Lasing in optically induced gap states in photonic graphene

We thank the referee for her/his valuable comments on our work. She/he mentions three points that need to be clarified. Here is our answer:

1.- About the possible effects of heating and electro-optic effects.
Thermo-optic effects caused by heating of the semiconductor could indeed lead to a local modification of the optical potential, which could explain the emergence of localised states. As mentioned by the referee, heating is avoided here by modulating the excitation beam with a low duty cycle. When revising the manuscript, we realised that the actual duty cycle is 8x10^-4 instead of 1e-6, with a repetition rate of 0.8kHz. We have corrected this point in the revised version. We have checked that the experimental results do not change when modifying the duty cycle around the value used in the experiment. In any case, any thermo-optic effect would result in a redshift of the local potential at high power, while we observe a blueshift. These arguments allow to safely discard thermal effects.
As for electro-optic effects, they are expected to be extremely weak compared to the modification of the local exciton potential induced by the generation of free carriers and excitons in the quantum wells by the excitation beam at 740 nm. A recent study shows that in microcavities, electro-optic effects may appear in the form of Stark shifts of the energy of the quantum well [A. Hayat et al., PRL 109, 33605 (2012)]. In that study it was shown that extremely high peak powers, only available in pulsed experiments, are needed to induce a blueshift of the order of what we observe: they report 250fs pulses of 2mJ/cm^2 to induce a blueshift of 0.5meV. This corresponds to an equivalent average cw power of 1000W for the spot we use in our experiments. We can thus safely disregard this effect. In the revised version we have added the sentence: “Electro-optics effects can be discarded to be at the origin of the local blueshift due to the very low cw powers used in our experiments compared to the high peak energies required to induce a blueshift via Stark effect [A. Hayat et al., PRL 109, 33605 (2012)].”

2.- About the evidence for lasing.
Our claim of lasing in gap states is supported by two features: (i) the observation of a nonlinear threshold in the emitted intensity as a function of the excitation density (Fig. 1e and Fig. 3g), and (ii) the linewidth reduction across the threshold, which attests the emergence of long temporal coherence. Following the referee’s suggestion, we have now included a detailed analysis of the linewidth as a function of the excitation power for the gap mode in Fig 1 and for the S1 gap mode in Fig. 3. A reduction of the linewidth of a factor of two is observed at threshold. At higher power, nonlinear effects such as spectral wandering due to fluctuating trapped charges degrade the linewidth. We have added a description of the linewidth behaviour as a function of power in the revised text.

3.- About the connection between photonic lattice simulators and the understanding of 2D materials.
We have modified the conclusion section of the manuscript to clarify the interest and potentialities of our study for the understanding and experimental exploration of defect states in two-dimensional lattices.