Fig. 4.

Effect of disorder on the topological microlaser. a Numerical calculations for the spectrum of a disordered lattice when an onsite perturbation is introduced to the third site from the right (highlighted in red), as indicated schematically at the top of the same panel. b The mode profile of the topological eigenstate, normalised with identity norm calculated from the perturbed tight-binding Hamiltonian, where the general characteristics of the zero mode persist with addition of small light intensities on the previously dark sublattice (labelled in yellow marks). c SEM image of the perturbed topological laser array with an on-top thick layer of polymer covering the corresponding ring. Scale bar: 10 µm. d Measured emission spectrum of the perturbed laser array showing the maintained single-mode lasing feature against the introduced onsite perturbation. e Measured mode profile of the perturbed laser array. Despite the introduced perturbation, single-mode lasing and its spatial profile remain in the whole range of pump power (up to 2.4 GW m⁻² that is ~3 times the lasing threshold) used in our experiment. This robustness arises from the topological robustness of the defect even with nonlinearity above the threshold (see Supplementary Note 2)