The short focal depth of a Gaussian beam limits the volumetric imaging speed of optical resolution photoacoustic microscopy (OR-PAM). A Bessel beam, which is diffraction free, provides a long focal depth, but its side lobes deteriorate image quality when the Bessel beam is directly employed to excite photoacoustic (PA) signals in OR-PAM. We present a nonlinear approach based on the Grueneisen relaxation effect to suppress the side-lobe artifacts in PA imaging. This method extends the focal depth of OR-PAM and speeds up volumetric imaging. We experimentally demonstrated a 1-mm focal depth with a lateral resolution and volumetrically imaged a carbon fiber and red blood cell samples.