Temperature dependence of transmission characteristics of multilayer film narrow bandpass filters

This report describes the temperature dependence of the transmission center wavelength in narrow bandpass filters made of cavity type multilayer films. The center wavelength shift is represented in relation to the properties of the film and substrate materials and the layer stacking structure. Approximate expressions are presented for estimating the wavelength shift by using a form such as the average of the optical path length increment ratio. It is possible to eliminate the temperature dependence by selecting a substrate with a suitable thermal expansion coefficient, whose value can be estimated by a simple expression.