Gives a broad description of optical bistability: from practical applications, as an optical transistor or optical memory element, to its phase transition interpretation. The theory is divided into three parts. The first is a simple discussion that covers most of the basic experimental effects and concepts of practical importance. The second part applies to atomic system where a semiclassical as well as a quantum-mechanical approach is possible. The third one discusses the mechanisms compatible with large nonlinearities observed in InSb and GaAs as semiconductors constitute the most promising materials for applications. Current experimental progress in all-optical and hybrid devices is also discussed and scaling example is presented to indicate the possibilities in high-speed all-optical signal processing.

https://iopscience.iop.org/article/10.1088/0034-4885/45/8/001/pdf

Optical bistability and related devices

In this, the first of two papers on the subject, we present an analysis of a non-linear optical system with a mode coupled to its second harmonic, exhibiting a rich variety of non-equilibrium steady-state transitions. Here we use a semiclassical analysis to examine the steady states and their stability, and thus predict the existence of various instabilities. We find that this system exhibits both first- and second-order phase transition-like behaviour, as well as having a hard mode transition. The application of this system as a switching device is also considered.

Non-equilibrium Transitions in Sub/Second Harmonic Generation

Optical bistability is a phenomenon which arises in the trans mission of light by an optical cavity filled with a resonant medium. Precisely, we consider a c-w laser beam which is injected into a resonant cavity tuned or nearly tuned to the incident light. The incident beam is partially transmitted, partially reflected and partially scattered by the cavity. When the cavity is empty the transmitted intensity is proportional to the incid ent intensity, where the proportionality constant depends on the cavity detuning. On the other hand, when the cavity is filled with material resonant or nearly resonant with the incident field the transmitted intensity is a nonlinear function of the incident intensity. In particular, under suitable conditions, the transmitted intensity varies discontinuously and exhibits a hysteresis cycle. This is the so-called Optical Bistability (OB). This phenomenon was predicted by SZ OKE and coworkers in 1969 [1]. Some years later McCA LL [2] performed a numerical treatment of OB in a Fabry-Perot cavity, which suggested the experiments of GIBBS, McCA LL and VENKA TESAN in Na and Ruby, in which the bistable response was nicely observed for the first time [3, 4]. These experiments have shown that this system is the basis for quite a number of device applications as optical memory, optical trans istor, clipper, limiter etc. These crucial results stimulated a very active theoretical research which bifurcated into two direc tions. The first channel was mainly interested in the device aspects of the phenomenon and in particular investigated the feasibility of electro-optical systems to produce bistability and related phenomena. A review of this approach can be found in [5]. The second channel [6 – 34] studies optical bistability as a fundamental chapter of the interaction between multiatomic systems and radiation. Precisely, it considers the optical bistable system as the passive counterpart of the laser. The semiclassical mean field of 0B has been developed in [6 – 12], the quantum statistical mean field theory in [13 – 23], the exact semiclassical treatment in a ring cavity in [24 – 25, 27 – 29], the numerical analysis in a Fabry-Perot cavity in [2,30 – 34].In particular the theory of 0B developed in [6 – 8, 10, 12 – 13, 18, 21,24 – 25, 27 – 29] has the following characteristics: it is completely microscopic, it is analytical, it takes propagation effects fully into account, it has been developed both at a semiclassical level, i.e. neglecting fluctuations and correlations, and at a fully quantum statistical level. In this paper we shall illustrate only the exact semiclassical theory in a ring cavity formulated in [24 – 25, 27 – 29].

Theory of Optical Bistability

On nonclassical effects in two-photon optical bistability and two-photon laser

We report what we believe to be the first systematic study of
Doppler-free, nonlinear absorption by use of cavity ringdown
spectroscopy. We have developed a variant of cavity ringdown
spectroscopy for the mid-infrared region between 9 and 11 µm,
exploiting the intracavity power buildup that is possible with
continuous-wave lasers. The infrared source consists of a
continuous-wave CO2 laser with 1-mW tunable infrared
sidebands that couple into a high-finesse stable resonator. We tune
the sideband frequencies to observe a saturated, Doppler-free Lamb dip
in the ν7, 111,10 ← 112,10
rovibrational transition of ethylene
(C2H4). Power studies of the Lamb dip
are presented to examine the intracavity effects of saturation on the
Lamb-dip linewidth, the peak depth, and the broadband
absorption.

Doppler-free nonlinear absorption in ethylene by use of continuous-wave cavity ringdown spectroscopy.

Optical bistabflity as a kind of first-order phase transition has been suggested and experimentally observed in an optical feedback system (1) as well as in a resonant absorber within an interferomcter ([ 2). A multiple-pass interferometer with a suitable nonlinear dispersive or absorptive mechanism can behave as a bistable optical system. The first suggestion was made by SZ6K~ et al. (1), and different versions have been shown to work with the nonlinearity due either to an atomic medium at resonance with the impinging field (2) or to an external feed-back system (3). We are here interested in the optical bistability arising from the collective behaviour of an atomic system. A general theory has been formulated in a series of papers by BONIFACIO and LVGIATO (4) to obtain absorptive and dispersive atomic bistability. As is well known from the first approaches (3) a difficulty of atomic bistability consists in inhomogeneous broadening due to the Doppler contribution of atom in a cell. We show here evidence of a bistable behaviour of an interferometer filled with a two-photon absorber and working in a travelling wave mode. This is the first step to derive, afterwards, a Doppler free atomic bistability (6) by absorbing photons from opposite directions and getting rid of the inhomogeneous line. We consider an n-level atom (fig. 1) where two relevant levels a and b with the same pari ty can be coupled by two-photon processes via all the other intermediate levels of suitable pari ty to satisfy the selection rules for one-photon processes. We introduce an interaction with a classical field that we write in the slowly varying envelope approximation as

F. T. Arecchi

Papers

Optical bistability in a resonant two-photon absorber