The infrared films with ultra-high reflection is the key and basic materials for the realization of low loss optical device, infrared stealth, etc.. According to the transmission matrix principle of multilayer optical films, the reflectance and transmittance expressions of one-dimensional photonic crystals were obtained, and the energy band structure of one-dimensional photonic crystals was analyzed. Using the principle of transmission matrix, we designed a 28-layer λ/4 one-dimensional photonic crystal structure with Ge and SiO₂ as dielectric materials. Also, the first and second band gaps of the photonic crystal calculated by the finite element method to be 2.01×10¹³~4.11×10¹³ Hz and 8.13×10¹³~1.02×10¹⁴ Hz, respectively. The optimized λ/4 one-dimensional photonic crystal structure has as low as 14 layers, thus achieving high reflections of 3~5 μm and 8~14 μm.