Wave spectrum at saturation and corresponding plasma wave-modes. Top panel: wave spectra in Fid simulation. The blue line for right-handed waves and red line for left-handed waves. Bottom panel: analytic dispersion relation of waves obtained by solving Eq. (16). The real part of ω (solid lines) and instability growth rate for the two polarizations that is the imaginary part of ω (dashed lines). The light-wave is shown with black solid line. The red star symbol at the top left side locates the intersection with ω = 2ω_pe line. Alfvén wave corresponds to low frequency and low-k part of red and blue solid lines. At kR_L,cr 1 the two branches separate into Whistler (blue solid line) and ion-cyclotron (red solid line). Vertical arrows in bottom panel locate the transition into ion-cyclotron regime (at kd_i = 1) for left-handed waves, and electron-cyclotron regime kd_e = 1 for right-handed waves. The lower red star symbol locates the intersection between the ion-cyclotron branch (red solid line) and Ω_ce – 3kυ_th,i (red dotted line).