time domain are 30nm×30nm×30nm (~λ/50) and 0.05fs, respectively. This mesh layout results in a calculation volume of 36μm×2.4μm×2.7μm, corresponding to 1200×80×90 cells. An electric dipole oriented in the y-direction is placed at the central part of the coupled waveguides and a continuous sinusoidal wave Jy = sin(ωt) , where ω is the angular frequency, is assigned to the dipole as the temporal current signature for the excitation. To obtain a steady-state result, 4000 time steps is used to allow the field evolved to a constant distribution in regardless of the location of the excitation.

Fig. 2 (a) Top view of the mesh layout, boundaries, and the orientation of the dipole excitation of the coupled rib plasmonic waveguides. (b) Cross-sectional view of the simulation arrangement.

3. Results and discussion

Fig. 3. Electric field distributions. (a)(b) Cross-section view of the Ey and the Ez component, respectively. (c)(d) Top view of the Ey and the Ez component, respectively. The excited wavelength is 1.55μm.
Fig. 4. Modal effective indices and the corresponding propagation losses for the coupled plasmonic waveguides with various structural parameters. The excited wavelength is 1.55μm.

The dispersion characteristics are further analyzed by scanning the carrier frequency of the excitation from 180THz to 230THz, corresponding to the wavelength ranging from 1.30μm to 1.67μm. As shown in Fig. 5, the coupled rib PWs shows a linear dispersion relation with only slightly dependence on the structural parameters. This result indicates a constant dispersion coefficient over a broad frequency range of ~50THz. The correspondent propagation loss is also calculated which shows a flat spectrum over the same frequency range, as shown in Fig. 6. These peculiar properties may allow the realization of a wide-band operation, dispersion compensator free, nano-scaled lightwave circuits.

Fig. 5. The dispersion relation of the coupled rib plasmonic waveguide
Fig. 6. The loss spectrum of the coupled rib plasmonic waveguide

4. Conclusions

We systematically analyze the propagation characteristics of the supermode supported by two coupled semi-infinite rib plasmonic waveguides using 3D-FDTD method. Fast Fourier transformation (FFT) is used for the determination of the propagation constant and the attenuation coefficient. It is found that only one supermode can exist regardless of the height of the gap between the two coupled rib plasmonic waveguides. The lowest propagation loss found is 0.0257 dB/μm, which is lower than that of a CPP in V-groove by 1.7 times, and the associated lateral field confinement is comparable to that of the CPPs. This result indicates that we have successfully compromised the field localization and the propagation loss at the same time. In addition, the investigated waveguide has a constant dispersion coefficient with a flat attenuation spectrum (< 0.05 dB/μm) over 30THz. Moreover, the structure is easier to fabricate due to the all-planar structural features and it is expected that these properties can be useful for lightwave transporting in a nano-photonic circuit.

Note that during the preparation of this manuscript, a paper that treats a similar problem using effective-index method was published [26

26. S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14,73241 (2006). [CrossRef]

].

Acknowledgments

References and links

1.

J. R. Krenn, “Nanoparticle waveguide: watching energy transfer,” Nature Materials 2,210 (2003). [CrossRef] [PubMed]

2.

J. -C. Weeber, et. al., “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B 64,045411 (2001). [CrossRef]

3.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22,475–477 (1997). [CrossRef] [PubMed]

4.

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23,1331–1333 (1998). [CrossRef]

5.

S. A. Maier, et al. , “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Materials 2,229–232 (2003). [CrossRef] [PubMed]

6.

B. E. Sernelius, Surface modes in physics, 1st ed. (Wiley-VCH, Berlin, 2001).

7.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60,663 (2002). [CrossRef]

8.

C. A. Pfeiffer, E. N. Economou, and K. L Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B 10,3038 (1974). [CrossRef]

9.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the Optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82,2590 (1999). [CrossRef]

10.

K. Tananka, M. Tanaka, and T. Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express 13,256 (2005). [CrossRef]

11.

L. Chen, Ja. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31,2133 (2006). [CrossRef] [PubMed]

12.

T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79,4583 (2001). [CrossRef]

13.

I. V. Novikov and A. A. Marardudin, “Channel polaritons,” Phys. Rev. B 66,035403 (2002). [CrossRef]

14.

D. F. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29,1069 (2004). [CrossRef] [PubMed]

15.

S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, J. -Y Laluet, and W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,23 (2006). [CrossRef]

16.

S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, and W. Ebbesen, “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005). [CrossRef] [PubMed]

17.

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30,1186 (2005). [CrossRef] [PubMed]

18.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29,1209 (2004). [CrossRef] [PubMed]

19.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large Single-mode Rib Waveguides in Ge/Si-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27,1971 (1991). [CrossRef]

20.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, “Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap,” J. Appl. Phys. 100,013101 (2006). [CrossRef]

21.

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape dispersion, and losses,” Opt. Lett. 31,3447–3449 (2006). [CrossRef] [PubMed]

22.

K. S. Yee, “Numerical solution of initial boundary value problem involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14,302 (1966). [CrossRef]

23.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, “A frequency-dependent finite difference time domain formulation for dispersive materials,” IEEE Trans. Electromag. Comp. 32,222 (1990). [CrossRef]

24.

M. A. Ordal, R. J. Bell, R. W. Alexander, Jr. L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, W,” Appl. Opt. 24,4493 (1985). [CrossRef] [PubMed]

25.

G. X. Fan and Q. H. Liu, “An FDTD algorithm with perfectly matched layers for general dispersive media,” IEEE Trans. Antennas Propagat. 48,637 (2000). [CrossRef]

26.

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14,73241 (2006). [CrossRef]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(200.4650) Optics in computing : Optical interconnects
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 24, 2006
Revised Manuscript: January 16, 2007
Manuscript Accepted: January 16, 2007
Published: February 19, 2007

Citation
Sheng Hsiung Chang, Tsen Chieh Chiu, and Chao-Yi Tai, "Propagation characteristics of the supermode based on two coupled semi-infinite rib plasmonic waveguides," Opt. Express 15, 1755-1761 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1755


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References

  1. J. R. Krenn, "Nanoparticle waveguide: watching energy transfer," Nat. Mater. 2, 210 (2003). [CrossRef] [PubMed]
  2. J. -C. Weeber,  et al., "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 64, 045411 (2001). [CrossRef]
  3. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett. 22, 475-477 (1997). [CrossRef] [PubMed]
  4. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998). [CrossRef]
  5. S. A. Maier,  et al., "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003). [CrossRef] [PubMed]
  6. B. E. Sernelius, Surface modes in physics, 1st ed. (Wiley-VCH, Berlin, 2001).
  7. J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Non-diffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663 (2002). [CrossRef]
  8. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: Surface plasmons," Phys. Rev. B 10, 3038 (1974). [CrossRef]
  9. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, "Squeezing the Optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590 (1999). [CrossRef]
  10. K. Tananka, M. Tanaka, and T. Sugiyama, "Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides," Opt. Express 13, 256 (2005). [CrossRef]
  11. L. Chen, Ja. Shakya, and M. Lipson, "Subwavelength confinement in an integrated metal slot waveguide on silicon," Opt. Lett. 31, 2133 (2006). [CrossRef] [PubMed]
  12. T. Yatsui, M. Kourogi, and M. Ohtsu, "Plasmon waveguide for optical far/near-field conversion," Appl. Phys. Lett. 79, 4583 (2001). [CrossRef]
  13. I. V. Novikov and A. A. Marardudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002). [CrossRef]
  14. D. F. Pile and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069 (2004). [CrossRef] [PubMed]
  15. S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, J. -Y Laluet, and W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 23 (2006). [CrossRef]
  16. S. I. Bozhevolnyi, V. S. Volkov, E. Deavux, and W. Ebbesen, "Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves," Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]
  17. D. F. P. Pile and D. K. Gramotnev, "Plasmonic subwavelength waveguides: next to zero losses at sharp bends," Opt. Lett. 30, 1186 (2005). [CrossRef] [PubMed]
  18. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Opt. Lett. 29, 1209 (2004). [CrossRef] [PubMed]
  19. R. A. Soref, J. Schmidtchen, and K. Petermann, "Large Single-mode Rib Waveguides in Ge/Si-Si and Si-on-SiO2," IEEE J. Quantum Electron. 27, 1971 (1991). [CrossRef]
  20. D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006). [CrossRef]
  21. E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, "Channel plasmon-polaritons: modal shape dispersion, and losses," Opt. Lett. 31, 3447-3449 (2006). [CrossRef] [PubMed]
  22. K. S. Yee, "Numerical solution of initial boundary value problem involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302 (1966). [CrossRef]
  23. R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite difference time domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222 (1990). [CrossRef]
  24. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr. L. L. Long, and M. R. Querry, "Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, W," Appl. Opt. 24, 4493 (1985). [CrossRef] [PubMed]
  25. G. X. Fan and Q. H. Liu, "An FDTD algorithm with perfectly matched layers for general dispersive media," IEEE Trans. Antennas Propag. 48, 637 (2000). [CrossRef]
  26. S. I. Bozhevolnyi, "Effective-index modeling of channel plasmon polaritons," Opt. Express 14, 73241 (2006). [CrossRef]

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