## Response of an acousto-optic device with feedback to time-varying inputs

Applied Optics, Vol. 31, Issue 11, pp. 1842-1852 (1992)

http://dx.doi.org/10.1364/AO.31.001842

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### Abstract

We investigate the response of an acousto-optic bistable device to time-varying acoustic inputs. The device modeled by a two-hump one-dimensional autonomous nonlinear map in which the (implied) is justifiably period is determined by the feedback time of the device. Our newly added time-varying input has a map period much greater than the feedback time and for simplicity is taken in the form of a periodic square pulse. We use numerical simulation and a matrix method to predict the general behavior of the output intensity at specific instants of time. Background knowledge, viz., general comments on the nature of one-two-hump one-dimensional maps and their distinction, is also presented in a unified fashion to aid in and the understanding of the dynamics of the device. We find that novel changes of the output period can occur for significant feedback amplitudes, and that these changes can be sensitively controlled.

© 1992 Optical Society of America

**History**

Original Manuscript: January 2, 1990

Published: April 10, 1992

**Citation**

Partha P. Banerjee, Uday Banerjee, and Harvey Kaplan, "Response of an acousto-optic device with feedback to time-varying inputs," Appl. Opt. **31**, 1842-1852 (1992)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-11-1842

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### References

- E. Ott, C. Grebogi, J. A. Yorke, “Experimental control of chaos” in Chaos, D. K. Campbell, ed. (American Institute of Physics, New York, 1990), pp. 153–172.
- W. L. Ditto, S. N. Rauseo, M. L. Spano, “Experimental control of chaos,” Phys. Rev. Lett. 65, 3211–3214 (1990). [CrossRef] [PubMed]
- J. Singer, Y.-Z. Wang, H. H. Bau, “Controlling a chaotic system,” Phys. Rev. Lett. 66, 1123–1125 (1991). [CrossRef] [PubMed]
- A. J. Irwin, S. J. Fraser, R. Kapral, “Stochastically induced coherence in bistable systems,” Phys. Rev. Lett. 64, 2343–2346 (1990). [CrossRef] [PubMed]
- A. Hubler, E. Luscher, “Resonant stimulation and control of nonlinear oscillators,” Naturwissenschaften 76, 67–69 (1989). [CrossRef]
- P. P. Banerjee, A. Ghafoor, “Design of a binary parallel optical processor,” Appl. Opt. 27, 4766–4770 (1988). [CrossRef] [PubMed]
- H. M. Gibbs, Optical Bistability (Academic, New York, 1985).
- A. Korpel, Acousto-Optics (Dekker, New York, 1989).
- J. Chrostowski, C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982). [CrossRef]
- J. Chrostowski, R. Vallee, C. Delisle, “Self-pulsing and chaos in acoustooptic bistability,” Can. J. Phys. 61, 1143–1148 (1983). [CrossRef]
- H. Jerominek, C. Delisle, J. Y. D. Pomerleau, R. Tremblay, “Bistability, optical regenerative oscillations and chaos in an integrated acoustoopic device,” Can. J. Phys. 63, 227–233 (1985). [CrossRef]
- F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982). [CrossRef]
- M. W. Derstine, H. M. Gibbs, F. A. Hopf, D. L. Kaplan, “Alternate paths to chaos in optical bistability,” Phys. Rev. A 27, 3200–3208 (1983). [CrossRef]
- H.-J. Zhang, J.-H. Dai, P.-Y. Wang, F.-L. Zhang, G. Xu, S.-P. Yang, “Chaos in liquid-crystal optical bistability,” in Directions in Chaos (2), H. B. Lin, ed. (World Scientific, Singapore, 1988), pp. 46–89.
- F. T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49, 1217–1220 (1982). [CrossRef]
- L. A. Lugiato, L. M. Narducci, D. K. Bandy, C. A. Pennise, “Breathing, spiking and chaos in a laser with injected signal,” Opt. Commun. 46, 64–68 (1983). [CrossRef]
- E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20, 130–141 (1963). [CrossRef]
- J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
- M. LeBerre, E. Ressayre, A. Tallet, H. M. Gibbs, “High-dimension chaotic attractors of a nonlinear ring cavity,” Phys. Rev. Lett. 56, 274–277 (1986). [CrossRef]
- J. Belair, L. Glass, “Universality and self-similarity in the bifurcations of circle maps,” Physica 16D, 143–154 (1985).
- P. Collet, J. P. Eckmann, Iterated Maps on the Interval as Dynamical Systems (Birkhauser, Boston, 1980).
- N. Metropolis, M. L. Stein, P. R. Stein, “On finite limit sets for transformation on the unit interval,” J. Comb. Theory 15, 25–44 (1973). [CrossRef]
- P. Mandel, R. Kapral, “Subharmonic and chaotic bifurcation structure in optical bistability,” Opt. Commun. 47, 151–156 (1983). [CrossRef]
- Starting values of x that are sufficiently close to any subbasin boundary, such as the position of a vertical line in Fig. 4, each of which acts as an unstable fixed point, will iterate for a long time according to the linearized map in the neighborhood of that point before leaving that neighborhood.
- In order to show that the hundredth iterate represents a period-four orbit rather than, for instance, four fixed-point attractors, we can graphically compound the map with its hundredth iterate, e.g., f101 = f0100° f, by the usual method [see H. Kaplan, Am. J. Phys. 55, 1023 (1987)]. [CrossRef]
- P. Cvitanovic, “Invariant measurement of strange sets in terms of limit cycles,” Phys. Rev. Lett. 61, 2729–2732 (1988). [CrossRef] [PubMed]

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