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Entry  Thu Jun 21 03:07:27 2012, Zach, Optics, Configuration, Parameter selection / mode definition geom_bowtie.pnggeom_non-bowtie.png

EDIT 2 (ZK): As with the previous post, all plots and calculations here are done with my MATLAB cavity modeling utility, ArbCav.

EDIT (ZK): Added input q parameters for OMMT 

found the nice result that the variation in the optimal length vs. variation in the mirror RoC is roughly linear within the ±1% RoC tolerance. So, we can choose two baseline mode definitions (one for each mirror topology) and then adjust as necessary following our RoC measurements.

Bowtie

For R = 2.5 m, the optimal length (see previous post) is LRT = 1.150 m, and the variation in this is dLRT/dR ~ +0.44 m/m.

Here is an illustration of the geometry:

geom_bowtie.png

The input q parameters, defined at the point over the edge of the OMC slab where the beam first crosses---(40mm, 150mm) on the OptoCad drawing---are, in meters:

  • qix = - 0.2276 + 0.6955 i
  • qiy = - 0.2276 + 0.6980 i

 

Non-bowtie

For R = 2.5 m, the optimal length is LRT = 1.246 m, and the variation in this is also dLRT/dR ~ +0.44 m/m.

Geometry:

geom_non-bowtie.png

q parameters, defined as above:

  • qix = - 0.0830 + 0.8245 i
  • qiy = - 0.0830 + 0.8268 i
Entry  Wed Jun 20 20:37:45 2012, Zach, Optics, Configuration, Topology / parameter selection 8x

EDIT (ZK): All the plots here were generated using my MATLAB cavity modeling tool, ArbCav. The utility description is below. The higher-order mode resonance plots are direct outputs of the function. The overlap plots were made by modifying the function to output a list of all HOM resonant frequencies, and then plotting the closest one as a function of cavity length. This was done for various values of highest mode order to consider, as described in the original entry.

Description:

This function calculates information about an arbitrary optical cavity. It can plot the cavity geometry, calculate the transmission/reflection spectrum, and generate the higher-order mode spectrum for the carrier and up to 2 sets of sidebands.

The code accepts any number of mirrors with any radius of curvature and transmission, and includes any astigmatic effects in its output.

As opposed to the previous version, which converted a limited number of cavity shapes into linear cavities before performing the calculation, this version explicitly propagates the gouy phase of the beam around each leg of the cavity, and is therefore truly able to handle an arbitrary geometry.

----------------Original Post----------------

I expressed concern that arbitrarily choosing some maximum HOM order above which not to consider makes us vulnerable to sitting directly on a slightly-higher-order mode. At first, I figured the best way around this is to apply an appropriate weighting function to the computed HOM frequency spacing. Since this will also have some arbitrariness to it, I have decided to do it in a more straightforward way. Namely, look at the spacing for different values of the maximum mode number, nmax, and then use this extra information to better select the length.

Assumptions:

  • The curved mirror RoC is the design value of 2.50±0.025 m
  • The ±9 MHz sidebands will have ~1% the power of the other fields at the dark port. Accordingly, as in Sam's note, their calculated spacing is artificially increased by 10 linewidths.
  • The opening angle of 4º is FIXED, and the total length is scaled accordingly

Below are the spacing plots for the bowtie (flat-flat-curved-curved) and non-bowtie (flat-curved-flat-curved) configurations. Points on each line should be read out as "there are are no modes of order N or lower within [Y value] linewidths of the carrier TEM00 transmission", where N is the nmax appropriate for that trace. Intuitively, as more orders are included, the maxima go down, because more orders are added to the calculation.

*All calculations are done using my cavity simulation function, ArbCav. The mode spacing is calculated for each particular geometry by explicitly propagating the gouy phase through each leg of the cavity, rather than by finding an equivalent linear cavity*

 ovlp_bowtie.pngovlp_non-bowtie.png

Since achievable HOM rejection is only one of the criteria that should be used to choose between the two topologies, the idea is to pick one length solution for EACH topology. Basically, one maximum should be chosen for each plot, based on how how high an order we care about.

Bowtie

For the bowtie, the nmax = 20 maximum at L = 1.145 m is attractive, because there are no n < 20 modes within 5 linewidths, and no n < 25 modes within ~4.5 linewidths. However, this means that there are also n < 10 modes within 5 linewidths, while they could be pushed (BLUE line) to ~8.5 linewidths at the expense of proximity to n > 15 modes.

Therefore, it's probably best to pick something between the red and green maxima: 1.145 m < L < 1.152 m.

By manually inspecting the HOM spectrum for nmax = 20, it seems that L = 1.150 m is the best choice. In the HOM zoom plot below and the one to follow, the legend is as follows

  • BLUE: Carrier
  • GREEN: +9 MHz
  • RED: -9 MHz
  • CYAN: +45 MHz
  • BLACK: -45 MHz

spect_zoom_bowtie.png

Non-bowtie

Following the same logic as above, the most obvious choice for the non-bowtie is somewhere between the red maximum at 1.241 m and the magenta maximum at 1.248 m. This still allows for reasonable suppression of the n < 10 modes without sacrificing the n < 15 mode suppression completely.

Upon inspection, I suggest L = 1.246 m

spect_zoom_non-bowtie.png

I reiterate that these calculations are taking into account modes of up to n ~ 20. If there is a reason we really only care about a lower order than this, then we can do better. Otherwise, this is a nice compromise between full low-order mode isolation and not sitting directly on slightly higher modes.

 

RoC dependence

One complication that arises is that all of these are highly dependent on the actual RoC of the mirrors. Unfortunately, even the quoted tolerance of ±1% makes a difference. Below is a rendering of the RED traces (nmax = 20) in the first two plots, but for R varying by ±2% (i.e., for R = 2.45 m, 2.50 m, 2.55 m).

ovlp_vs_R_bowtie.pngovlp_vs_R_non-bowtie.png

The case for the non-bowtie only superficially seems better; the important spacing is the large one between the three highest peaks centered around 1.24 m.

Also unfortunately, this strong dependence is also true for the lowest-order modes. Below is the same two plots, but for the BLUE (nmax = 10) lines in the first plots.

 ovlp_vs_R_N10_bowtie.pngovlp_vs_R_N10_non-bowtie.png

Therefore, it is prudent not to pick a specific length until the precise RoC of the mirrors is measured.

 

Conclusion

Assuming the validity of looking at modes between 10 < n < 20, and that the curved mirror RoC is the design value of 2.50 m, the recommended lengths for each case are:

  • Bowtie: LRT = 1.150 m
  • Non-bowtie: LRT = 1.246 m

 HOWEVER, variation within the design tolerance of the mirror RoC will change these numbers appreciably, and so the RoC should be measured before a length is firmly chosen.

Entry  Wed Jun 20 00:10:53 2012, Koji, Facility, General, Hole on the wall was patched P6191706.jpg

P6191706.jpg

Entry  Sat Jun 16 08:53:09 2012, Koji, General, General, To Do List 

Facility

Mechanics

  • Work 
    •  
  • Design
    • How do we hold the PDs, QPDs, and black glass - we put 2 PDs and 2 QPDs on the PD mounting blacket.
    •  
  •  
  • Test
     
  • Things to be tested
    • New suspension scheme (cup & cone design)
    • Balancing the plates
    • Dummy metal payload?
  • => Suspending test with a suspension cage for a Faraday isolator@CIT
    • Supporting block for the suspension cage (to mimic the OMC suspension)
  • Things to be designed
    • Wire end (cone)
    • Diode holding structures
      PD/QPD/PZT holding structure
  • PZT alignment
  • Prototyping with metal parts?
  • UV glue? (heat) / gluing test
  • Balance / ballast
     
  • Solid works

Optics

  • Mirrors to be delivered ~Aug
  • Design down select
    • Between "Single output & BS" vs "Two outputs & no BS"
  • Mode design
  • Finalization of scattering paths / PD angles etc
     
  • Things to be decided / confirmed:
    • How to handle optics / assemblies (Talk to the prev people)
    • First contact? (Margot: applicable to a short Rc of ~2.5m)
    • Gluing templates to be designed (how to handle it?)
  • Things to be tested:
    • R&T of each mirror
    • Cavity ref/trans/finesse
    • PD QE / incident angle
       
  • What PD do we use?
     
  • CCD beam analyzer (Zach: It is fixed.)
     
  • PD angle measurement
  • Obtain EG&G 3mm PDs

Electronics

  • Electronics / CDS electronics / software
     
  • Things to be tested
    • QPD/PD pre-selections (QE/noise)
    • Functionality test of QPD/PD/PZT

Shipping, storage etc


Jun/July
    - Lab renovtion
    - Mechanics design
    - Glue training
Aug
    - Mirror delivery
    - Basic optics test
Sept
    - Cavity test
    - Suspending test
NOV~DEC
    - Shipping to LLO

Open questions
    Two optical designs
    Procedure
    Modeling
    Clamp design / stencil design
    gluing-installation procedure

Entry  Fri Jun 15 15:45:49 2012, Koji, General, General, OMC Plan 

LIGO Document G1200683-v1:
aLIGO OMC fabrication and testing plan

aLIGO OMC wiki

ELOG V3.1.3-