Abstract

A recent modal theory of nonlinear planar resonators is applied to the analysis of the steady transmission characteristics of the two-beam nonlinear Fabry–Perot interferometer. An analytical study, based on the plane-wave approximation, is presented that shows the potential applications of the device. In particular, a flip-flop mode of operation, derived from a pitchfork bifurcation, is predicted. Its salient feature is to require only positive triggering pulses.

© 1990 Optical Society of America

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References

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  1. M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
    [Crossref]
  2. M. Haelterman, M. Tolley, G. Vitrant, J. Appl. Phys. 67, 2725 (1990).
    [Crossref]
  3. M. Haelterman, G. Vitrant, R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990).
    [Crossref]
  4. G. Carter, Y. Chen, Appl. Phys. Lett. 42, 643 (1983).
    [Crossref]
  5. G. Vitrant, “Effets transverses et bistabilité optique dans les résonateurs optiques à nonlinéarité de type Kerr,” thèse d’état (Université Joseph Fourier, Grenoble, France, 1989).
  6. M. Haelterman, “Contribution à l’étude théorique de l’optique nonlinéaire dans les guides et les cavités,” dissertation (Université Libre de Bruxelles, Bruxelles, Belgium, 1989).
  7. A. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
    [Crossref]
  8. K. Otsuka, K. Ikeda, Opt. Lett. 12, 599 (1987).
    [Crossref] [PubMed]
  9. T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
    [Crossref]
  10. K. Otsuka, Opt. Lett. 14, 72 (1989).
    [Crossref] [PubMed]
  11. J.-L. Chern, J. K. McIver, Opt. Lett. 15, 186 (1990).
    [Crossref] [PubMed]

1990 (3)

1989 (2)

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

K. Otsuka, Opt. Lett. 14, 72 (1989).
[Crossref] [PubMed]

1987 (1)

1984 (1)

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

1983 (1)

G. Carter, Y. Chen, Appl. Phys. Lett. 42, 643 (1983).
[Crossref]

1982 (1)

A. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[Crossref]

Carter, G.

G. Carter, Y. Chen, Appl. Phys. Lett. 42, 643 (1983).
[Crossref]

Chen, Y.

G. Carter, Y. Chen, Appl. Phys. Lett. 42, 643 (1983).
[Crossref]

Chern, J.-L.

Danckaert, J.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

Haelterman, M.

M. Haelterman, M. Tolley, G. Vitrant, J. Appl. Phys. 67, 2725 (1990).
[Crossref]

M. Haelterman, G. Vitrant, R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990).
[Crossref]

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

M. Haelterman, “Contribution à l’étude théorique de l’optique nonlinéaire dans les guides et les cavités,” dissertation (Université Libre de Bruxelles, Bruxelles, Belgium, 1989).

Ikeda, K.

Kaplan, A.

A. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[Crossref]

Kitano, M.

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

Mandel, P.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

McIver, J. K.

Meystre, P.

A. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[Crossref]

Ogawa, T.

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

Okamoto, T.

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

Otsuka, K.

Reinisch, R.

Thienpont, H.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

Tolley, M.

M. Haelterman, M. Tolley, G. Vitrant, J. Appl. Phys. 67, 2725 (1990).
[Crossref]

Veretenicoff, I.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

Vitrant, G.

M. Haelterman, M. Tolley, G. Vitrant, J. Appl. Phys. 67, 2725 (1990).
[Crossref]

M. Haelterman, G. Vitrant, R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990).
[Crossref]

G. Vitrant, “Effets transverses et bistabilité optique dans les résonateurs optiques à nonlinéarité de type Kerr,” thèse d’état (Université Joseph Fourier, Grenoble, France, 1989).

Yabuzaki, T.

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

Appl. Phys. Lett. (1)

G. Carter, Y. Chen, Appl. Phys. Lett. 42, 643 (1983).
[Crossref]

J. Appl. Phys. (1)

M. Haelterman, M. Tolley, G. Vitrant, J. Appl. Phys. 67, 2725 (1990).
[Crossref]

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

Opt. Commun. (2)

A. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[Crossref]

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, I. Veretenicoff, Opt. Commun. 74, 238 (1989).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (1)

T. Yabuzaki, T. Okamoto, M. Kitano, T. Ogawa, Phys. Rev. A 29, 1964 (1984).
[Crossref]

Other (2)

G. Vitrant, “Effets transverses et bistabilité optique dans les résonateurs optiques à nonlinéarité de type Kerr,” thèse d’état (Université Joseph Fourier, Grenoble, France, 1989).

M. Haelterman, “Contribution à l’étude théorique de l’optique nonlinéaire dans les guides et les cavités,” dissertation (Université Libre de Bruxelles, Bruxelles, Belgium, 1989).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the two-beam nonlinear Fabry–Perot interferometer. The axes 0x and 0y define the plane of incidence, θr and θl are the angles of incidence, and a, b and r, l are the amplitudes of the incident and transmitted beams, respectively.

Fig. 2
Fig. 2

Transmission characteristics R(A) and L(A) under the symmetric illumination condition: A = B and identical angles of incidence Δr = Δl = 2.4. Dashed curves correspond to unstable states.

Fig. 3
Fig. 3

Transmission characteristics R(A) and L(A) of the biased system with the same detunings as those of Fig. 2. The holding intensity B = 3 is chosen in the asymmetric regime domain of Fig. 2. Dashed curves correspond to unstable states.

Equations (9)

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d 2 E t ( x ) / d x 2 + [ β m 2 + i ρ m 2 + γ | E t ( x ) | 2 ] E t ( x ) = i ρ m 2 E i ( x ) ,
E i ( x ) = a ( x ) exp ( i β r x ) + b ( x ) exp ( i β l x ) ,
E t ( x ) = r ( x ) exp ( i β r x ) + l ( x ) exp ( i β l x ) .
2 i β r d r ( x ) d x + ( i ρ m 2 δ r 2 ) r ( x ) + γ [ | r ( x ) | 2 + 2 | l ( x ) | 2 ] r ( x ) = i ρ m 2 a ( x ) ,
2 i β l d l ( x ) d x + ( i ρ m 2 δ l 2 ) l ( x ) + γ [ 2 | r ( x ) | 2 + | l ( x ) | 2 ] l ( x ) = i ρ m 2 b ( x ) ,
R 3 + 4 R 2 L + 4 R L 2 2 Δ r R 2 4 Δ r RL + ( 1 + Δ r 2 ) R = A ,
L 3 + 4 L 2 R + 4 L R 2 2 Δ l L 2 4 Δ l LR + ( 1 + Δ l 2 ) L = B ,
( R L ) [ R 2 + RL + L 2 2 Δ ( L + R ) + Δ 2 + 1 ] = 0 .
9 R 3 6 Δ R 2 + ( Δ 2 + 1 ) R = A .

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