Compressive-sensing based damped multi-mode extraction with nonuniform spatial sampling

•Multi-modes are extracted by compressive sensing(CS) with nonuniform spatial samples.•Similar accuracy in modal extraction is achieved using 75% less spatial samples.•Accurate sample location required by conventional methods is reduced by using CS.•Nuclear norm CS is more appropriate to reconstruct off-grid signals with damping.•Proposed method can be applied in different waveguides for multi-mode extraction.