Abstract

We theoretically investigate waveguide power splitters with parallel output ports by the time-domain coupled-mode theory. Conditions for perfect transmission and zero reflection are obtained that are different from the idea of a structure with a perfect T-type branch and two perfect bends. Using theoretical analysis, waveguide power splitters in two-dimensional square-lattice photonic crystals are modeled and optimized. Their transmission properties are simulated by using the finite-difference time-domain method, and an excellent agreement has been found with the present analysis.

© 2009 Optical Society of America

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References

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  1. A. Mekis, J. C. Chen, I. Kurland, S. 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]
  2. S. G. Johson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23, 1855-1857 (1998).
    [CrossRef]
  3. S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162-165 (2001).
    [CrossRef]
  4. S. Kim, I. Park, and H. Lim, “Proposal for ideal 3-dB splitters-combiners in photonic crystals,” Opt. Lett. 30, 257-259 (2005).
    [CrossRef] [PubMed]
  5. S. Boscolo and M. Midrio, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching,” Opt. Lett. 27, 1001-1003 (2002).
    [CrossRef]
  6. T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
    [CrossRef]
  7. I. Park, H.-S. Less, H.-J. Kim, K.-M. Moon, S.-G. Lee, B.-H. O, S.-G. Park, and E. -H. Lee, “Photonic crystal power-splitter based on directional coupling,” Opt. Express 12, 3599-3604 (2004).
    [CrossRef] [PubMed]
  8. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  9. C. Manolatou, S. G. Johson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682-1692 (1999).
    [CrossRef]
  10. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1999).
    [CrossRef]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).
  12. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972-2974 (2006).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2004 (2)

I. Park, H.-S. Less, H.-J. Kim, K.-M. Moon, S.-G. Lee, B.-H. O, S.-G. Park, and E. -H. Lee, “Photonic crystal power-splitter based on directional coupling,” Opt. Express 12, 3599-3604 (2004).
[CrossRef] [PubMed]

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

2002 (1)

2001 (1)

1999 (2)

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

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1999).
[CrossRef]

1998 (1)

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. 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]

Bermel, P.

Boscolo, S.

Burr, G.

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. 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]

Fallahi, M.

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

Fan, S.

Farjadpour, A.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).

Haus, H. A.

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Johson, S. G.

Kim, H.-J.

Kim, S.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. 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, E. -H.

Lee, S.-G.

Less, H.-S.

Lim, H.

Liu, T.

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

Manolatou, C.

Mansuripur, M.

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. 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.

Moon, K.-M.

O, B.-H.

Park, I.

Park, S.-G.

Rodriguez, A.

Roundy, D.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1999).
[CrossRef]

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

S. G. Johson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23, 1855-1857 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. 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]

Zakharian, A. R.

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

J. Lightwave Technol. (2)

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. , 22, 2842-2846 (2004).
[CrossRef]

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

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

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. 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]

Other (2)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).

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

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Figures (5)

Fig. 1
Fig. 1

Schematic of theoretical model for waveguide splitter. The black regions represent the waveguides and the white circles represent the resonator.

Fig. 2
Fig. 2

Top panel: Schematic view of the 201 a × 25 a computational cell, where cavity A 1 is located in the center. The field amplitude is monitored at points A and B, which are placed in the input and output guides of the splitter, respectively. The distance between the two output waveguides is 6 a . Bottom panel: Field amplitude recorded at points A and B as a function of time. The pulses reflected by and transmitted through the splitter as well as the pulses reflected from the edges of the cell are easily discernible.

Fig. 3
Fig. 3

Transmission coefficients for the power splitter shown in the top panel of Fig. 2. The inset is the spectral profile of three input pulses.

Fig. 4
Fig. 4

(a) Structure of the power splitter with d = 3 a . (b) Transmission spectra calculated by the finite-different time-domain method. The inset is the electric field distribution at frequency ω 0 = 0.393 ( 2 π c a ) . The electric field is polarized along the axis of dielectric columns.

Fig. 5
Fig. 5

(a) Structure of the power splitter with d = 4 a in two-dimensional photonic crystals made from a square lattice. (b) Transmission spectra calculated by the finite-different time-domain method. Solid line for the structure with r c = 0.20 a , r x = 0.055 a ; dashed line for the structure r c = 0.235 a , r x = 0.0 .

Equations (10)

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d a 1 d t = j ω 1 a 1 ( 1 τ 11 + 2 τ 12 ) a 1 + ( S + 11 2 τ 11 + 2 S + 12 2 τ 12 ) ,
d a 2 d t = j ω 2 a 2 ( 1 τ 21 + 1 τ 22 ) a 2 + S + 21 2 τ 21 ,
S i j = S + i j + 2 τ i j a i .
β d = n π
R = | S 11 S + 11 | 2 = ( ω ω 0 ) 2 + ( 1 τ 1 2 τ 2 ) 2 ( ω ω 0 ) 2 + ( 1 τ 1 + 2 τ 2 ) 2 ,
T = | S 22 S + 11 | 2 = 4 τ 1 τ 2 ( ω ω 0 ) 2 + ( 1 τ 1 + 2 τ 2 ) 2 ,
ω 0 = τ 12 ω 1 + 2 τ 21 ω 2 τ 12 + 2 τ 21 ,
1 τ 1 = τ 12 τ 11 1 τ 12 + 2 τ 21 ,
1 τ 2 = 1 τ 12 + 2 τ 21 .
1 τ 11 = 2 τ 12 ,

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