I made some simulation to study the change that the heater setup can induce on the Radius of Curvature of the ETM.
First, I used a non-sequential ray tracing software (Zemax) to calculate the heat pattern. I made a CAD of the elliptical reflector and I put a radiative element inside it (similar to the rod-heater 30mm long, 3.8mm diameter that we ordered), placing it in such a way that the heater tip is as close as possible to the ellipse first focus. (figure 1)
Then, by putting a screen at the second focus of the ellipse (where we suppose to place the mirror HR surface), I could find the projected heat pattern, as shown in figure 2 and 3 (section). Notice that the scale is in INCH, even if the label says mm. As you can see, the heat pattern is pretty broad, but still enough to induce a RoC change.
In order to compute the mirror deformation induced by this kind of pattern, I used this map produced with Zemax as absorption map in COMSOL. I considered ~1W total power absorbed by the mirror (just to have a unitary number).
The mirror temperature and deformation maps induced by this heat pattern are shown in figures 4 and 5.
RoC change evaluation
Then I had to evaluate the RoC change. In particular, I did it by fitting the Radius of Curvature over a circle of radius:
where is the waist of tha Gaussian mode on the ETMY (5mm) and n is the mode order. This is a way to approximately know which is the Radius of Curvature as "seen" by each HOM, and is shown in figure 6 (the RoC of the cold mirror is set to be 57.37m). Of course, besides being very tiny, the difference in RoC strongly depends on the heat pattern.
Gouy phase variation
Considering this absorbed power, the cavity Gouy phase variation between hot and cold state is roughly 15kHz (I leave to the SURFs the details of the calculation).
So the still unaswered questions are:
- which is the minimum variation we are able to resolve with our measurement
- how much heating power do we expect to be projected onto the mirror surface (I'll make another entry on that)