A beamsplitter is an optical element that allows part of an electromagnetic wave to pass through while reflecting the other part. A simple dielectric can therefore serve as a beamsplitter. Consider the dielectric illustrated above with index of refraction n,thickness d,and Fresnel reflection and transmission coefficients r and t , and let and , and incident electric field intensity . Let be the phase of the single-reflected beam, the phase of the doubly-reflected beam, and so on. Then the zeroth-order term is







where is the phase difference upon passing through the dielectric. Similarly, the first-order term is















and the second-order term is












Therefore, by induction,


Now define

If all rays are collected,








so the power transmission is

But

where k is the wavenumber and l is the distance difference, and



Writing

then gives

The plots above show T as a function of frequency for various beamsplitter thicknesses.

Note that only the rays up to n = k are included, then