SESAM mode locked femtosecond laser at higher frequency up to gigahertz repetition rate suffers from the tendency for Q-switching instabilities. Increasing the pump power and decreasing the spot size at both the laser crystal and SESAM could help to stabilize the cw mode-locking of a gigahertz ultrafast laser. However, this is limited by the available laser diode pump power and may result in SESAM damage. Two photon absorption (TPA) effect in SESAM will generate ‘roll over’ effect of nonlinear reflectivity curve, which will decrease the critical pulse energy and critical pump power for cw mode-locking. By designing SESAM structures, we could optimize the ‘roll over’ effect and suppress the Q-switching instabilities. From simulation, we find out that enhanced SESAM with a cap layer thickness of 116nm and first GaAs layer thickness of 517nm will lead to a minimum critical pump power of 12.1W for our designed 1GHz laser cavity.