Abstract

Two orthogonal light polarizations in a waveguide overcoupled to microring resonators can propagate as fast and slow light. Which polarization is fast (slow) is determined by input polarization and the number of resonators.

© 2007 Optical Society of America

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  1. F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
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  2. Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
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  5. M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef] [PubMed]
  9. J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
    [CrossRef]

2007 (6)

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[CrossRef] [PubMed]

C. Fietz and G. Shvets, Opt. Lett. 32, 1683 (2007).
[CrossRef] [PubMed]

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C. Shih, Opt. Express 15, 7000 (2007).
[CrossRef] [PubMed]

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

2006 (4)

Q. Xu and M. Lipson, Opt. Lett. 31, 341 (2006).
[CrossRef] [PubMed]

G. Shvets and M. Tushentsov, J. Mod. Opt. 53, 2507 (2006).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803 (2006).
[CrossRef]

2004 (2)

A. A. S. L. Maleki, A. B. Matsko, and V. S. Ilchenko, Opt. Lett. 29, 626 (2004).
[CrossRef] [PubMed]

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

2003 (1)

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

2002 (1)

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

1999 (1)

1996 (1)

K. Ogusu, IEEE J. Quantum Electron. 32, 1537 (1996).
[CrossRef]

1982 (1)

Barwics, T.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Bianucci, P.

Boyd, R. W.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847 (1999).
[CrossRef]

Brunner, N.

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Chiao, R. Y.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Chodorow, M.

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Fietz, C.

Fietz, C. R.

Gisin, N.

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847 (1999).
[CrossRef]

Hickmann, J. M.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Ilchenko, V. S.

Ippen, E. P.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Kärtner, F. X.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Legré, M.

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Lipson, M.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[CrossRef] [PubMed]

Q. Xu and M. Lipson, Opt. Lett. 31, 341 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Maleki, A. A. S. L.

Manipatruni, S.

Matsko, A. B.

McCormick, C. F.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Mitsugi, S.

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803 (2006).
[CrossRef]

Morehead, J. J.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803 (2006).
[CrossRef]

Ogusu, K.

K. Ogusu, IEEE J. Quantum Electron. 32, 1537 (1996).
[CrossRef]

Popovic, M. A.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Rakich, P. T.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Robertson, J. W.

Ropers, C.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Scarani, V.

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Schmidt, B.

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Shakya, J.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Shaw, H. J.

Shih, C.

Shvets, G.

Smith, H. I.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Socci, L.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Solli, D. R.

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

Stokes, L. F.

Tushentsov, M.

G. Shvets and M. Tushentsov, J. Mod. Opt. 53, 2507 (2006).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Watts, M. R.

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Wegmuller, M.

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Xu, Q.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[CrossRef] [PubMed]

Q. Xu and M. Lipson, Opt. Lett. 31, 341 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

K. Ogusu, IEEE J. Quantum Electron. 32, 1537 (1996).
[CrossRef]

J. Mod. Opt. (2)

G. Shvets and M. Tushentsov, J. Mod. Opt. 53, 2507 (2006).
[CrossRef]

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Nat. Photonics (3)

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

T. Barwics, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (1)

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

D. R. Solli, C. F. McCormick, C. Ropers, J. J. Morehead, R. Y. Chiao, and J. M. Hickmann, Phys. Rev. Lett. 91, 143906 (2003).
[CrossRef] [PubMed]

N. Brunner, V. Scarani, M. Wegmuller, M. Legré, and N. Gisin, Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Fast–slow light setup: a square-cross-section (polarization degenerate) Si bus waveguide is horizontally coupled to a rectangular-cross-section (nondegenerate) Si microring resonator. Both the bus and the microring are embedded in Si O 2 . We operate at a frequency where only the vertical (TM) polarization of the waveguide is near resonance. The light entering through the bus is assumed to be in a mixed ( TE + TM ) polarization state, with the mixing angle θ.

Fig. 2
Fig. 2

Phase (dashed) and magnitude (solid) of the transmission coefficient for N microrings coupled to a single bus. Mixing angle θ = 30 ° ; ω is the frequency detuning from resonance. At resonance ( ω = 0 ) , the fast group delay for N = 2 is 58 ps with a bandwidth of 10 GHz , and the fast group delay for N = 4 is 54 ps with a bandwidth of 9 GHz .

Fig. 3
Fig. 3

Same as in Fig. 2, except θ = 60 ° . At resonance ( ω = 0 ) , the fast group delay for N = 1 (incoming polarization) is 2 ps with a bandwidth of 110 GHz , and the slow group delay for N = 2 (incoming polarization) is 58 ps with a bandwidth of 10 GHz .

Fig. 4
Fig. 4

Group delay, transmission, and bandwidth versus mixing angle θ. All numbers are at resonance ω = 0 . The behavior of the transmitted light is largely characterized by whether it passes by an even or odd number of rings.

Equations (2)

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T 1 = ( cos θ sin θ ) ( A N 0 0 1 ) ( cos θ sin θ ) = A N cos 2 θ + sin 2 θ ,
T 2 = ( cos ( θ + π 2 ) sin ( θ + π 2 ) ) ( A N 0 0 1 ) ( cos θ sin θ ) = sin 2 θ 2 ( 1 A N ) .

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