Abstract

We present a novel technique for vertical coupling of light guided by nanoscale plasmonic slot waveguides (PSWs). A triangularly-shaped plasmonic slot waveguide rotator is exploited to attain such coupling with a good efficiency over a wide bandwidth. Using this approach, light propagating in a horizontal direction is efficiently coupled to propagate in the vertical direction and vice versa. We also propose a power divider configuration to evenly split a vertically coupled light wave to two horizontal channels. A detailed parametric study of the triangular rotator is demonstrated with multiple configurations analyzed. This structure is suitable for efficient coupling in multilevel nano circuit environment.

© 2013 Optical Society of America

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  1. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
    [CrossRef]
  2. A. Biberman and K. Bergman, “Optical interconnection networks for high-performance computing systems,” Rep. Prog. Phys.75(4), 046402 (2012).
    [CrossRef] [PubMed]
  3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
    [CrossRef]
  4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
    [CrossRef] [PubMed]
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
    [CrossRef] [PubMed]
  6. I. Choi and Y. Choi, “Plasmonic nanosensors: review and prospect,” IEEE J. Sel. Top. Quantum Electron.18(3), 1110–1121 (2012).
    [CrossRef]
  7. M. H. El Sherif, O. S. Ahmed, M. H. Bakr, and M. A. Swillam, “Polarization-controlled excitation of multilevel plasmonic nano-circuits using single silicon nanowire,” Opt. Express20(11), 12473–12486 (2012).
    [CrossRef] [PubMed]
  8. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
    [CrossRef] [PubMed]
  9. P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
    [CrossRef]
  10. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 311102 (2005).
    [CrossRef]
  11. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005).
    [CrossRef] [PubMed]
  12. W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
    [CrossRef] [PubMed]
  13. M. A. Swillam and A. S. Helmy, “Feedback effects in plasmonic slot waveguides examined using a closed-form model,” IEEE Photon. Technol. Lett.24(6), 497–499 (2012).
    [CrossRef]
  14. M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
    [CrossRef]
  15. S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
    [CrossRef]
  16. F. D. T. D. Lumerical, Lumerical Soultions, Inc. http://www.lumerical.com
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  18. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
    [CrossRef]

2012 (4)

A. Biberman and K. Bergman, “Optical interconnection networks for high-performance computing systems,” Rep. Prog. Phys.75(4), 046402 (2012).
[CrossRef] [PubMed]

I. Choi and Y. Choi, “Plasmonic nanosensors: review and prospect,” IEEE J. Sel. Top. Quantum Electron.18(3), 1110–1121 (2012).
[CrossRef]

M. A. Swillam and A. S. Helmy, “Feedback effects in plasmonic slot waveguides examined using a closed-form model,” IEEE Photon. Technol. Lett.24(6), 497–499 (2012).
[CrossRef]

M. H. El Sherif, O. S. Ahmed, M. H. Bakr, and M. A. Swillam, “Polarization-controlled excitation of multilevel plasmonic nano-circuits using single silicon nanowire,” Opt. Express20(11), 12473–12486 (2012).
[CrossRef] [PubMed]

2010 (3)

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

2007 (1)

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
[CrossRef]

2006 (3)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

2005 (2)

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 311102 (2005).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2002 (1)

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

1999 (1)

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Ahmed, O. S.

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Bakr, M. H.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bergman, K.

A. Biberman and K. Bergman, “Optical interconnection networks for high-performance computing systems,” Rep. Prog. Phys.75(4), 046402 (2012).
[CrossRef] [PubMed]

Biberman, A.

A. Biberman and K. Bergman, “Optical interconnection networks for high-performance computing systems,” Rep. Prog. Phys.75(4), 046402 (2012).
[CrossRef] [PubMed]

Bowers, J. E.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Brongersma, M. L.

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Cai, W.

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Chen, A.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Choi, I.

I. Choi and Y. Choi, “Plasmonic nanosensors: review and prospect,” IEEE J. Sel. Top. Quantum Electron.18(3), 1110–1121 (2012).
[CrossRef]

Choi, Y.

I. Choi and Y. Choi, “Plasmonic nanosensors: review and prospect,” IEEE J. Sel. Top. Quantum Electron.18(3), 1110–1121 (2012).
[CrossRef]

Chuyanov, V.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Dagli, N.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Dalton, L. R.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

El Sherif, M. H.

El-Sayed, I. H.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
[CrossRef]

El-Sayed, M. A.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
[CrossRef]

Fan, S.

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 311102 (2005).
[CrossRef]

Garner, S. N.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Han, Z.

He, S.

Helmy, A. S.

M. A. Swillam and A. S. Helmy, “Feedback effects in plasmonic slot waveguides examined using a closed-form model,” IEEE Photon. Technol. Lett.24(6), 497–499 (2012).
[CrossRef]

Jain, P. K.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
[CrossRef]

Lee, S.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Liu, B.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Liu, L.

Okuno, Y.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Raburn, M.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Rauscher, K.

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Shin, W.

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

Steier, W. H.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Swillam, M. A.

M. H. El Sherif, O. S. Ahmed, M. H. Bakr, and M. A. Swillam, “Polarization-controlled excitation of multilevel plasmonic nano-circuits using single silicon nanowire,” Opt. Express20(11), 12473–12486 (2012).
[CrossRef] [PubMed]

M. A. Swillam and A. S. Helmy, “Feedback effects in plasmonic slot waveguides examined using a closed-form model,” IEEE Photon. Technol. Lett.24(6), 497–499 (2012).
[CrossRef]

Veronis, G.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 311102 (2005).
[CrossRef]

Yacoubian, A.

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Adv. Mater. (1)

W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater.22(45), 5120–5124 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 311102 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. N. Garner, S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. H. Steier, and L. R. Dalton, “Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron.35(8), 1146–1155 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

M. Raburn, B. Liu, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, “3-D photonic circuit technology,” IEEE J. Sel. Top. Quantum Electron.8(4), 935–942 (2002).
[CrossRef]

I. Choi and Y. Choi, “Plasmonic nanosensors: review and prospect,” IEEE J. Sel. Top. Quantum Electron.18(3), 1110–1121 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. A. Swillam and A. S. Helmy, “Feedback effects in plasmonic slot waveguides examined using a closed-form model,” IEEE Photon. Technol. Lett.24(6), 497–499 (2012).
[CrossRef]

Mater. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Nano Today (1)

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today2(1), 18–29 (2007).
[CrossRef]

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (1)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmonic slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Rep. Prog. Phys. (1)

A. Biberman and K. Bergman, “Optical interconnection networks for high-performance computing systems,” Rep. Prog. Phys.75(4), 046402 (2012).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Other (2)

F. D. T. D. Lumerical, Lumerical Soultions, Inc. http://www.lumerical.com

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

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Figures (17)

Fig. 1
Fig. 1

A plasmonic slot waveguide (PSW).

Fig. 2
Fig. 2

The transmission efficiency at different points along the PSW.

Fig. 3
Fig. 3

The rectangular rotator.

Fig. 4
Fig. 4

The transmission (T) and reflection (R) of the rectangular rotator.

Fig. 5
Fig. 5

The right triangular PSW.

Fig. 6
Fig. 6

The TPSW in a vertical-to-horizontal light bending configuration with a monitor placed 400.0 nm from the straight waveguide edge and h = 400.0 nm

Fig. 7
Fig. 7

The transmission efficiency (T) and reflection (R) for the first configuration in Fig. 6. The width (w) of the TPSW is changed by moving the vertical plane containing the points 2 and 3. The width of the vertical waveguide and the height of the horizontal waveguide are kept fixed at 400.0 nm. The height of the triangular PSW is fixed at h = 400.0 nm.

Fig. 8
Fig. 8

The transmission efficiency for the second configuration in Fig. 6. The width (w) of the TPSW is changed using point 1 only while keeping the height h fixed at 400.0 nm. The width of the vertical waveguide and the height of the horizontal waveguide are kept at 400.0 nm. Points 2 and 3 are placed 100.0 nm to the right side of the vertical PSW.

Fig. 9
Fig. 9

The transmission efficiency (T) and reflection (R) for changing (h) with monitor 100 nm from the TPSW edge. The width of the vertical PSW is 400.0 nm while the width of the TPSW (w) is kept unchanged at 500.0 nm.

Fig. 10
Fig. 10

TPSW with the horizontal PSW height fixed at Hw = 400.0 nm, with monitor placed 100.0 nm from triangle edge.

Fig. 11
Fig. 11

The transmission efficiency (T) and reflection (R) for different (h). The horizontal PSW is fixed at a height Hw = 400.0 nm near the uppermost corner of the TPSW. The width of the vertical PSW is 400.0 nm while the width of the TPSW (w) is kept unchanged at 500.0 nm.

Fig. 12
Fig. 12

The transmission efficiency (T) for 200.0 nm horizontal and vertical PSWs and h = 200.0 nm and 300.0 nm.

Fig. 13
Fig. 13

The normalized transmission of the TPSW as compared to a straight PSW for different widths (w). The height of the TPSW (h) is fixed at 400.0 nm.

Fig. 14
Fig. 14

The light bending stair case structure.

Fig. 15
Fig. 15

The transmission and reflection of the stair case configuration as compared to the triangular section and rectangular section of the same dimensions.

Fig. 16
Fig. 16

Vertical power splitter/combiner.

Fig. 17
Fig. 17

Transmission (T) and reflection (R) for different (h2) of the triangular section power splitter.

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