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Physical Review A

Mirrorless optical bistability condition

Richard M. Friedberg, Sven R. Hartmann, Jamal T. Manassah

Published Apr 1, 1989• 56 citations
Publisher

Abstract

The mirrorless optical bistability problem is approached by analyzing the local relationship between the population inversion and the intensity of the laser excitation source. The active mechanism leading to bistability is the nonlinear Lorentz shift that changes sign along with the population inversion. Homogeneous broadening works against bistability. For a collision-broadened gas these factors are related and we show that the relationship is such that optical bistability is forbidden.

DOI
10.1103/physreva.39.3444

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Physical Review A•Jan 1, 1996•71 citations
The mirrorless optical bistability problem is approached by analyzing the local relationship between the population inversion and the intensity of the laser excitation source. The active mechanism leading to bistability is the nonlinear Lorentz shift that changes sign along with the population inversion. Homogeneous broadening works against bistability. For a collision-broadened gas these factors are related and we show that the relationship is such that optical bistability is forbidden.
Introduction Usage has reserved the expression optical bistability mostly for coherently driven passive systems. An atomic system is called passive when there is no population inversion. This is the case, for example, of a system at thermal equilibrium. On the contrary, the laser that we have described in Chapter 1 is a driven active system, because a population inversion is created. The laser equations we have studied so far describe an incoherently driven laser. However, nothing prevents driving a lasing cavity with a coherent field emitted by another laser. This is realized in a whole class of lasers that are used mainly as frequency converters. In optical bistability (OB), the driving field is usually a coherent field. Thus we have to account for two differences between the laser and the optically bistable system: (1) In OB, there is no inversion of population: 〈| A 2 |〉>〈| B 2 |〉, in the notation of Chapter 1. Hence, in the absence of interaction with a field, the population difference D relaxes toward a negative value. (2) The pumping is coherent, meaning that an external laser field is added to the cavity field. Using the single-mode equations (1.48)–(1.50), we have to change the sign of D and D a (which amounts to keeping D defined in (1.34) as it is but changing P into – P and A into – A ) and to add a source term in the equation for the complex field amplitude.
A new type of active optical bistability is described: frequency bistability as well as light intensity bistability. The device is quite simple—a laser with a passive filter. The gain medium of the laser is homogeneously broadened and has a broad fluorescence spectrum much greater than the longitudinal mode interval. The passive filter, in fact, is a set of mirrors with reflectivity varying with frequency. Its center frequency, that is, the frequency of maximum reflectivity, is different from that of the gain medium. The mechanism of this bistability is making use of the nonlinearity of both gain medium and passive filter vs frequency.
A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
Heat conduction and propagation of the electromagnetic field as well as temperature-dependent absorption are considered in a model for mirrorless optical bistability. The effects of temperature and laser-frequency detuning are calculated and discussed. It is shown that the multiple bistability of output intensity as a function of input intensity can be induced and controlled by the temperature boundary conditions. It is emphasized that changes in these boundary conditions determine the details of the transmission characteristics.
A theoretical modeling analysis is presented to study the optical bistability exhibited in the oscillation of an inhomogeneously broadened quasi-three-level laser. All the major characteristics of optical bistability depend on two normalized parameters, f and xa, which are defined by f = Isat,a/Isat,m and xa = 2αa0pa/δ and are related to measurable properties of the laser medium. In comparison with the case of a homogeneously broadened laser, the essential condition for the occurrence of such bistability, f < xa/(xa + 1), turns out to be the same, whereas the intensities at the up- and down-thresholds are substantially increased and the bistability range is reduced.
The bistable response of linear molecular aggregates modeled as linear chains of two-level systems is shown. We carry out analytical and numerical calculations of the aggregate population by means of the system of coupled nonlinear equations for the density matrices of individual molecules. Our conclusion is that bistable behavior of the population results from the dependence of resonance frequency of the aggregate on the number of excited molecules. \textcopyright{} 1996 The American Physical Society.