Abstract

The coupling efficiency of grating couplers is derived for a Gaussian incident beam. Its optimum value depends on the beam waist and on the position of a light spot with respect to the coupler edge for given grating parameters. The characteristic coupling length has been experimentally determined for the grating coupler studied. Relative measurements of the coupling efficiency as a function of incident beam characteristics are in good agreement with the numerical results.

© 1997 Optical Society of America

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References

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  1. P. Vincent, “Differential methods,” in Electromagnetic theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 101–121.
    [Crossref]
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    [Crossref]
  3. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction gratings,” in Proc. IEEE 73, 894–937 (1985).
  4. T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
    [Crossref]
  5. H. Kogelnik, “Theory of dielectric waveguide,” in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, Berlin, 1985), pp. 13–81.
  6. K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
    [Crossref]
  7. M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), Chap. 5, pp. 123–157.
    [Crossref]
  8. M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).
  9. A. Jacques, D. B. Ostrowsky, “The grating coupler: comparison of theoretical and experimental results,” Opt. Commun. 13, 74–77 (1975).
    [Crossref]
  10. L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  13. R. Ulrich, “Theory of the prism-film coupler by plane wave analysis,” J. Opt. Soc. Am. 60, 1337–1350 (1970).
    [Crossref]
  14. R. Orobtchouk, “Modélisation et étude de composants pour l’optique intégrée silicium sur isolant (SIMOX) à λ = 1,3 µm,” thèse de doctorat No. 4106 (Université Paris-Sud, Orsay, France, 1996), pp. 60–99.
  15. D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
    [Crossref]

1995 (1)

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

1991 (1)

1990 (1)

1986 (1)

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction gratings,” in Proc. IEEE 73, 894–937 (1985).

1980 (1)

1977 (1)

M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).

1975 (1)

A. Jacques, D. B. Ostrowsky, “The grating coupler: comparison of theoretical and experimental results,” Opt. Commun. 13, 74–77 (1975).
[Crossref]

1973 (1)

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

1970 (2)

Chang, K. C.

Chang, W. S. C.

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction gratings,” in Proc. IEEE 73, 894–937 (1985).

Gupta, M. C.

Jacques, A.

A. Jacques, D. B. Ostrowsky, “The grating coupler: comparison of theoretical and experimental results,” Opt. Commun. 13, 74–77 (1975).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguide,” in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, Berlin, 1985), pp. 13–81.

Koster, A.

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

Laval, S.

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

Li, L.

Maystre, D.

M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction gratings,” in Proc. IEEE 73, 894–937 (1985).

Nevière, M.

M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), Chap. 5, pp. 123–157.
[Crossref]

Nishihara, H.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

Orobtchouk, R.

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

R. Orobtchouk, “Modélisation et étude de composants pour l’optique intégrée silicium sur isolant (SIMOX) à λ = 1,3 µm,” thèse de doctorat No. 4106 (Université Paris-Sud, Orsay, France, 1996), pp. 60–99.

Ostrowsky, D. B.

A. Jacques, D. B. Ostrowsky, “The grating coupler: comparison of theoretical and experimental results,” Opt. Commun. 13, 74–77 (1975).
[Crossref]

Pascal, D.

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

Rosembaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

Sapori, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

Shah, V.

Suhara, T.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

Tamir, T.

Tien, P. K.

Ulrich, R.

Vincent, P.

M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).

P. Vincent, “Differential methods,” in Electromagnetic theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 101–121.
[Crossref]

Appl. Opt. (2)

Electron. Lett. (1)

D. Pascal, R. Orobtchouk, S. Laval, A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photo resist,” Electron. Lett. 31, 914–915 (1995).
[Crossref]

IEEE J. Quantum Electron. (2)

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

K. Ogawa, W. S. C. Chang, B. L. Sapori, F. J. Rosembaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[Crossref]

J. Opt. (1)

M. Nevière, D. Maystre, P. Vincent, “Application du calcul à l’étude théorique des anomalies des réseaux recouverts de diélectrique,” J. Opt. 4, 231–242 (1977).

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

A. Jacques, D. B. Ostrowsky, “The grating coupler: comparison of theoretical and experimental results,” Opt. Commun. 13, 74–77 (1975).
[Crossref]

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction gratings,” in Proc. IEEE 73, 894–937 (1985).

Other (4)

H. Kogelnik, “Theory of dielectric waveguide,” in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, Berlin, 1985), pp. 13–81.

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), Chap. 5, pp. 123–157.
[Crossref]

R. Orobtchouk, “Modélisation et étude de composants pour l’optique intégrée silicium sur isolant (SIMOX) à λ = 1,3 µm,” thèse de doctorat No. 4106 (Université Paris-Sud, Orsay, France, 1996), pp. 60–99.

P. Vincent, “Differential methods,” in Electromagnetic theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 101–121.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Gaussian light beam incident on a grating coupler.

Fig. 2
Fig. 2

Coupling efficiency versus the distance between the beam center and the coupler edge for various values of the beam waist and two different grating coupling lengths: (a) Lc = 200 µm, (b) Lc = 440 µm.

Fig. 3
Fig. 3

Maximum coupling efficiency and normalized optimum position of the incident beam on the input coupler as a function of the ratio between the beam waist radius and the grating coupling length.

Fig. 4
Fig. 4

Experimental device.

Fig. 5
Fig. 5

Decoupled light intensity recorded along the output grating coupler.

Fig. 6
Fig. 6

Decoupled light intensity measured as a function of the incident beam position on the input coupler for various beam waist radii.

Fig. 7
Fig. 7

Maximum coupling efficiency and optimum position of the incident beam on the input coupler as a function of the beam waist radius: experimental points compared with theoretical curves.

Equations (11)

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

Eyiinc0, zi=E0inc exp-zi2w02.
Eyiinc0, z=E0inc exp-z2w12,
w1=w0/cos θ0.
Eyd=-+ pkz-kzoux, z, kzdkz,
ux, z, kz=vmx, kzkz-kz,p expjkz+m 2πΛz,
kz,p=1/2Lc.
rz=-j -+ pξexpjξzξ-jkz,pdξ,
Eydx, z=jrzvmx, kzoexpjkzo+m 2πΛz.
ddz rz+kz,prz=E0inc exp-z2w12,
rz=E0incw1π1/22 expw1216Lc2-z2Lc×1+erfzw1-w14Lc.
ηzc=kz,p+m2π/Λrzc2-+vmx2dx.

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