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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 3 — Feb. 5, 2007
  • pp: 1211–1221
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Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides

Georgios Veronis and Shanhui Fan  »View Author Affiliations


Optics Express, Vol. 15, Issue 3, pp. 1211-1221 (2007)
http://dx.doi.org/10.1364/OE.15.001211


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Abstract

We theoretically investigate the properties of compact couplers between high-index contrast dielectric slab waveguides and two-dimensional metal-dielectric-metal subwavelength plasmonic waveguides. We show that a coupler created by simply placing a dielectric waveguide terminated flat at the exit end of a plasmonic waveguide can be designed to have a transmission efficiency of ~70% at the optical communication wavelength. We also show that the transmission efficiency of the couplers can be further increased by using optimized multisection tapers. In both cases the transmission response is broadband. In addition, we investigate the properties of a Fabry-Perot structure in which light is coupled in and out of a plasmonic waveguide sandwiched between dielectric waveguides. Finally, we discuss potential fabrication processes for structures that demonstrate the predicted effects.

© 2007 Optical Society of America

1.Introduction

Because of the predicted attractive properties of MDM waveguides, people have started to explore such structures experimentally. In particular, Dionne et al. [15

15. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6,1928–1932 (2006). [CrossRef] [PubMed]

] have recently demonstrated waveguiding in a quasi-two-dimensional MDM geometry experimentally, showing clear evidence of a subwavelength guided mode with substantial propagation distances. With this as a background, it is important to explore the coupling of a dielectric slab waveguide into such a quasi-two-dimensional MDM geometry.

The remainder of the paper is organized as follows. In Section 2 we describe the simulation methods used for the analysis of the coupler structures. The results obtained using these methods for the various coupler designs are presented in Section 3. Finally, our conclusions are summarized in Section 4.

2. Simulation method

We use a two-dimensional finite-difference frequency-domain (FDFD) method [19

19. S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19,2018–2029 (2002). [CrossRef]

, 20

20. G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29,2288–2290 (2004). [CrossRef] [PubMed]

] to theoretically investigate the properties of the couplers. This method allows us to directly use experimental data for the frequency-dependent dielectric constant of metals such as silver [21

21. Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1985).

], including both the real and imaginary parts, with no further approximation. Perfectly matched layer (PML) absorbing boundary conditions are used at all boundaries of the simulation domain [22

22. J. Jin, The Finite Element Method in Electromagnetics, (Wiley, New York, 2002).

]. Due to the rapid field variation at the metal-dielectric interfaces, a very fine grid resolution of ~1 nm is required at the metal-dielectric interfaces to adequately resolve the local fields. On the other hand, a grid resolution of ~λ/20 is sufficient in the dielectric waveguide regions of the simulation domain. For example the required grid size in air at λ0 =1.55 μm is ~77.5 nm which is almost two orders of magnitude larger than the required grid size at metal-dielectric interfaces. We therefore use a nonuniform orthogonal grid [23

23. A. Taflove, Computational Electrodynamics, (Artech House, Boston, 1995).

] to avoid an unnecessary computational cost. We found that by using such a grid our results are accurate to ~0.05%.

We also note that due to reciprocity [24

24. D. M. Pozar , Microwave Engineering, (Wiley, New York, 1998).

] the transmission efficiency from the dielectric to the plasmonic waveguide Tdp is equal to the transmission efficiency from the plasmonic to the dielectric waveguide Tpd. However the corresponding reflection coefficients Rdp and Rpd are not equal, since the power lost to radiation modes in the vacuum depends on whether the input waveguide is the dielectric or the plasmonic waveguide.

3.Results

Fig. 1. (a) Power transmission efficiency (blue line) of a coupler between a dielectric and a MDM waveguide as a function of the width of the plasmonic waveguide wp at λ0 =1.55 μm calculated using FDFD. The coupler, created by placing the dielectric waveguide terminated flat at the exit end of the MDM waveguide, is shown in the inset. Results are shown for wd = 300 nm. Also shown is the transmission efficiency, if the metal in the MDM waveguide is lossless (black line), or perfect electric conductor (red line). (b) Coupler reflection coefficients Rdp (blue line), and Rpd (red line) as a function of the width of the plasmonic waveguide wp. All other parameters are as in Fig. 1(a). Experimental data are used for the dielectric constant of the metal, including both the real and imaginary parts.

In general we found that for a given width of the subwavelength MDM waveguide wp, there is an optimum width of the dielectric waveguide wd which maximizes the transmission efficiency and vice versa. We also found that for a given wd the optimum wp is significantly smaller than wd. This is due to the fact that a subwavelength MDM waveguide collects light from an area significantly larger than its cross-sectional area [25

25. H. Henke, H. Fruchting, and R. Winz, “Diffraction by a flanged parallel-plate waveguide and a slit in a thick screen,” Radio Sci. 14,11–18 (1979). [CrossRef]

]. More precisely, the transmission cross section of a MDM waveguide (in the unit of length in two dimensions), defined as the transmitted power into the waveguide normalized by the incident plane wave power flux, is significantly larger than its geometric cross-sectional area. As an example, we found that the transmission cross section of a MDM waveguide with wp =50 nm is ~185 nm at λ0 =1.55 μm. On the other hand, the transmission cross section of dielectric waveguides is approximately equal to their geometrical area. For example, for a waveguide consisting of a silicon slab surrounded by air with wd =320 nm we found that the transmission cross section is ~340 nm at λ0 =1.55 μm.

Fig. 2. (a) Transmission efficiency as a function of ϵp for wp =50 nm. All other parameters are as in Fig. 1(a). Experimental data are used for the dielectric constant of the metal, including both the real and imaginary parts. (b) Transmission efficiency as a function of wd for wp =50 nm (blue line), wp =100 nm (red line). All other parameters are as in Fig. 1(a). Experimental data are used for the dielectric constant of the metal, including both the real and imaginary parts.

In Figs. 3(a) and 3(b) we show the profiles of the magnetic and electric field respectively for a coupler with wd =300 nm, wp =50 nm (Fig. 1(a)). The power is incident from the left so that the incident and reflected waves result in an interference pattern in the dielectric waveguide. We note that the electric field intensity is significantly enhanced in the MDM waveguide with respect to the dielectric waveguide, while similar enhancement is not observed for the magnetic field intensity. This can be understood if we note that from Maxwell’s equations we haveEy=1jωεHzx=γjωεHz, so that for the Poynting vector we have S=12Re(EyHz*)βωεHz2ωεβEy2, where γ = α + jβ is the propagation constant of the mode. Thus, for the magnetic field enhancement we have HzpHzp2~wdwpβdεdβpεp, while for the electric field enhancement we have EypEyp2~wpwpεdβdεpβp. The observed field enhancements (Fig. 3) are consistent with these relations.

As mentioned above, a simple coupler created by placing a dielectric waveguide terminated flat at the exit end of a MDM waveguide (inset of Fig. 1(a)), can be designed to have transmission efficiency of 68%. To further increase the transmission, we design a coupler consisting of a multisection taper shown in Fig. 4(a). Such tapers, consisting of a number of waveguide sections, have been used as couplers between dielectric waveguides with highly different widths [31

31. M. M. Spuhler, B. J. Offrein, G. L. Bona, R. Germann, I. Massarek, and D. Erni, “A very short planar silica spot-size converter using a nonperiodic segmented waveguide,” J. Lightwave Technol. 16,1680–1685 (1998). [CrossRef]

, 32

32. B. Luyssaert, P. Vandersteegen, D. Taillaert, P. Dumon, W. Bogaerts, P. Bienstman, D. Van Thourhout, V. Wiaux, S. Beckx, and R. Baets, “A compact photonic horizontal spot-size converter realized in silicon-on-insulator,” IEEE Photon. Technol. Lett. 17,73–75 (2005). [CrossRef]

, 33

33. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23,2462–2468 (2005). [CrossRef]

]. It has been shown theoretically and confirmed experimentally that they can be designed to have higher transmission efficiency than conventional tapers of the same length with linear or parabolic shapes [32

32. B. Luyssaert, P. Vandersteegen, D. Taillaert, P. Dumon, W. Bogaerts, P. Bienstman, D. Van Thourhout, V. Wiaux, S. Beckx, and R. Baets, “A compact photonic horizontal spot-size converter realized in silicon-on-insulator,” IEEE Photon. Technol. Lett. 17,73–75 (2005). [CrossRef]

, 33

33. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23,2462–2468 (2005). [CrossRef]

]. The coupler design used here consists of a number of dielectric waveguide and MDM waveguide sections. The widths of these sections are optimized using a genetic global optimization algorithm in combination with FDFD. More specifically, we use a microgenetic algorithm which has been shown to reach the near-optimal region much faster than large population genetic algorithms [34

34. K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proceedings of the SPIE 1196,289–296 (1989).

, 35

35. B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12,3313–3326 (2004). [CrossRef] [PubMed]

]. Using this approach we designed a coupler with 93% transmission efficiency for wd =300 nm, wp =50 nm at λ0 =1.55 μm. In this design we use 4 dielectric waveguide sections and 4 MDM waveguide sections. The lengths of all waveguide sections are li =50 nm. Their widths w 1,w 2,…,w 8 are optimized using the microgenetic algorithm, while the number of dielectric and MDM sections as well as their lengths are kept fixed during the optimization process. The designed coupler is extremely compact with a total length of 400 nm. The magnetic field profile for this optimized coupler design is shown in Fig. 4(b).

Fig. 3. (a) Profile of the magnetic field amplitude |H| for wd =300 nm, wp =50 nm (Fig. 1(a)). (b) Profile of the electric field amplitude |E| for wd =300 nm, wp =50 nm.

Both the simple coupler of Fig. 1(a) and the multisection taper of Fig. 4(a) were optimized at a single wavelength of λ0 =1.55 μm. In Fig. 5 we show the transmission efficiency of these couplers as a function of wavelength. We observe that in both cases the transmission efficiency is close to its maximum value in a broad range of wavelengths. This is due to the fact that in both cases the high transmission efficiency is not associated with any strong resonances. Similar broadband responses are observed in couplers between dielectric waveguides with highly different widths based on multisection tapers [32

32. B. Luyssaert, P. Vandersteegen, D. Taillaert, P. Dumon, W. Bogaerts, P. Bienstman, D. Van Thourhout, V. Wiaux, S. Beckx, and R. Baets, “A compact photonic horizontal spot-size converter realized in silicon-on-insulator,” IEEE Photon. Technol. Lett. 17,73–75 (2005). [CrossRef]

, 33

33. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23,2462–2468 (2005). [CrossRef]

], and in multisection impedance matching transformers used in microwave circuits [24

24. D. M. Pozar , Microwave Engineering, (Wiley, New York, 1998).

].

In Fig. 6(a) we show a Fabry-Perot cavity structure consisting of a MDM waveguide of length l sandwiched between two dielectric waveguides. In this structure light is coupled from the wavelength-sized input dielectric waveguide to a subwavelength MDM waveguide, and then coupled back to the output dielectric waveguide. We excite the fundamental TM mode in the input dielectric waveguide and measure the power coupled into the fundamental mode of the output dielectric waveguide. The transmission efficiency of this structure as a function of the length l of the MDM waveguide section is shown in Fig. 6(b). We observe oscillations typical in the response of a Fabry-Perot structure. Such a device could be potentially used in nonlinear or sensing applications in which the large field enhancement achieved at metal-dielectric interfaces of plasmonic waveguides is desirable. Light could be transfered on chip with low loss dielectric waveguides and coupled efficiently in and out of the plasmonic waveguide-based device.

Fig. 4. (a) Schematic of a coupler consisting of a multisection taper. (b) Profile of the magnetic field amplitude |H| of the optimized coupler design for wd =300 nm, wp =50 nm and 8 waveguide sections. The optimized widths of the dielectric waveguide sections are w 1 =420 nm, w 2 =440 nm, w 3 =440 nm, w 4 =340 nm, while the widths of the MDM waveguide sections are w 5 =330 nm, w 6 =40 nm, w 7 =40 nm, w 8 =120 nm.

We also theoretically investigated couplers between silica-silicon-silica dielectric slab waveguides and two-dimensional silver-silica-silver MDM plasmonic waveguides. We note that such a coupler device can be made by first fabricating the dielectric slab waveguide using a Separation by IMplantation of Oxygen (SIMOX) process [36

36. P. Koonath, K. Kishima, T. Indukuri, and B. Jalali, “Sculpting of three-dimensional nano-optical structures in silicon,” Appl. Phys. Lett. 83,4909–4911 (2003). [CrossRef]

, 37

37. P. Koonath, T. Indukuri, and B. Jalali, “Vertically-coupled micro-resonators realized using three-dimensional sculpting in silicon,” Appl. Phys. Lett. 85,1018–1020 (2004). [CrossRef]

]. Such a process enables the fabrication of silicon/silica waveguiding structures [36

36. P. Koonath, K. Kishima, T. Indukuri, and B. Jalali, “Sculpting of three-dimensional nano-optical structures in silicon,” Appl. Phys. Lett. 83,4909–4911 (2003). [CrossRef]

, 37

37. P. Koonath, T. Indukuri, and B. Jalali, “Vertically-coupled micro-resonators realized using three-dimensional sculpting in silicon,” Appl. Phys. Lett. 85,1018–1020 (2004). [CrossRef]

]. A portion of the dielectric slab waveguide can then be removed using lithography and etching processes. This step can then be followed by deposition of metal, oxide, and metal layers. Fig. 7 shows a schematic of the proposed structure. We found that if silica (Fig. 7) is used instead of air (Fig. 1) the calculated results for the transmission efficiency are qualitatively the same. We also found that for the simple coupler created by placing the dielectric waveguide terminated flat at the exit end of the MDM waveguide very similar high transmission efficiencies are achieved in both the air (Fig. 1) and silica (Fig. 7) cases at the optical communication wavelength.

Fig. 5. Transmission efficiency as a function of wavelength for the couplers of Fig. 1(a) (blue line) and Fig. 4(a) (red line). In both cases the coupler parameters were optimized at a single wavelength of λ0 =1.55 μm.
Fig. 6. (a) Schematic of a Fabry-Perot cavity structure consisting of a MDM waveguide sandwiched between two dielectric waveguides. (b) Transmission efficiency for the structure of Fig. 6(a) as a function of l at λ0 =1.55 μm. Results are shown for wd =300 nm, wp =50 nm.

4.Conclusions

Fig. 7. Schematic of a coupler structure in which a silica-silicon-silica dielectric slab waveguide is coupled to a two-dimensional silver-silica-silver MDM waveguide.

Acknowledgments

This research was supported by DARPA/MARCO under the Interconnect Focus Center and by AFOSR grant FA 9550-04-1-0437.

References and links

1.

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]

2.

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]

3.

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. 60,663–669 (2002). [CrossRef]

4.

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]

5.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2,229–232 (2003). [CrossRef] [PubMed]

6.

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

7.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182,539–554 (1969). [CrossRef]

8.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82,1158–1160 (2003). [CrossRef]

9.

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86,211101 (2005). [CrossRef]

10.

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30,3359–3361 (2005). [CrossRef]

11.

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

12.

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. 87,261114 (2005). [CrossRef]

13.

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]

14.

M. Lipson, “Guiding, modulating, and emitting light on Silicon - Challenges and opportunities,” J. Lightwave Technol. 23,4222–4238 (2005). [CrossRef]

15.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6,1928–1932 (2006). [CrossRef] [PubMed]

16.

P. Ginzburg, D. Arbel, and M. Orenstein, “Efficient coupling of nano-plasmonics to micro-photonic circuitry,” in Conference on Lasers and Electro-optics (Optical Society of America, 2005), paper CWN5.

17.

L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31,2133–2135 (2006). [CrossRef] [PubMed]

18.

M. Hochberg, T. Baehr-Jones, C. Walker, and A. Scherer, “Integrated plasmon and dielectric waveguides,” Opt. Express 12,5481–5486 (2004). [CrossRef] [PubMed]

19.

S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19,2018–2029 (2002). [CrossRef]

20.

G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29,2288–2290 (2004). [CrossRef] [PubMed]

21.

Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1985).

22.

J. Jin, The Finite Element Method in Electromagnetics, (Wiley, New York, 2002).

23.

A. Taflove, Computational Electrodynamics, (Artech House, Boston, 1995).

24.

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

25.

H. Henke, H. Fruchting, and R. Winz, “Diffraction by a flanged parallel-plate waveguide and a slit in a thick screen,” Radio Sci. 14,11–18 (1979). [CrossRef]

26.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83,2845–2848 (1999). [CrossRef]

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P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2,48–51 (2000). [CrossRef]

28.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175,265–273 (2000). [CrossRef]

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Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86,5601–5603 (2001). [CrossRef] [PubMed]

30.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90,213901 (2003). [CrossRef] [PubMed]

31.

M. M. Spuhler, B. J. Offrein, G. L. Bona, R. Germann, I. Massarek, and D. Erni, “A very short planar silica spot-size converter using a nonperiodic segmented waveguide,” J. Lightwave Technol. 16,1680–1685 (1998). [CrossRef]

32.

B. Luyssaert, P. Vandersteegen, D. Taillaert, P. Dumon, W. Bogaerts, P. Bienstman, D. Van Thourhout, V. Wiaux, S. Beckx, and R. Baets, “A compact photonic horizontal spot-size converter realized in silicon-on-insulator,” IEEE Photon. Technol. Lett. 17,73–75 (2005). [CrossRef]

33.

B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23,2462–2468 (2005). [CrossRef]

34.

K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proceedings of the SPIE 1196,289–296 (1989).

35.

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12,3313–3326 (2004). [CrossRef] [PubMed]

36.

P. Koonath, K. Kishima, T. Indukuri, and B. Jalali, “Sculpting of three-dimensional nano-optical structures in silicon,” Appl. Phys. Lett. 83,4909–4911 (2003). [CrossRef]

37.

P. Koonath, T. Indukuri, and B. Jalali, “Vertically-coupled micro-resonators realized using three-dimensional sculpting in silicon,” Appl. Phys. Lett. 85,1018–1020 (2004). [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:
Optics at Surfaces

History
Original Manuscript: November 6, 2006
Revised Manuscript: January 17, 2007
Manuscript Accepted: January 17, 2007
Published: February 5, 2007

Citation
Georgios Veronis and Shanhui Fan, "Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides," Opt. Express 15, 1211-1221 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1211


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References

  1. 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]
  2. 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]
  3. J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Nondiffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663-669 (2002). [CrossRef]
  4. 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]
  5. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003). [CrossRef] [PubMed]
  6. 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]
  7. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969). [CrossRef]
  8. K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003). [CrossRef]
  9. F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101 (2005). [CrossRef]
  10. G. Veronis and S. Fan, "Guided subwavelength plasmonic mode supported by a slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005). [CrossRef]
  11. L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 6645-6650 (2005). [CrossRef] [PubMed]
  12. 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, 261114 (2005). [CrossRef]
  13. 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]
  14. M. Lipson, "Guiding, modulating, and emitting light on Silicon - Challenges and opportunities," J. Lightwave Technol. 23, 4222-4238 (2005). [CrossRef]
  15. J. A. Dionne, H. J. Lezec, and H. A. Atwater, "Highly confined photon transport in subwavelength metallic slot waveguides," Nano Lett. 6, 1928-1932 (2006). [CrossRef] [PubMed]
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