Profile of Beam Headed to Indium Cavity

We took a profile of the beam after the faraday headed to the cavity. To compute the beam parameters, I fit parameters to a TEM00 mode instead of using the beamspotsize python package to calculate parameters since that package allows M^2 to float, and the beam waist is inside the Faraday and unaccessible. Taking the folding mirror after the faraday to be z = 0, the waist is located at z = -102.5mm +- 26.1mm and the waist spot size is w0 = 55.0um +- 5.1um. The attached figure shows the curve fit results.

CMTF Optical Cavity Properties

We're preparing to set up a Pound-Drever-Hall lock to lock a Mephisto laser to a stable, indium optical cavity. The cavity has mirrors labeled "Y1-1037-0-0.50cc" and "PR1-1064-99-IF-1037-UV" the Y1 mirror looks to be a high-reflector with a zero-degrees angle-of-incidence and a 0.5 meter radius of curvature. The PR1 mirror looks to be a flat mirror coated to be 99% reflective at 1064nm on a 1037-UV substrate. Based on these parameters, we expect the cavity to have a finesse of F = -2*Pi/ln(R1*R2) = 625 where R1 = 1.00 and R2 = 0.99. The spacing between the mirrors is approximately 255mm and the mirror radii of curvature are r1 = 500mm and r2 = infinity so the cavity stability factor is g = (1 - L/r1)*(1 - L/r2) = (1 - 255/500)*1 = 0.49 so the cavity has a large stability margin. (Cavities are stable as long as 0 < g < 1 and are unstable otherwise.)

Added Faraday to Beam Path in CMTF at Fermilab

We added a lens, lambda/4, lambda/2, and a faraday isolator to the beam path on the CMTF table after the EOM. The faraday has 58mW of incident power and 50mW of transmitted power after tuning up the polarization with the waveplates and the beam position relative to the faraday using the lens. Before, we had problems with the beam clipping on the sides of the faraday when we tried to add it to the setup. After these alignment steps, the beam coming out of the faraday looks clean and gaussian -- see the attached image file.

Added EOM to CMTF Table

We added an EOM phase modulator to the optics table in the CMTF at Fermilab. There's 63.3 mW of power incident on the EOM and 60.6 mW of transmitted power through the EOM.

Bowtie Cavity Length Calculation and Update

To get the round trip Gouy phase of the cavity to 1/3, the total round trip length should be 2.4 m.

 

Current mirror locations: (X,Y) =  (10.655 in, 1.1033 in)

Current total round trip length = 4*X+4*sqrt(X²+Y²) = 85.47 in = 2.17 m

Need 2.4 m, so need to add 0.23 m = 9 in

This means every mirror needs to go 9 in / 8 = 1.125 in back

8 comes from 4 mirrors and the round trip

 

New mirror locations: (X,Y) =  (11.779 in, 1.163 in)

New total round trip length = 4*X+4*sqrt(X²+Y²) = 94.46 in = 2.40 m

 

Thus, I plan on buying sixteen 1.125 in spacers for the every mirror.

Preparing to add Phase Modulator EOM to Beam Path

We're going to add a Newfocus 4064 phase modulator (EOM) to the beam path to allow us to set up a PDH lock. We plan to place the phase modulator at the waist position of the beam. The waist size is 100um and the EOM has a 2mm diameter so we should have plenty of clearance. The EOM has a maximum intensity of 20 W/mm^2, and our beam has 60mW of power with a 100um waist giving a peak intensity of 4 W/mm^2, safely below the EOM's damage threshold.

Initial Beam Profile of Laser 256 in FermiLab's CMTF

An initial beam profile measurement of laser 256 at Fermilab indicates that it has a waist of 658 +- 173 um located at the front of the laser, a divergence angle of 6.36 +- 0.98 mrad, and a M^2 value of 6.17 +- 1.88. Since the waist is at the front of the laser and the beam needs to be attenuated before measuring it, I couldn't get any data points within 1 Rayleigh range of the waist, so the measured M^2 value is likely far from the true value. I measured the beam with a Thorlabs DCC1545M CCD camera and used the laserbeamsize python package to measure D4sigma beam diameters and characterize the beam waist, divergence, and M^2. The attached image shows the measured data and calculated beam parameters.

8 m Interferometer Vacuum Calculation

Calculation for Pfeiffer Vacuum Calculator:

Central vessel:

Treating as a cylinder

11.9 inch radius

11 inch height

 

V = pi*r^2*h = 4900 in^3 = 0.080 m^3

SA = 2*pi*r*h + 2*pi*r^2 = 1,700 in^2 = 1.1 m^2

End cube:

Treating as a cube, even though the inside is more spherical

L = 10 in

 

V = L^3 = 1,000 in^3 = 0.016 m^3

SA = 6*L^2 = 600 in^2 = 0.39 m^2

 

Tubes:

4 inch radius

275 in height (two 10 ft tubes + 1 ft T = 6.4 m, round up to 7 m including gate valve, reducer, etc)

V = pi*r^2*h = 13,800 in^3 = 0.23 m^3

SA = 2*pi*r*h = 6,900 in^2 = 4.5 m^2

 

Total:

Vessel + 5 Cubes + 2.1 Tubes (power recylcer ~0.7m):

V = 0.643 m^3 = 643 L

SA = 12.5 m^2

 

Assumed desorption: 1e-8 mbar*l/(s*cm²)

Assumed leak rate: 3e-9 mbar*l/s

Can then figure out what pumps and how many to use using the calculator

Cavity length with 1.6m ROC Mirror in cavities

BTgeom_gouyph_1C.pdf Shows the round-trip Gouy phase (fractional) of the cavity with the 1.6m optic as a function of the total round trip length. We want a Gouy phase of 0.33333 to filter, so the total round trip length should be 2.4m.

Lasers at Fermilab

I am working with Hudson Loughlin. He is visiting from MIT. We powered on the Mephisto laser 255 (formerly the L IFO of the Holometer). At Injection current of 2.017 and crystal temperatur of 24.57, we read 1.514 W using the Thorlabs power meter.

Temporary Piezo Purchase and Install for Filter Cavities

Because the Noliac order is delayed until mid to late August, we bought 4 Thorlabs PA44M3KW Piezo Rings for the Filter Cavities. The idea is to stack two of them in the piezo top where one Noliac NAC 2125-H08 will go. The set screws hold them as intended.

ULine Cabinet Inventory List

Entire mouser order is in the uline cabinet. Using this google sheet to track what goes where. Anyone with this link + a caltech address should be able to edit it.

Gain Margin and Phase Margin Relation

Using the calculated \( H_\infty \) limited controllers in the attached plot I show that as \( \gamma \) decreases the phase margin and the gain margin both increase. It also shows that the gain and phase margin are strongly correlated. In the plot the gamma is represented by the colors in the color bar and the current LIGO controller is shown as a blue triangle. The different lines of points are diffrent F1 gains and show that the relation between the gain margin and the phase margin is not always linear. However, generally speaking, this shows that gain margin and phase margin can be used somewhat interchangeably in this case. I'm not sure if this extends to all admissible controllers.

Mathjax? Adding Latex to the Logbook

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