Here is a simulation of the relative FP-cavity gain vs the CEP for a Finesse of 23000 and taking into account the Menhir laser optical spectrum and several CVBG parameters.
I added the commented Matlab code to produce this plot.
| Xinyi Lu wrote: |
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These days, Ronic, Daniele and I achieved stable cavity locking with the menhir pulsed laser.
- After vacuuming, the current cavity finesse is now about 23,000. The diameter of the cavity mode is w_x=2.2mm, w_y=2.7mm.
- We had to compensate for frequency drift by manually adjusting the cavity length to keep locking.
Now the problem is that CEP's compensation range is not enough. The laser CEP is drifting from day to day. We adjusted the CEP by tuning the pump current of the menhir laser, but the adjustment range was not enough.
- The laser pump current is varied in the locking state and the variation of repetition rate is recorded. The current range is 850mA to 950mA and the repetition rate changes by 24 Hz. The calculation process is shown in Figure 3.
- By calculation, the variation of CEP caused by the variation of laser current is only π/2, which we hope is 2π.
- For Gamma Factory, the target FSR is 40 MHz, so the 4-pulse stack provides 4 times CEP tuning range to meet the requirements. But for our experiment, it seems not enough now.
The next step is to evaluate the gap to the maximum gain and draw the curve of CEP. Then we will discuss solutions.
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clear
clc
c=3e8; % speed of light
% laser parameters
lambda0=1031.6e-9; % central wavelength (m)
dlambda0=6.2e-9; % spectral LW (m)
Frep0=160.3e6; % laser repetition rate (Hz)
CEP0=0; % arbitrary CEP value (rad)
% CVBG parameters
CVBG=3; % choose the version of the CVBG
switch CVBG
case 1
% N40-05
lambda1=1031.61e-9; % central wavelength (m)
dlambda1=2.2e-9; % spectral LW (m)
case 2
% N40-01
lambda1=1031.55e-9; % central wavelength (m)
dlambda1=1.92e-9; % spectral LW (m)
case 3
%N40-20
lambda1=1031.64e-9; % central wavelength (m)
dlambda1=2.49e-9; % spectral LW (m)
end
lambda_min=lambda1-dlambda1/2; % minimum wavelength limit of the CVBG
lambda_max=lambda1+dlambda1/2; % maximum wavelength limit of the CVBG
% wavelength vector
lambda=linspace(lambda0-5*dlambda0,lambda0+5*dlambda0,1e5);
% laser power vs wavelentgth
Plas=Plaser(lambda,lambda0,dlambda0,0,1);
% laser power after CVBG vs wavelentgth
Pcvbg=Plaser(lambda,lambda0,dlambda0,lambda_min,lambda_max);
figure(1)
clf
plot(lambda*1e9,Plas)
hold on
plot(lambda*1e9,Pcvbg)
grid on
xlabel('wavelength (nm)')
ylabel('laser power (a.u)')
title('laser spectral power before and after CVBG')
legend('before CVBG','after CVBG')
nmin=floor(c/lambda_max/Frep0); % minimum laser resonance index
nmax=ceil(c/lambda_min/Frep0); % maximum laser resonance index
nmean=(nmin+nmax)/2; % average laser resonance index
nv=nmin:nmax; % vector of resonance indexes
flas=(nv+CEP0/2/pi)*Frep0; % vector of laser frequencies
lambda=c./flas; % new vector of wavelength for the laser
% laser power after CVBG vs wavelentgth
Pcvbg=Plaser(lambda,lambda0,dlambda0,lambda_min,lambda_max);
figure(2)
clf
plot(lambda*1e9,Pcvbg)
grid on
xlabel('wavelength (nm)')
ylabel('laser power (a.u)')
title('laser spectral power after CVBG')
% FP-cavity description
FSR=Frep0; % Free Spectral Range of the FP-cavity
F=23000; % Finesse of the FP-cavity
LW=FSR/F; % FP-cavity linewidth definition
N=1e3; % Nb of CEP simulation steps
cepv=linspace(-2*pi,2*pi,N); % CEP vector
Gcav=zeros(1,N); % FP-cavity gain vector initialization
for k=1:N
dfrep=-cepv(k)/2/pi/(nmean+cepv(k)/2/pi)*FSR; % dfrep = frep - FSR
df=(nv-nmean).*dfrep; % df = flas(n) - n*FSR
T=Airy(df,LW); % power FP-cavity gain vs df
Gcav(k)=sum(T.*Pcvbg)/sum(Pcvbg); % total FP-cavity gain
end
figure(3)
clf
hold on
plot(cepv/pi,Gcav)
grid on
xlabel('CEP/pi (rad/rad)')
ylabel('Relative cavity gain (a.u)')
title('Relative cavity gain vs CEP')
%legend('cvbg N40-05','cvbg N40-01','cvbg N40-20')
% Laser power after CVBG function
function Pcvbg=Plaser(lambda,lambda0,dlambda0,lambda_min,lambda_max)
Plas=sech(1.7625*(lambda-lambda0)/dlambda0).^2;
Tcvbg=lambda>=lambda_min & lambda<=lambda_max;
Pcvbg=Plas.*Tcvbg;
end
% FP-cavity Airy function
function T=Airy(df,LW)
T=1./(1+(2*df/LW).^2);
end
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