Abstract

In this Letter we employ the general coupled-mode equations of the nonlinear directional coupler and demonstrate that the switching characteristics of prototypical nonlinear racetrack-resonator structures may differ considerably from those obtained when the standard, generally incorrect, coupled-mode equations are used.

© 2012 Optical Society of America

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References

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    [CrossRef]

2009

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

2008

2007

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef]

2003

J. E. Heebner and R. W. Boyd, Proc. SPIE 4969, 185 (2003).

2002

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

2001

1997

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

1996

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

1991

1990

1988

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

1982

A. A. Maier, Sov. J. Quantum Electron. 12, 1490 (1982).
[CrossRef]

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[CrossRef]

Absil, P.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

Adachi, T.

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

Agrawal, G. P.

Aitchison, J. S.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Ankiewicz, A.

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

Assanto, G.

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Boyd, R. W.

J. E. Heebner and R. W. Boyd, Proc. SPIE 4969, 185 (2003).

Bristow, A. D.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Capmany, J.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Fraile-Pelaez, F. J.

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Grover, R.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, Proc. SPIE 4969, 185 (2003).

Ho, P.-T.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

Ibrahim, T.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

Imai, M.

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

Imai, Y.

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

Iyer, R.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[CrossRef]

Joannopoulos, J. D.

Johnson, F.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

Johnson, S. G.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Lin, Q.

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Maier, A. A.

A. A. Maier, Sov. J. Quantum Electron. 12, 1490 (1982).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Mookherjea, S.

Muriel, M. A.

Painter, O. J.

Schneider, M. A.

Smirl, A. L.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Takamatsu, K.

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Van, V.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

van Driel, H. M.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. D. Bristow, R. Iyer, J. S. Aitchison, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 90, 101112 (2007).
[CrossRef]

Electron. Comm. Jpn., Part II

M. Imai, T. Adachi, K. Takamatsu, and Y. Imai, Electron. Comm. Jpn., Part II 79, 32 (1996).

IEEE J. Quantum Electron.

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, IEEE J. Sel. Top. Quantum Electron. 8, 705 (2002).
[CrossRef]

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Nat. Photon.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

Proc. SPIE

J. E. Heebner and R. W. Boyd, Proc. SPIE 4969, 185 (2003).

Sov. J. Quantum Electron.

A. A. Maier, Sov. J. Quantum Electron. 12, 1490 (1982).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Electric field profile of the quasi-TM mode in (a) 2D and (c) 3D presentation, and (b) the add-drop filter structure showing its main dimensions.

Fig. 2.
Fig. 2.

Drop (solid blue) and through (dashed green) power outputs of the nonlinear add-drop, predicted using the inaccurate (left) and complete (right) equations for the NLDCs.

Fig. 3.
Fig. 3.

Power at the drop port when the device is operated out of resonance. The solid blue curve is obtained with the NLDCs described by the inaccurate equations, while the true bistable characteristic, obtained with Eqs. (1)–(2), is represented by the dashed green curve.

Equations (5)

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

ia=11N2[(MNG)aiα2(1N2)a+(GNM)b+(Q1NQ3)|a|2a+(Q2NQ3)(2a|b|2+b2a*)+(Q3NQ2)(2|a|2b+b*a2)+(Q3NQ1)|b|2b],
ib=same with{ba},
Q1=C1(ωc)234χ(3)Ea(b)4ds,
Q2=C1(ωc)234χ(3)Ea2Eb2ds,
Q3=C1(ωc)234χ(3)Eb(a)3Ea(b)ds.

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