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Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Experimental study of the response of a bad cavity bistable system to fast light switch-on

W. E. Schulz, W. R. MacGillivray, M. C. Standage

Published Dec 18, 1984• 3 citations
Publisher

Abstract

Abstract Preliminary results are reported on the response of an intrinsic bistable system to the rapid switch-on of an injected light field. The bistable system consists of a linear array of 25 sodium atomic beams contained in a low finesse Fabry—Perot etalon. The beams are aligned perpendicular to the direction of propagation of the cavity field and are collimated sufficiently to resolve the D-line ground state 32S1/2 hyperfine structure. The etalon conditions are such that the cavity lifetime is an estimated 6 ns compared with the atomic lifetime of 16 ns; hence the system approaches the bad cavity limit in which the atom dynamics should be observable. The radiation from a single-mode ring dye laser is switched on to the bistable system in approximately 1 ns. Although preliminary results show low branch to high branch switching there is no evidence of the expected nutational oscillations.

DOI
10.1098/rsta.1984.0130

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Physical Review A•Oct 1, 1983•143 citations
Abstract Preliminary results are reported on the response of an intrinsic bistable system to the rapid switch-on of an injected light field. The bistable system consists of a linear array of 25 sodium atomic beams contained in a low finesse Fabry—Perot etalon. The beams are aligned perpendicular to the direction of propagation of the cavity field and are collimated sufficiently to resolve the D-line ground state 32S1/2 hyperfine structure. The etalon conditions are such that the cavity lifetime is an estimated 6 ns compared with the atomic lifetime of 16 ns; hence the system approaches the bad cavity limit in which the atom dynamics should be observable. The radiation from a single-mode ring dye laser is switched on to the bistable system in approximately 1 ns. Although preliminary results show low branch to high branch switching there is no evidence of the expected nutational oscillations.
Experiments were performed on a bistable system consisting of a low finesse cavity and sodium atoms as the nonlinear medium. The atoms were excited by a dye laser system tuned to the D lines. Both ring and Fabry-Perot configurations were employed, and steady-state as well as transient behaviour was investigated. Flat mirrors of approximately 93% reflectivity were used in all experiments. With sodium vapour as the medium, experiments were performed in steady state, and a marked difference was observed in the behaviour of the Fabry-Perot cavity as compared to the ring set-up. This discrepancy could be explained when the sodium transition was modelled as a three - level lambda -type system, where the Doppler width is of the same order of magnitude as the ground state splitting. In this case the atoms with a Doppler shift close to half the ground state splitting have a major influence on the macroscopic refractive index. Extensive computer simulations were performed using this three -level model, and good qualitative agreement between experiment and theory was obtained for both types of cavity. A vacuum system containing a multiple atomic beam apparatus was constructed in order to reduce the Doppler width. Both the ring and the Fabry-Perot configuration could be set up inside the vacuum chamber.. The steady-state experiments displayed bistability when the laser intensity, laser frequency or cavity frequency were cycled. At higher atomic densities the system showed instabilities and multiple switching.
A bistable system consisting of an optical cavity with a medium of sodium atomic beams has been subjected to square pulses of light resonant with a D transition. The lifetimes of the field in the cavity and of the atomic medium are approximately equal. The system transmission data recorded has been compared with simulated data calculated from a theoretical model which treats the atomic energy configuration associated with the D lines as a three-level, lambda-type. Good qualitative agreement is obtained showing the system switching on to the high transmission branch. In particular, as the intensity of the input pulse ends, from the high intensity side, to the low to high branch transition threshold, switching is delayed by a time which is more than one order of magnitude longer than the field and atomic lifetimes.
The influence of noise on an optical bistable system in the vicinity of one of the bifurcation points is investigated by studying the transient response to a step input of light. The experiment is performed under absorptive conditions in a sodium-filled nonlinear Fabry-Perot in the bad cavity limit. Alternatively, a bistable electronic circuit (Schmitt trigger) is shown to exhibit the same type of behavior while admitting more detailed studies. On the monostable side of the bifurcation point, we observe a transient bimodality as well as a shift of the average switching delay to shorter times with increasing noise. Both results are in accord with a recent prediction by Broggi and Lugiato. We also present indications that the average switching time is smoothly connected with the lifetime of the metastable state on the bistable side of the bifurcation point.
In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip times. The slowing down of the cavity response occurs when the incident intensity is approximately equal to the critical switching intensity. This effect is called critical slowing down. As a result, the response of the cavity is much slower than what could be expected from the steady state analysis. The reflected intensity and the change in round-trip phase have similar dynamic response. In this research, the matlap programs are used to study the switching dynamics of a Fabry-Perot etalon.
In this work, the external switching dynamics of a Fabry-Perot etalon are studied via optical bistability system simulation. The simulated set-up of this investigation consists of two laser beams; the first beam is continuous (CW) which is considered as a biasing beam and capable of holding the bistable system for a certain range, which we are interested in, from a point that is very close self-switching to a point where the switching is unachievable. The second beam is modulated by passing the first beam through an acousto-optic modulator (AOM) to produce pulses with a minimum rise time and is used as an external source (coherent switching). In this work, we obtained the optical bistable loops by applying absorption coefficient (α) = 20cm-1, e sample etalon thickness (D) = 110μm, forward mirror reflectivity (Rf) = 0.6, and backward mirror reflectivity (Rb) = 0.95. The steady state characteristic of an initial detuning of the cavity (φ0) = 0.8 was studied at the conditions of no external input pulse intensity (M(t) = 0) and switching that takes place at Is(ON)= 0.57mW and Is(OFF) = 0.4mW.
Observations of steady-state hysteresis in absorptive bistability are reported for well-collimated atomic beams of sodium within a traveling-wave interferometer. The atomic medium approximates a system of homogeneously broadened "two-level" atoms, and effects due to standing waves are eliminated. The experiment thus represents the first demonstration of optical bistability under conditions that have been widely employed in theoretical models. Absolute measurements of switching intensities versus atomic cooperativity CCC are reported, and a preliminary comparison with Gaussian-beam theory is made.