Fig. 1: Spectral sensitivity of network lasers to pump profile.

a Fluorescence image of a photonic network with interconnected dye-doped polymer nanofibers. As a guide to the eye, we highlight the graph topology (edges as blue lines, nodes as orange dots) over a few links as an example. Inset: scanning electron microscopy image of a node of the network formed by annealing two nanofibers (scale bar = 1 μm). The nanofibers have diameters in the range 200–500 nm and function as single-mode waveguides for light emitted by the dye. b Lasing spectrum of the network in a obtained with uniform illumination (blue) and with a slightly modified pump pattern (yellow), both at pump fluence of 1.5 mJ cm⁻² pulse⁻¹. The insets show the respective pump patterns; the illumination area on sample is 300 × 480 μm² and the modified pattern has pump removed from a small area 60 × 60 μm² in the centre of the illuminated rectangle. c A model planar photonic network modelled as a Buffon graph that is open at the boundaries. We highlight edges with more than 50% of the maximal amplitude of the electric field for a delocalised mode (orange edges, mode 1) and a localised mode (green edges, mode 2). d Numerical calculations of the lasing spectrum from the Buffon network in c obtained with netSALT. Spectra at pump power D₀ = 0.01 (SALT units) show ~ 50 lasing modes within the gain spectrum of dye (red dashed line). Note the suppression of mode 1 when changing from uniform pumping (blue, pump profile in inset) to a pump missing the two edges supporting the largest electric field amplitudes for mode 1 (yellow, pump profile in inset).