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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 13 — Jun. 27, 2005
  • pp: 4818–4827
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FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice

W. M. Saj  »View Author Affiliations


Optics Express, Vol. 13, Issue 13, pp. 4818-4827 (2005)
http://dx.doi.org/10.1364/OPEX.13.004818


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Abstract

We present a 2D plasmon waveguide in the form of rows of silver nanorods in hexagonal lattice, that may be used for creating a medium with novel effective electromagnetic properties. Transport of energy due to surface plasmon coupling is investigated with Finite Difference Time Domain method for visible range wavelengths from 400 to 750 nm. For 500 to 750 nm range two-mode nature of the waveguide is shown in simulations. Attenuation factors and group velocities are calculated for transmitted modes.

© 2005 Optical Society of America

1. Introduction

In the last years there is a great interest in materials like photonic crystals and metamaterials that exhibit novel optical properties because of their subwavelength structure. Shvets [1

1. G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67, 035109 (2003). [CrossRef]

] proposed a 2D medium with desired properties that can be composed of a net of waveguides exhibiting those properties. The medium is a negative refractive index material made of narrow channel plasmon waveguides. Recently, a waveguiding periodic arrangement of metal slits was presented [2

2. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for Designing Metallic Metamaterials with a High Index of Refraction,” Phys. Rev. Lett. 94, 197401 (2005). [CrossRef] [PubMed]

] as a method of constructing medium with high refractive index.

We propose a plasmon waveguide based on hexagonal lattice of silver rods that could be a base for 2D net medium with refractive index given by light propagation constant in a single waveguide. Light propagates only in one direction in the waveguide and space isotropy of wavefront propagation in the whole medium is established by different orientations of waveguides. This is an advantage over full photonic crystal structures where isotropy of photonic band is required [3

3. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10, 696 (2000). [CrossRef]

].

Plasmon waveguides are useful in construction of optical metamaterials because of their small size. Plasmons are coupled oscillations of electromagnetic field and of electrons excited on a surface of a conductor. Surface plasmons concentrate and locally enhance light intensity [4

4. H. Raether, Surface Plasmons (Springer, Berlin1988).

, 5

5. C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

]. This property stimulates investigations on nanoscale plasmonic devices because of their possible applications in near field optics, sensing and data storage [5

5. C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

12

12. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977 [CrossRef] [PubMed]

].

Surface plasmons offer a possibility of transporting energy with concentration of light below the diffraction limit [6

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

, 7

7. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

, 9

9. T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001). [CrossRef]

, 11

11. K. Tanaka, M. Tanaka, and T. Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express 13, 256–266 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-256 [CrossRef] [PubMed]

13

13. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Optics Letters 29, 1069–1071 (2004). [CrossRef] [PubMed]

]. A few types of plasmon waveguides were proposed and investigated previously [7

7. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

16

16. S. A. Maier, Guiding of electromagnetic energy in subwavelength periodic metal structures, PhD Thesis, (California Institut of Technology, Pasadena2003).

]. These were attempts to employ surface plasmon propagation along wires, small metal strips [7

7. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

10

10. R. Zia, 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]

, 12

12. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977 [CrossRef] [PubMed]

] or grooves in metal [13

13. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Optics Letters 29, 1069–1071 (2004). [CrossRef] [PubMed]

]. In another approach coupling between plasmons on metal particles and guiding energy by chain of particles was used [14

14. 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]

16

16. S. A. Maier, Guiding of electromagnetic energy in subwavelength periodic metal structures, PhD Thesis, (California Institut of Technology, Pasadena2003).

].

In our structure, coupling between surface plasmons on neighboring silver rods arranged in hexagonal lattice is employed. Previously, a dielectric structure of nanopillars in square lattice for waveguiding energy was proposed in [17

17. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, “Nanopillars photonic crystal waveguides,” Opt. Express 12, 617–622 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617 [CrossRef] [PubMed]

] and light propagation in channels in metallic photonic crystal was examined in [18

18. F. I. Baida, D. Van Labeke, Y. Pagani, B. Guizal, and M. Al Naboulsi, “Waveguiding through a two-dimensional metallic photonic crystal,” J. Microscopy 213, 144–148 (2004). [CrossRef]

]. Resonant coupling of surface plasmons on two metallic nanowires was studied in detail in [19

19. J. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-12-655 [CrossRef]

].

The structure is made of alternating two and three silver nanorods of diameter d=100 nm and lattice constant Λ=200 nm placed in a material with refractive index n=1. It has waveguiding properties in the visible range. We analyze modes and find their propagation constants. The guided modes form four pairs of bands with different field distribution. Propagation of waves is simulated using Finite Difference Time Domain method and estimation of energy losses along the waveguide are made for several wavelengths from the range 400–750 nm.

2. FDTD simulations

We assume that dielectric function of silver is described by Drude model

ε(ω)=εωp2[ω(ω+iΓ)]1.
(1)

In the simulations we employ the following parameters ε=3.70, ωp=13673 THz and Γ=27.35 THz The parameters were calculated by Sönnichsen [5

5. C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

] from experimental data on reflection and transmission of 25–50 nm thick silver films obtained for the wavelength range 0.188–1.9 µm by Johnson and Christy [20

20. P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

].

Fig. 1. Real (left) and imaginary parts (right) of the dielectric function of silver: experimental results [20] and the best fit curves for the wavelength range 0.188–1.9 µm obtained using Drude model with parameters ε∞=3.70, ωp=13673 THz and Γ=27.35 THz [5].

Real Reε(λ) and imaginary Imε(λ) parts of the dielectric permittivity function of silver calculated according to Drude model are plotted in Fig. 1. In the wide range of wavelengths for which measurements [20

20. P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

] were made the continuous lines are the best fit curves. In the optical range of our interest, however, we observe a serious discrepancy between the measured values of imaginary part of ε(λ) of silver and the best fit curve. Roughly, the mismatch can be estimated on the level of factor of two. It means that in the visible range absorption losses in silver are underestimated when the Drude model with parameters calculated by Sönnichsen is accepted. Additional absorption losses may result from high surface to volume ratio of the nanowires used to construct the waveguide [5

5. C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

].

We assume uniformity of the structure and electromagnetic field in the y direction and choose magnetic component of the field parallel to rods (TE mode). Thus, considered field components are Ex, Ez, Hy and Poynting vector length |P|=((Ex Hy)2+(Ez Hy)2)1/2 describes the density of energy.

For simulations we use our own implementation of FDTD method [21

21. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, MA2000).

, 22

22. W. M. Saj, Application of Finite Difference Time Domain Method to Modeling of Photonic Crystal Fibers, Msc Thesis (in Polish) (Warsaw University, Warsaw2003).

]. It uses second order difference equations to compute evolution of electromagnetic field on discrete computational grid. It is able to simulate propagation from finite in space sources like Gaussian or Hermite-Gaussian within volumes limited by periodic Bloch conditions and Uniaxial Perfectly Matched Layers (UPML) as the absorbing boundary conditions. UPML are used to simulate free space surrounding investigated structure. Computations are performed on a PC with 2.8 GHz CPU and 4 GB RAM.

Fig. 2. Computation area (a) was used to analyze modes and (b) was used to simulate propagation.

Figure 2(b) shows a cross section of the waveguide used to study propagation. Size of the simulation region is 5000 nm×2500 nm and space discretization step is Δr=5 nm. The x axis polarized electromagnetic TE wave originates from finite in space Gaussian or Hermite -Gaussian sources positioned at z=0 plane. The sources of different symmetry excite corresponding modes [17

17. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, “Nanopillars photonic crystal waveguides,” Opt. Express 12, 617–622 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617 [CrossRef] [PubMed]

]. To avoid numerical switch-on effects amplitude of sources increases from zero to its maximum value during the first three periods. Time discretization step is Δtr/2c=8.34×10-18 s. Simulation area is surrounded by 10 layers thick UPML boundary to cancel possible artificial reflections from the edge. For each wavelength we calculate intensity as an average of Poynting vector lengths over 5 wave periods taken after 10000 time steps.

3. Results

3.1. Waveguide modes in the visible range

The visible range modes for the first Brillouin Zone (BZ) of the waveguide are shown in Fig. 3(a) as plots interpolated between the calculated values of wavevectors k. The observed dispersion curves form four bands with negative dispersion and another four symmetric bands with respect to the center of BZ with positive dispersion. Each pair of curves represents different structure of the field, see Fig. 3(b, 1–3). Three lowest pairs of branches have energy concentrated within the waveguide. The fourth pair of branches corresponds to a mode with energy concentrated outside the waveguide, see Fig. 3(b, 4). The branch with positive dispersion almost matches the free space dispersion curve for all frequencies and is probably a numerical artifact. The asymmetry of the field in this case is a result of asymmetry of initial field distribution and is connected with the fact that this curve represents two joined beams that propagate in free space on the edges of simulation volume weakly interacting with the structure.

Fig. 3. (a) Mode dispersion curves plotted on frequency values calculated using FDTD for assumed wavenumbers in the z direction. (b) Intensity distributions for modes pointed with arrows on the dispersion diagram. Pseudocolors are separately normalized to maximum values.

3.2. Light propagation in the waveguide

In propagation simulations we excite single modes with desired symmetry using appropriate sources [17

17. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, “Nanopillars photonic crystal waveguides,” Opt. Express 12, 617–622 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617 [CrossRef] [PubMed]

]. In the waveguide propagation of light of wavelength of 600 nm is observed for excitation with both Gaussian and Hermite-Gaussian beams. In the first case, energy is concentrated along the z axis the waveguide. In the second case, due to another shape of the incident beam light propagates mainly between outer nanorods, what can be seen on Figs. 4 and 5. Fields of the output beams preserve Gaussian and Hermite-Gaussian distributions.

Fig. 4. Intensity distributions in the waveguide with Gaussian (left) and Hermite-Gaussian (right) incident beams at 600 nm wavelength. Intensities are obtained as Poynting vector lengths averaged over 5 periods of the source.
Fig. 5. Cross-sections of intensity distribution in the waveguide with Gaussian (left column) and Hermite-Gaussian (right column) incident beams at 600 nm wavelength. Intensities are calculated at distances z=3130, 3300 and 4000 nm from the input plane.

In the waveguide energy flows from one set of surface plasmons coupled on two rods to the subsequent set excited on three rods and so on. Difference in intensity distributions results from symmetry of the incident field with respect to the waveguide axis, as it is shown in Figs. 6 and 7.

Fig. 6. Magnetic field component Hy of the propagating beam (left, 1.35 MB). Flow of energy in the waveguide (right, 1.56 MB). Both animations are made for Gaussian beam illumination at 600 nm wavelength for the region 1000 nm≤z≤3000 nm and 750 nm≤x≤1750 nm.
Fig. 7. Magnetic field component Hy of the propagating beam (left, 1.82 MB). Flow of energy in the waveguide (right, 2.45 MB). Both animations are made for Hermite-Gaussian beam illumination at 600 nm wavelength for the region 1000 nm ≤z≤3000 nm and 750 nm≤x≤ 1750 nm.

Figure 8 shows an example of situation where due to off-axis illumination we observe both symmetric and antisymmetric field distributions in the waveguide. We observe serpentine propagation of energy that is interpreted as an effect of symmetric and antisymmetric fields beating and makes a clear evidence that there is a difference in propagation constants between them.

Fig. 8. Intensity profile for off-axis illumination of the waveguide. The shift of the source is 250 nm and illumination wavelength is 600 nm.

For 600 nm illumination wavelength we calculate the group velocities of symmetric and antisymmetric waves by tracking positions of chosen energy maxima (Fig. 9). We obtain vg=0.84c and vg=0.98c for the symmetric and the antisymmetric fields, correspondingly.

Fig. 9. Positions of chosen single maximum values of Poynting vectors for Gaussian (left) and Hermite-Gaussian (right) fields. Linear fits give values of group velocities calculated for 600 nm wavelength incident beam.

3.3 Attenuation

Attenuation of energy in the proposed plasmon waveguide composed of metallic nanorods is high. Figure 10 shows decrease of propagating energy for Gaussian and Hermite-Gaussian illuminating beams calculated for 400, 500, 600 and 700 nm wavelengths.

Fig. 10. Plots of propagating energy for Gaussian (left) and Hermite-Gaussian (right) illuminating beams calculated for different wavelengths. Each point corresponds to integration along the x axis of the intensity (Poynting vector length averaged in time).

In Fig. 11 we show attenuation factors calculated for several wavelengths in the range 400–750 nm. The results are obtained from comparison of intensity integrated over the x axis at the input (z=0 nm) and output (z=4000 nm) planes. Both in the input and output planes time averaged Poynting vector lengths are integrated. In the input plane the incident field and that reflected from the input section are taken into account. In the output plane integration includes only the transmitted field. For 500 nm and longer wavelengths the symmetric waves have lower attenuation than the antisymmetric ones. For both fields the rapid increase of attenuation at shorter wavelengths and minimum losses at 550 nm are observed. At 500 nm and 550 nm Gaussian beams we observe interference patterns.

Fig. 11. Attenuation factors calculated for both types of illumination and various wavelengths. Results are obtained from comparison of energy at input (z=0 nm) and output (z=4000 nm) planes.

4. Discussion of propagation results

To match results of propagation simulations in the waveguide illuminated with Gaussian and Hermite-Gaussian beams of given time frequency with the mode description we record temporary field distributions along the waveguide length and find its space frequencies in the z direction. The results of that procedure are of low precision, however Fig. 12 shows that we observe modes of the positive dispersion branch from the first BZ as well as modes of the negative dispersion branch of the second BZ. Beating between the modes from the two branches is responsible for the interference pattern in Fig. 10. The difference of propagation constants well corresponds to observed pattern periodicity.

Fig. 12. Space frequencies of symmetric and antisymmetric fields that propagate in the waveguide and their corresponding time frequencies. Green line indicates the edge of BZ.

Figure 3(a) and 12 show that propagation of symmetric and antisymmetric field distributions in the waveguide is connected mainly with the first and the second branch of modes, correspondingly. Values of group velocities calculated from propagation of wave maxima are in good agreement with those assessed from positive slopes of dispersion curves. At certain wavelengths attenuation factors shown in Fig. 11 considerably change values. It results from the fact that each mode has its maximum frequency of propagation. Maximum frequencies of mode dispersion curves (branches 1 and 2 in Fig. 3(a)) and frequencies where attenuation changes abruptly are in qualitative agreement.

5. Conclusions

In the proposed waveguide composed of silver nanorods arranged in hexagonal lattice transfer of energy is due to surface plasmon coupling. In the photonic crystal structure we observe propagation of modes of various field distributions. In the visible range from 500 to 750 nm only two symmetric and antisymmetric modes are guided. We find that theoretical values of attenuation factors change from 3.6 to 14.9 dB/µm and from 10.0 to 17.6 dB/µm for symmetrical and antisymmetrical modes, respectively. For both modes attenuation reaches maximum at 425 nm and minimum at 550 nm. Further analysis of geometrical parameters and properties of the waveguide should lead to lower attenuation. The 2D medium composed of a net of such waveguides may be useful in photonic devices.

Acknowledgments

References and Links

1.

G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67, 035109 (2003). [CrossRef]

2.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for Designing Metallic Metamaterials with a High Index of Refraction,” Phys. Rev. Lett. 94, 197401 (2005). [CrossRef] [PubMed]

3.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10, 696 (2000). [CrossRef]

4.

H. Raether, Surface Plasmons (Springer, Berlin1988).

5.

C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

6.

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

7.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

8.

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Surface plasmon propagation in microscale metal stripes,” Appl. Phys. Lett. 79, 51–53 (2001). [CrossRef]

9.

T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001). [CrossRef]

10.

R. Zia, 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]

11.

K. Tanaka, M. Tanaka, and T. Sugiyama, “Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,” Opt. Express 13, 256–266 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-256 [CrossRef] [PubMed]

12.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977 [CrossRef] [PubMed]

13.

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Optics Letters 29, 1069–1071 (2004). [CrossRef] [PubMed]

14.

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]

15.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000). [CrossRef]

16.

S. A. Maier, Guiding of electromagnetic energy in subwavelength periodic metal structures, PhD Thesis, (California Institut of Technology, Pasadena2003).

17.

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, “Nanopillars photonic crystal waveguides,” Opt. Express 12, 617–622 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617 [CrossRef] [PubMed]

18.

F. I. Baida, D. Van Labeke, Y. Pagani, B. Guizal, and M. Al Naboulsi, “Waveguiding through a two-dimensional metallic photonic crystal,” J. Microscopy 213, 144–148 (2004). [CrossRef]

19.

J. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-12-655 [CrossRef]

20.

P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

21.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, MA2000).

22.

W. M. Saj, Application of Finite Difference Time Domain Method to Modeling of Photonic Crystal Fibers, Msc Thesis (in Polish) (Warsaw University, Warsaw2003).

23.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995). [CrossRef]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Research Papers

History
Original Manuscript: April 14, 2005
Revised Manuscript: June 6, 2005
Published: June 27, 2005

Citation
W. Saj, "FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice," Opt. Express 13, 4818-4827 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-4818


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References

  1. G. Shvets, �??Photonic approach to making a material with a negative index of refraction,�?? Phys. Rev. B 67, 035109 (2003). [CrossRef]
  2. J. T. Shen, P. B. Catrysse, and S. Fan, �??Mechanism for Designing Metallic Metamaterials with a High Index of Refraction,�?? Phys. Rev. Lett. 94, 197401 (2005). [CrossRef] [PubMed]
  3. M. Notomi, �??Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,�?? Phys. Rev. B 62, 10, 696 (2000). [CrossRef]
  4. H. Raether, Surface Plasmons (Springer, Berlin 1988).
  5. C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).
  6. W. L. Barnes, A. Dereux and T. W. Ebbesen, �??Surface plasmon subwavelength optics,�?? Nature 424, 824 �??830 (2003). [CrossRef] [PubMed]
  7. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn and J. P. Goudonnet, �??Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,�?? Phys. Rev. B 60, 9061�?? 9068 (1999). [CrossRef]
  8. B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, �??Surface plasmon propagation in microscale metal stripes,�?? Appl. Phys. Lett. 79, 51�??53 (2001). [CrossRef]
  9. T. Yatsui, M. Kourogi, and M. Ohtsu , �??Plasmon waveguide for optical far/near-field conversion,�?? Appl. Phys. Lett. 79, 4583�??4585 (2001). [CrossRef]
  10. R. Zia, 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]
  11. K. Tanaka, M. Tanaka, and T. Sugiyama, �??Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides,�?? Opt. Express 13, 256�??266 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-256">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-256</a> [CrossRef] [PubMed]
  12. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, �??Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,�?? Opt. Express 13, 977�??984 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977</a> [CrossRef] [PubMed]
  13. D. F. P. Pile, D. K. Gramotnev, �??Channel plasmon-polariton in a triangular groove on a metal surface,�?? Optics Letters 29, 1069�??1071 (2004). [CrossRef] [PubMed]
  14. 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]
  15. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, �??Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,�?? Phys. Rev. B 62, R16356�??R16359 (2000). [CrossRef]
  16. S. A. Maier , Guiding of electromagnetic energy in subwavelength periodic metal structures, PhD Thesis, (California Institut of Technology, Pasadena 2003).
  17. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, �??Nanopillars photonic crystal waveguides,�?? Opt. Express 12, 617�??622 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-617</a> [CrossRef] [PubMed]
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