Abstract

We propose a novel way to enhance the Sagnac effect by using a nonlinear ring interferometer. Specifically, we take advantage of the nonlinearly induced nonreciprocity of counterpropagating waves caused by the formation of an index grating in the nonlinear medium.

© 1981 Optical Society of America

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References

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  1. For a comprehensive review, see E. Post, Rev. Mod. Phys. 39, 475 (1967).
    [CrossRef]
  2. M. O. Scully, in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer- Verlag, Heidelberg, 1979), p. 21.
  3. R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
    [CrossRef]
  4. A. E. Kaplan, P. Meystre, Opt. Commun. (to be published).
  5. As shown in Fig. 2, the enhancement factor η becomes less than 1 for some values of the pump intensity. This corresponds to a reduction of the Sagnac effect in the vicinity of the onset of symmetric bistability4(Δth=−3,Ath=8/93). ηmin and the minimizing pump intensity Amin are again given by Eqs. (9) and (10) but with the opposite signs before the radicals.
  6. D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
    [CrossRef]

1980 (1)

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
[CrossRef]

1967 (1)

For a comprehensive review, see E. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

1966 (1)

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
[CrossRef]

Garmire, E.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, P. Meystre, Opt. Commun. (to be published).

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
[CrossRef]

Meystre, P.

A. E. Kaplan, P. Meystre, Opt. Commun. (to be published).

Miller, D. A. B.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
[CrossRef]

Post, E.

For a comprehensive review, see E. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

Scully, M. O.

M. O. Scully, in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer- Verlag, Heidelberg, 1979), p. 21.

Smith, S. D.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
[CrossRef]

Wherrett, B. S.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
[CrossRef]

Opt. Commun. (1)

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980)
[CrossRef]

Phys. Rev. Lett. (1)

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966);R. L. Carman, R. Y. Chiao, P. L. Kelley, Phys. Rev. Lett. 17, 1281 (1966);B. Ya. Zeldovich, Brief Communications in Physics of the Lebedev Institute (Lebedev Physical Institute, Moscow, 1970), No. 5, p. 20;M. Sargent, Appl. Phys. 9, 127 (1976);A. E. Kaplan, Opt. Lett. 6, 361 (1981).
[CrossRef]

Rev. Mod. Phys. (1)

For a comprehensive review, see E. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

Other (3)

M. O. Scully, in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer- Verlag, Heidelberg, 1979), p. 21.

A. E. Kaplan, P. Meystre, Opt. Commun. (to be published).

As shown in Fig. 2, the enhancement factor η becomes less than 1 for some values of the pump intensity. This corresponds to a reduction of the Sagnac effect in the vicinity of the onset of symmetric bistability4(Δth=−3,Ath=8/93). ηmin and the minimizing pump intensity Amin are again given by Eqs. (9) and (10) but with the opposite signs before the radicals.

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Figures (2)

Fig. 1
Fig. 1

Rotating ring resonator with nonlinear medium and two pumping beams of equal intensity.

Fig. 2
Fig. 2

Enhancement factor η as a function of the dimensionless pump intensity A for various values of the dimensionless frequency detuning Δ: 1, Δ = 0; 2, Δ = 3 ( 1 0.2 ); 3, Δ = 3 ( 1 2 / 35 ); 4, Δ = 3 ( 1 1 / 35 ); 5, Δ = 3.

Equations (13)

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Δ 1 NL = 2 ( | E 1 | 2 + 2 | E 2 | 2 ) , Δ 2 NL = 2 ( | E 2 | 2 + 2 | E 1 | 2 ) .
E ( x ) = E 1 ( x ) e ikx + E 2 ( x ) e ikx .
P NL E | E | 2 = ( E 1 e ikx + E 2 e ikx ) [ ( | E 1 | 2 + | E 2 | 2 ) + ( E 1 E 2 * e 2 ikx + c . c . ) ] = E 1 e ikx ( | E 1 | 2 + 2 | E 2 | 2 ) + E 2 e ikx ( | E 2 | 2 + 2 | E 1 | 2 ) ( + rapidly varying terms ) ,
E j = E I ( γ c / γ T ) 1 + i γ 1 [ ν ν 0 + ( 1 ) j ω s + ν 0 Δ j NL L s / L ] .
ω s = 4 S ω r K 0 / L
I j = 2 | E j | 2 L s ν 0 / L γ , A = γ c 2 | E I | 2 L s ν 0 / L γ T .
A = I j { 1 + [ Δ + ( 1 ) j Ω + I j + 2 I 3 j ] 2 } .
A = I 0 [ 1 + ( Δ + 3 I 0 ) 2 ] .
ζ 1 = ζ 2 = ( η 1 ) Ω ,
η = 1 + ( Δ + 3 I 0 ) 2 1 + ( Δ + 3 I 0 ) ( Δ + I 0 ) .
A = ( 2 / 3 ) [ Δ ( 3 Δ 2 5 ) ± ( 3 Δ 2 1 ) ( Δ 2 3 ) 1 / 2 ] .
η max = 1 / [ 2 ( Δ 2 + 1 ) 1 / 2 ] .
A max = 2 ( Δ 2 + 1 ) [ ( Δ 2 + 1 ) 1 / 2 + 1 ] 2 / 3 Δ 3 .

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