Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Topical Meeting on Optical Bistability (OB)

Optimised instability thresholds in a nonlinear Ring-Cavity

W. J. Firth, Scott Sinclair

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Optical bistability (OB) and instabilities in passive ring resonators containing Kerr media are described by the delay-differential system [1]: where E(t) is the intracavity field, τ the medium response time and ϕO the cavity mistuning. The nonlinear phase shift is denoted by ϕ(t).
DOI
10.1364/obi.1988.we.5

Related papers

OPTIMISED INSTABILITY THRESHOLDS IN A NONLINEAR RING CAVITY CONTAINING A KERR MEDIUM

W. J. Firth, Scott Sinclair

Stability analysis of an arbitrary finesse ring cavity containing a Kerr medium reveals an absolute minimum threshold for the driving intensity necessary for realisation of self-pulsing instabilities. This threshold is minimised not only with respect to cavity mistuning, but also with respect to the medium response time. The instability threshold is typically six times that for optical bistability. We have also generalised this model to include the effects of transverse diffusion.

Le Journal de Physique Colloques•Jun 1, 1988•0 citations

Absolute minimum instability thresholds in a nonlinear ring cavity containing a Kerr medium

W. J. Firth, Scott Sinclair

Stability analysis of an arbitrary-finesse ring cavity containing a Kerr medium of arbitrary response time reveals an absolute minimum threshold for the driving intensity necessary for realization of self-pulsing instabilities. This threshold is minimized not only with respect to cavity mistuning but also with respect to the medium's response time. The instability threshold is typically six times that for optical bistability.

Optics Letters•Mar 1, 1988•1 citation

Instability Thresholds in General Nonlinear Ring Resonators

W. J. Firth, Scott Sinclair

By considering a passive ring cavity with linear absorption in the dispersive limit, a unified analysis is presented for tuning-optimized minimum instability thresholds; the treatment is general, allowing consideration of arbitrary material response times, cavity tuning and finesse. In the adiabatic limit (τ → 0) the results reduce to the usual Ikeda map. The case of long medium-response time (τ → ∞) is treated in some detail in the high-finesse limit; these conditions being of particular relevance to semiconductor laser amplifiers. It is found analytically that in the high-finesse limit, both optical bistability and self-pulsing instabilities should exhibit the same low-threshold behaviour. An analytical expression is derived for the ‘instability threshold curve’, A 2 B against B for minimum A 2, in the mapping limit.

Journal of Modern Optics•Mar 1, 1988•3 citations

Bistability in nonideal double-ring cavities

Albert T. Rosenberger, Jeong-Mee Kim

Optical bistability in double-ring cavities, in which a ring cavity containing a nonlinear medium is nested within another ring cavity, has been considered and has been shown to exhibit frustrated instabilities,1 multistability,2 and threshold and response time reduced relative to a single-ring cavity.3

Annual Meeting Optical Society of America•Jan 1, 1993•0 citations

A nonlinear passive ring cavity: optical bistability

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

In Chapter 9 we discussed the case of a nonlinear cavity containing an active medium. In this framework, the outstanding phenomenon which arises is laser emission, and we calculated the stationary solutions for the ring laser. In this chapter, instead, we turn our attention to the passive nonlinear cavity and in this framework the outstanding phenomenon is optical bistability , i.e. the existence of two distinct stable stationary states that coexist for the same fixed values of the parameters in play. This phenomenon can arise also in the case of an active system contained in a cavity, as we have already noted in Section 9.1 and as we will discuss further in connection with the laser with injected signal, but it became popular from the studies of nonlinear passive optical cavities in the 1970s and 1980s. In contrast to the laser case, in the passive configuration we use an input coherent field, which is injected into the cavity. We discussed this case in Chapter 8 and derived a general equation for the transmission of the cavity (Eq. (8.23)), which we used for an empty cavity and for a linear cavity in Sections 8.4 and 8.5, respectively. In this chapter we will discuss the full nonlinear configuration. It is customary to identify two extreme cases of optical bistability called absorptive optical bistability and dispersive or refractive optical bistability . In both cases an essential ingredient to obtain the bistable behavior is the feedback action exerted by the mirrors of the cavity. In the purely absorptive configuration, in which there is exact resonance among the frequencies of the input field, of the atoms and of the cavity, the other essential ingredient is the saturable nonlinearity of the absorption. In the dispersive case, instead, the main feature is the nonlinearity of the refractive index. These two cases will be illustrated in Sections 11.1 and 11.2, respectively, both “exactly” and in the low-transmission limit.

Cambridge University Press eBooks•Feb 28, 2015•0 citations

Polarization patterns in a passive ring-cavity

J.B. Geddes, Jerome V. Moloney, Ewan M. Wright +1 more

A ring-cavity system, filled with an isotropic nonlinear medium and driven by a linearly polarized coherent input field, has been the subject of intense study over the last decade. This system can show a number of non-equilibrium phase transitions, including optical bistability (OB), and transverse pattern formation. The instability responsible for pattern formation then simply serves to drive the system from the unstable lower branch to the stable upper branch. This conclusion, however, is based on the assumption that the internal field in the nonlinear ring-cavity preserves its polarization state as that of the input field. Here we extend the mean field model to include polarization effects.>

Nonlinear Optics•Dec 17, 2002•0 citations
By considering a passive ring cavity with linear absorption in the dispersive limit, a unified analysis is presented for tuning-optimized minimum instability thresholds; the treatment is general, allowing consideration of arbitrary material response times, cavity tuning and finesse. In the adiabatic limit (τ → 0) the results reduce to the usual Ikeda map. The case of long medium-response time (τ → ∞) is treated in some detail in the high-finesse limit; these conditions being of particular relevance to semiconductor laser amplifiers. It is found analytically that in the high-finesse limit, both optical bistability and self-pulsing instabilities should exhibit the same low-threshold behaviour. An analytical expression is derived for the ‘instability threshold curve’, A 2 B against B for minimum A 2, in the mapping limit.
In Chapter 9 we discussed the case of a nonlinear cavity containing an active medium. In this framework, the outstanding phenomenon which arises is laser emission, and we calculated the stationary solutions for the ring laser. In this chapter, instead, we turn our attention to the passive nonlinear cavity and in this framework the outstanding phenomenon is optical bistability , i.e. the existence of two distinct stable stationary states that coexist for the same fixed values of the parameters in play. This phenomenon can arise also in the case of an active system contained in a cavity, as we have already noted in Section 9.1 and as we will discuss further in connection with the laser with injected signal, but it became popular from the studies of nonlinear passive optical cavities in the 1970s and 1980s. In contrast to the laser case, in the passive configuration we use an input coherent field, which is injected into the cavity. We discussed this case in Chapter 8 and derived a general equation for the transmission of the cavity (Eq. (8.23)), which we used for an empty cavity and for a linear cavity in Sections 8.4 and 8.5, respectively. In this chapter we will discuss the full nonlinear configuration. It is customary to identify two extreme cases of optical bistability called absorptive optical bistability and dispersive or refractive optical bistability . In both cases an essential ingredient to obtain the bistable behavior is the feedback action exerted by the mirrors of the cavity. In the purely absorptive configuration, in which there is exact resonance among the frequencies of the input field, of the atoms and of the cavity, the other essential ingredient is the saturable nonlinearity of the absorption. In the dispersive case, instead, the main feature is the nonlinearity of the refractive index. These two cases will be illustrated in Sections 11.1 and 11.2, respectively, both “exactly” and in the low-transmission limit.
A ring-cavity system, filled with an isotropic nonlinear medium and driven by a linearly polarized coherent input field, has been the subject of intense study over the last decade. This system can show a number of non-equilibrium phase transitions, including optical bistability (OB), and transverse pattern formation. The instability responsible for pattern formation then simply serves to drive the system from the unstable lower branch to the stable upper branch. This conclusion, however, is based on the assumption that the internal field in the nonlinear ring-cavity preserves its polarization state as that of the input field. Here we extend the mean field model to include polarization effects.>