Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Bistability and instability in passive and active optical systems with a general ring cavity model

Shufen Tian, Xijun Fan

Published Oct 28, 1992• 0 citations

Abstract

In this paper, the general ring cavity model of passive and active optical systems is presented. In the mean field and the Gaussian one transverse mode approximations, the steady state and stability properties of the systems are analyzed for mixed absorptive and dispersive cases. It is found that when the transmissivity ratio M (equals T1/T2) varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode, and the instability domain on the steady state curve varies obviously. The mode-pulling formula and bistable threshold with varying values of M are also discussed.

DOI: 10.1117/12.130441

Related papers

Analysis of ring cavity optically bistable systems with two partially reflecting mirrors of unequal transmissivity

Liguo Luo, Chen Jishu

The general ring cavity optically bistable systems with two partially reflecting mirrors of unequal transmissivity are analysed. In the mean field approximation, the steady state equation is given, and the linear stability analysis of the steady states is performed. It is found that when the ratio of transmissivity T_1/T_2 varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode. It is pointed out that in the mean field approximation there are many systems with (?)≡CT_1/L_v(?)1 and also many systems with (?)1. The self-pulsing instability is observed in the latter systems.

Jan 1, 19880 citations

Instabilities in passive and active optical systems with a Gaussian transverse intensity profile

L. A. Lugiato, R. J. Horowicz, G. Strini +1 more

In this paper we analyze the steady-state and stability properties of bistable optical systems, lasers with an injected signal, and ordinary free-running lasers. The starting point of our study is a unified model of a ring cavity containing a finite-size cylindrical sample of homogeneously broadened two-level atoms, and capable of supporting a single field mode with a Gaussian transverse profile. After solving the equations of motion in the steady state, we carry out a linear stability analysis of the stationary solutions, identify the domains of unstable operation of each of the three systems, and compare in detail the results of this work with those of earlier plane-wave uniform-field calculations. In the case of the laser with an injected signal, we find a significant enhancement of the instability domain relative to the plane-wave limit. A similar conclusion holds for mixed absorptive and dispersive optical bistability, although the enhancement of the domain of instability is less pronounced. Unstable behavior is predicted to occur for experimentally accessible values of the bistability parameter, and to be favored by the absence of bistability and by the selection of atomic and cavity detunings having opposite signs. This configuration ensures that the instability will be responsible for the emergence of undamped output pulsations of the type that will make the bistable system behave as an optical clock.

Physical Review ASep 1, 198447 citations

Off-resonant-mode instabilities in mixed absorptive and dispersive optical bistability

M. L. Asquini, L. A. Lugiato, H. J. Carmichael +1 more

We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.

Physical Review AJan 1, 198614 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 eBooksFeb 28, 20150 citations

ANALYSIS OF RING CAVITY OPTICAL BISTABLE SYSTEM WITH SINGLE OUTPUT

Lan Luo, Jian-Guan Chen

The ring cavity optical bistable system with single output is presented and analyzed. The steady state equation in the purely absorptive and resonant condition is given. The steady state curves in the mean field limit all exhibit a reverse S shape, and the critical value of the bistable cooperative coefficient C is equal to 2. The central section of the reverse S-shaped steady state curve proves to be always unstable. Moreover, a part of the steady state curve on the right hand of the central section may also lose its stability.

Jan 1, 19870 citations

RING CAVITY OPTICAL BISTABLE SYSTEM WITH SINGLE OUTPUT DRIVEN BY A GAUSSIAN BEAM

Xiangsuo Fan, Shuang Tian

The single output ring cavity optical bistable systems driven by a Gaussian beam are studied.The steady state equation is obtained and the linearized stability is analysed under the purely absorptive and resonant conditions using mean field approximation. The results show that the steady state light intensity curves still exhibit a reverse S shape but the unstable range in the case of Gaussian beam drive is manifestly different from that of plane wave beam drive.

Jan 1, 19890 citations