Integrated optical technologies for quantum computing based on linear optics have been under active development in the recent decade. However, the nonlinear optical interactions ‘on a chip’ offer new unexplored functionalities and may play a key role. Recently a new class of nonlinear system has emerged in which light and matter play equally important roles. The basic building blocks of these systems are quantum states of matter coupled to enhanced optical fields found in microstructures. One example is the microcavity exciton-polariton: a mixed light-matter quasiparticle, resulting from the strong coupling of quantum well (QW) excitons to cavity photons.
Microcavity exciton-polaritons have numerous advantages over bare photons and excitons. For instance, due to the excitonic component, they exhibit weaker diffraction and tighter localisation, and the strong interparticle interactions result in lower operational powers ~fJ/mm2 and faster switching speeds ~a few ps. Polariton waves can be confined in structures with sub-micron size, which opens up possibilities for fabrication of polaritonic integrated circuits based on structured semiconductor microcavities on a chip. Laterally etched microcavity wires  (Fig. 1a) enhance further the polaritonic nonlinearities and thus are a particularly promising integration platform due to broad transparency window, mature fabrication technology and the possibility of monolithic integration with semiconductor diode lasers and VCSELs. In this respect, new theories and numerical methods are needed to model the nonlinear polariton dynamics in non-planar microcavity wires.
This work is focused on the largely unexplored nonlinear functionality of polaritons and the potential of self-organised structures, such as bright polariton solitons , to be exploited for signal processing in polaritonic networks on a chip. We aim at designing novel polariton devices based on polariton soliton logic.
We have developed a driven-dissipative mean-field model of the polariton nonlinear dynamics in non-planar microcavity wires . For a realistic microcavity wire, we found that the conventional for planar microcavities bistability evolves into complex multistability [Fig. 1b] and discussed its origin in detail. In contrast to the single-mode polariton solitons in planar microcavities, polariton solitons in microcavity wires exhibit a complex spatial multi-mode structure. Under suitable conditions, different modes within the polariton soliton wave packet interact among themselves in such a way as to give rise to a self-localisation mechanism that prevents the pulse from broadening (Fig. 1c). We have developed a modal expansion method  to investigate the nonlinear mechanisms behind localisation, and attempt to find a means to leverage the inter-modal interactions for the development of polaritonic integrated circuits. The multi-mode solitons deserve special attention, since they are capable of propagating further along an imperfect microcavity wire than their single-mode counterparts.
Using our 2D model, we investigate polariton soliton propagation in microcavity wires with different widths — with a view to designing integrated polaritonic devices . We simulate polariton soliton propagation in tilted and tapered microcavity wires, and determine the maximum tilt angle for which the soliton persists. Finally, we demonstrate numerically a new coherent propagation phenomenon of a radiating polariton soliton exhibiting periodic collapses and revivals, and identify regimes for existence of this new class of polariton solitons.
Further details will be presented at the NUSOD 2017 conference in Copenhagen (paper ThA1).
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