Abstract

In a study concerned with second-harmonic generation at grating couplers, Kull et al. [Opt. Lett. 16, 1930 (1991)] observed a curious phenomenon in which the second-harmonic efficiency exhibits dips, instead of peaks, when the angle of incidence of the pump beam is scanned through its resonant value. This surprising result has not been explained. It is our aim to show that this effect is closely related to the existence of nonlinear zeros.

© 1995 Optical Society of America

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References

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  1. M. Kull, J. L. Coutaz, R. Meyrueix, Opt. Lett. 16, 1930 (1991).
    [CrossRef] [PubMed]
  2. M. Nevière, E. Popov, R. Reinisch, J. Opt. Soc. Am. A 12, 513 (1995).
    [CrossRef]
  3. R. Reinisch, M. Nevière, Phys. Rev. B 28, 1870 (1983).
    [CrossRef]
  4. C. Vassalo, Théorie des guides d’ondes électromagnétiques (CNET-ENST, Eyrolles, Paris, 1985).
  5. H. Kogelnik, in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, New York, 1975), pp. 13–81.
    [CrossRef]
  6. M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed (Springer-Verlag, New York, 1980), pp. 123–157.
    [CrossRef]
  7. R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
    [CrossRef]
  8. E. Popov, M. Nevière, J. Opt. Soc. Am. B 11, 1555 (1994).
    [CrossRef]

1995 (1)

1994 (1)

1992 (1)

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

1991 (1)

1983 (1)

R. Reinisch, M. Nevière, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

Coutaz, J. L.

Kogelnik, H.

H. Kogelnik, in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, New York, 1975), pp. 13–81.
[CrossRef]

Kull, M.

Meyrueix, R.

Nevière, M.

M. Nevière, E. Popov, R. Reinisch, J. Opt. Soc. Am. A 12, 513 (1995).
[CrossRef]

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

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

R. Reinisch, M. Nevière, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

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

Popov, E.

Reinisch, R.

M. Nevière, E. Popov, R. Reinisch, J. Opt. Soc. Am. A 12, 513 (1995).
[CrossRef]

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

R. Reinisch, M. Nevière, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

Vassalo, C.

C. Vassalo, Théorie des guides d’ondes électromagnétiques (CNET-ENST, Eyrolles, Paris, 1985).

Vincent, P.

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

Vitrant, G.

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

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

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

Opt. Commun. (1)

R. Reinisch, M. Nevière, P. Vincent, G. Vitrant, Opt. Commun. 91, 51 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

R. Reinisch, M. Nevière, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

Other (3)

C. Vassalo, Théorie des guides d’ondes électromagnétiques (CNET-ENST, Eyrolles, Paris, 1985).

H. Kogelnik, in Integrated Optics, T. Tamir, ed., Vol. 7 of Topics in Applied Physics (Springer-Verlag, New York, 1975), pp. 13–81.
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

Experimental configuration used in Ref. 1. The large arrow represents the pump light coupled to either a guided mode or a surface plasmon.

Fig. 2
Fig. 2

Angular dependence of the SH specular amplitude. Periodicity, 1.66 μm; groove depth, 0.08 μm. (a) Pump wavelength λ1 = 1.319 μm, SH wavelength λ2 = 0.6595 μm. The thickness of the PUCS film is 2.92 μm. The refractive indices n have the following values: nPUSC(λ1 = 1.319 μm) = 1.57 + i0.00004, nAg(λ1 = 1.319 μm) = 0.05976 + i8.3668, nPUSC(λ2 = 0.6595 μm) = 1.585 + i0.0027, nAg(λ2 = 0.6595 μm) = 0.09363 + i3.5361. (b) Pump wavelength λ1 = 1.064 μm, SH wavelength λ2 = 0.532 μm. The thickness of the PUCS film is 3.05 μm. The refractive indices n have the following values: nPUSC(λ1 = 1.064 μm) = 1.574802 + i0.00004, nAg(λ1 = 1.064 μm) = 0.13 + i7.474, nPUSC(λ2 = 0.532 μm) = 1.6010998 + i0.0593343, nAg(λ2 = 0.532 μm) = 0.051 + i3.16622.

Fig. 3
Fig. 3

Data from Ref. 1: (a) angular dependence of the specularly reflected SH peak power for λ1 = 1.319 μm and λ2 = 0.6595 μm, (b) angular dependence of the specularly reflected SH peak power for λ1 = 1.064 μm and λ2 = 0.532 μm.

Equations (12)

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( B 2 ω ) = ( S 2 ω ) ( A 2 ω ) .
g ω = t β - β 1 p A i ,
β = k 0 sin θ + q 2 π d ,
P i NL ( 2 ω ) = ɛ 0 χ i j h ( 2 ω ) E i ( ω ) E h ( ω ) ,
B 2 ω , n ( h ) = D n ( h ) [ β - β 1 p ( h ) ] 2 [ 2 β - β 2 p ( h ) ] .
lim h 0 B 2 ω , n ( h ) = δ 0 , n R 2 ω ,
D 0 ( h = 0 ) = R 2 ω [ β - β 1 p ( h = 0 ) ] 2 [ 2 β - β 2 p ( h = 0 ) ] .
[ β - β 1 p ( h = 0 ) ] 2 [ 2 β - β 2 p ( h = 0 ) ] .
β 11 z ( h = 0 ) = β 12 z ( h = 0 ) = β 1 p ( h = 0 ) , β 2 z ( h = 0 ) = β 2 p ( h = 0 ) .
B 2 ω , 0 ( h ) = R 2 ω [ β - β 11 z ( h ) ] [ β - β 12 z ( h ) ] [ 2 β - β 2 z ( h ) ] [ β - β 1 p ( h ) ] 2 [ 2 β - β 2 p ( h ) ] .
B 2 ω , 0 ( h ) = a ( h ) + b ( h ) [ β - β 1 p ( h ) ] 2 + c ( h ) [ 2 β - β 2 p ( h ) ] + d ( h ) [ β - β 1 p ( h ) ] 2 [ 2 β - β 2 p ( h ) ] .
2 Re [ β 1 p ( h ) ] = Re [ β 2 p ( h ) ] .

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