We study the properties of propagating polariton wave-packets and their connection to the stability of doubly charged vortices. Wave-packet propagation and related photoluminescence spectra exhibit a rich behaviour dependent on the excitation regime. We show that, because of the non-quadratic polariton dispersion, doubly charged vortices are stable only when initiated in wave-packets propagating at small velocities. Vortices propagating at larger velocities, or those imprinted directly into the polariton optical parametric oscillator (OPO) signal and idler are always unstable to splitting.
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