We experimentally demonstrate and analyze two different techniques for apodizing the nonlinear coupling in aperiodically poled MgO:LiNbO₃ (APPLN) used in an ultrabroadband optical parametric chirped pulse amplifier (OPCPA). With an adiabatic increase of the nonlinear coupling, a smooth gain spectrum and spectral phase is preserved during amplification in such media. The two approaches we explore are poling period apodization (PPA) and duty cycle apodization (DCA). For the first implementation of the apodized APPLN amplifier we use a constant chirp-rate in the grating k-vector. The nonlinear coupling is apodized over 10% of the total length at each side of the APPLN chip. This allows us to achieve high-intensity output pulses with clean temporal structure.