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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 21 — Oct. 12, 2009
  • pp: 19033–19040
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Nanoplasmonic couplers and splitters

Rami A. Wahsheh, Zhaolin Lu, and Mustafa A. G. Abushagur  »View Author Affiliations


Optics Express, Vol. 17, Issue 21, pp. 19033-19040 (2009)
http://dx.doi.org/10.1364/OE.17.019033


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Abstract

In this paper, we present novel designs and analysis of ultra-compact couplers and 1 × 2 splitters based on plasmonic waveguides. Numerical simulation shows coupling efficiency up to 88% for the former one and 45% for each branch for the latter one. The proposed coupler design has the advantages of improving the alignment tolerance of the plasmonic waveguide with respect to the dielectric waveguide and broadening the spectrum response of the splitter.

© 2009 OSA

1. Introduction

It is necessary to use dielectric waveguides to connect the plasmonic devices to the light source and detector so that the propagation losses due to the metallic interaction are dramatically reduced. To achieve that, several different coupling methods have been proposed to increase the coupling efficiency from a dielectric waveguide into a plasmonic waveguide, such as direct coupling [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

], multi-section taper [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

], λ/4 coupler [7

7. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15(11), 6762–6767 (2007). [CrossRef] [PubMed]

], adiabatic tapered coupler [8

8. D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett. 89(4), 041111 (2006). [CrossRef]

], and nonadiabatic tapered coupler [8

8. D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett. 89(4), 041111 (2006). [CrossRef]

,9

9. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Express 31, 3288–3290 (2006).

]. Also, several different T- and Y-shaped splitters have been proposed [10

10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

14

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

]. Splitters are used in optical circuit elements and devices such as Mach-Zehnder interferometers (MZIs) [15

15. B. Wang and G. P. Wang, “Surface Plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Express 29, 1992–1994 (2004).

17

17. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. (to be published).

] because they are considered as the platform for the optical sensors. In Y-junctions, the radius of curvature plays an important role in reducing radiation losses and increasing the size of the fabricated devices [10

10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

,11

11. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24(1), 477–494 (2006). [CrossRef]

]. In T-junctions, the intersection area should be designed to increase the coupling efficiency and reduce back reflection. Coupling efficiency can be increased using a resonant cavity at the intersection area [12

12. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]

], using photonic crystal waveguides [13

13. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22(6), 1191–1198 (2005). [CrossRef]

], or using plasmonic waveguides [14

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

].

A recent numerical simulation demonstrated a coupling efficiency of 68% by directly coupling light from a 300 nm wide silicon waveguide into a 40 nm silver-air-silver plasmonic waveguide [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

]. Coupling efficiency was further improved to 93% by using a multi-section taper of a length of 400 nm, which was designed by a genetic global optimization algorithm and analyzed with a finite-difference frequency-domain methodology. In this work, we propose a direct yet efficient short plasmonic coupler of a length of 33 nm to increase the coupling efficiency between a silicon waveguide and a silver-air-silver plasmonic waveguide. Based on the coupler, we also propose a splitter that delivers light from a silicon waveguide into two plasmonic waveguides. To the best of our knowledge, this is the first time that one reports a 1 × 2 splitter from a silicon waveguide into two MDM plasmonic waveguides. The coupling efficiency and the spectrum response of both devices are investigated using the two- dimensional (2D) finite-difference time-domain method [18

18. A. Taflove, Computational Electrodynamics (Artech, Norwood, MA, 1995).

] with a uniform mesh size of 1 nm to accurately capture the change of the field at the interface between the dielectric and plasmonic waveguides. The fundamental transverse magnetic mode is excited in the single-mode dielectric waveguide and the transmitted power is measured by a power monitor that is placed close to the interface with the single-mode plasmonic waveguide [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

]. Then, the coupling efficiency is calculated by normalizing the transmitted power with respect to the input power. The perfectly matched layer is used to attenuate the field within its region without back reflection [19

19. J. P. Berenger, “A perfectly matched layer for the absorption for electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

]. The metal losses are included in our simulations and the relative permittivity of the silver at the free-space wavelength λo = 1.55 µm using the commercial software FullWAVE from RSOFT is −103.7 + 8.1j.

In order to validate our results, we started by simulating the structure proposed by Veronis and Fan [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

] and obtained the same coupling efficiency (68%) by directly coupling light from a 300 nm wide silicon waveguide into a 40 nm silver-air-silver plasmonic waveguide. By analyzing the numerical results, it is obvious that the light wave from the dielectric waveguide excites surface plasmon polaritons (SPPs) along the dielectric-plasmonic boundaries and the SPPs will be “funneled” into the MDM plasmonic waveguides. This funneling process can conceptually explain why light can be efficiently coupled from a large (300 nm) dielectric waveguide into a tiny (40 nm) dielectric slot MDM waveguide. Recently, we found that the coupling efficiency can be greatly improved simply by incorporating a rectangular air-gap (i.e., slot waveguide) and hence preventing transverse “funneling leakage” at the interface between the dielectric waveguide and the MDM plasmonic waveguide [20

20. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient couplers and splitters from dielectric waveguides to plasmonic waveguides”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FThS4. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2008-FThS4

]. Herein, we present the design steps and numerical results for the proposed air-gap couplers (AGCs) and splitters.

2. Air-gap coupler design

First, we consider an ultra-short matching rectangular AGC inside the plasmonic waveguide at the interface with silicon, as shown in Fig. 1(a)
Fig. 1 (a) Schematic of the basic proposed coupler (top view). (b) Coupling efficiency as a function of the coupler’s width W and length L. (c) Field distribution of the coupled light at λo = 1.55 µm for the air-gap coupler.
. In the 2D simulation, we varied the dimensions of the coupler and measured the corresponding coupling efficiency. The dependence of the coupling efficiency on the coupler’s width W and length L is shown in Fig. 1(b). We found that coupling efficiency had a maximum value when W matches the width of the silicon waveguide. In particular, the coupling efficiency is above 87.7% for 30 nm < L < 40 nm and is maximized for L = 33 nm (coupling efficiency = 88.1%). Tapering the edges of the rectangular AGC can further increase the coupling efficiency to 90% [20

20. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient couplers and splitters from dielectric waveguides to plasmonic waveguides”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FThS4. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2008-FThS4

], but doing so will also increase the fabrication complexity. In this work, we only consider the rectangular AGC and optimize its length as 40 nm to match that of the width of the plasmonic waveguide. The field distribution of the coupled light for the rectangular AGC is shown in Fig. 1(c).

Veronis and Fan [6

6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

] found that to maximize the coupling efficiency between the dielectric waveguide and the plasmonic waveguide, there is an optimal width of the dielectric waveguide for a given width of the plasmonic waveguide. As shown in Fig. 2
Fig. 2 Coupling efficiency for the basic structure [Fig. 1(c)] as a function of the dielectric waveguide’s width.
, the optimal width of the dielectric waveguide is 300 nm when the width of the plasmonic waveguide is 40 nm. We found that this dependency is broadened when using our proposed AGC. Increasing the size of the dielectric waveguide from 300 nm to 500 nm resulted in a decrease in the coupling efficiency by about 15% as opposed to 45% for the case without using the AGC.

In our couplers, the rectangular air-gap plays an important role in increasing both the coupling efficiency (as shown in Fig. 1) and improving the alignment tolerance of the plasmonic waveguide with respect to the dielectric waveguide (as shown in Figs. 3 and 4). To verify this, we made several additional simulations and found that without using the AGC the plasmonic mode was excited at the interface between metal and silicon that had a different mode size than that of the MDM waveguide. After using the AGC, the plasmonic mode size partially matched that of the MDM waveguide because the AGC formed a cavity between the metal and silicon, which enabled more power to couple into the MDM waveguide. When the AGC does not have the same width as that of the silicon waveguide, the SPP excitation starts from the area that is not covered with the AGC. Then the SPP is coupled inside the AGC and propagates towards the MDM waveguide and couples into the MDM waveguide, as shown in Fig. 5(a)
Fig. 5 The electric field distribution when (a) the width of the AGC does not match that of the silicon waveguide, (b) the width of the AGC matches that of the silicon waveguide and the MDM waveguide is at the center, and (c) the width of the AGC matches that of silicon waveguide and the MDM waveguide is not at the center.
. When AGC covers the whole silicon area and the MDM waveguide is at the center, as shown in Fig. 5(b), the SPP excitation starts at an equal distance from the MDM waveguide and then is coupled into the MDM waveguide. When the MDM waveguide is not at the center, SPP excitation starts away from the MDM waveguide before it is coupled into the MDM waveguide [Fig. 5(c)]. This proves that the MDM waveguide introduces transverse metal boundaries that prevent the transverse leakage of SPPs and consequently increases the coupling efficiency.

We can further explain why one structure has higher coupling efficiency than another. For example, the coupling efficiency for the structure shown in Fig. 1(c) has the highest coupling efficiency (about 88%) because the SPP excitation starts at equidistance from both sides of the centered MDM waveguide and are “funneled” into the MDM waveguide. In another example, the coupling efficiency for the structure shown in Fig. 5(a) is less than that for the structure shown in Fig. 1(c) because part of the excited SPP propagates away from the AGC and also the excited SPP mode at the interface between silicon and metal travels towards the AGC, which has a different dielectric material (air). On the other hand, when the width of the AGC is higher than that of the silicon waveguide, the AGC does not act as a cavity because the bottom of the extra length is terminated by air and not by silicon. Thus, the coupling efficiency dropped dramatically.

3. Splitter design

In the first method, we designed a 3-dB splitter by increasing the separation distance g1 between the two MDM waveguides [as shown in Fig. 6(a)
Fig. 6 (a) Schematic of the splitter structure without the air-gap coupler. (b) Coupling efficiency as a function of the separation distance g1. (c) Field distribution for the structure shown in Fig. 6(a) for g1 = 160 nm.
] until maximum coupling is achieved. We found that the maximum coupling efficiency is about 37% for each branch when g1 = 160 nm, as shown in Figs. 6(b) and 6(c). This configuration has the advantage in easy fabrication.

The efficiency can be further increased using the air-gap coupler. In the second method, we designed a 3-dB splitter by increasing the separation distance g2 between the two MDM waveguides [as shown in Fig. 7(a)
Fig. 7 (a) Schematic of the splitter structure with the air-gap coupler. (b) Coupling efficiency as a function of the separation distance g2. (c) Field distribution for the structure shown in Fig. 7(a) for g2 = 260 nm.
] until maximum coupling is achieved. The increase in g2 was done after the addition of the rectangular AGC. We found that the maximum coupling efficiency is about 45% for each branch for g2 = 260 nm, as shown in Figs. 7(b) and 7(c). Over 90% of power in total can be delivered into two MDM plasmonic waveguides.

The splitting ratio can be easily controlled by the position of the MDM waveguides WR and WL, as shown in Fig. 8(a)
Fig. 8 (a) Schematic of the asymmetric splitter structure. (b) Coupling efficiency as a function of the displacement D2. (c) Field distribution for D2 = 150 nm.
. Before shifting WL, the displacement between the two waveguides was 260 nm, which resulted in a coupling efficiency of 45%. As expected, we found that as D2 increases, coupling efficiency into the shifted waveguide decreases and coupling efficiency into the fixed waveguide increases [as shown in Fig. 8(b)]. Figure 8(c) shows the coupling efficiency ratio between WL and WR for D2 = 150 nm. Even when there is no overlap between the shifted MDM waveguide and silicon waveguide, the coupled power is about 10% in WL.

Another way to control the splitting ratio is by varying the width of MDM waveguides W1 and W2, as shown in Fig. 9(a)
Fig. 9 (a) Schematic of the asymmetric splitter structure. (b) Coupling efficiency as a function of W2. (c) Field distribution for W2 = 100 nm and W1 = 40 nm.
. We found that as the width of W2 increases from 40 nm to 100 nm, the coupling efficiency in W2 increases slightly from 45% to 47%, while the coupling efficiency in a 40 nm wide W1 decreases from 45% to 28% [as shown in Fig. 9(b)]. The field distribution for W2 = 100 nm and W1 = 40 nm is shown in Fig. 9(c).

4. Spectrum analysis

The proposed couplers and splitters can also operate at a broad frequency range. To show that, we varied the wavelength of the light source and measured the corresponding coupling efficiency. The coupling efficiency with respect to wavelength for the structures shown in Figs. 1(c) (with and without AGC), 5(c), and 6(c) is shown in Fig. 10(a)
Fig. 10 Spectrum of the structures shown in Fig. 1(c) (with and without the AGC) and Figs. 5(c) and 6(c).
. Using AGC broadens the spectrum range around the communication wavelength 1.55 µm for all structures. Using two plasmonic waveguides in addition to AGC broadens the spectrum over longer range. The wavelength dependent of the permittivity of metal is not very clear because the coupling efficiency is measured close to the interface with silicon. If the coupling efficiency is measured far away from the interface, then it will be obvious that the losses of the metal increase significantly as the wavelength decreases.

5. Conclusions

To summarize, we showed that a matching coupler at the interface between a dielectric waveguide and a plasmonic waveguide can be designed to increase the coupling efficiency as well as the alignment tolerance when aligning a dielectric waveguide to a plasmonic waveguide. In addition, based on the efficient couplers, nano-scale plasmonic 1 × 2 splitters can be designed with a coupling efficiency of 45% for each branch that operates at the optical telecom wavelength. The splitting ratio can be controlled by varying either the relative position or width of the two branches. Finally, we investigated the spectrum of the proposed structures and found that using the air-gap coupler broadens the spectrum around the optical communication wavelength. Two potential applications of our proposed coupler and splitter: a directional coupler and a Mach-Zehnder interferometer are presented in [17

17. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. (to be published).

].

References and links

1.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

2.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. 21(12), 2442–2446 (2004). [CrossRef]

3.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

4.

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

5.

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, “Smallest possible electromagnetic mode volume in a dielectric cavity,” IEE Proc., Optoelectron. 145(6), 391–397 (1998). [CrossRef]

6.

G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]

7.

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15(11), 6762–6767 (2007). [CrossRef] [PubMed]

8.

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett. 89(4), 041111 (2006). [CrossRef]

9.

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Express 31, 3288–3290 (2006).

10.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

11.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24(1), 477–494 (2006). [CrossRef]

12.

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]

13.

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22(6), 1191–1198 (2005). [CrossRef]

14.

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

15.

B. Wang and G. P. Wang, “Surface Plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Express 29, 1992–1994 (2004).

16.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]

17.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. (to be published).

18.

A. Taflove, Computational Electrodynamics (Artech, Norwood, MA, 1995).

19.

J. P. Berenger, “A perfectly matched layer for the absorption for electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

20.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient couplers and splitters from dielectric waveguides to plasmonic waveguides”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FThS4. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2008-FThS4

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Integrated Optics

History
Original Manuscript: July 21, 2009
Revised Manuscript: September 14, 2009
Manuscript Accepted: September 22, 2009
Published: October 7, 2009

Citation
Rami A. Wahsheh, Zhaolin Lu, and Mustafa A. G. Abushagur, "Nanoplasmonic couplers and splitters," Opt. Express 17, 19033-19040 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19033


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References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  2. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. 21(12), 2442–2446 (2004). [CrossRef]
  3. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]
  4. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]
  5. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, “Smallest possible electromagnetic mode volume in a dielectric cavity,” IEE Proc., Optoelectron. 145(6), 391–397 (1998). [CrossRef]
  6. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15(3), 1211–1221 (2007). [CrossRef] [PubMed]
  7. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15(11), 6762–6767 (2007). [CrossRef] [PubMed]
  8. D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett. 89(4), 041111 (2006). [CrossRef]
  9. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Express 31, 3288–3290 (2006).
  10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]
  11. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24(1), 477–494 (2006). [CrossRef]
  12. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]
  13. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22(6), 1191–1198 (2005). [CrossRef]
  14. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]
  15. B. Wang and G. P. Wang, “Surface Plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Express 29, 1992–1994 (2004).
  16. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]
  17. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. (to be published).
  18. A. Taflove, Computational Electrodynamics (Artech, Norwood, MA, 1995).
  19. J. P. Berenger, “A perfectly matched layer for the absorption for electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]
  20. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient couplers and splitters from dielectric waveguides to plasmonic waveguides”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FThS4. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2008-FThS4

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