Abstract

The self-imaging effect based on symmetrical interference in multimode layer-by-layer photonic crystal waveguides (PhCWs), is numerically studied with finite-difference time-domain simulations. With the properties of twofold images, a kind of three-dimensional (3D) PhCW-based power splitters with an ultracompact size using complete photonic bandgaps is proposed, calculated, and analyzed. The presented structure can be extended for the design of M×N power splitters for 3D photonic integrated circuits applications.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. B.-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
    [CrossRef]
  7. H. J. Kim, I. Park, B. H. O, S. G. Park, E. H. Lee, and S. G. Lee, “Self-imaging phenomena in multi-mode photonic crystal line-defect waveguides: application to wavelength de-multiplexing,” Opt. Express 12, 5625–5633 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. P. Kohli, C. Christensen, and J. Muehlmeier, “Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities,” Appl. Phys. Lett. 89, 231103 (2006).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. T. B. Yu, Q. J. Wang, J. Zhang, J. Y. Yang, and S. F. Yu, “Ultracompact 2×2 photonic crystal waveguide power splitter based on self-imaging effect realized by asymmetrical interference,” IEEE Photon. Technol. Lett. 23, 1151–1153 (2011).
    [CrossRef]
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    [CrossRef]
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2011 (2)

S.-Y. Su, L. Tang, and T. Yoshie, “Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing,” Opt. Lett. 36, 2266–2268 (2011).
[CrossRef]

T. B. Yu, Q. J. Wang, J. Zhang, J. Y. Yang, and S. F. Yu, “Ultracompact 2×2 photonic crystal waveguide power splitter based on self-imaging effect realized by asymmetrical interference,” IEEE Photon. Technol. Lett. 23, 1151–1153 (2011).
[CrossRef]

2010 (4)

2009 (2)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

2008 (4)

T. Yu, H. Zhou, Z. Gong, J. Yang, X. Jiang, and M. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D 41, 095101 (2008).
[CrossRef]

R.-J. Liu, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103, 094514 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

R.-J. Liu, Z.-Y. Li, F. Zhou, and D.-Z. Zhang, “Waveguide coupler in three-dimensional photonic crystal,” Opt. Express 16, 5681–5688 (2008).
[CrossRef]

2006 (3)

2004 (2)

2003 (2)

B.-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

Z.-Y. Li, and K.-M. Ho, “Waveguides in three-dimensional layer-by-layer photonic crystals,” J. Opt. Soc. Am. B 20, 801–809 (2003).
[CrossRef]

2000 (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

1999 (1)

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75, 3739–3741 (1999).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[CrossRef]

1994 (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

1990 (1)

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef]

Asano, T.

B.-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Busch, K.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Cheng, B.-Y.

R.-J. Liu, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103, 094514 (2008).
[CrossRef]

Christensen, C.

P. Kohli, C. Christensen, and J. Muehlmeier, “Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities,” Appl. Phys. Lett. 89, 231103 (2006).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75, 3739–3741 (1999).
[CrossRef]

Essig, S.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Euser, T. G.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Fallahi, M.

Fan, S. H.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Feng, Z.-F.

R.-J. Liu, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103, 094514 (2008).
[CrossRef]

Fleming, J. G.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Freymann, G. V.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Gong, Z.

T. Yu, H. Zhou, Z. Gong, J. Yang, X. Jiang, and M. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D 41, 095101 (2008).
[CrossRef]

Gralak, B.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Ho, K.-M.

Imada, M.

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Ishizaki, K.

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

Jiang, X.

T. Yu, H. Zhou, Z. Gong, J. Yang, X. Jiang, and M. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D 41, 095101 (2008).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice (Kluwer Academic, 2002).

Johnson, S. G.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice (Kluwer Academic, 2002).

Kawashima, S.

Kim, H. J.

Kohli, P.

P. Kohli, C. Christensen, and J. Muehlmeier, “Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities,” Appl. Phys. Lett. 89, 231103 (2006).
[CrossRef]

Kristensen, M.

Kruger, A. C.

Ledermann, A.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Lee, E. H.

Lee, L. H.

Lee, S. G.

Li, B.

Li, Z.

Li, Z.-Y.

Liu, R.-J.

R.-J. Liu, Z.-Y. Li, F. Zhou, and D.-Z. Zhang, “Waveguide coupler in three-dimensional photonic crystal,” Opt. Express 16, 5681–5688 (2008).
[CrossRef]

R.-J. Liu, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103, 094514 (2008).
[CrossRef]

Liu, T.

Malureanu, R.

Mansuripur, M.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Molenaar, A. J.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Moloney, J. V.

Muehlmeier, J.

P. Kohli, C. Christensen, and J. Muehlmeier, “Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities,” Appl. Phys. Lett. 89, 231103 (2006).
[CrossRef]

Nakamori, T.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Noda, S.

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

B.-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75, 3739–3741 (1999).
[CrossRef]

O, B. H.

Okano, M.

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Ota, Y.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Park, I.

Park, S. G.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[CrossRef]

Polman, A.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Satpathy, S.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[CrossRef]

Song, B.-S.

B.-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Staude, I.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Su, S.-Y.

Suzuki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Takahashi, S.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Tang, L.

Thiel, M.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Vos, W. L.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

Wang, M.

T. Yu, H. Zhou, Z. Gong, J. Yang, X. Jiang, and M. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D 41, 095101 (2008).
[CrossRef]

Wang, Q. J.

T. B. Yu, Q. J. Wang, J. Zhang, J. Y. Yang, and S. F. Yu, “Ultracompact 2×2 photonic crystal waveguide power splitter based on self-imaging effect realized by asymmetrical interference,” IEEE Photon. Technol. Lett. 23, 1151–1153 (2011).
[CrossRef]

Wegener, M.

G. V. Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 2038–1052 (2010).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Yang, J.

T. Yu, H. Zhou, Z. Gong, J. Yang, X. Jiang, and M. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D 41, 095101 (2008).
[CrossRef]

Yang, J. Y.

T. B. Yu, Q. J. Wang, J. Zhang, J. Y. Yang, and S. F. Yu, “Ultracompact 2×2 photonic crystal waveguide power splitter based on self-imaging effect realized by asymmetrical interference,” IEEE Photon. Technol. Lett. 23, 1151–1153 (2011).
[CrossRef]

Yoshie, T.

Yu, S. F.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic diagram of 3D layer-by-layer photonic crystal. (b) Top view diagram of Y-type waveguide constructed by removing a middle part with a width wg from each single rectangular rod within a same layer.

Fig. 2.
Fig. 2.

Dispersive curves of Y-type photonic crystal waveguides shown in Fig. 1(b) for (a) wg=0.7a and (b) wg=3.2a. The insets show the supercell structures.

Fig. 3.
Fig. 3.

(a) Top view of a junction connecting a 3D PhCW for wg=0.7a and that for wg=3.2a. (b) Top view of 3D PhCW power splitter.

Fig. 4.
Fig. 4.

(a) Field and (b) Poynting distribution in the 3D junction shown in Fig. 3(a) within the guiding layer. (c) Poynting distribution in the proposed 3D PhCW-based power splitter within the guiding layer shown in Fig. 3(b). The working wavelength is 1.55 μm.

Fig. 5.
Fig. 5.

Transmittance of the two output ports in the 3D multimode photonic crystal waveguide-based power splitter shown in Fig. 3(b).

Tables (1)

Tables Icon

Table 1. Mode Properties of the Layer-by-Layer PhCW in Fig. 1(b) for wg=3.2a at the Working Frequency a/λ=0.4

Equations (1)

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L=2nπ/(k0k2)n=1,2,3,.

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