Abstract

In this Letter we propose a rigorous and generalized approach for the design of integrated optical bent directional couplers (DCs) based on the coupled mode theory and super mode theory. The full vectorial finite-element method is used for the calculation of effective indices of optical modes propagating into the waveguides constituting the DCs. The flexibility and robustness of this general modelling approach is demonstrated by simulating several directional coupling configurations, as those based on cosine S-bend and double arc bent waveguides. Furthermore, some numerical results have been validated by comparison with the three-dimensional semi-vectorial beam propagation method.

© 2014 Optical Society of America

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References

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  1. H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).
  2. J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.
  3. R. J. McCosker, G. E. Town, Sens. Actuator B-Chem. 150, 417 (2010).
  4. S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).
  5. H. Morino, T. Maruyama, K. Iiyama, 18th OptoElectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching (OECC/PS, 2013), pp. 1–2.
  6. Q. Xu, D. Fattal, R. G. Beausoleil, Opt. Express 16, 4309 (2008).
    [CrossRef]
  7. J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
    [CrossRef]
  8. A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
    [CrossRef]
  9. Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
    [CrossRef]
  10. D. Dai, J. E. Bowers, Opt. Express 19, 18614 (2011).
    [CrossRef]
  11. A. Prinzen, M. Waldow, H. Kurz, Opt. Express 21, 17212 (2013).
    [CrossRef]
  12. A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).
  13. F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
    [CrossRef]
  14. G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
    [CrossRef]
  15. K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
    [CrossRef]
  16. Comsol Multiphysics by COMSOL (2005).
  17. RSoft BeamProp by SYNOPSYS (2013).

2013 (2)

S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).

A. Prinzen, M. Waldow, H. Kurz, Opt. Express 21, 17212 (2013).
[CrossRef]

2011 (1)

2010 (1)

R. J. McCosker, G. E. Town, Sens. Actuator B-Chem. 150, 417 (2010).

2009 (1)

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

2008 (3)

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Q. Xu, D. Fattal, R. G. Beausoleil, Opt. Express 16, 4309 (2008).
[CrossRef]

2006 (2)

Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
[CrossRef]

K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
[CrossRef]

2005 (2)

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

1994 (1)

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Arakawa, Y.

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

Beausoleil, R. G.

Beggs, D. M.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Bhatnagar, A.

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Bowers, J. E.

D. Dai, J. E. Bowers, Opt. Express 19, 18614 (2011).
[CrossRef]

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

Bulgan, E.

S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).

Chalapati, K.

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Cheben, P.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Chu, T.

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

Costa, R.

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Cusmai, G.

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Dai, D.

D. Dai, J. E. Bowers, Opt. Express 19, 18614 (2011).
[CrossRef]

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

De Leonardis, F.

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

Delage, A.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Dell’Olio, F.

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

Densmore, A.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Farrell, G.

Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
[CrossRef]

Fattal, D.

Freir, T.

Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
[CrossRef]

Gorajoobi, S. B.

S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).

Hammer, M.

K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
[CrossRef]

Hiremath, K. R.

K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
[CrossRef]

Houdre, R.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Iiyama, K.

H. Morino, T. Maruyama, K. Iiyama, 18th OptoElectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching (OECC/PS, 2013), pp. 1–2.

Ishida, S.

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

Jagerska, J.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Janz, S.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Kaykisiz, M. M.

S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).

Krauss, T. F.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Kumar, R.

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Kurz, H.

Lamontagne, B.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Lapointe, J.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Le Thomas, N.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Liang, D.

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

Maruyama, T.

H. Morino, T. Maruyama, K. Iiyama, 18th OptoElectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching (OECC/PS, 2013), pp. 1–2.

Mashanovich, G. Z.

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

McCosker, R. J.

R. J. McCosker, G. E. Town, Sens. Actuator B-Chem. 150, 417 (2010).

McKinnon, R. W.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Melloni, A.

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Morichetti, F.

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Morino, H.

H. Morino, T. Maruyama, K. Iiyama, 18th OptoElectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching (OECC/PS, 2013), pp. 1–2.

O’Brien, D.

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

Passaro, V. M. N.

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

Patro, Y. G. K.

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Post, E.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Prinzen, A.

Rosotti, P.

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Schmid, J. H.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Stoffer, R.

K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
[CrossRef]

Storey, C.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Suresh Nair, K. R.

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

Tang, Y.

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

Town, G. E.

R. J. McCosker, G. E. Town, Sens. Actuator B-Chem. 150, 417 (2010).

Waldow, M.

Waldron, P.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Wang, J.

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

Wang, Q.

Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
[CrossRef]

Xu, D.-X.

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

Xu, Q.

Yamada, H.

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

Appl. Phys. Lett. (1)

J. Jagerska, N. Le Thomas, R. Houdre, D. M. Beggs, D. O’Brien, T. F. Krauss, Appl. Phys. Lett. 92, 151106 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Bhatnagar, K. R. Suresh Nair, R. Kumar, K. Chalapati, Y. G. K. Patro, IEEE Photon. Technol. Lett. 6, 1004 (1994).
[CrossRef]

J. Lightw. Technol. (2)

A. Delage, D.-X. Xu, R. W. McKinnon, E. Post, P. Waldron, J. Lapointe, C. Storey, A. Densmore, S. Janz, B. Lamontagne, P. Cheben, J. H. Schmid, J. Lightw. Technol. 27, 1172 (2009).

S. B. Gorajoobi, M. M. Kaykisiz, E. Bulgan, J. Lightw. Technol. 31, 3469 (2013).

J. Opt. A (1)

F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, F. De Leonardis, J. Opt. A 10, 064003 (2008).
[CrossRef]

Opt. Commun. (2)

Q. Wang, G. Farrell, T. Freir, Opt. Commun. 259, 133 (2006).
[CrossRef]

K. R. Hiremath, R. Stoffer, M. Hammer, Opt. Commun. 257, 277 (2006).
[CrossRef]

Opt. Express (3)

Opt. Quantum Electron. (1)

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, Opt. Quantum Electron. 37, 343 (2005).
[CrossRef]

Proc. SPIE (1)

H. Yamada, T. Chu, S. Ishida, Y. Arakawa, Proc. SPIE 6019, paper 60192X (2005).

Sens. Actuator B-Chem. (1)

R. J. McCosker, G. E. Town, Sens. Actuator B-Chem. 150, 417 (2010).

Other (4)

Comsol Multiphysics by COMSOL (2005).

RSoft BeamProp by SYNOPSYS (2013).

J. Wang, D. Liang, Y. Tang, D. Dai, J. E. Bowers, Asia Communications and Photonics Conference, OSA Technical Digest (OSA, 2012), paper ATh1B.5.

H. Morino, T. Maruyama, K. Iiyama, 18th OptoElectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching (OECC/PS, 2013), pp. 1–2.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of DC based on S-cosine (a) and arc and (b) bend waveguide (BWG) coupled to a straight bus waveguide (SWG).

Fig. 2.
Fig. 2.

Coupling length as a function of the coupler gap for a DC based on a SOI rib waveguide (Wrib=500nm, Htot=400nm, Hrib=220nm) designed at λop=1.55μm.

Fig. 3.
Fig. 3.

Simulation of the DC formed by a cosine S-bent rib waveguide coupled to a straight rib waveguide with geometrical parameters: Li=35μm, Ltr=25μm, g0=0.3μm, D=2μm.

Fig. 4.
Fig. 4.

3D semi-vectorial BPM simulation of DC based on S-cosine bent SOI rib waveguides with geometrical parameters: Li=35μm, Ltr=25μm, g0=0.3μm, D=2μm.

Fig. 5.
Fig. 5.

Simulation of DC formed by an arc bent-rib waveguide coupled to a straight-rib waveguide with geometrical parameters: Li=35μm, Ltr=18.75μm, g0=0.3μm, R=25μm.

Fig. 6.
Fig. 6.

3D semi-vectorial BPM simulation of the DC based on arc bent SOI rib waveguides with geometrical parameters: Li=35μm, Ltr=18.75μm, g0=0.3μm, R=25μm.

Fig. 7.
Fig. 7.

Coupling length as a function of the coupler gap for a DC based on a SOI slot waveguide (Wslot=180nm, Htot=310nm, Hslot=250nm, gslot=100nm) designed at λop=1.55μm.

Fig. 8.
Fig. 8.

Simulation of the DC formed by an arc bent rib-slot waveguide coupled to a straight rib-slot waveguide with geometrical parameters: Li=15μm, Ltr=22.5μm, g0=0.3μm, R=30μm.

Equations (12)

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

dX(z)dziδX(z)=iκc(z)eiϑ(z)Y(z),dY(z)dz+iδY(z)=iκc(z)eiϑ(z)X(z),
ϑ(z)=0z[Δβ(ζ)Δβ(0)]dζ,
δ=Δβ(0)2,
Δβ(z)=2πλop[neff,Y(z)neff,X(z)].
neff,Y(z)={neff,BWGz[0,Ltr][Ltr+Li,Li+2Ltr]neff,SWGz]Ltr,Ltr+Li[,neff,X(z)=neff,SWGz[0,Li+2Ltr].
Δβ(z)={2πλop(neff,BWGneff,SWG)z[0,Ltr][Ltr+Li,Li+2Ltr]0z[0,Li+2Ltr],
ϑ(z)={0z[0,Ltr]2δLiz]Ltr,Ltr+Li[2δ(zLtr)z[Ltr+Li,Li+2Ltr],
Lc=λop2(neff,Sneff,A).
Lc(z)=AeBgc(z),
κc(z)=π2Lc(z).
gc(z)={g0+(Dg0)2·(1+cos(πzLtr))z[0,Ltr]g0z]Ltr,Ltr+Li[g0+(Dg0)2·(1cos(π|z(Ltr+Li)|Ltr))z[Ltr+Li,Li+2Ltr].
gc(z)={g0+R147R2+24Rz16z2z[0,Ltr]g0z]Ltr,Ltr+Li[g0+R1416Li224LiR+7R2+32Liz+24Rz16z2z[Ltr+Li,Li+2Ltr].

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