Calibration of the polariton density
This protocol is extracted from research article:
Strongly interacting dipolar-polaritons
Sci Adv, Oct 19, 2018; DOI: 10.1126/sciadv.aat8880

To derive the relation between the number of photons emitted via the grating coupler and the density of the polaritons, we first used the following rate equation model for polaritons that propagate along the outcouplingEmbedded Image(5)where γ = γr + γnr is the overall decay rate, γnr is the nonradiative decay along the ITO channel under the output grating, and γr is the added loss due to the outcoupling of polaritons through the grating. In Fig. 6, we plotted the spatial distribution of the emitted PL from the area of the grating for F = 0. Because the emitted intensity is given byEmbedded Image(6)we foundEmbedded Image(7)where Embedded Image. By integrating over the emitted intensity, we could relate the total number of emitted photons Nph to the polariton density, which arrived to the grating n0 (see the Supplementary Materials for a more detailed derivation), and obtainedEmbedded Image(8)

An image of the grating when it is illuminated by white light (bottom) and the normalized PL along the grating, measured for F = 0 (top).

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