I think the way to go is to go backwards from the cavity:

1. Adjust the length of the triangle to make the FSR smaller (easier to tune the lasers to a closer resonance)
2. Keepiing the curved mirror curvature as is, pick the length such that the HOM resonances are far away. In my attached notebook, I do this for the Mariner input mode cleaner. Its based on Shruti's earlier analysis, but with cooler colors. The main to make sure of is that the HOM of the lower sideband don't resonate. Should be easy as long as the transverse mode spacing is > the modulation frequency. If the mode spacing is too much than a HOM of the upper sideband could also resonate.
3. Based on the waist of that cavity, figure out a simple mode-matching solution with a single lens(?) and the ~1 mm beam that the fiber launcher can produce (check w profiler or razor blade).
4. We should hook up the little Watec video camera to look at the cavity transmission. Its much more informative than the photodiode. There is a B&W CRT monitor on the optics cabinet that we can use.

I also looked into the monotonic beatnote claim. Turns out that the Moku was set to compare the phase of the beat note relative to a internal 30 MHz signal. So the phase on the display was just integrating away. I set it back to acquire the frequency by itself, and the Moku frequency display now looks like some tiny random noise as it should. Whoever gets to the Moku next, please save the data and send it to me with dropbox.caltech.edu. Whoever knows the Moku's gmail should set up a Dropbox account for it so we can just save there all the time.

The beat note was initially at 174 MHz and I moved the temperature of the lasers around until I got the beat down to 40 MHz. Along the way, I noticed that beat note disappears for some settings of the temperature set point. I think that this is mode-hopping of the lasers, but it seems kind of outrageous if the mode-hop free region is only 100 MHz or so. Is it actually multi-mode behavior (thus making the laser so noisy that its basically broadband) or is there some other reason the beat goes away?

I also got the new laser working (with the beam scan laptop), and it says that its stable. So the next step is to bring over the blue PM fiber that runs to the green monster table and figure out how to get it onto the table in way where it won't immediately be stepped on. Then we're ready for the infinite hat method.

Does anyone know how to calculate what stability we would need for the fiber so as to be able to measure laser noise below the level of the RIO Planex?

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   "source": [
    "# Mariner: Higher Order Mode Analysis of IMC for Mariner Phase-I trial\n",
    "\n",
    "\n",
    "### Questions:\n",