Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

Abstract

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schrödinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques.

Wigner instability analysis of the damped Hirota equation

“…By following the incoherent MI analysis in the celebrated Wigner-function framework [11,13,54], we show that the Kerr interaction is more resilient to the third-orderdispersion stabilizing effects than the higher-order nonlinear interaction. We also see the SS contribution in conjunction with the Landau-type damping may augment the unstable spectrum in agreement with previous works dealing with generalized NLSEs [37,38]. Nonetheless any (first-order) instability signature eventually disappears by the action of strong damping strengths.…”

“…At first sight, we may appreciate that the instability growth rate significantly differs from the result (9) obtained via the Benjamin-Feir analysis (this is retrieved in the limit p 0 → 0). As similarly noted in the context of four-state atomic systems [37,38], the Eq. ( 12) unveils an intricate interplay between the highernonlinear corrections and a frequency bandwith: the contribution from the SS interaction to the instability growth rate exclusively couples to the Landau damping.…”

“…To summarize, we have shown that the incoherent modulation analysis reveals new features about the MI of the Hirota equation which are unappreciated by following the standard Benjamin-Feir treatment [21]: we found out that the Landau damping in conjunction with the SS interaction enhances up the instability features rendering an extended unstable spectrum [37,38]. On the other side, the instability structure arising from the Kerr interaction is significantly resilient to the stabilizing effects of the TOD, while the self-steepening contribution may be eventually cancelled out.…”

“…( 9) follows that the growth rate characteristic of the Benjamin-Feir instability is insensible to this. However, this situation drastically changes in presence of the Landau damping [51], and it is less clear how the TOD influences the instability structure owing to higher-nonlinear interactions [37,38]. We illustrate in the Figure 1 the results obtained from the numerical computation of the (maximum) MI gain (i.e.…”

“…Today it is broadly accepted that the (coherent) modulation instability (MI) is one of the principal physical mechanism explaining the rising of amplitude-growing periodic perturbations from unstable quasi-continuous pulses [19,20,21] (see also [22]). For instance, the baseband-type MI has been shown to be fundamental for the formation of rogue waves in the NLSE [10,19,23,24,25,26,27], the Hirota equation [11,28], and others higher-order generalized equations Email address: a.valido@iff.csic.es (Antonio A. Valido) [29,30,31,32,33,34,35,36,37,38]. Unfortunately, the MI mechanism is fragile to the unavoidable dissipation and noise (which commonly render stabilizing effects) present in most interesting situations, so a complete understanding of the experimental observation of extreme wave events driven by the MI starts by addressing the influence of realistic damping effects.…”