Abstract

We provide an improved surface-mode photonic crystal (PhC) T-junction waveguide, combine it with an improved PhC bandgap T-junction waveguide, and then provide an ultracompact 1×4 TM-polarized beam splitter. The energy is split equally into the four output waveguides. The maximal transmission ratio of each output waveguide branch equals 24.7%, and the corresponding total transmission ratio of the ultracompact 1×4 beam splitter equals 98.8%. The normalized frequency of maximal transmission ratio is 0.397(2πc/a), and the bandwidth of the ultracompact 1×4 TM-polarized beam splitter is 0.0106(2πc/a). To the best of our knowledge, this is the first time such a high-efficiency 1×4 beam splitter exploiting the nonradiative surface mode as a guided mode has been proposed. Although we only employed a 1×4 beam splitter, our design can easily be extended to other 1×n beam splitters.

© 2012 Optical Society of America

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  1. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
    [CrossRef]
  2. 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]
  3. S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
    [CrossRef]
  4. S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002).
    [CrossRef]
  5. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
    [CrossRef]
  6. S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
    [CrossRef]
  7. D. Y. Zhao and X. Y. Jiang, “Vertical surface emitting open coupled-cavities based on photonic crystal surface modes,” Appl. Optics 47, 1729–1733 (2008).
    [CrossRef]
  8. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  9. C. Manolatou, S. G. Johnson, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999).
    [CrossRef]
  10. S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
    [CrossRef]
  11. Q. Wang, L. L. Zhang, and Q. Li, “Beam splitting at the output of photonic crystal waveguides with discrete surface point defects,” Opt. Express 18, 24245–24257 (2010).
    [CrossRef]
  12. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
    [CrossRef]
  13. S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
    [CrossRef]
  14. B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
    [CrossRef]
  15. H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
    [CrossRef]
  16. W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. A 21, 289–295 (2004).
    [CrossRef]

2011 (1)

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

2010 (1)

2009 (1)

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

2008 (1)

D. Y. Zhao and X. Y. Jiang, “Vertical surface emitting open coupled-cavities based on photonic crystal surface modes,” Appl. Optics 47, 1729–1733 (2008).
[CrossRef]

2005 (3)

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
[CrossRef]

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

2004 (2)

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. A 21, 289–295 (2004).
[CrossRef]

2003 (1)

2002 (1)

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002).
[CrossRef]

2001 (1)

2000 (1)

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)

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

Chen, W.

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

Fan, S. H.

S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[CrossRef]

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002).
[CrossRef]

S. H. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[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]

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

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

García-Vidal, F. J.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Haus, H. A.

Jensen, J. S.

Jia, W.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Jiang, B.

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

Jiang, L. Y.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Jiang, X. Y.

D. Y. Zhao and X. Y. Jiang, “Vertical surface emitting open coupled-cavities based on photonic crystal surface modes,” Appl. Optics 47, 1729–1733 (2008).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kim, J. E.

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Kim, W. J.

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. A 21, 289–295 (2004).
[CrossRef]

Kivshar, Y. S.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

Lee, S. G.

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Li, H. P.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Li, Q.

Li, X. Y.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Liu, A. J.

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

Manolatou, C.

Martín-Moreno, L.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

Moreno, E.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Morrison, S. K.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

O’Brien, J. D.

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. A 21, 289–295 (2004).
[CrossRef]

Oh, S. S.

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Parka, H. Y.

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

Qiang, H. X.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Sigmund, O.

Suh, W.

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]

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

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[CrossRef]

Wang, Q.

Zhang, L. L.

Zhao, D. Y.

D. Y. Zhao and X. Y. Jiang, “Vertical surface emitting open coupled-cavities based on photonic crystal surface modes,” Appl. Optics 47, 1729–1733 (2008).
[CrossRef]

Zheng, W. H.

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

Zhou, W. J.

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

Appl. Optics (1)

D. Y. Zhao and X. Y. Jiang, “Vertical surface emitting open coupled-cavities based on photonic crystal surface modes,” Appl. Optics 47, 1729–1733 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002).
[CrossRef]

S. G. Lee, S. S. Oh, J. E. Kim, and H. Y. Parka, “Line-defect-induced bending and splitting of self-collimated beams in two dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[CrossRef]

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. A 21, 289–295 (2004).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

B. Jiang, A. J. Liu, W. Chen, W. J. Zhou, and W. H. Zheng, “The optimization of large gap—midgap ratio photonic crystal with improved bisection-particle swarm optimization,” Opt. Commun. 284, 226–230 (2011).
[CrossRef]

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282, 3012–3017(2009).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (3)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. B 77, 3787–3790 (1996).
[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]

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Other (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (6)

Fig. 1.
Fig. 1.

(a) SMW1 T-junction waveguide. (b) 1a×20a supercell. (c) Surface mode (9×supercell, nine repetitious periods in the x direction). (d) Dispersion relation curves of the surface modes for the different radii of surface rods.

Fig. 2.
Fig. 2.

(a) 1×9 supercell of the straight PhC waveguide. (b) Band structure of the straight PhC waveguide. The bandgap of the periodic PhC ranges from 0.28602(2πc/a) to 0.42073(2πc/a).

Fig. 3.
Fig. 3.

(a) SMW1 T-junction waveguide. (b) Schematic model of the SMW1 T-junction waveguide using the coupled-mode theory. (c) PhC T-junction waveguide. (d) Schematic model of the PhC T-junction waveguide using the coupled-mode theory.

Fig. 4.
Fig. 4.

(a) Improved SMW1 T-junction waveguide. (b) Transmission ratios of the original SMW1 T-junction waveguide (lower red curve) and the improved SMW1 T-junction waveguide (upper black curve). (c) Improved PhC T-junction waveguide. (d) Transmission ratios of the traditional PhC T-junction waveguide (lower red curve) and the improved PhC T-junction waveguide (upper black curve).

Fig. 5.
Fig. 5.

(a) The ultracompact 1×4 beam splitter. (b) Transmission ratio of the ultracompact 1×4 beam splitter.

Fig. 6.
Fig. 6.

The steady-state field distribution of the improved 1×4 beam splitter with frequency 0.397(2πc/a).

Equations (4)

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

dFdt=iω0Fn=14F/τn+n=132τnsn+sn=sn++2τiF.
R(ω)==|s1|2|s1+|2=(ωω0)2+(1τ1n=241τn)2(ωω0)2+(1τ1+n=241τn)2,T12==|s2|2|s1+|2=4τ1τ2(ωω0)2+(1τ1+n=241τn)2,T13==|s3|2|s1+|2=4τ1τ3(ωω0)2+(1τ1+n=241τn)2,T14==|s4|2|s1+|2=4τ1τ4(ωω0)2+(1τ1+n=241τn)2.
1/τ1=1/τ2+1/τ3+1/τ4=2/τ2+1/τ4.
1/τ1=1/τ2+1/τ3.

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