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Message ID: 4260     Entry time: Tue Feb 8 13:26:11 2011
Author: Aidan 
Type: Summary 
Category: Green Locking 
Subject: Temperature dependence of phase change of green on reflection 

 I did a quick back of the envelope calculation of the expected green phase change on reflection from the aLIGO ITM.

The phase change per nm, K1 = delta phi/delta Lambda, around 532nm is ~1.5 degrees/nm (from the LMA data) [this number is approximately 100x smaller at 1064nm]

I assumed that very small changes in the thickness of the coating appear equivalent to shifting the spectra for reflection/transmission/phase-change-on-reflection up or down by delta lambda, where

delta Lambda/Lambda = delta h/h

where h is the total thickness of the coating and delta h is the change in the thickness of the coating.

Assume that delta h/h = alpha deltaT, where alpha is the coefficient of thermal expansion and delta T is the change in temperature. (approximately 1K)

Then delta phi = K1* Lambda * alpha * delta T = 1.5 degrees/nm * 532nm * 10^-5 K^-1 * 1.0 K =  8 * 10^-3 degrees.

Assume that 360 degree phase change corresponds to one FSR.

Therefore, the frequency shift due to temperature change in the coating = 8*10^-3/360 * FSR = 2.2 *10^-5 * FSR.

Therefore, the expected frequency shift per degree temperature change = 2.2*10^-5 * FSR [Hz/K]

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