Fig. 4. Non-Hermitian skin effect in multi-mode laser arrays.

a Schematic of the microring laser array where the length of the links is set to be central wavelength $\beta L\to \left(m+1/2\right)\pi$ to observe multi-mode behavior. b, c, f, g Multi-mode lasing operation in 2-element Hatano–Nelson system with the aforementioned link phase condition. The output intensity (incoherent superposition of two modes) is tilted towards right end (b, c) and left end (f, g), respectively. d, e, h, i Multi-mode lasing behaviors in 5-element systems. The output intensity localizes at the right end (d, e) when the upper links are pumped, and left side (h, i) when the lower ones are illuminated. These results confirm that the non-Hermitian skin effect universally applies to all modes and their incoherent (intensity) superposition. The number of the data points in the spectra is 288