Calculation model for spectral coefficient’s first and second order partial derivatives of multilayer optical coatings with respect to layer parameters

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings, an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness, real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix. This partial derivative computation model characterizes the same applicable condition and universality in physics with the matrix theory mentioned above. Thus it can also be applied to any homogenous and isotropic layered multilayer system.