Abstract
We investigate and analyze temporal soliton interactions with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency), via split step Fourier numerical simulation. Truncated Airy pulses, which remain self-similar during propagation and have a ballistic trajectory in the retarded time frame, can interact with a nearby soliton by its accelerating wavefront property. We find by tracking the fundamental parameters of the emergent soliton-time position, amplitude, phase and frequency-that they alter due to the primary collision with the Airy main lobe and the continuous co-propagation with the dispersed Airy background. These interactions are found to resemble coherent interactions when the initial time separation is small and incoherent at others. This is due to spectral content repositioning within the Airy pulse, changing the nature of interaction from coherent to incoherent. Following the collision, the soliton intensity oscillates as it relaxes. The initial parameters of the Airy pulse such as initial phase, amplitude and time position are varied to better understand the nature of the interactions.
Highlights
Airy wave packets were first introduced in the context of quantum mechanics as a curiosity [1], exhibiting a solution to the Schrödinger equation which both maintains its form and continuously accelerates, in opposition to conventional wisdom
Since the truncated Airy pulse has the same center frequency and must maintain its first moment, it never completely crosses over the soliton; the wavefront consisting of the main lobe, which has been designed to maintain its identity within the collision range, and subsequent lobes, do cross the soliton. (The Airy with our truncation coefficient of a = 0.005 was designed to decay to half peak power at ξ = 16.7, beyond the collision zone.) the Airy-soliton interactions are classified as incomplete collisions, defined as having either an initial temporal overlap or a terminal overlap after the collision, as opposed to complete collisions
We have demonstrated the unique attributes of the interaction between a colliding Airy pulse and a soliton pulse at the same center frequency through split-step Fourier method simulations
Summary
Airy wave packets were first introduced in the context of quantum mechanics as a curiosity [1], exhibiting a solution to the Schrödinger equation which both maintains its form and continuously accelerates, in opposition to conventional wisdom. Solitons have been extensively studied in both the spatial [24] and temporal domains [25], the latter out of interest for application in optical communications [26,27] These studies have included soliton interactions, both coherent [21,28,29] (interactions between successive pulses in a bit stream) and incoherent [27,30] (collisions between pulses of different wave division multiplexing (WDM) channels, due to group velocity mismatch), and soliton perturbations from the stable solution [31,32,33,34,35,36,37,38,39]. We are interested to study whether the soliton will behave as an impenetrable barrier (as an event horizon) [42]—or rather analogously a shepherding pulse [43]—or whether the Airy probe can control the soliton propagation parameters [34], or as a collision perturbation [32], albeit the Airy can potentially have infinite energy (if non-truncated)
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