Abstract
We present an analysis of temporal modulation instability in a ring array of coupled optical fibers. Continuous-wave signals are shown to be unstable to perturbations carrying discrete angular momenta, both for normal and anomalous group velocity dispersion. We find the frequency spectrum of modulation instability is different for each perturbation angular momentum and depends strongly on the coupling strength between fibers in the ring. Twisting the ring array also allows the frequency spectra to be tuned through the induced tunnelling Peierls phase.
Highlights
Modulation instability (MI) of plane waves in anomalously-dispersive optical fibers with a self-focusing Kerr nonlinearity is one of the most well-known phenomena in nonlinear optics [1]
This temporal MI of discrete angular momentum signals has been little explored compared to the well-known azimuthal instability pointed out above
A Peierls phase introduced by coiling the ring around its propagation axis adds a further degree of depth and potential control to these spectra, but it is by no means necessary to observe this novel MI
Summary
Modulation instability (MI) of plane waves in anomalously-dispersive optical fibers with a self-focusing Kerr nonlinearity is one of the most well-known phenomena in nonlinear optics [1]. Continuous-wave signals subject to MI break up into a train of pulses as fluctuations grow through the nonlinearity, resulting in a characteristic spectrum of a pair of symmetric sidebands about the signal’s original frequency It has been observed in higher dimensional systems, in particular as an azimuthal instability of optical vortices in continuous self-focusing quadratic [2], Kerr [3, 4], saturable [5, 6] and defocusing Kerr [7] nonlinear media. We show that plane wave supermodes of fiber arrays as shown in figure 1 can be unstable in the presence of perturbations and that the gain spectra of these perturbations depends on their angular momenta Until now, this temporal MI of discrete angular momentum signals has been little explored compared to the well-known azimuthal instability pointed out above. We examine how twisting the array can introduce (or suppress) unstable modes, depending on the coupling between neighbouring cores in the ring
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