Abstract

By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates ε, the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2πε12 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well.

© 2009 Optical Society of America

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  1. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. A. Yariv and X. K. Sun, Opt. Express 15, 9147 (2007).
    [CrossRef] [PubMed]
  8. M. Galarza, D. Van Thourhout, R. Baets, and M. Lopez-Amo, Opt. Express 16, 8350 (2008).
    [CrossRef] [PubMed]
  9. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (2)

2007 (1)

2005 (1)

F. Xia, V. M. Menon, and S. R. Forrest, IEEE J. Sel. Top. Quantum Electron. 11, 17 (2005).
[CrossRef]

2003 (1)

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).
[CrossRef]

2002 (2)

T. Bakke, C. T. Sullivan, and S. D. Mukherjee, J. Lightwave Technol. 20, 1188 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

2001 (1)

S. R. Park and B. H. O, IEEE Photon. Technol. Lett. 13, 675 (2001).
[CrossRef]

1998 (1)

1997 (1)

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

1996 (1)

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

1994 (2)

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

1993 (1)

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

1991 (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

1986 (1)

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

1973 (1)

A. Yariv, IEEE J. Quantum Electron. 9, 919 (1973).
[CrossRef]

Baets, R.

Bakke, T.

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Billes, L.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

Burkhard, H.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Carenco, A.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Fiedler, F.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Forrest, S. R.

F. Xia, V. M. Menon, and S. R. Forrest, IEEE J. Sel. Top. Quantum Electron. 11, 17 (2005).
[CrossRef]

Galarza, M.

Gobel, R.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

Greus, C.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Hasumi, Y.

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

Hubner, B.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Janning, H.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Kasaya, K.

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

Kawano, K.

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

Kempf, B.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Kewitsch, A. S.

Kohtoku, M.

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

Kondo, S.

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

Kondo, Y.

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

Kuphal, E.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Lifante, G.

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).
[CrossRef]

Lopez-Amo, M.

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

Meichenin, D.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Menon, V. M.

F. Xia, V. M. Menon, and S. R. Forrest, IEEE J. Sel. Top. Quantum Electron. 11, 17 (2005).
[CrossRef]

Mersali, B.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Mitomi, O.

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

Mukherjee, S. D.

Naganuma, M.

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

Noguchi, Y.

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

O, B. H.

S. R. Park and B. H. O, IEEE Photon. Technol. Lett. 13, 675 (2001).
[CrossRef]

Okamoto, M.

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

Ougazzaden, A.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Park, S. R.

S. R. Park and B. H. O, IEEE Photon. Technol. Lett. 13, 675 (2001).
[CrossRef]

Rakuljic, G. A.

Ries, R.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Ronneberg, E.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Sekine, S.

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

Sigogne, D.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Simon, J. C.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

Sullivan, C. T.

Sun, X. K.

Takeuchi, H.

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

Valiente, I.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Van Thourhout, D.

Vassallo, C.

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

Vollrath, G.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Willems, P. A.

Xia, F.

F. Xia, V. M. Menon, and S. R. Forrest, IEEE J. Sel. Top. Quantum Electron. 11, 17 (2005).
[CrossRef]

Yariv, A.

Yoshimoto, N.

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

Zengerle, R.

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

Electron. Lett. (4)

K. Kasaya, Y. Kondo, M. Okamoto, O. Mitomi, and M. Naganuma, Electron. Lett. 29, 2067 (1993).
[CrossRef]

D. Sigogne, A. Ougazzaden, D. Meichenin, B. Mersali, A. Carenco, J. C. Simon, I. Valiente, C. Vassallo, and L. Billes, Electron. Lett. 32, 1403 (1996).
[CrossRef]

K. Kawano, M. Kohtoku, N. Yoshimoto, S. Sekine, and Y. Noguchi, Electron. Lett. 30, 353 (1994).
[CrossRef]

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

IEE Proc.-J: Optoelectron. (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc.-J: Optoelectron. 138, 343 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. 9, 919 (1973).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

B. Hubner, G. Vollrath, R. Ries, C. Greus, H. Janning, E. Ronneberg, E. Kuphal, B. Kempf, R. Gobel, F. Fiedler, R. Zengerle, and H. Burkhard, IEEE J. Sel. Top. Quantum Electron. 3, 1372 (1997).
[CrossRef]

F. Xia, V. M. Menon, and S. R. Forrest, IEEE J. Sel. Top. Quantum Electron. 11, 17 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. R. Park and B. H. O, IEEE Photon. Technol. Lett. 13, 675 (2001).
[CrossRef]

N. Yoshimoto, K. Kawano, Y. Hasumi, H. Takeuchi, S. Kondo, and Y. Noguchi, IEEE Photon. Technol. Lett. 6, 208 (1994).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Other (1)

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Model of the adiabatic mode transformer based on two coupled waveguides 1 and 2, placed in close proximity to each other. The geometry of waveguide 2 is gradually varied along the z direction. Light is coupled in at plane z = z i ( = 0 ) and out at plane z = z f . The modal profiles of the local modes e e and e o are listed at the input, phase-matching, and output planes.

Fig. 2
Fig. 2

Coupling efficiency as a function of the transformer length L ( = z f z i ) for devices designed with γ distributions of tan [ arcsin ( u ) ] , u, u 3 , and sin ( u ) . The optimal design with γ distributed with tan [ arcsin ( u ) ] has the smallest length to achieve the same level of adiabatic mode transformation.

Fig. 3
Fig. 3

Fraction of power in modes e e and e o along the + z direction in a 200 - μ m -long mode transformer with the optimal design. The equiripple behavior for both modes indicates the minimal power scattering.

Equations (11)

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

e e ( z ) = 1 2 ( 1 δ / S ) 1 2 ( 1 + δ / S ) 1 2 e i β e z = e ̃ e e i β e z ,
e o ( z ) = 1 2 ( 1 + δ / S ) 1 2 ( 1 δ / S ) 1 2 e i β o z = e ̃ o e i β o z ,
j = e , o [ ( z a j ) e ̃ j + a j ( z e ̃ j ) ] exp [ i 0 z β j ( z ) d z ] = 0 .
d a o d z = ( 1 4 i κ ( 1 + γ 2 ) 3 2 d γ d z ) d d z ( e 2 i S ¯ z ) ,
a o = ( 1 2 κ ( 1 + γ 2 ) 3 2 d γ d z ) e i S ¯ z sin ( S ¯ z ) ,
a o 1 2 κ ( 1 + γ 2 ) 3 2 d γ d z ,
1 2 κ ( 1 + γ 2 ) 3 2 d γ d z ε 1 2 .
γ = u 1 u 2 = tan [ arcsin ( u ) ] ,
d d z [ b 1 b 2 ] = [ i β 1 i κ i κ i β 2 ] [ b 1 b 2 ] C [ b 1 b 2 ] ,
[ b 1 ( z + Δ z ) b 2 ( z + Δ z ) ] = exp ( C ( z ) Δ z ) [ b 1 ( z ) b 2 ( z ) ] ,
C ( z ) = i β ¯ ( z ) I + i κ [ γ ( z ) 1 1 γ ( z ) ] ,

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