Sideway scattered second-harmonic spectra emitted from a 1064-nm-laser-produced plasma have been observed to originate from nonlinear coupling near the critical surface. The time evolution of the second-harmonic optical density confirmed the possibility that a plasmon issued from the resonant absorption of the incident beam can recombine with a photon (omega0) to give a transverse wave of frequency 2omega0. A plasmon issued from a parametric decay instability may also, by coalescence with an incident photon, give a transverse wave at a shifted second-harmonic frequency. The threshold of such a combination is determined. Moreover, irregular plasma-parameter variations and the perturbed spatial uniformity of the incident beam appear to alter the second-harmonic spectra. An oscillatory structure of the optical density of the observed second harmonic is interpreted as a result of the coupling physics involved and of laser-beam filamentation.