  Large bandgap semiconductor microwires constitute a very advantageous
alternative to planar microcavities in the context of room temperature strong
coupling regime between exciton and light. In this work we demonstrate that in
a GaN microwire, the strong coupling regime is achieved up to room temperature
with a large Rabi splitting of 125 meV never achieved before in a Nitride-based
photonic nanostructure. The demonstration relies on a method which doesn't
require any knowledge \'a priori on the photonic eigenmodes energy in the
microwire, i.e. the details of the microwire cross-section shape. Moreover,
using a heavily doped segment within the same microwire, we confirm
experimentally that free excitons provide the oscillator strength for this
strong coupling regime. The measured Rabi splitting to linewidth ratio of 15
matches state of the art planar Nitride-based microcavities, in spite of a much
simpler design and a less demanding fabrication process. These results show
that GaN microwires constitute a simpler and promising system to achieve
electrically pumped lasing in the strong coupling regime.
