[Yuta, Jenne]
We have both calculated, and agree on the numbers for, the PRC gain for carrier and sideband.
We are using the measured arm cavity (power) loss of 150ppm....see elog 5359.
We get a PRC gain for the CARRIER (nonflipped folding) of 21, and PRC gain (flipped folding) of 20. This is a 4.7% loss of carrier buildup.
We get a PRC gain for the SIDEBANDS (nonflipped folding) of 69, and PRC gain (flipped folding) of 62. This is an 8.8% loss of sideband buildup.
The only difference between the "flipped" and "nonflipped" cases are the L_PR# values  for "nonflipped", I assume no loss of PR2 or PR3, but for the "flipped" case, I assume 1500ppm, as in Rana's email. Also, all of these cases assume perfect mode matching. We should see what the effect of poor mode matching is, once Jamie finishes up his calculation.
Why, one might ask, are we getting cavity buildup of ~20, when Kiwamu always quoted ~40? Good question! The answer seems, as far as Yuta and I can tell, to be that Kiwamu was always using the reflectivity of the ITM, not the reflectivity of the arm cavity. The other alternative that makes the math work out is that he's assuming a loss of 25ppm, which we have never measured our arms to be so good.
For those interested in making sure we haven't done anything dumb:
ppm = 1e6;
%     
% PRM PR2 PR3 ITM ETM
T_PRM = 0.05637;
t_PRM = sqrt(T_PRM);
L_PRM = 0 *ppm;
R_PRM = 1  T_PRM  L_PRM;
r_PRM = sqrt(R_PRM);
T_PR2 = 20 *ppm;
t_PR2 = sqrt(T_PR2);
L_PR2 = 1500 *ppm;
R_PR2 = 1  T_PR2  L_PR2;
r_PR2 = sqrt(R_PR2);
T_PR3 = 47 *ppm;
t_PR3 = sqrt(T_PR3);
L_PR3 = 1500 *ppm;
R_PR3 = 1  T_PR3  L_PR3;
r_PR3 = sqrt(R_PR3);
T_ITM = 0.01384;
t_ITM = sqrt(T_ITM);
L_ITM = 0;%100 *ppm;
R_ITM = 1  T_ITM  L_ITM;
r_ITM = sqrt(R_ITM);
T_ETM = 15 *ppm;
t_ETM = sqrt(T_ETM);
L_ETM = 0 *ppm;
R_ETM = 1  T_ETM  L_ETM;
r_ETM = sqrt(R_ETM);
rtl = 150*ppm; % measured POWER round trip loss of arm cavities.
rtl = rtl/2; % because we need the sqrt of the exp() for ampl loss....see Siegman pg414.
eIkx_r = exp(1i*2*pi);
r_cav_res = r_ITM + (t_ITM^2 * r_ETM * eIkx_r * exp(rtl)) / (1  r_ITM*r_ETM * eIkx_r * exp(rtl) );
eIkx_ar = exp(1i*pi);
r_cav_antires = r_ITM + (t_ITM^2 * r_ETM * eIkx_ar * exp(rtl)) / (1  r_ITM*r_ETM * eIkx_ar * exp(rtl) );
%% PRC buildup gain
g_antires = t_PRM*eIkx_ar / (1r_PRM*r_PR2*r_PR3*r_cav_antires*eIkx_ar);
G_ar = g_antires^2;
G_ar = abs(G_ar) % Just to get rid of the imag part that matlab is keeping around.
g_res = t_PRM*eIkx_r / (1r_PRM*r_PR2*r_PR3*r_cav_res*eIkx_r);
G_r = g_res^2;
G_r = abs(G_r)
