The following elog is in support of Evan's upcoming elog on last nights TCS transient (turning off TCS) Bottom line: The contrast defect (CD) can be modeled as CD = CD_0 + pi^2/8 * D^2*w^4/lambda^2 where: CD : contrast defect CD_0 : residual contrast defect, not due to ITM RoC mismatch D : Diopter change in (one) ITM, double pass, i.e. D=2*( 1/R_new - 1/R_old ) w : beam spot radius on the ITM, nominally 53mm lambda: wave length = 1.064e-6m Derivation: - incident beam: |Psi> = N exp(-r^2/w^2) - ITMX reflection operator: exp(i*k*D*r^2/2) - ITMY reflection operator: 1 - reflected field: |r> = |Psi> * exp(i*k*D*r^2/4) * cos(k*D*r^2/4) - dark port field: |t> = |Psi> * exp(i*k*D*r^2/4) * i sin(k*D*r^2/4) - Power in dark port due to RoC mismatch:= k^2*D^2*w^4/32 = pi^2/8 * D^2*w^4/lambda^2 The bottom line formula for contrast defect follows from this. Some other useful expressions: - Power reflected from the Michelson: = 1 - = 1 - pi^2/8 * D^2*w^4/lambda^2 Note that this power will be in a different mode, so the mode matching into the recycling cavity is expected to change. And for reference, some Gaussian integrals: h_n := h_n = n/4 w^2 h_(n-2) h_0 = 1 h_2 = 1/2 w^2 h_4 = 1/2 w^4 h_6 = 3/4 w^6 h_8 = 3/2 w^8
Stefan, Evan
Since we turned off the TCS last night and left PRMI locked on carrier, we have roughly 8 hours of good data that tells us the (1) the contrast defect and (2) the behavior of the ITM thermal lens as a function of time. To extract these quantities, we did the following:
In principle, we can also use the above data to extract the mode-matching into the PRMI as a function of time. Perhaps we will pursue this later.