Abstract

Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.

© 2001 Optical Society of America

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References

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  1. M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
    [CrossRef]
  2. H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
    [CrossRef]
  3. A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
    [CrossRef]
  4. M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
    [CrossRef]
  5. H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
    [CrossRef]
  6. J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
    [CrossRef]
  7. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999).
    [CrossRef]
  8. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
    [CrossRef]
  9. J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals and lightwave devices using the scattering matrix method,” J. Lightwave Technol. 17, 1500–1508 (1999).
    [CrossRef]
  10. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  11. K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969).
  12. For a review, see K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993); and A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  13. J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microwave Opt. Technol. Lett. 10, 319–323 (1995).
    [CrossRef]

1999

1997

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

1996

A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
[CrossRef]

1995

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microwave Opt. Technol. Lett. 10, 319–323 (1995).
[CrossRef]

1994

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

1989

M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Agarwal, A. M.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Baba, T.

Chen, J. C.

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microwave Opt. Technol. Lett. 10, 319–323 (1995).
[CrossRef]

Cheng, R.-S.

H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
[CrossRef]

Chu, P. L.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

Fan, S.

C. Manolatou, S. G. Johnson, 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 (1997).
[CrossRef]

Foresi, J. S.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Hatami-Hanza, H.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

Haus, H. A.

Hu, M. H.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

Huang, J. Z.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

Ikeda, M.

Joannopoulos, J. D.

C. Manolatou, S. G. Johnson, 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 (1997).
[CrossRef]

Johnson, S. G.

Kawakami, S.

M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Kersten, P.

A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Klekaump, A.

A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
[CrossRef]

Lederer, M. J.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

Levy, M.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

Li, K.

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microwave Opt. Technol. Lett. 10, 319–323 (1995).
[CrossRef]

Liao, L.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Lim, D. R.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Lin, H.-B.

H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
[CrossRef]

Manolatou, C.

Minakata, M.

M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Osgood, R. M.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

Rangaraj, M.

M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Rehm, W.

A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
[CrossRef]

Scanrmozzino, R.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

Skinner, I. M.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

Su, J.-Y.

H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
[CrossRef]

Villeneuve, P. R.

C. Manolatou, S. G. Johnson, 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 (1997).
[CrossRef]

Wang, W.-S.

H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
[CrossRef]

Yonekura, J.

IEEE J. Quantum Electron.

H.-B. Lin, J.-Y. Su, R.-S. Cheng, and W.-S. Wang, “Novel optical single-mode asymmetric Y-branches for variable power splitting,” IEEE J. Quantum Electron. 35, 1092–1096 (1999).
[CrossRef]

IEEE Photonic Technol. Lett.

M. H. Hu, J. Z. Huang, R. Scanrmozzino, M. Levy, and R. M. Osgood, “A low-loss and compact waveguide Y-branch using refractive-index tapering,” IEEE Photonic Technol. Lett. 9, 203–205 (1997).
[CrossRef]

J. Lightwave Technol.

J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals and lightwave devices using the scattering matrix method,” J. Lightwave Technol. 17, 1500–1508 (1999).
[CrossRef]

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

M. Rangaraj, M. Minakata, and S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, and I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–214 (1994).
[CrossRef]

A. Klekaump, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996).
[CrossRef]

Microwave Opt. Technol. Lett.

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microwave Opt. Technol. Lett. 10, 319–323 (1995).
[CrossRef]

Nature

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

Proc. SPIE

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, “Small radius bends and large angle splitters in SOI waveguides,” Proc. SPIE 3007, 112–118 (1997).
[CrossRef]

Other

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

K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969).

For a review, see K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993); and A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the theoretical model for waveguide branches. The gray regions represent the waveguides, and the white circle represents a resonator. S+i and S-i are the input and output wave amplitudes at the ith port, respectively.

Fig. 2
Fig. 2

Prediction of the theoretical model as shown in Fig. 1, assuming that the wave is incident from port 1 and that the output ports are symmetric. Plotted here is the intensity-transmission coefficient into port 2, as a function of the ratio between the decay rates into the input and an output waveguide.

Fig. 3
Fig. 3

Top panel: Schematic view of the 140a×180a computational cell, where a is the lattice constant. The field amplitude is monitored at points A and B, which are placed in the input and output guides of the branch, respectively. The output guide is separated from the edge of the cell by ten periods of rods. Bottom panel: Field amplitude recorded at points A and B, as a function of time. The pulses reflected by and transmitted through the branch, as well as the pulses reflected from the edges of the cell, are easily discernible.

Fig. 4
Fig. 4

Intensity-transmission spectra through the waveguide branch shown in Fig. 3. The structure of the branching region is also shown in the inset.

Fig. 5
Fig. 5

Intensity-transmission spectra for waveguide-branch structures with (a) rt=0.03a, (b) rt=0.07a, and (c) rt=0.15a. The structures are shown in the inset of each panel. The rt denotes the radius of the smaller rods between the input and output waveguides.

Fig. 6
Fig. 6

Steady-state electric field distribution, at a frequency ω=0.41(2πc/a), for the waveguide-branch structures with rt=0.07a, as shown in Fig. 5(b). Red and blue represent large positive and negative fields, while white represents zero field.

Equations (11)

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

dadt=jω0a-ai1τi+iS+i2τi,
S-i=-S+i+2τia.
R=S-1S+12=-j(ω-ω0)+1τ1-1τ2-1τ3j(ω-ω0)+1τ1+1τ2+1τ32,
T2=S+2S+12=2τ1τ2j(ω-ω0)+1τ1+1τ2+1τ32,
T3=S+3S+12=2τ1τ3j(ω-ω0)+1τ1+1τ2+1τ32.
1τ1=1τ2+1τ3
S-=T·S+.
T=αβββαβββα,
|α|2+2|β|2=1,
|β|2+αβ*+α*β=0.
|α|2=11+8 cos2 φ19,

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