The quantum efficiency of an InAs/InAsSb type-II superlattice (T2SL) high operating temperature (HOT) long-wavelength infrared (LWIR) photodetector may be significantly improved by integrating a two-dimensional subwavelength hole array in a metallic film (2DSHA) with the detector heterostructure. The role of the metallic grating is to couple incident radiation into surface plasmon polariton (SPP) modes whose field overlaps the absorber region. Plasmon-enhanced infrared photodetectors have been recently demonstrated and are the subject of intensive research. Optical modelling of the three-dimensional detector structure with subwavelength metallic components is challenging, especially since its operation depends on evanescent wave coupling. Our modelling approach combines the 3D finite-difference time-domain method (FDTD) and the rigorous coupled wave analysis (RCWA) with a proposed adaptive data-point selection for calculation time reduction. We demonstrate that the 2DSHA-based detector supports SPPs in the Sommerfeld-Zenneck regime and waveguide modes that both enhance absorption in the active layer.