Abstract

The feasibility of nanometric practical optical waveguide circuits based on surface plasmon polariton gap waveguides (SPGWs) is investigated in detail through three-dimensional simulations. H-plane planar branching waveguide circuits of subwavelength scale are shown to be possible using SPGWs. The waveguide characteristics of the circuits are found to be highly sensitive to the dimensions of the optical circuit, indicating that highly accurate computer-aided design and simulations are necessary for the construction of practical SPGW-based optical circuits.

© 2005 Optical Society of America

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References

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  1. C.  Manolatou, S. G.  Johnson, S.  Fan, P. R.  Villeneuve, H. A.  Haus, J. D.  Joannopoulos, “High-density integrated optics,” J. Lightwave Tech. 17, 1682–1692 (1999).
    [CrossRef]
  2. J. D.  Joannopoulos, R. D.  Meade, J. N.  Winn, Photonic Crystals, Princeton University Press (1995).
  3. J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
    [CrossRef]
  4. S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
    [CrossRef]
  5. T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
    [CrossRef]
  6. T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
    [CrossRef]
  7. H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
    [CrossRef]
  8. K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
    [CrossRef]
  9. K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits: Open-type surface plasmon polariton gap waveguide,” Jpn. J. Appl. Phys. 42, L585–L588 (2003).
    [CrossRef]
  10. E. K.  Miller, L.  Medgyesi-Mitschnag, E. H.  Newsman ed., Computational Electromagnetics Frequency-Domain Method of Moments, Institute of Electrical and Electronics Engineers, Inc. (1992).
  11. J. H.  Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations, (John Wiley & Sons, Inc. New York, 1991).
  12. P.  Zwamborn, P. M.  van den Berg, “The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems”, IEEE Trans on MTT 40, 1757–1766 (1992).
    [CrossRef]
  13. R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
    [CrossRef]

2004 (1)

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

2003 (2)

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

K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits: Open-type surface plasmon polariton gap waveguide,” Jpn. J. Appl. Phys. 42, L585–L588 (2003).
[CrossRef]

2002 (1)

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

2001 (2)

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
[CrossRef]

1999 (1)

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

1997 (1)

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

1992 (1)

P.  Zwamborn, P. M.  van den Berg, “The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems”, IEEE Trans on MTT 40, 1757–1766 (1992).
[CrossRef]

Atwater, H. A.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Aussenegg, F. R.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Barrett, R.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Berry, M.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Brongersma, M. L.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Chan, T. F.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Demmel, J.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Ditlbacher, H.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Donato, J.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Dongarra, J.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Eijkhout, V.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Fan, S.

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

Fukuda, H.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Goto, T.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Haus, H. A.

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

Joannopoulos, J. D.

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

J. D.  Joannopoulos, R. D.  Meade, J. N.  Winn, Photonic Crystals, Princeton University Press (1995).

Johnson, S. G.

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

Katagiri, Y.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Kik, P. G.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Kobayashi, I.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Kobayashi, T.

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Kourogi, M.

T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
[CrossRef]

Krenn, J. R.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Leitner, A.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Maier, S. A.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Manolatou, C.

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

Meade, R. D.

J. D.  Joannopoulos, R. D.  Meade, J. N.  Winn, Photonic Crystals, Princeton University Press (1995).

Meltzer, S.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Mitsuoka, Y.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Morimoto, A.

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Nakano, Y.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Ohtsu, M.

T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
[CrossRef]

Pozo, R.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Requicha, A. A. G.

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Romine, C.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Schider, G.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Shinojima, H.

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

Takahara, J.

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Taki, H.

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Tanaka, K.

K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits: Open-type surface plasmon polariton gap waveguide,” Jpn. J. Appl. Phys. 42, L585–L588 (2003).
[CrossRef]

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

Tanaka, M.

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

K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits: Open-type surface plasmon polariton gap waveguide,” Jpn. J. Appl. Phys. 42, L585–L588 (2003).
[CrossRef]

van den Berg, P. M.

P.  Zwamborn, P. M.  van den Berg, “The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems”, IEEE Trans on MTT 40, 1757–1766 (1992).
[CrossRef]

van der Vorst, H.

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

Villeneuve, P. R.

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

Wang, J. H.

J. H.  Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations, (John Wiley & Sons, Inc. New York, 1991).

Winn, J. N.

J. D.  Joannopoulos, R. D.  Meade, J. N.  Winn, Photonic Crystals, Princeton University Press (1995).

Yamagishi, S.

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Yatsui, T.

T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
[CrossRef]

Zwamborn, P.

P.  Zwamborn, P. M.  van den Berg, “The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems”, IEEE Trans on MTT 40, 1757–1766 (1992).
[CrossRef]

Adv. Mat. (1)

S. A.  Maier, M. L.  Brongersma, P. G.  Kik, S.  Meltzer, A. A. G.  Requicha, H. A.  Atwater, “Plasmonics - A route to nanoscale optical devices,” Adv. Mat. 13, 1501–1505 (2001).
[CrossRef]

Appl. Phys. Lett. (4)

T.  Yatsui, M.  Kourogi, M.  Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001).
[CrossRef]

T.  Goto, Y.  Katagiri, H.  Fukuda, H.  Shinojima, Y.  Nakano, I.  Kobayashi, Y.  Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84, 852–854 (2004).
[CrossRef]

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

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

IEEE Trans on MTT (1)

P.  Zwamborn, P. M.  van den Berg, “The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems”, IEEE Trans on MTT 40, 1757–1766 (1992).
[CrossRef]

J. Lightwave Tech. (1)

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

Jpn. J. Appl. Phys. (1)

K.  Tanaka, M.  Tanaka, “Simulations of nanometric optical circuits: Open-type surface plasmon polariton gap waveguide,” Jpn. J. Appl. Phys. 42, L585–L588 (2003).
[CrossRef]

Opt. Lett. (1)

J.  Takahara, S.  Yamagishi, H.  Taki, A.  Morimoto, T.  Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 4765–477 (1997).
[CrossRef]

Other (4)

J. D.  Joannopoulos, R. D.  Meade, J. N.  Winn, Photonic Crystals, Princeton University Press (1995).

R.  Barrett, M.  Berry, T. F.  Chan, J.  Demmel, J.  Donato, J.  Dongarra, V.  Eijkhout, R.  Pozo, C.  Romine, H.  van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
[CrossRef]

E. K.  Miller, L.  Medgyesi-Mitschnag, E. H.  Newsman ed., Computational Electromagnetics Frequency-Domain Method of Moments, Institute of Electrical and Electronics Engineers, Inc. (1992).

J. H.  Wang, Generalized Moment Method in Electromagnetics: Formulation and Computer Solution of Integral Equations, (John Wiley & Sons, Inc. New York, 1991).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of an subwavelength-scale H-plane planar optical circuit with SPGWs

Fig. 2.
Fig. 2.

Optical intensities for (a) two-port, (b) three-port, and (c) four-port circuits consisting of straight SPGWs. White rectangular the shows the region C x×C y shown in Fig. 1.

Fig. 3.
Fig. 3.

Optical intensities for (a) two-port, (b) three-port, and (c) four-port circuits with round structures. White rectangle indicates the region C x×C y in Fig. 1.

Fig. 4.
Fig. 4.

(a) Two-dimensional distribution of optical intensity on the plane indicated by the dotted line in Fig. 3 (c). (b) One-dimensional distribution. White rectangle in (a) denotes the region Cy ×Cz shown in Fig. 1.

Fig. 5.
Fig. 5.

Optical intensities for (a) k 0 h=1.0, (b) k 0 h=0.6, and (c) k 0 h=0.2, where h is the height of the ridge structure given by h=C z-g in Fig. 1. White rectangle indicates the region Cx ×Cy shown in Fig. 1.

Fig. 6.
Fig. 6.

Optical intensities for (a) k 0 g=0.3 (b), (b) k 0 g=0.2 and (c) k 0 g=0.1. White rectangle indicates the region Cx ×Cy in Fig. 1.

Fig. 7.
Fig. 7.

Optical intensities for (a) k 0 w=0.1, (b) k 0 w=0.2, and (c) k 0 w=0.4. White rectangle indicates the region Cx ×Cy in Fig. 1.

Fig. 8.
Fig. 8.

Optical intensities for an interrupted port. The white rectangle in (b) indicates the region Cx ×Cy in Fig. 1.

Fig. 9.
Fig. 9.

(a) Structure of seven-port branching circuit with k 0 w=0.1, k 0 g=0.1, and k 0 h=1.0. (b) Two-dimensional distribution of optical intensity. White rectangle in (b) indicates the region Cx ×Cy in Fig. 1.

Fig. 10.
Fig. 10.

One-dimensional distribution of optical intensities along the white broken line for seven-ports branching circuit in Fig. 9 (b).

Equations (3)

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E i ( x ) = D ( x ) ε r ( x ) ( k 0 2 + ) A ( x )
A ( x ) = ( 1 ε 0 ) V { [ ε r ( x ) ε 0 ] ε r ( x ) } G ( x x ) D ( x ) dv
G ( x x ) = exp ( j k 0 x x ) ( 4 π x x )

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