A quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium. This system displays bistability and hysteresis in the semiclassical solutions. Quantum fluctuations are included via a Fokker-Planck equation in a generalised P representation. The transmitted light shows a transition from a single-peaked spectrum to a double-peaked spectrum above the threshold of the lower branch. Fluctuations in the field are reduced on the upper branch and both photon bunching and photon antibunching are predicted, for different operating points. An exact solution obtained for the steady-state generalised P function shows decidedly non-equilibrium behaviour, e.g. the lack of a Maxwell construction.

https://iopscience.iop.org/article/10.1088/0305-4470/13/2/034/pdf

Quantum theory of optical bistability. I. Nonlinear polarisability model

We report the observation of optical stability for a plane parallel semiconductor crystal which forms a Fabry‐Perot interferometer using only the natural reflectivity of its surfaces. Nonlinear transmission is observed for cw laser intensities above ∼ 100 W/cm2 for radiation at 1895 cm−1 near the energy gap of InSb at 5 K. The effect is interpreted in terms of a very large intensity‐dependent refractive index giving a 5λ/2 optical thickness change for an intensity of ∼2 kW/cm2. Clear bistability is seen in fifth‐order interference, the first such observation above first order in an intrinsic, one‐element system, in addition to regions exhibiting signal amplification. The same crystal also shows strong modulation of the transmission of one laser beam induced by a second, with real signal gain, thus demonstrating an ’’optical transistor.’’

Optical bistability and signal amplification in a semiconductor crystal: applications of new low‐power nonlinear effects in InSb

Recent fabrication advances have enabled compact semiconductor microring resonators to be fabricated with high-finesse values and picosecond cavity lifetimes. These devices have potential applications in optical signal processing as all-optical switches, multiplexers and logic gates. Theoretical analysis shows a maximum reduction in the switching power proportional to the fourth power of the field enhancement in the microring. An enhancement in the wavelength conversion efficiency by four-wave mixing which is proportional to the eighth power of the field enhancement is also predicted and experimentally confirmed. Experimental results demonstrating bistability, picosecond switching using pump and probe excitation, optical time-division demultiplexing, spatial pulse routing and four-wave mixing in GaAs-AlGaAs microring resonators are reported. Apart from the bistable response, which was thermally induced, the nonlinear effects observed in the microrings were caused by the two-photon absorption process. Applications of microrings to realize all-optical logic gates are also proposed.

Optical signal processing using nonlinear semiconductor microring resonators

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

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

A Fabry-Perot interferometer filled with a medium whose refractive index depends upon intensity has a multiple-valued transmission-vs-intensity characteristic. When the incident light is circularly polarized, and the nonlinearity is only cubic in the fields, Maxwell's equations may be solved exactly for the plane-parallel resonator field in terms of elliptic functions. An accurate approximate analysis is given for more general cases, including resonators with spherical mirrors and finite beams, where self-focusing is important. The theory is developed to yield design information for operation as an optical switch, "transistor," and power limiter.

F. S. Felber

Papers

Theory of a lossless nonlinear Fabry-Perot interferometer