Cause of reduced transmitted power in the defocusing diamond lattice when the flat band exits the dispersive band

Explain the cause of the significantly reduced transmitted power observed in the diamond lattice with defocusing nonlinearity when the coupling parameter c3>2 places the flat band outside the dispersive bands, despite the existence of a turning point and the occurrence of supratransmission for driving amplitudes above threshold at the flat-band frequency. Identify the dynamical or spectral mechanism that suppresses long-range power transmission under these conditions.

Background

By scanning transmitted power versus the driving amplitude and coupling parameters, the paper finds that when the flat band moves relative to the dispersive bands (tuned via c3 with c1=c2=1), the supratransmission threshold can persist even when the drive frequency lies within or outside the dispersive bands.

For the defocusing diamond lattice with c3>2, a turning point exists and supratransmission occurs; however, the transmitted power becomes significantly smaller than expected. The underlying reason for this reduction is not identified, motivating a targeted investigation of the responsible nonlinear dynamics or spectral features.