# Theory of optically controlled anisotropic polariton transport in semiconductor double microcavities

## TL;DR

This paper presents a theoretical study of the optical control of the optical spin Hall effect in semiconductor double microcavities, revealing how spin textures and anisotropic transport can be manipulated via external optical excitation.

## Contribution

It introduces a theoretical framework using spinor-polariton Gross-Pitaevskii equations to analyze and control the OSHE in double microcavities, highlighting the role of exciton interactions and polariton density.

## Key findings

- Controlled rotation of spin textures in momentum space.
- Identification of effective magnetic field components for optical control.
- Numerical solutions demonstrating tunable anisotropic transport.

## Abstract

Exciton polaritons in semiconductor microcavities exhibit many fundamental physical effects, with some of them amenable to being controlled by external fields. The polariton transport is affected by the polaritonic spin-orbit interaction, which is caused by the splitting of transverse-electric and transverse-magnetic (TE-TM) modes. This is the basis for a polaritonic Hall effect, called optical spin Hall effect (OSHE), which is related to the formation of spin/polarization textures in momentum space, determining anisotropic ballistic transport, as well as related textures in real space. Owing to Coulombic interactions between the excitonic components of the polaritons, optical excitation of polaritons can affect the OSHE. We present a theoretical analysis of the OSHE and its optical control in semiconductor double microcavities, i.e. two optically coupled cavities, which are particularly well suited for the creation of polaritonic reservoirs that affect the spin-texture-forming polaritons. The theory is formulated in terms of a set of double-cavity spinor-polariton Gross-Pitaevskii equations. Numerical solutions feature, among other things, a controlled rotation of the spin texture in momentum space. The theory also allows for an identification of the effective magnetic field component that determines the optical control in phenomenological pseudo-spin models in terms of exciton interactions and the polariton density in the second lower polariton branch.