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Holographic acoustic lenses (HALs), also known as acoustic holograms, are used for generating unprecedented complex focused ultrasound (FU) fields. HALs store the phase profile of the desired wavefront, which is used to reconstruct the acoustic pressure field when illuminated by a single acoustic source. Nonlinear effects occur as the sound intensity increases, leading to distorted and asymmetric waveforms. Here, the k-space pseudospectral method is used to perform homogeneous three-dimensional nonlinear acoustic simulations with power law absorption. An in-depth analysis is performed to study the evolution of holographic-modulated FU fields produced by HALs as the excitation amplitude increases. It is shown that nonlinear waveform distortion significantly affects the reconstruction of the pressure pattern when compared to the linear condition. Diffraction and nonlinear effects result in an asymmetric waveform with distinct positive and negative pressure patterns at the target plane. Peak positive pressure distribution becomes more localized around the areas with the highest nonlinear distortion. The peak signal-to-distortion ratio (PSDR) at the target plane falls while the nonuniformity index (NUI) rises. As a result of harmonic generation, the heat deposition distribution becomes highly localized with a significant increase in the NUI. Nonlinear effects have also been shown to flatten the peak negative pressure distribution while having minimal effect on the PSDR or NUI. However, nonlinear effects are shown to be critical for accurately predicting cavitation zones. Findings will pave the way for HALs implementation in high-intensity applications and prompt the incorporation of nonlinear acoustics into the notion of computer-generated holography.