Abstract

Hybrid-mode waveguides consisting of a metal surface separated from a high index medium by a low index spacer have attracted much interest recently. Power is concentrated in the low index spacer region for this waveguide. Here we investigate the properties of the hybrid mode in detail and numerically demonstrate the possibility of realizing compact waveguide bends using this wave guiding scheme.

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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    [CrossRef]
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  7. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
    [CrossRef]
  8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. M. Yan and M. Qiu, “Compact optical waveguides based on hybrid index and surface-plasmon-polariton guidance mechanisms,” Act. Passive Electron. Compon. 52461, (2007).
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  12. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [CrossRef]
  13. M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
    [CrossRef]
  19. Electromagnetics Module User’s Guide (Comsol, 2007).
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  21. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer, Berlin, 1988).
  22. FDTD Solutions Reference Guide, (Lumerical Solutions, 2009).

2009 (2)

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
[CrossRef]

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009).
[CrossRef] [PubMed]

2008 (2)

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

2007 (2)

M. Yan and M. Qiu, “Compact optical waveguides based on hybrid index and surface-plasmon-polariton guidance mechanisms,” Act. Passive Electron. Compon. 52461, (2007).

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007).
[CrossRef] [PubMed]

2006 (4)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

2005 (3)

2003 (2)

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

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

1997 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Aussenegg, F. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Barnes, W. L.

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

Bartal, G.

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

Berini, P.

Boltasseva, A.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
[CrossRef]

Buckley, R.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Dai, D.

Dereux, A.

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

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Ditlbacher, H.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Drezet, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

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

Fan, S.

Freude, W.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
[CrossRef]

Fujii, M.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
[CrossRef]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

He, S.

Hohenau, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Homola, J.

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kjaer, K.

Kobayashi, T.

Krenn, J. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Larsen, M. S.

Leitner, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Leosson, K.

Leuthold, J.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
[CrossRef]

Morimoto, A.

Nikolajsen, T.

Oulton, R. F.

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Pile, D. F.

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Qiu, M.

M. Yan and M. Qiu, “Compact optical waveguides based on hybrid index and surface-plasmon-polariton guidance mechanisms,” Act. Passive Electron. Compon. 52461, (2007).

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Steinberger, B.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Stepanov, A. L.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

Takahara, J.

Taki, H.

Veronis, G.

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Yamagishi, S.

Yan, M.

M. Yan and M. Qiu, “Compact optical waveguides based on hybrid index and surface-plasmon-polariton guidance mechanisms,” Act. Passive Electron. Compon. 52461, (2007).

Zhang, X.

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Act. Passive Electron. Compon. (1)

M. Yan and M. Qiu, “Compact optical waveguides based on hybrid index and surface-plasmon-polariton guidance mechanisms,” Act. Passive Electron. Compon. 52461, (2007).

Anal. Bioanal. Chem. (1)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripe on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of sub-wavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. 21(6), 362–364 (2009).
[CrossRef]

J. Lightwave Technol. (1)

N. J. Phys. (1)

R. F. Oulton, G. Bartal, D. F. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008).
[CrossRef]

Nat. Photonics (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Nature (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Other (5)

M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” CLEO/QELS 2007, http://www.opticsinfobase.org/abstract.cfm?uri=CLEO-2007-JThD112 .

Electromagnetics Module User’s Guide (Comsol, 2007).

E. D. Palik, Handbook of optical constants of solids, (Academic Press, Inc. 1985).

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer, Berlin, 1988).

FDTD Solutions Reference Guide, (Lumerical Solutions, 2009).

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Figures (14)

Fig. 1
Fig. 1

Schematic of the infinite width hybrid waveguide and the coordinate system used.

Fig. 2
Fig. 2

Field intensity plots of hybrid mode for tspacer = 100 nm and thi = 60 nm, εspacer = 2, εhi = 12, εcover = 1 (a) magnetic field, Hx (b) electric field Ey and Ez (c) guided power for hybrid mode and SP mode at silver dielectric interface. All quantities are normalized.

Fig. 3
Fig. 3

Schematic of the two dimensional waveguide.

Fig. 4
Fig. 4

Effects of varying waveguide width and spacer height for h = 60 nm, (a) real part of effective mode index (b) propagation distance (μm) (c) mode size (μm).

Fig. 5
Fig. 5

Effects of varying waveguide width and spacer height for h = 100 nm, (a) real part of effective mode index (b) propagation distance (μm) (c) mode size (μm).

Fig. 6
Fig. 6

Normalized guided power density of the hybrid mode for the parameters mentioned in Table 2.

Fig. 7
Fig. 7

Dispersion of the proposed guide for waveguide dimensions mentioned in Table 2. (a) mode size (b) propagation distance and real part of effective mode index.

Fig. 8
Fig. 8

(a) Schematic of the two dimensional hybrid guide on SOI wafer (b) normalized guided power density for waveguide dimensions w/ = 100 nm, h/ = 60 nm, d / = 100 nm, H = 1 μm.

Fig. 9
Fig. 9

Variations of the hybrid mode characteristics with the permittivity of surrounding medium for waveguide dimensions mentioned in Table 2. (a) mode size (b) propagation distance and real part of effective mode index.

Fig. 10
Fig. 10

Variation of propagation distance for SP at silver-dielectric interface as a function of permittivity of the dielectric medium

Fig. 11
Fig. 11

Transmission through 90 degree bends for different bend radii for two different cover materials (a) air (b) silica. Spacer medium is silica for both straight and bend sections.

Fig. 12
Fig. 12

Ey field intensity for a 90 degree bend with bend radius 1.5 μm when cover medium is (a) air (b) silica. Spacer layer is silica for both straight and bend sections.

Fig. 13
Fig. 13

Transmission through 90 degree bend for different bend radii for two different cover materials (a) air (b) silica. Spacer is silicon nitride in bend and silica in straight sections.

Fig. 14
Fig. 14

Ey field intensity for a 90 degree bend with bend radius of 1.5 μm when cover medium is (a) air (b) silica. Spacer layer is silica nitride in bend and silica is straight sections.

Tables (2)

Tables Icon

Table 1 Effects of changing different dimensions on waveguide performance

Tables Icon

Table 2 Details of material properties and waveguide dimensions for the finite width hybrid waveguide

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

t × ( ε r i 1 t × H t ) t ( μ r i 1 t H t ) ( k 0 2 μ r i β 2 ) H t = 0
δ S P = 1 k 0 ( ε m + ε d ε m ε d ) 3 / 2 ( ε m ) 2 ε m

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