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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16596–16603
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Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves

Il-min Lee, Jaehoon Jung, Junghyun Park, Hwi Kim, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 16596-16603 (2007)
http://dx.doi.org/10.1364/OE.15.016596


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Abstract

We have studied the dispersion characteristics of single-mode channel plasmon polaritons (CPPs) with step-trench-type groove waveguides. From the numerical simulations using the finite-element method, the modal shapes and the complex propagation constants of the CPPs over a wide spectral range were obtained. It is shown that the dispersion characteristics of the step-trench-type CPP waveguide, which is composed of a step trench with a stacking nature, show an intermediate feature between the narrow and broad trenches. The results show that this configuration allows for a well-confined CPP with a moderate propagation loss at the wavelengths investigated.

© 2007 Optical Society of America

1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves that are bound to a metal-dielectric interface and are coupled to the oscillations of the free electrons in the metal [1

1. H. Rather, Surface Plasmons (Springer-Verlag, Berlin, 1988).

]. There has been much interest in utilizing SPPs, because electromagnetic waves are able to be confined in a small cross-section located perpendicular to their direction of propagation while most of their energy is confined to the interface [2

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

4

4. S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007). [CrossRef]

].

In particular, there have been many suggestions of SPP waveguide structures that can implement highly confined electromagnetic waves able to be propagated with a moderate loss [3

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

, 5

5. 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]

7

7. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005). [CrossRef] [PubMed]

]. For example, long-range SPPs (LRSPPs) based on thin metal films or stripes have been intensively investigated [6

6. P. Berini, “Plasmon-polariton modes guided by a metal film of finite width,” Opt. Lett. 24, 1011–1013 (1999). [CrossRef]

]. However, this type of waveguide is limited in high integration for wide field extension to the surrounding dielectric media [2

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

, 6

6. P. Berini, “Plasmon-polariton modes guided by a metal film of finite width,” Opt. Lett. 24, 1011–1013 (1999). [CrossRef]

]. In contrast, by using metal cladding, the field can be confined tightly in a small cross-section. Although the propagation length for this type of waveguide is generally limited to a few tens of micrometers, many investigations have been reported on this configuration, owing to its potential for high integration [7

7. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005). [CrossRef] [PubMed]

15

15. V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and W. Ebbesen, “Wavelength selective nanophotonics components utilizing channel plasmon polaritons,” Nano Lett. 7, 880–884 (2007). [CrossRef] [PubMed]

] and among these investigations, channel plasmon polaritons (CPPs) are especially interesting. Since the first theoretical proposition of CPPs [8

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

], many experimental and theoretical investigations have been carried out [8

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

14

14. E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” J. Lightwave Technol. 25, 2547–2562 (2007). [CrossRef]

]. Recently, experiments into CPPs utilizing optical devices operating at telecommunication wavelengths, such as waveguide bends, splitters, interferometers, and resonators have been reported [10

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

, 15

15. V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and W. Ebbesen, “Wavelength selective nanophotonics components utilizing channel plasmon polaritons,” Nano Lett. 7, 880–884 (2007). [CrossRef] [PubMed]

]. Among the various geometries that have been proposed, there have been two representative groove types: a triangular (V-shaped) type and a rectangular (trenched) type.

2. The dispersion characteristics of conventional CPP waveguides

As a first step, we will briefly review several important characteristics of the two conventional CPP waveguide configurations. To examine the dispersion characteristics of CPPs in several geometries, we numerically simulated representative examples of conventional CPP waveguides by using FEM mode calculation method with COMSOL [16]. Through this paper, the effective index and the propagation length are defined as follows: neff=Re(β/k 0), and Lprop=1/Im(β), where β and k 0 are complex propagation constants of SPP and free space, respectively.

Fig. 1. The effective indices of the fundamental CPP modes in V-shaped, broad, and narrow trenches. The two upper insets show geometrical schematic drawings of the V-shaped (left) and trench (right) waveguides. The frequency-dependent propagation lengths for these configurations are depicted in the lower inset. The depth of all the geometries was set to the same value, d=1.2 µm. The top-most opening widths were: w=523 nm (V-shape), w 1=523 nm (trench), and w 2=120 nm (trench).

3. A step-trench CPP waveguide

A schematic diagram of our step-trench waveguide is shown in Fig. 2. This structure can be understood as two trenches with different widths forming a simple stack in the direction oriented vertically to the metal surface.

Fig. 2. A schematic diagram of our proposed step-trench waveguide.

The dispersion characteristics and corresponding propagation lengths of step-trench CPPs having different geometrical parameters are shown in Fig. 3. In our calculations, the top opening width, w 1, and the total groove depth, d, were set to the same values as the geometries shown in Fig. 1. The width of the narrow region, w 2, in Fig. 2 was also set to the same value as that shown in Fig. 1. By keeping the same width of the structures, we varied the depth, d 1, of the upper broad region from 200 nm to 1000 nm, while fixing the total depth of the groove as 1200 nm.

Fig. 3. The dispersion characteristics of step-trench-type CPPs for different depths. The inset shows the results for the corresponding propagation lengths. The upper trench depth, d 1, was varied from 200 to 1000 nm (depicted as ‘Up 200 nm’-‘Up 1000 nm’). In all cases, the total depth was fixed at d=1.2 µm. The results for the conventional trenches shown in Fig. 1 are represented as black lines.

Fig. 4. (Movie) Normalized modal energy distribution. The white curves denote the contour lines for -10 dB power drops from the peak power, and the thin gray lines denote the geometrical boundaries. In all cases, the top opening width and the total groove depth were fixed to have the same values of 523 and 1200 nm, respectively. For the step trenches, the depth of the upper trench was: (a) 600 and (b) 800 nm. The width of the narrow lower trench in (a) and (b) was 120 nm. The wavelength-dependent evolution of the modal energy distribution are shown in movies with a file size of: (a) 211, (b) 218, (c) 249 and (d) 237 KB [Media 1] [Media 2] [Media 3] [Media 4].

We carried out further investigations into the mode confinement to obtain more insight into this trade-off between propagation length and mode confinement. Because of the surface wave nature of the SPPs, when we consider the mode confinement to estimate the coupling or crosstalk between two parallel waveguides, the main concern is the lateral (parallel to the x-axis in Fig. 4) mode diameter at the interface. We define the lateral mode radius 3dB r as the distance of -3 dB power drop point from the waveguide’s symmetrical plane. Figure 5(a) shows the wavelength-dependent 3dB r variations over wavelength range.

Fig. 5. Numerical results of: (a) the wavelength-dependent lateral mode radius, and (b) the propagation length. The brown horizontal line in (a) depicts a distance of half the opening-width of the waveguide (261.5nm).

As shown in Fig. 5(a), the value of 3dB r in the short wavelength regime corresponds to that of narrow trench. As the wavelength increases, an abrupt jump to large values of 3dB r (which corresponds to broad trench value) was observed. This abrupt jump originates from the increasing intensity of the wedge mode at the edge of the upper broad trench. This wedge mode effect can also be observed in V-shaped trenches in the wavelength range of 800–900 nm in Fig. 5(a), but from the discontinuous shape of the step-trench, the ‘jump’ occurs more suddenly in our proposed structure than in the V-shaped structure. As the depth of the upper trench in the step-trench waveguide increases, the wavelength of this abrupt jump shifts to lower values. This can be envisaged by considering that as the depth of the upper broad trench increases, the nature of the broad trench dominates. Although the saturated 3dB r values in the long wavelength regime are larger than those of a V-shaped waveguide, the propagation length in Fig. 5(b) shows that the propagation lengths in this regime are also larger than in V-shaped CPP waveguides. As mentioned above, the trade-off between mode confinement and the propagation length can be observed in Figs. 5(a) and 5(b). However, when compared to the V-shaped waveguide, one can find that for typical geometric configurations, both the smaller 3dB r and the longer propagation length can be achieved. For example, the ‘UP 900 nm’ configuration, as depicted by the purple line in Fig. 5, shows a longer propagation length with a smaller mode radius for operation wavelengths of about 900–1000 nm. Moreover, we expect that when the depth of the upper trench is carefully selected, this spectral range can be increased.

To treat the trade-off between several configurations, we defined a figure-of-merit (FOM) as,

FOM=PropagationlengthLateralmoderadius=Lr3dB.
(1)

From the definition in Eq. (1), a large value of FOM implies a long propagation length or a small mode radius. Our results are shown in Fig. 6.

Fig. 6. Figure-of-merit for several waveguide configurations.

In Fig. 6, in most of our configurations, the value of the FOM was better than that of the V-shaped waveguide. Compared to a the broad trench waveguide, at shorter wavelengths before the occurrence of the abrupt jump shown in Fig. 5(a), the value of the FOM of step-trench-type structure is better. For example, for a configuration with a shallow upper trench, such as ‘Up 600 nm’ or ‘Up 700 nm’, the value of the FOM is superior over most of the spectral range. Here, we need to mention that the value of the FOM in the short wavelength regime is slightly worse than that of a narrow trench, even for shallow upper trench configurations. However, when we consider the fabrication process that needs to be applied for mass-production, such as ‘nanoimprinting’ [18

18. S. H. Ko, I. Park, H. Pen, C. P. Gigoropoulos, A. P. Pisano, C. K. Luscombe, and J. M. Frechet, “Direct nanoimprinting of metal nanoparticles for nanoscale electronics fabrication,” Nano Lett. 7, 1869–1877 (2007). [CrossRef] [PubMed]

, 19

19. H. L. Chen, S. Y. Chuang, H. C. Cheng, C. H. Lin, and T. C. Chu, “Directly patterning metal films by nanoimprint lithography with low-temperature and low-pressure,” Microelectron. Eng. 83, 893–896 (2006). [CrossRef]

], our proposed step-trench configuration is the most appropriate choice versus the needs of fabricating a deep and narrow trench. Moreover, when the inter-waveguide crosstalk is the main parameter of concern rather than the propagation length, which is expected to be important in highly integrated applications at telecommunication wavelengths, a configuration such as ‘Up 600 nm’, as shown in Figs. 5 and 6, would be a good example that easily satisfies the requirements.

4. Conclusions

We have suggested and numerically investigated the step-trench-type CPP waveguide configuration. From our results, our proposed waveguide structure shows an intermediate nature between its composing two (narrow and broad) trenches, which gives us a simple, but useful, guideline and more degrees of freedom in designing this type of waveguide. The mode confinement of the step-trench-type waveguide is better than that of conventional V-shaped or trenched waveguides with the same opening width when the geometrical parameters are properly selected. Considering the figure-of-merit defined to evaluate the trade-off between the mode confinement and the propagation length, our proposed structure shows an advantageous feature. Our proposed configuration is an appropriate structure for highly integrated photonic devices with a diminishing degree of difficulty during fabrication, compared to the case of making narrow and deep trenches.

Acknowledgment

The authors acknowledge the support by the Ministry of Science and Technology of Korea and Korea Science and Engineering Foundation through the Creative Research Initiative Program (Active Plasmonics Applications Systems).

References and links

1.

H. Rather, Surface Plasmons (Springer-Verlag, Berlin, 1988).

2.

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

3.

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

4.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90, 051113 (2007). [CrossRef]

5.

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]

6.

P. Berini, “Plasmon-polariton modes guided by a metal film of finite width,” Opt. Lett. 24, 1011–1013 (1999). [CrossRef]

7.

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005). [CrossRef] [PubMed]

8.

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

9.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]

10.

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

11.

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467–9476 (2006). [CrossRef] [PubMed]

12.

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]

13.

G. Vernois and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007). [CrossRef]

14.

E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” J. Lightwave Technol. 25, 2547–2562 (2007). [CrossRef]

15.

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and W. Ebbesen, “Wavelength selective nanophotonics components utilizing channel plasmon polaritons,” Nano Lett. 7, 880–884 (2007). [CrossRef] [PubMed]

16.

http://www.comsol.com/

17.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]

18.

S. H. Ko, I. Park, H. Pen, C. P. Gigoropoulos, A. P. Pisano, C. K. Luscombe, and J. M. Frechet, “Direct nanoimprinting of metal nanoparticles for nanoscale electronics fabrication,” Nano Lett. 7, 1869–1877 (2007). [CrossRef] [PubMed]

19.

H. L. Chen, S. Y. Chuang, H. C. Cheng, C. H. Lin, and T. C. Chu, “Directly patterning metal films by nanoimprint lithography with low-temperature and low-pressure,” Microelectron. Eng. 83, 893–896 (2006). [CrossRef]

OCIS Codes
(230.7380) Optical devices : Waveguides, channeled
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 15, 2007
Revised Manuscript: November 21, 2007
Manuscript Accepted: November 27, 2007
Published: November 29, 2007

Citation
Il-min Lee, Jaehoon Jung, Junghyun Park, Hwi Kim, and Byoungho Lee, "Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves," Opt. Express 15, 16596-16603 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16596


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References

  1. H. Rather, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  2. R. Zia, M. D. Selker, P. B. Catrysse, and M. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A 21, 2442-2446 (2004). [CrossRef]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003). [CrossRef] [PubMed]
  4. S. Kim, H. Kim, Y. Lim, and B. Lee, "Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings," Appl. Phys. Lett. 90, 051113 (2007). [CrossRef]
  5. 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]
  6. P. Berini, "Plasmon-polariton modes guided by a metal film of finite width," Opt. Lett. 24, 1011-1013 (1999). [CrossRef]
  7. L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 6645-6650 (2005). [CrossRef] [PubMed]
  8. I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002). [CrossRef]
  9. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]
  10. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laulet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006). [CrossRef] [PubMed]
  11. S. I. Bozhevolnyi, "Effective-index modeling of channel plasmon polaritons," Opt. Express 14, 9467-9476 (2006). [CrossRef] [PubMed]
  12. 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]
  13. G. Vernois and S. Fan, "Modes of subwavelength plasmonic slot waveguides," J. Lightwave Technol. 25, 2511-2521 (2007). [CrossRef]
  14. E. Feigenbaum and M. Orenstein, "Modeling of complementary (void) plasmon waveguiding," J. Lightwave Technol. 25, 2547-2562 (2007). [CrossRef]
  15. V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and W. Ebbesen, "Wavelength selective nanophotonics components utilizing channel plasmon polaritons," Nano Lett. 7, 880-884 (2007). [CrossRef] [PubMed]
  16. http://www.comsol.com/>
  17. A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005). [CrossRef]
  18. S. H. Ko, I. Park, H. Pen, C. P. Gigoropoulos, A. P. Pisano, C. K. Luscombe, and J. M. Frechet, "Direct nanoimprinting of metal nanoparticles for nanoscale electronics fabrication," Nano Lett. 7, 1869-1877 (2007). [CrossRef] [PubMed]
  19. H. L. Chen, S. Y. Chuang, H. C. Cheng, C. H. Lin, and T. C. Chu, "Directly patterning metal films by nanoimprint lithography with low-temperature and low-pressure," Microelectron. Eng. 83, 893-896 (2006). [CrossRef]

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