Transfer-matrix method in optics

Summary

The transfer-matrix method computes the reflection and transmission of a plane wave by a stack of flat homogeneous layers. Each layer is described by a $2 \times 2$ matrix that maps the tangential fields at one face to those at the other. The matrix of the whole stack is the product of the layer matrices, and the reflection and transmission coefficients follow from it. It is the standard tool for anti-reflection coatings, dielectric mirrors and thin-film interference, and it extends the Fresnel equations from one interface to many. It should not be confused with ray transfer matrix analysis, which uses $2 \times 2$ matrices for rays in geometrical optics.