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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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

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

2009

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

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

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

2004

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]

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]

2003

2002

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

2001

2000

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

1996

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

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.

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.

J. Opt. Soc. Am. A

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

Opt. Commun.

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

Phys. Rev. B

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Metrics