Abstract

Based on a series of 1x2 beam splitters, novel direct excitation of slow-light from input- to output-region in photonic crystal waveguides is investigated theoretically and experimentally. The study shows that the slow-light excitation provides over 50 nm bandwidth for TE-polarized light splitting between two output ports, and co-exists together with self-imaging leading to ~20 nm extra bandwidth. The intensity of the direct excitation is qualitatively explained by the overlap integral of the magnetic fields between the ground input- and excited output-modes. The direct excitation of slow light is practically lossless compared with transmission in a W1 photonic crystal waveguides, which broadens the application-field for slow-light and further minimizes the size of a 1x2 splitter.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (1)

2008 (3)

D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

2007 (1)

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

2006 (4)

Y. Zhang, Z. J. Li, and B. J. Li, “Multimode interference effect and self-imaging principle in two-dimensional silicon photonic crystal waveguides for terahertz waves,” Opt. Express 14(7), 2679–2689 (2006).
[CrossRef] [PubMed]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14(20), 9444–9450 (2006).
[CrossRef] [PubMed]

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

2005 (2)

A. Têtu, M. Kristensen, L. H. Frandsen, A. Harpøth, P. I. Borel, J. S. Jensen, and O. Sigmund, “Broadband topology-optimized photonic crystal components for both TE and TM polarizations,” Opt. Express 13(21), 8606–8611 (2005).
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005).
[CrossRef]

2004 (3)

2002 (1)

2001 (1)

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Baets, R.

Beckx, S.

Beggs, D. M.

Bogaerts, W.

Borel, P. I.

Boscolo, S.

Chong, H.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

De la Rue, R. M.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Dumon, P.

Fage-Pedersen, J.

Fallahi, M.

Fan, S. H.

Frandsen, L. H.

Gong, Z.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

Harpøth, A.

Haus, H. A.

Huang, S. Y.

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

Jensen, J. S.

A. Têtu, M. Kristensen, L. H. Frandsen, A. Harpøth, P. I. Borel, J. S. Jensen, and O. Sigmund, “Broadband topology-optimized photonic crystal components for both TE and TM polarizations,” Opt. Express 13(21), 8606–8611 (2005).
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005).
[CrossRef]

Jiang, X. Q.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kim, H. J.

Krauss, T. F.

Kristensen, M.

Krüger, A. C.

Lavrinenko, A. V.

Lee, H.

Lee, H. S.

Lee, S. G.

Li, B. J.

Li, W.

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

Li, Z. J.

Liao, Q. H.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

Liu, T.

Malureanu, R.

Manolatou, C.

Mansuripur, M.

McIntyre, D.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Midrio, M.

Moloney, J. V.

Moon, K. M.

O, B.-H.

O’Faolain, L.

O'Faolain, L.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Park, I.

Park, S.-G.

Shi, J. F.

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

Sigmund, O.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005).
[CrossRef]

A. Têtu, M. Kristensen, L. H. Frandsen, A. Harpøth, P. I. Borel, J. S. Jensen, and O. Sigmund, “Broadband topology-optimized photonic crystal components for both TE and TM polarizations,” Opt. Express 13(21), 8606–8611 (2005).
[CrossRef] [PubMed]

Têtu, A.

Thoms, S.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Thorhauge, M.

Wang, D. S.

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

Wang, M. H.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

White, T. P.

Wiaux, V.

Wouters, J.

Yang, J. Y.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

Yu, T. B.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

Yuan, X.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Zakharian, A. R.

Zhang, M.

Zhang, Y.

Zhou, H. F.

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

Zhuang, Y. X.

Electron. Lett. (2)

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005).
[CrossRef]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A, Pure Appl. Opt. 9(1), 37–42 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. D Appl. Phys. (1)

T. B. Yu, H. F. Zhou, Z. Gong, J. Y. Yang, X. Q. Jiang, and M. H. Wang, “Ultracompact multiway beam splitters using multiple coupled photonic crystal waveguides,” J. Phys. D Appl. Phys. 41(9), 095101 (2008).
[CrossRef]

Nat. Photonics (1)

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Opt. Eng. (1)

S. Y. Huang, J. F. Shi, D. S. Wang, and W. Li, “Power splitters with different output power levels built with two-dimensional photonic crystals,” Opt. Eng. 45(2), 020503 (2006).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

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Figures (5)

Fig. 1
Fig. 1

Dispersion diagram for the even guided TE polarization of the PhCWs calculated using 3D PWE method, where the right axis shows the corresponding wavelength, λ, in free space for Λ = 380 nm. a) the single W1 PhCW, b) the triple multimode region, and c) the dual waveguide output. The super-cells are shown in the insets. The upper cyan shaded band indicates the region where the MMI self-imaging can occur in MMI region and the gray part represents the region where the novel excitation may happen.

Fig. 2
Fig. 2

(a)-(c) SEM micrographs of splitters with Ln = 0, 3 and 7Λ.

Fig. 3
Fig. 3

(a) Simulated normalized TE-polarized transmission by 3D FDTD for the splitters (b) measured normalized TE-polarized transmission for the splitters. Self-imaging excitation bands are shown highlighted with cyan pattern.

Fig. 4
Fig. 4

The transverse profile of the magnetic field Hy for the even modes in (a) the MMI region and (b) the input- and output-regions. The different frequencies are marked in Fig. 1(a)-(c).

Fig. 5
Fig. 5

The overlap integral of eigenmodes between the magnetic fields (Hz ) of the PhCW splitter input- and output- regions obtained from 2D PWE method for the modes shown in Fig. 1(a) and Fig. 1(c).

Equations (4)

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ψ ( x , z ) = c 0 ψ 0 ( x , z ) e j β 0 z + c 2 ψ 2 ( x , z ) e j β 2 z ,
L 0 = π | β 0 β 2 | ,
v g = d ϖ d k = c 0 n g ,
M ( λ ) = | H g * ( τ ) H e ( τ ) | d τ H g * ( τ ) H g ( τ ) d τ H e * ( τ ) H e ( τ ) d τ ,

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