Abstract

We study efficient injectors for coupling light from z-invariant ridge waveguides into slow Bloch modes of single-row defect photonic crystal waveguides. Two-dimensional vectorial computations performed with a Bloch mode theory approach predict that very high efficiencies (>90%) can be achieved for injector lengths of only a few wavelengths in length, even for small group velocities in the range of c100c400. This result suggests that photonic crystal devices operating with slow waves can be interfaced with classical waveguides without sacrificing compactness.

© 2007 Optical Society of America

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References

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2007 (4)

N. Ozaki, Y. Kitagawa, Y. Takata, N. Ikeda, Y. Watanabe, A. Mizutani, Y. Sugimoto, and K. Asakawa, Opt. Express 15, 6974 (2007).
[CrossRef]

G. Lecamp, J. P. Hugonin, and P. Lalanne, Opt. Express 15, 11042 (2007).
[CrossRef] [PubMed]

P. Velha, J. P. Hugonin, and P. Lalanne, Opt. Express 15, 6102 (2007).
[CrossRef] [PubMed]

P. Pottier, M. Gnan, and R. M. De La Rue, Opt. Express 15, 6569 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (5)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

G. Lecamp, P. Lalanne, J. P. Hugonin, and J. M. Gérard, IEEE J. Quant. Electron. 41, 1323 (2005).
[CrossRef]

X. Yang and C. W. Wong, Opt. Express 13, 4723 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, S. Johnson, and J. Joannopoulos, Opt. Express 13, 7145 (2005).
[CrossRef] [PubMed]

J. Khurgin, Opt. Lett. 30, 2778 (2005).
[CrossRef] [PubMed]

2004 (2)

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

IEEE J. Quant. Electron. (1)

G. Lecamp, P. Lalanne, J. P. Hugonin, and J. M. Gérard, IEEE J. Quant. Electron. 41, 1323 (2005).
[CrossRef]

Nat. Mater. (1)

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

Nature (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Phys. World (1)

T. F. Krauss, Phys. World 19(2), 32 (2006).

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Figures (3)

Fig. 1
Fig. 1

Interface between two PhCWs supporting slow (W1) and fast ( W ) Bloch modes at the same frequencies. (a) H y 2 distribution for λ = 1.615 μ m ( n g = 100 ) . The right inset is a cut of H y 2 on the waveguide z axis. (b) Dispersion diagram of the fundamental guided Bloch modes of the waveguides. The lines represents the air light lines of the two waveguides.

Fig. 2
Fig. 2

Performance of a two-cell injector heterostructure for coupling between fast and slow PhCW Bloch modes. (a) Sketch of the two-cell geometry. The background represents the H y 2 distribution calculated for an incident illumination from the fundamental W Bloch mode at λ = 1.615 μ m ( n g = 100 ) . (b) Tolerance of the coupling efficiency T as a function of the periods, a 1 and a 2 , of the injector for λ = 1.615 μ m ( n g = 100 ) . (c) Coupling efficiency as a function of the group index of the slow W1 PhC-Bloch mode. Solid curve, a 1 = 0.925 a and a 2 = 1.038 a ( n g = 100 ) , as marked with a star in (b); dotted curve, a 1 = 0.867 a and a 2 = 1.064 a ( n g = 100 ) ; dashed curve, abrupt interface ( a 1 = a 2 = a ) . The top horizontal scale represents the distance in GHz from the cutoff frequency, λ = 1.616 μ m .

Fig. 3
Fig. 3

Light injection from a z-invariant waveguide into a W1 slow Bloch mode. (a) Two-step injection geometry. N represents the number of periods of the fast PhCW W section. The superimposed background is defined as before. (b) Total coupling efficiency T t as a function of the group index of the slow PhC Bloch mode for different values of N, and for a 1 = 0.925 a and a 2 = 1.038 a [star in Fig. 2b]. Curve T represents the coupling efficiency between the ridge and the W waveguide, and the curve labeled direct coupling represents the coupling efficiency from the ridge waveguide to W1, a = a 1 = a 2 = a in (a).

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