• B K Goswami

Articles written in Pramana – Journal of Physics

• Nonlinear resonance phenomena of a doped fibre laser under cavity-loss modulation: Experimental demonstrations

Our experiments with an erbium-doped fibre ring laser (CW, single transverse mode and multiaxial mode) with an intracavity LiNbO3 electro-optic modulator (EOM) display the characteristic features of a nonlinear oscillator (e.g., harmonic and period-2 sub-harmonic resonances) when the EOM driver voltage is modulated periodically. Harmonic resonance leads to period-1 bistability and hysteresis. Inside the period-2 sub-harmonic resonance region, the laser exhibits Feigenbaum sequence and generalized bistability.

• Flip-ﬂop between soft-spring and hard-spring bistabilities in the approximated Toda oscillator analysis

We study theoretically the effect of truncating the nonlinear restoring force (exp $(\Phi)−1 = \Sum^{\infty}_{n=1} \Phi^n/n!$) in the bistability pattern of the periodically driven, damped one-degree-of-freedom Toda oscillator that originally exhibits soft-spring bistability with counterclockwise hysteresis cycle. We observe that if the truncation is made third order, the harmonic bistability changes to hard-spring type with a clockwise hysteresis cycle. In contrast, for the fourth-order truncation, the bistability again becomes soft-spring type, overriding the effect of third-order nonlinearity. Furthermore, each higher odd-order truncation attempts to introduce hard-spring nature while each even-order truncation turns to soft-spring type of bistability. Overall, the hard-spring effect of every odd-order nonlinear term is weaker in comparison to the soft-spring effect of the next even-order nonlinear term. As a consequence, higher-order approximations ultimately converge to the soft-spring nature. Similar approximate analysis of Toda lattice has in recent past revealed remarkably similar ﬂip-ﬂop pattern between stochasticity (chaotic behaviour) and regularity (integrability).

• # Pramana – Journal of Physics

Volume 96, 2022
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Posted on July 25, 2019

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