Density calibration procedure
This protocol is extracted from research article:
Strongly interacting dipolar-polaritons
Sci Adv, Oct 19, 2018; DOI: 10.1126/sciadv.aat8880

The expression in Eq. 8 is used to derive the density of the polaritons given tp = 280 ps, Δy = 17 μm, d = 100 μm, and Embedded Image (see the Supplementary Materials). The value of Embedded Image is the same as the one calculated by fitting to Eq. 4. The group velocity, vg, which is the mean velocity of the polaritons, was extracted from the fits to the coupled oscillator model. From those fits, the population at each excitonic fraction χx(β) [or photonic fraction χph(β)] is found, from which the mean polaritonic fractions and the mean velocity are extracted. Nph is acquired from the counts of the ICCD, where we used the following calibration routine: First, we quantified the loss of the optical setup, using a laser beam traversing along the whole optical path of the system and measuring the relative transmitted power at the CCD (yielding a transmission of 0.4). Then, we directly measured the conversion between counts on the ICCD to incident photons. Using the above procedure, we extracted the conversion between photons entering the measurement system to counts on the ICCD. In addition, we also used a finite-difference time-domain simulation of the optical WG mode propagation under the output grating to find the ratio between the number of photons that are emitted toward the objective side to the number of photons that are emitted toward the substrate side. We found this ratio to be roughly unity, which adds a factor of 2 to the conversion between ICCD counts to polaritons. Because the angular emission spread from the sample (in the y direction, perpendicular to the WG-polariton propagation direction) is ~30°, while the effective optical acceptance of the setup (limited by the slit of the spectrometer in the Fourier configuration) lets only 0.73° in, we multiplied the counts to polariton conversion factor by 31/0.73 ≃ 42.

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