Determine "Dichroic Contribution Matrix"

[Jashcraf]

There are two unconstrained dichroic filters whose coating recipes we do not know. Given that the polarization operator is a function of phase thickness, test combinations of alternating HL refractive indices that make for a dichroic filter. Some optimization may be necessary

Ideal data product is a N x N matrix where each step is an additional HL layer, and the elements of the matrix are the average retardance of the jones pupil

[Jashcraf]

First we kind of need to understand the dichroic design space. We know the following about thin film design

• Designs are reported using HML, which represents a quarter wave stack of a film of High (H), Medium (M), or Low (L) refractive index
• The condition on physical thickness for a quarter wave stack is $d = \lambda/8n$

From Macleod, we are shown a couple of recipes for dichroic filters.

• [L/2 H L/2]^s is a shortpass filter
• [H/2 L H/2]^s is a longpass filter
• Any bandpass filter can be made with a series of these two

But, I don't know how to engineer the center wavelength or bandwidth of either of these filters.

[Jashcraf]

Ah, it was a skill issue all along. Start from the beginning.

So the building blocks of thin film optical filters are alternating stacks of quarter wave optical thickness (QWOT) layers centered on some design wavelength. This determines the center wavelength of the bandpass filter. The $\Delta g$ value, given by the following formula determines the width of the transmissive region.

Let's try this out for a Hafnia (H) and Silica (L) coating. The $\Delta g$ for this coating at the design wavelength is ~ 0.08

Looks like it works!

[Jashcraf]

Still working on this, moving forward using Jake Heath's 2020 SPIE proceedings talking about Dichroic beamsplitters at 45 degree angle of incidence.

For a "worst-cast", we can assign some of the matrices from Table 2 to each of the dichroics and spin the fast axis.

$\lambda = 630nm$, nearly a HWP

There's some phase unwrapping here, which causes the signals of greater than half a wave

$\lambda = 650nm$, nearly a QWP

This is a much smoother contour, with a very apparent global minimum and much greater retardance

[Jashcraf]

These are the space of all possible retardance values, but we need to understand what best represents the retardance.

[Jashcraf]

These were the phases of the jones matrices