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IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)

Optical bistability in a fiber ring cavity with synchronous pulsed pump: anomalous and normal dispersion

Jorge García Mateos

Published Dec 17, 2002• 2 citations
Publisher

Abstract

Passive fiber cavities are basic nonlinear optical systems that are described by simple models - however they have a rich spectrum of complex behaviors (optical bistability, period-doubling bifurcations, chaos, modulational instability). From a practical point of view their study would have direct implications in the understanding of more complex cavity-based optical devices such as fiber lasers, Fabry-Perot lasers or APM lasers. Moreover, passive fiber cavities have potential applications in telecommunications as ultra-short pulse generators and as optical memories using their bistable behavior. This work is a contribution to the study of this bistable behavior with pulsed input, so that the device studied could be used for pulsed optical memory storage.

DOI
10.1109/leos.1994.586592

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Passive fiber cavities are basic nonlinear optical systems that are described by simple models - however they have a rich spectrum of complex behaviors (optical bistability, period-doubling bifurcations, chaos, modulational instability). From a practical point of view their study would have direct implications in the understanding of more complex cavity-based optical devices such as fiber lasers, Fabry-Perot lasers or APM lasers. Moreover, passive fiber cavities have potential applications in telecommunications as ultra-short pulse generators and as optical memories using their bistable behavior. This work is a contribution to the study of this bistable behavior with pulsed input, so that the device studied could be used for pulsed optical memory storage.
Optical storage devices are essential elements of future ultra-high bit-rate fiber communications systems in which they will find applications to various vital functions. Pulse pattern storage has been demonstrated in various fiber loop devices [1] that involve pulse control techniques in order to provide timing stability of the bit patterns. Most of these stabilization techniques are based on electrooptic modulation which limits the bit rates to a tenth of Gb/s. Moreover, erasing the data in these storage fiber loops requires switching off the system elect rooptically. Individual bit addressing is therefore impossible, which considerably restricts the functionality of the devices. We investigate here the possibility of developing a new type of all-optical fiber loop storage device. This device consists of a simple nonlinear passive fiber ring resonator synchronously and coherently pumped by a cw mode-locked train of ultrashort pulses. It is well known that this system exhibits rich nonlinear dynamics, in particular, optical bistability which is a feature naturally suited for applications to optical storage. However, erasing the data in an optical bistable element requires to switch off the holding beam and is therefore not practical. Recently, Haelterman et al. [2] have studied the polarization dynamics of nonlinear dispersive ring cavities with cw pump and have shown that these devices exhibit a polarization symmetry breaking characterized by a pitchfork bifurcation. This feature can be applied to the development of a set-reset flip-flop all-optical fiber loop pulsed memory. This work aims at presenting the results of a preliminary investigation of such a storage device.
We present a method for calculating the dynamic input–output characteristics of a nonlinear fiber ring resonator caused by a change in input intensity. It is based on an original method developed by Bischofberger and Shen [Phys. Rev. A 19, 1169 (1979)] to study a transient nonlinear Fabry–Perot resonator. We treat a double-coupler fiber ring resonator, in which two types of optical bistability (transmission bistability and reflection bistability) are available and present the illustrative numerical results for a few cavity parameters. This analysis will be useful for a future experimental verification of optical bistability in fiber ring resonators and for the design of fiber bistable devices.
Dispersive optical bistability and instabilities leading to period doubling, higher harmonics, and chaos in an all-optical passive quantum system are discussed theoretically and experimentally. These phenomena have been observed for a wide range of operating conditions in ring and Fabry-Perot resonators containing ammonia molecular gas as the nonlinear medium. Laser input intensity, gas pressure, and cavity tuning are the main control parameters in observation of these effects. The experimental results are well modeled by our generalization of standard two-level system theory to include standing-wave, reservoir, and transverse effects.
The subject of spontaneous pulsations in Optical Bistability has stimulated considerable interest following its prediction by Bonifacio, and Lugiato1 in the framework of the plane-wave, ring cavity model and the realization by McCall2 of an electro-optical converter of cw coherent light into pulsed radiation. In a subsequent important development Ikeda3 showed that, in the dispersive case, the Bonifacio-Lugiato instability leads to chaotic behavior (optical turbulence). This was later observed in a hybrid device by Gibbs, et al4.
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.
We present an analysis of the dynamic behavior of a nonlinear fiber ring resonator when an optical pulse with an arbitrary shape envelope is incident into it through a fiber directional coupler. The transient analysis is based on the extension of a well-known multiple-beam interference method to non-linear transmission problems. The steady-state analyses reported so far predict that the ring resonator exhibits reflection optical bistability in the input-output characteristics under appropriate conditions. But, our transient analysis shows that a nearly periodical oscillation of the transmitted power always takes place at a suitable initial detuning when the resonator has no loss or a small loss. It seems that the present instability is caused by the repetition of accumulation and release of the power in the ring resonator. We can obtain a bistable hysteresis loop by introducing a loss to the directional coupler. The dynamic behavior of bistability in a nonlinear fiber ring resonator with coupler loss is then investigated. It is found that a remarkable undershoot and overshoot occur in the switch-off curve and switch-on curve, respectively.