resonatorprofile: should transfer function scale with sqrt(power)

[stestoll]

Currently, resonatorprofile returns a transfer function that is normalized such that it equals 1 at resonance, independent of unloaded Q and coupling coefficient. Since this transfer function represents the B1 profile, it might be useful to have it scale with the square root of the admitted/transmitted power. This way, it would be clear that the B1 field at the sample not only depends on loaded Q, but on the coupling as well.

Demonstration that compares two situations with identical loaded Q, but different unloaded Q and different coupling coefficients:

nu = linspace(9,10,1001);
nu0 = 9.5;

Qu1 = 200; beta1 = 1;
Qu2 = 400; beta2 = 3;
QL1 = Qu1/(1+beta1);
QL2 = Qu2/(1+beta2);

% Transmtted/admitted power
Ptrans1 = resonatorprofile(nu,nu0,Qu1,beta1,'powertransmission');
Ptrans2 = resonatorprofile(nu,nu0,Qu2,beta2,'powertransmission');

% Normalized transfer function
H_norm1 = resonatorprofile(nu,nu0,Qu1,beta1,'transferfunction');
H_norm2 = resonatorprofile(nu,nu0,Qu2,beta2,'transferfunction');

% Transfer function, including dependence on coupling
xi = nu/nu0-nu0./nu;
H1 = 2*sqrt(beta1)./(1+beta1+1i*Qu1*xi);
H2 = 2*sqrt(beta2)./(1+beta2+1i*Qu2*xi);

% Plotting
tiledlayout(1,3)
nexttile
plot(nu,Ptrans1,nu,Ptrans2);
title('Power transmission coefficient')
legend(sprintf('Q_u=%d, \\beta=%d, Q_L=%g',Qu1,beta1,QL1),...
  sprintf('Q_u=%d, \\beta=%d, Q_L=%g',Qu2,beta2,QL2))
legend boxoff

nexttile
plot(nu,abs(H_norm1),nu,abs(H_norm2));
title('Transfer function, normalized to max 1')

nexttile
plot(nu,abs(H1),nu,abs(H2));
title('Transfer function, \propto sqrt(power)')