Modulation-Instability in odd non-linear waves

 

Modulation Instability (MI) is an ubiquitous phenomenon; It has been catalogued under various names, and manifests in diverse systems ranging from water waves to lasers. In this work, we study the interplay of MI and parity breaking (in particular odd viscosity) in a hydrodynamic system of surface gravity waves. We derive a generalised non-linear Schrodinger equation (NLSE) with an odd-viscosity dependent stability criterion for amplitude modulation. We find that the parity breaking effects result in different stability criterion for left and right moving modes of NLSE. 

In the end, we show that similar phenomena can arise in 1D dielectrics through the introduction of parity-breaking terms. We provide two different models as possible non-reciprocal optical platforms that realise the generalised NLSE.