The ATLAS Tile Calorimeter (TileCal) is a sampling hadronic calorimeter composed of alternating layers of thin steel absorbers and plastic scintillators. The emitted light is collected by wavelength-shifting fibres and transported to photomultipliers (PMTs), where the light is transformed into electric signals and digitized on-detector into seven readout samples using analog-to-digital converters (ADCs). The PMTs can be calibrated using the laser system, which delivers laser pulses from the service cavern via optical fibres to monitor and correct for PMT gain drifts. In this poster, we investigate the linearity of the PMT response using laser calibration runs with varying intensities of laser light, with special interest in the performance of new R11187 PMTs, which will replace approximately 10% of the legacy PMTs, particularly those in highly irradiated regions.