In the authors' previous work, the effect of a plasmonic metal hole array (MHA) as integrated on the infrared (IR) photodetector was demonstrated and its performance particularly at a normal incidence was analysed. However, in IR imaging, the associated optics or lens focuses and collimates the light to the detector, which in turn causes the incident light to bend with various angles. Since the MHA is integrated on top of the detector, it is critical to investigate its sensitivity against the angle of incidence and how it impacts the overall sensing capability. The splitting of the surface plasmon polariton (SPP) resonances due to MHA is reported here, since the incident angle varies. In the experiment, the SPP structure has been fabricated by a two-dimensional (2D) square array of subwavelength circular holes penetrating the gold film. The transmission spectra of the SPP structure in a mid-IR range have been measured for various incident angles. An interesting phenomenon is observed here, that is, the first- and second-order bimodal plasmonic spectra split into three or more peaks as the incident angle increases. Consistency in the experimental results with the simulation is found.