**[size=+3]Symmetric Immersed Beamsplitter**

We are required to design an immersed beamsplitter all of whose layers are dielectric and symmetric. An N-layer design is symmetric if layer number i is the same material and thickness as layer number N-i+1. The coating is immersed in glass (index 1.52) and must operate in the wavelength range 450-750 nm at 45 degrees. It should transmit 50% of S-polarized light. There is no requirement for P polarization.

The beauty of symmetric dielectric designs is that the phase difference between reflected and transmitted light is 90 degrees. This property is independent of the incident angle, polarization, or the fraction of light reflected/transmitted. This property derives from the fact that a symmetric dielectric coating is equivalent to a single layer of a non-real material.

Using TFCalc's capability of grouping layers, it is relatively easy to design symmetric coatings. We put the first and last layer in the same group; the second and second-to-the-last layer in another group, etc. Then we optimize groups instead of layers. A little experimentation showed that 11 layers (in six groups) would probably be enough for this design. The performance of this design is shown below. The long thin rectangle indicates the optimization target that was used.