Lorentzian dispersion template is overtruncated

[stestoll]

clear, clc

Sys.lw = [0 10];

Exp.Field = 340;
Exp.mwRange = [9 10];
Exp.Harmonic = 0;
Exp.mwPhase = pi/2;

[f,spc] = pepper(Sys,Exp);
plot(f,spc);

[cerium1925]

Preliminary testing shows that the Lorentz line template function has no bugs.

test code: clc, clear, clf;

x = linspace(-10, 10, 1e3);
x0 = 0;
fwhm = 1;

subplot(2, 2, 1);
[yabs, ydisp] = lorentzian(x, x0, fwhm, -1);
plot(x, yabs, 'r'); hold on;
plot(x, ydisp, 'b');
legend('Absorption', 'Dispersion');
xlabel('x');
ylabel('Amplitude');

subplot(2, 2, 2);
[yabs, ydisp] = lorentzian(x, x0, fwhm, 0);
plot(x, yabs, 'r'); hold on;
plot(x, ydisp, 'b');
legend('Absorption', 'Dispersion');
xlabel('x');
ylabel('Amplitude');

subplot(2, 2, 3);
[yabs, ydisp] = lorentzian(x, x0, fwhm, 1, pi/2);
plot(x, yabs, 'r'); hold on;
plot(x, ydisp, 'b');
legend('Absorption', 'Dispersion');
xlabel('x');
ylabel('Amplitude');

subplot(2, 2, 4);
[yabs, ydisp] = lorentzian(x, x0, fwhm, 2, pi);
plot(x, yabs, 'r'); hold on;
plot(x, ydisp, 'b');
legend('Absorption', 'Dispersion');
xlabel('x');
ylabel('Amplitude');

For Gaussian and Lorentzian functions, the fixed parameters adopted here may introduce potential bugs. It has been found that for the same lw, for Gaussian and Lorentzian line modes, x0T, wT, xT are different, which should not make a difference. . .

I don't quite understand why fixed parameters are used here, but preliminary tests have found that the current bug can be fixed by changing this "reduction factor" to 1e3 or larger.

[stestoll]

Yes, you are spot on. Extending the range over which the template lineshape is evaluated reduces this truncation error.

The issue is that for a reasonably accurate dispersion template (ie. falling off to at least 0.25e-2 of its maximum, or better), it would need to be about 800 fwhm linewidths wide. The absorption template only needs 20 fwhm linewidths.

 clc, clear

x0 = 0;
fwhm = 1;

xabs = linspace(-1,1,1e4)*20*fwhm;
yabs = lorentzian(xabs,x0,fwhm,0,0);
yabs = yabs/max(yabs);

xdisp = linspace(-1,1,1e4)*800*fwhm;
ydisp = lorentzian(xdisp,x0,fwhm,0,pi/2);
ydisp = ydisp/max(ydisp);

tol = 0.25e-2;

tiledlayout(2,1)
nexttile
semilogy((xabs-x0)/fwhm,yabs);
xlabel('(x-x0)/fwhm')
ylabel('abs/max(abs)');
grid on
yline(tol,Color='r')
title('Lorentzian absorption')

nexttile
semilogy((xdisp-x0)/fwhm,abs(ydisp));
xlabel('(x-x0)/fwhm')
ylabel('disp/max(disp)');
grid on
yline(tol,Color='r')
title('Lorentzian dispersion')