Monday, November 03, 2014

The Optical Interference Matrix

Designing thin films is engineering an optical interference matrix. Phase shift at an interface produces interference. At the air to substrate interface and the layer to layer interface a phase shift takes place. When it comes down to it it's as simple as that and you should start to think of your designs as such.

I've heard many people claim that AR coatings need to have the last deposited layer be a material that is of "low" index.
What does that mean?
Designation of high or low or medium index is relative. It's relative to the substrate, the medium in which the optical system operates in, and the other material(s) used in the coating.

A simple example is a single layer AR coating.
On glass having an index of 1.9 a single layer of MgF2 will result in near 0%R at the design wavelength (1.38 being very close to the square root of 1.9).
On Ge a single layer AR could be made of ZnS having a refractive index of 2.2 resulting in a reflection of ~1.3%R (2.2 being close to the square root of 4).
The refractive index of ZnS is much higher than the index of MgF2, but much lower than the refractive index of Ge.

Comparing these two simple examples we can see that there is the same phase shift occurring at the air to film interface and the film to substrate interface regardless of the actual refractive index.

Going further with multi-layer AR coatings we can see with the design;
85.08L 43.3H 46.2L 27.73H (where nL=1.46 and nH= 2.2) on glass the result is an anti-reflection thin film at 532nm (a frequency doubled 1064 laser). (click to enlarge image)

Now this design may be impractical but it illustrates my point. An AR coating ending in a "high" index layer.
But it's important to keep in mind that the phase shift at the air to film interface is going to be the same no matter what the last deposited layer is (the medium to film boundary layer). The other layers in this multi-layer example are the rest of the optical interference matrix engineered to result in low reflection at the desired wavelength(s).

Looking at your design as an optical interference matrix this way increases your choices of materials. You can start to use harder / environmentally resistant materials as boundary layers, a third material to induce a phase shift change in the matrix at some point in your multi-layer, or choosing materials where equipment or deposition methods may be a limiting factor.

To see more about this and more examples watch Episode 9 of Coaters Tech videos.


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