Abstract

A compact beam splitter consisting of three branches of periodic dielectric waveguides (PDW) is designed and analyzed theoretically. Both the symmetrical and asymmetrical configurations of the beam splitter are studied. The band structure for the guided modes is calculated by using finite-difference time-domain (FDTD) method with Bloch-type boundary conditions applying in an appropriate supercell. The field patterns for the whole structure and the transmissions for the output ports are calculated using the multiple scattering method. By utilizing the co-directional coupling mechanism, the light injected into the input branch can be efficiently transferred into the two output branches if the phase matching conditions are satisfied. The coupling length is short and the broad-band requirement can be achieved. Bending loss is small and high transmission (above 95 %) can be preserved for arbitrarily bent PDW if the bend radius of each bend exceeds five wavelengths. This feature indicates that the periodic dielectric waveguide beam splitter (PDWBS) is a high efficiency device for power redistribution while avoiding the lattice orientation restriction of the photonic crystal waveguides (PCW).

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals-Molding the Flow of Light (Princeton University Press, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  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. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  4. S.-H. Fan, S. G. Johnson, J. D. Joannopoulos, G. Manoatou, and H. A. Haus, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B 18, 162-165 (2001).
    [CrossRef]
  5. S. Boscolo, M. Midrio, and T. F. Krauss, "Y junctions in photonic crystal channel waveguides: high transmission and impedance matching," Opt. Lett. 27, 1001-1003 (2002).
    [CrossRef]
  6. C. C. Chen, H. T. Chien, and P. G. Luan, "Photonic crystal beam splitter," Appl. Opt. 43, 6187, (2004).
    [CrossRef] [PubMed]
  7. S.-Y. Shi, A. Sharkawy, G.-H. Chen, D.M. Pustai, and D.W. Prather "Dispersion-based beam splitter in photonic crystal," Opt. Lett. 29, 617-619 (2004).
    [CrossRef] [PubMed]
  8. X.-F. Yu, and S.-H. Fan, "Bends and splitters for self-collimated beams in photonic crystal," Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
  9. S. G. Lee, S. S. Oh, J. E. Kim, H. Y. Parka, and C. S. Kee, "Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 181106 (2005).
    [CrossRef]
  10. P. Pottier, S. Mastroiacovo, and R. M. D. L. Rue, "Power and polarization beam-splitters, mirrors, and integrated interferometers based on air-hole photonic crystals and lateral large index-contrast waveguides," Opt. Express 14, 5617-5633 (2006).
    [CrossRef] [PubMed]
  11. T. Liu, A. R. Zakharian,M. Fallahi, J. V. Moloney, andM.Mansuripur, "Multimode Interference-Based Photonic Crystal Waveguide Power Splitter," J. Lightwave Technol. 22, 2842-2846 (2004).
    [CrossRef]
  12. N. Yamamoto, T. Ogawa, and K. Komori, "Photonic crystal directional coupler switch with small switching length and bandwidth," Opt. Express 14, 1223-1229 (2006).
    [CrossRef] [PubMed]
  13. P. G. Luan, and K. D. Chang, "Transmission characteristics of finite periodic dielectric waveguides," Opt. Express 14, 3263-3272 (2006).
    [CrossRef] [PubMed]
  14. A. Yariv, P. Yeh, Optical Waves in Crystals (John Wiley & Sons, New York, 1984).
  15. Y. Y. Chen and Z. Ye, "Acoustic Attenuation by Two-Dimensional Arrays of Rigid Cylinders," Phys. Rev. Lett. 87, 1843011-4 (2001).
    [CrossRef]
  16. Y. Zhang and B.-J. Li, "Photonic crystal-based bending waveguides for optical interconnections," Opt. Express 14, 5723-5732 (2006).
    [CrossRef] [PubMed]

2006 (4)

2005 (1)

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

2004 (3)

2003 (1)

X.-F. Yu, and S.-H. Fan, "Bends and splitters for self-collimated beams in photonic crystal," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

2002 (1)

2001 (2)

S.-H. Fan, S. G. Johnson, J. D. Joannopoulos, G. Manoatou, and H. A. Haus, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B 18, 162-165 (2001).
[CrossRef]

Y. Y. Chen and Z. Ye, "Acoustic Attenuation by Two-Dimensional Arrays of Rigid Cylinders," Phys. Rev. Lett. 87, 1843011-4 (2001).
[CrossRef]

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Boscolo, S.

Chang, K. D.

Chen, C. C.

Chen, G.-H.

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chen, Y. Y.

Y. Y. Chen and Z. Ye, "Acoustic Attenuation by Two-Dimensional Arrays of Rigid Cylinders," Phys. Rev. Lett. 87, 1843011-4 (2001).
[CrossRef]

Chien, H. T.

Fallahi, M.

Fan, S.-H.

X.-F. Yu, and S.-H. Fan, "Bends and splitters for self-collimated beams in photonic crystal," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

S.-H. Fan, S. G. Johnson, J. D. Joannopoulos, G. Manoatou, and H. A. Haus, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B 18, 162-165 (2001).
[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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Haus, H. A.

Joannopoulos, J. D.

S.-H. Fan, S. G. Johnson, J. D. Joannopoulos, G. Manoatou, and H. A. Haus, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B 18, 162-165 (2001).
[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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

Kee, C. S.

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

Kim, J. E.

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

Komori, K.

Krauss, T. F.

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Lee, S. G.

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

Li, B.-J.

Liu, T.

Luan, P. G.

Manoatou, G.

Mastroiacovo, S.

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Midrio, M.

Moloney, J. V.

Ogawa, T.

Oh, S. S.

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

Pottier, P.

Prather, D.W.

Pustai, D.M.

Rue, R. M. D. L.

Sharkawy, A.

Shi, S.-Y.

Villeneuve, P. R.

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Yamamoto, N.

Ye, Z.

Y. Y. Chen and Z. Ye, "Acoustic Attenuation by Two-Dimensional Arrays of Rigid Cylinders," Phys. Rev. Lett. 87, 1843011-4 (2001).
[CrossRef]

Yu, X.-F.

X.-F. Yu, and S.-H. Fan, "Bends and splitters for self-collimated beams in photonic crystal," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Zakharian, A. R.

Zhang, Y.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

X.-F. Yu, and S.-H. Fan, "Bends and splitters for self-collimated beams in photonic crystal," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

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

J. Lightwave Technol. (1)

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

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

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. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Y. Y. Chen and Z. Ye, "Acoustic Attenuation by Two-Dimensional Arrays of Rigid Cylinders," Phys. Rev. Lett. 87, 1843011-4 (2001).
[CrossRef]

Other (3)

A. Yariv, P. Yeh, Optical Waves in Crystals (John Wiley & Sons, New York, 1984).

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

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

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 (8)

Fig. 1.
Fig. 1.

(Color on line) (a1) and (b1): The two kinds of multimode PDWs consisting of three rows of dielectric rods. The size of the supercells for calculating the band structures is a×14a. (a2) and (b2) are the calculated band structures of these two waveguides (Choosing Ly = 1.3a.). The mode patterns are shown in the insets.

Fig. 2.
Fig. 2.

The coupling length Lc for the two cases in Fig.1 as functions of frequency. The length unit is the lattice constant a. (a) and (b) correspond to the structures in Fig. 1(a1) and (a2), respectively.

Fig. 3.
Fig. 3.

(a) The structure of the PDWBS. It consists of an input waveguide, the coupling section (b), two S-shaped waveguides (c), and two output (straight) waveguides. The coupling section is denoted by the solid line rectangle in (a), and its length is Lc . The Pi and Pa,b are the input and output power evaluated at the planes indicated in the figure, respectively. The band radius is chosen as R = 19.1a and the bend angle θ is arbitrary.

Fig. 4.
Fig. 4.

(Color on line) The one-arm transmission spectrum for the symmetric PDWBS as function of splitting angle. The horizontal and vertical axes are the reduced frequency a/λ and the splitting angle θsp , respectively.

Fig. 5.
Fig. 5.

(Color on line) The transmission spectra Ta,b (ω) for the asymmetric configuration of the PDWBS as functions of θb , taking θa to be fixed. Here “a” and “b” stand for the Arm a and Arm b , respectively. For θa = 0°, the calculated Ta (ω) and Tb (ω) are plotted in (a1) and (b1). For θa = 90°, the results are plotted in (a2) and (b2).

Fig. 6.
Fig. 6.

(Color on line) The transmission Tb as function of θa and θb . The reduced frequency of the incident beam is a/λ = 0.219. The horizontal and vertical axes are θa and θb , respectively.

Fig. 7.
Fig. 7.

(Color on line) The field patterns for the symmetric (a) and asymmetric (b) PDWBS.

Fig. 8.
Fig. 8.

(Color on line) The field distribution (real part) around the coupling section of the symmetric PDWBS. This result is obtained by using the FDTD method. The structure and simulation parameters are the same as that used in Fig. 7(a).

Equations (1)

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

L c = π k 1 k 2 .

Metrics