Observation of soliton explosions in a passively mode-locked fiber laser

Soliton explosions are among the most exotic dissipative phenomena studied in mode-locked lasers. In this regime, a dissipative soliton circulating in the laser cavity experiences an abrupt structural collapse, but within a few roundtrips returns to its original quasi-stable state. In this work we report on the first observation of such events in a fiber laser. Specifically, we identify clear explosion signatures in measurements of shot-to-shot spectra of an Yb-doped mode-locked fiber laser that is operating in a transition regime between stable and noise-like emission. The comparatively long, all-normal-dispersion cavity used in our experiments also permits direct time-domain measurements, and we show that the explosions manifest themselves as abrupt temporal shifts in the output pulse train. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.Comment: 5 pages, 5 figures, submitte

Bifurcations of Periodic Orbits in the Generalised Nonlinear Schr\"{o}dinger Equation

We focus on the existence and persistence of families of saddle periodic orbits in a four-dimensional Hamiltonian reversible ordinary differential equation derived using a travelling wave ansatz from a generalised nonlinear Schr{\"o}dinger equation (GNLSE) with quartic dispersion. In this way, we are able to characterise different saddle periodic orbits with different signatures that serve as organising centres of homoclinic orbits in the ODE and solitons in the GNLSE. To achieve our objectives, we employ numerical continuation techniques to compute these saddle periodic orbits, and study how they organise themselves as surfaces in phase space that undergo changes as a single parameter is varied. Notably, different surfaces of saddle periodic orbits can interact with each other through bifurcations that can drastically change their overall geometry or even create new surfaces of periodic orbits. Particularly we identify three different bifurcations: symmetry-breaking, period-$k$ multiplying, and saddle-node bifurcations. Each bifurcation exhibits a degenerate case, which subsequently gives rise to two bifurcations of the same type that occurs at particular energy levels that vary as a parameter is gradually increased. Additionally, we demonstrate how these degenerate bifurcations induce structural changes in the periodic orbits that can support homoclinic orbits by computing sequences of period-$k$ multiplying bifurcations

Generalized and multi-oscillation solitons in the Nonlinear Schr\"odinger Equation with quartic dispersion

We study different types of solitons of a generalized nonlinear Schr\"odinger equation (GNLSE) that models optical pulses traveling down an optical waveguide with quadratic as well as quartic dispersion. A traveling-wave ansatz transforms this partial differential equation into a fourth-order nonlinear ordinary differential equation (ODE) that is Hamiltonian and has two reversible symmetries. Homoclinic orbits of the ODE that connect the origin to itself represent solitons of the GNLSE, and this allows us to study the existence and organization of solitons with advanced numerical tools for the detection and continuation of connecting orbits. In this way, we establish the existence of connections from one periodic orbit to another, called PtoP connections. They give rise to families of homoclinic orbits to either of the two periodic orbits; in the GNLSE they correspond to generalized solitons with oscillating tails whose amplitude does not decay but reaches a nonzero limit. Moreover, PtoP connections can be found in the energy level of the origin, where connections between this equilibrium and a given periodic orbit, called EtoP connections, are known to organize families of solitons. As we show here, EtoP and PtoP cycles can be assembled into different types of heteroclinic cycles that give rise to additional families of homoclinic orbits to the origin. In the GNLSE, these correspond to multi-oscillation solitons that feature several episodes of different oscillations in between their decaying tails. As for solitons organized by EtoP connections only, multi-oscillation solitons are shown to be an integral part of the phenomenon of truncated homoclinic snaking.Comment: 25 Pages, 13 figure

Nonlinear optics of fibre event horizons

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here, we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.Comment: 7 pages, 5 figure

Complex switching dynamics of interacting light in a ring resonator

Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and widespread applications. The increasingly high finesse (or $Q$ factor) of such resonators means that nonlinear effects are unavoidable even for low power, making them attractive for nonlinear applications, including optical comb generation and second harmonic generation. In addition, light in these nonlinear resonators may exhibit chaotic behavior across wide parameter regions. Hence, it is necessary to understand how, where, and what types of such chaotic dynamics occur before they can be used in practical devices. We consider a pair of coupled differential equations that describes the interactions of two optical beams in a single-mode resonator with symmetric pumping. Recently, it was shown that this system exhibits a wide range of fascinating behaviors, including bistability, symmetry breaking, chaos, and self-switching oscillations. We employ here a dynamical system approach to identify, delimit, and explain the regions where such different behaviors can be observed. Specifically, we find that different kinds of self-switching oscillations are created via the collision of a pair of asymmetric periodic orbits or chaotic attractors at Shilnikov homoclinic bifurcations, which acts as a gluing bifurcation. We present a bifurcation diagram that shows how these global bifurcations are organized by a Belyakov transition point (where the stability of the homoclinic orbit changes). In this way, we map out distinct transitions to different chaotic switching behavior that should be expected from this optical device.Comment: 22 pages, 10 figure