Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters

In this study, an analytical model is developed to evaluate the effects of uniform and nonuniform temperature increases, as well as stress level, on the optical characteristics of three-cavity sub-nanometer bandpass filters fabricated using TiO₂ and SiO₂ film materials through ion-assisted deposition (IAD), taking into account the coupled photoelastic and thermo-optical effects. A more realistic stress analysis, which is capable of considering the effects of intrinsic and thermal stresses, bending moment as well as nonuniform temperature increase, is proposed and formulated for the first time. Various factors, including errors in film thickness, changes of refractive index and film thickness due to temperature increase and stress as well as the delamination gap along the layer interface, are then considered to evaluate their individual influence on optical characteristics of bandpass filters. The results show that the change of film thickness due to temperature increase and stress has a significant effect on center wavelength shift. Moreover, a significant degradation of the transmission curve due to nonuniform temperature increase was observed.