Publication: Purely absorptive bistability in double-ring cavities
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1986-03
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American Physical Society
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Abstract
A novel type of optical bistable configuration, namely the so-called double-ring (DR) device, is presented. The stationary solutions in the purely absorptive case for a homogeneously broadened atomic system are derived. In the mean-field limit it has been pointed out that use of a DR arrangement enables us to reduce both the length of the sample of the nonlinear medium and the response time of the device. Linear stability analyses have shown that the position and the length of the unstable regions of a given hysteresis cycle can be controlled, to a great extent, by means of the two new parameters of our DR scheme. Finally, it has been remarked that, in order to observe selfpulsing, the purely absorptive DR system. may present a similar behavior to that offered in the dispersive single-ring case.
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This work was supported by the Comision Asesora de Investigacion Cientifica y Tecnica (CAICyT) of Spain, under Project No. 213G/83.
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1 See, for example, E. Abraham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982), and references therein; see also S. L. McCall and H. M. Gibbs, in Dissipative Systems in Quantum Optics, edited by R. Bonifacio (Springer, Berlin, 1982), p. 93; and more recently the Proceedings of the Conference on Opti cal BistabiIity 2, edited by C. M. Bowden, H. M. Gibbs, and S. L. McCall (Plenum, New York, 1984).
2 R. Bonifacio and L. A. Lugiato, Lett. Nuovo Cimento 21, 505 (1978).
3 R. Bonifacio and L. A. Lugiato, Lett. Nuovo Cimento 21, 510 (1978); R. Bonifacio, M. Gronchi, and L. A. Lugiato, Opt. Commun. 30, 129 (1979).
4 L. A. Lugiato, Opt. Commun. 33, 108 (1980).
5 Double-ring situations have been recently considered by K. Ikeda and M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984). In this work the two-cavities scheme is presented as equivalent to the usual Fabry-Perot resonator and the respective equations of motion are reduced to double-delay differential equations.
6 Although in the present work we are analyzing the purely absorptive case, for the sake of generality, we shall consider in the calculations the complete set of five Maxwell-Bloch equations.
7 There exist other two passible values of tlat. See, R. Bonifacio and L. A. Lugiato, in Dissipative Systems in Quantum Optics, edited by R. Bonifacio (Springer, Berlin, 1982), p. 73. However, their real parts are strongly negative and cannot yield any unstable behavior.
8 R. Bonifacio and L. A. Lugiato, in Dissipative Systems in Quantum Optics, edited by R. Bonifacio (Springer, Berlin, 1982),p. 61.
9 As in Fig. 2, the points of the curve with negative slope are unstable because the resonant mode is unstable, whereas sidemode instability ( n =1) appears on the second unstable region of the HTB of the plot.