Abstract

We deal with second-harmonic generation in χ(2) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in χ(2) optical resonators.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [Crossref]
  2. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. Van Stryland, Opt. Lett. 17, 28 (1992);G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
    [Crossref] [PubMed]
  3. R. Reinisch, G. Vitrant, Prog. Quantum Electron. 18, 1 (1994), and references cited therein.
    [Crossref]
  4. R. Reinisch, M. Nevière, E. Popov, H. Akhouayri, Opt. Commun. 112, 339 (1994).
    [Crossref]
  5. 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]
  6. M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, New York, 1980), pp. 123–157.
    [Crossref]

1994 (2)

R. Reinisch, G. Vitrant, Prog. Quantum Electron. 18, 1 (1994), and references cited therein.
[Crossref]

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

1992 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Akhouayri, H.

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

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

DeSalvo, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Hagan, D. J.

Nevière, M.

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

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

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Popov, E.

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

Reinisch, R.

R. Reinisch, G. Vitrant, Prog. Quantum Electron. 18, 1 (1994), and references cited therein.
[Crossref]

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

Sheik-Bahae, M.

Stegeman, G. I.

Van Stryland, E.

Vassalo, C.

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]

Vitrant, G.

R. Reinisch, G. Vitrant, Prog. Quantum Electron. 18, 1 (1994), and references cited therein.
[Crossref]

Opt. Commun. (1)

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

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Prog. Quantum Electron. (1)

R. Reinisch, G. Vitrant, Prog. Quantum Electron. 18, 1 (1994), and references cited therein.
[Crossref]

Other (2)

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]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

χ(2) optical resonators considered in this Letter: (a) grating coupler of periodicity d, permitting guided-mode excitation, (b) prism coupler permitting guided-mode excitation (c) prism coupler in the Kretschmannn geometry permitting surface-plasmon excitation.

Fig. 2
Fig. 2

Response of a χ(2) optical resonator for detuning values Δ1 = 5 (long-dashed curve) Δ1 = 3.08 (solid curve; threshold values deduced from inequality (8) and Δ1 = 0 (short-dashed curve). neff,1 = 1.9100 + j1.4677 × 10−3; neff,2 = 1.9099 + j9.6401 × 10−4 where neff,ν (ν = 1, 2) is the effective index of mode p at ω(ν = 1) and that of mode m at 2ω(ν = 2); ψ = −0.808496°.

Equations (20)

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

d f 1 , p d x + j ( β γ 1 , p ) f 1 , p = j ω ξ 1 ( x ) f 2 , m f 1 , p * j τ i A i ( x ) ,
d f 2 , m d x + j ( 2 β γ 2 , m ) f 2 , m = j 2 ω ξ 2 ( x ) f 1 , p 2 .
c 1 , p ( x ) = f 1 , p ( x ) exp [ j ( β γ 1 , p ) x ] ,
c 2 , m ( x ) = f 2 , m ( x ) exp [ j ( 2 β γ 2 , m ) x ] .
( Δ 1 j ) F 1 + exp ( j ψ 1 ) F 2 F 1 * + A i = 0 ,
( Δ 2 j ) F 2 + exp ( j ψ 2 ) F 1 2 = 0 ,
f 1 , p = 1 ω ( γ 1 , p γ 2 , m 2 | ξ 1 ξ 2 | ) 1 / 2 F 1 ,
f 2 , m = γ 1 , p ω | ξ 1 | F 2 ,
A i = γ 1 , p ω τ i ( γ 1 , p γ 2 , m 2 | ξ 1 ξ 2 | ) 1 / 2 A i ,
Δ 1 = β γ 1 , p γ 1 , p ,
Δ 2 = 2 β γ 2 , m γ 2 , m ,
ξ ν = | ξ ν | exp ( j ψ ν ) ( ν = 1 , 2 ) ,
γ ν = γ ν + j γ ν ( ν = 1 , 2 ) .
Δ 2 = 2 γ 1 , p γ 2 , m γ 2 , m + 2 γ 1 , p γ 2 , m Δ 1 .
[ ( j Δ 1 ) + exp ( j ψ ) j Δ 2 | F 1 | 2 ] F 1 = A i ,
ψ = ψ 1 + ψ 2 .
2 [ a sin ψ + b cos ψ ] > 3 ( a 2 + b 2 ) ,
a sin ψ + b cos ψ < 0.
Δ 1 Δ 2 1 > | Δ 1 + Δ 2 | 3 .
χ eff ( 3 ) = 2 ω 2 ξ 1 ξ 2 2 β γ 2 ,

Metrics