Abstract

Diffraction gratings can be used to achieve phase matching between the fundamental modes of a slab or confined waveguide. Compared with the usual techniques such as quasi-, Čerenkov, and intermodal phase matching, the matching method used here involves spatial harmonics of the guided electromagnetic field that are generated by the corrugated grating. This grating acts simultaneously as a linear waveguide coupler at both the pump and harmonic frequencies. Using the third spatial harmonic, we report what we believe to be the first observation of grating-assisted phase-matched second-harmonic generation between counterpropagating TM0 modes of an organic waveguide.

© 1995 Optical Society of America

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References

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  1. K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
    [CrossRef]
  2. V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.
  3. G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
    [CrossRef]
  4. Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
    [CrossRef]
  5. Z. Weissman, A. Hardy, IEEE J. Quantum Electron. 28, 1848 (1992).
    [CrossRef]
  6. S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
    [CrossRef]
  7. C. L. Tang, P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
    [CrossRef]
  8. E. Popov, M. Nevière, J. Opt. Soc. Am. B 11, 1555 (1994).
    [CrossRef]
  9. R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
    [CrossRef]
  10. M. Nevire, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
    [CrossRef]

1994 (3)

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

E. Popov, M. Nevière, J. Opt. Soc. Am. B 11, 1555 (1994).
[CrossRef]

1993 (2)

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

1992 (1)

Z. Weissman, A. Hardy, IEEE J. Quantum Electron. 28, 1848 (1992).
[CrossRef]

1973 (1)

C. L. Tang, P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

1972 (1)

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

Akhouayri, H.

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

Azumai, Y.

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

Bey, P.

C. L. Tang, P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

Hardy, A.

Z. Weissman, A. Hardy, IEEE J. Quantum Electron. 28, 1848 (1992).
[CrossRef]

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

le Barny, P.

V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.

Lemoine, V.

V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

Nevière, M.

E. Popov, M. Nevière, J. Opt. Soc. Am. B 11, 1555 (1994).
[CrossRef]

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

Nevire, M.

M. Nevire, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

Pocholle, J. P.

V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.

Popov, E.

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

E. Popov, M. Nevière, J. Opt. Soc. Am. B 11, 1555 (1994).
[CrossRef]

Reinisch, R.

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

Rikken, G. L. J. A.

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

Robin, P.

V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

Seppen, C. J. E.

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

Somekh, S.

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

Staring, E. G. J.

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

Tang, C. L.

C. L. Tang, P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

Venhuizen, A. H. J.

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

Weissman, Z.

Z. Weissman, A. Hardy, IEEE J. Quantum Electron. 28, 1848 (1992).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

Yariv, A.

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

Appl. Phys. Lett. (2)

G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, A. H. J. Venhuizen, Appl. Phys. Lett. 62, 2483 (1993).
[CrossRef]

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. L. Tang, P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, IEEE J. Quantum Electron. 30, 1596 (1994).
[CrossRef]

Z. Weissman, A. Hardy, IEEE J. Quantum Electron. 28, 1848 (1992).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

Opt. Commun. (1)

R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
[CrossRef]

Other (2)

M. Nevire, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

V. Lemoine, J. P. Pocholle, P. le Barny, P. Robin, in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 379–432.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the device with the corrugated grating on the glass substrate and para-nitroaniline/poly(methyl methacrylate) (PNA-PMMA) as the guiding NL layer. The arrows in the air designate the incident beam and the reflected orders. The arrows in the guiding layer correspond to the TM0 modes at the fundamental and harmonic wavelengths phase matched through the wave vector associated with the grating.

Fig. 2
Fig. 2

SH efficiency measured as a function of the incident angle in the specular reflected order for two different wavelengths of the pump beam. The phase-matching condition is fulfilled at λ = 1046.5 nm and θ = 35.72°. SHG, second-harmonic generation.

Fig. 3
Fig. 3

Numerical calculations of the SH efficiency with the plane-wave assumption versus the incident angle corresponding to the experimental data shown in Fig. 2.

Equations (6)

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H z ω ( x , y ) = p H z , p ω ( y ) exp [ i ( k 0 ω n eff ω + p 2 π d ) x ] ,
H z 2 ω ( x , y ) p , q H z , p ω ( y ) H z , q ω ( y ) × exp { i [ 2 k 0 ω n eff ω + ( p + q ) 2 π d ] x } .
H z 2 ω ( x , y ) = m H z , m 2 ω ( y ) exp [ i ( k 0 2 ω n eff 2 ω + m 2 π d ) x ] .
2 k 0 ω Re ( n eff ω ) ± k 0 2 ω Re ( n eff 2 ω ) + ( p ω + q ω + m 2 ω ) ( 2 π / d ) = 0.
- k 0 ω Re ( n eff TM 0 ω ) - l 2 π d = k 0 ω sin θ 1 ,
1 2 [ k 0 2 ω Re ( n eff TM 0 2 ω ) - l 2 π d ] = k 0 ω sin θ 2 .

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