Contents
First problem is, given rho and d, find z and d_0
d=0.3;
lambda=10.59e-6;
bprime=pi*d^2/4/lambda;
f=(0.1:0.1:5)*bprime;
qinv=-1./f - 1i/bprime;
q=1./qinv;
z=real(q);
b=imag(q);
d_0=sqrt(b*4*lambda/pi);
fig12=figure;plot(f/1000,-z/1000,'k');
moose=axis;
axis([0,moose(2),0,moose(4)]);
hold on;plot([0,moose(4)],[0,moose(4)],'k--',...
[1,1]*bprime/1000,[0,moose(4)],'k-.',...
[0,moose(2)],[1,1]*bprime/2/1000,'k-.');
grid on;
hold off;
xlabel('f, Focal Length, km');
ylabel('-z, Distance to Waist, km');
Now show the wasit diameter.
fig13=figure;plot(f/1000,d_0*100,'k',...
[0,bprime/1000],[0,4/pi*lambda/d*bprime*100],'k--',...
[0,f(end)]/1000,[1,1]*d*100,'k--');
grid on;
xlabel('f, Focal Length, km');
ylabel('d_0, Waist Diameter, cm');
for three plots of axial irradiance with dfferent f
zplot=(0:10:10000);
fplot=[200,1000,5000];
[zp,fp]=meshgrid(zplot,fplot);
qinvp=-1./fp - 1i/bprime;
qp=1./qinvp;
zzerop=real(qp);
bp=imag(qp);
d_0p=sqrt(bp*4*lambda/pi);
dp=d_0p.*sqrt(1+((-zp-zzerop)./bp).^2);
pp=2./(pi*(dp/2).^2);
fig14=figure;loglog(zplot/1000,pp,'k-',...
fplot(1)*[1,1]/1000,[1e-2;1e6],'k-.',...
fplot(2)*[1,1]/1000,[1e-2;1e6],'k-.',...
fplot(3)*[1,1]/1000,[1e-2;1e6],'k-.');
grid on;
hold on;
moose=axis;axis([moose(1:2),1e-2,1e5]);
xlabel('z, Distance, km');
ylabel('I_0/P, m^{-2}');
hold off;
Beam diameter along the path
test=zplot<2500;
fig15=figure;plot(zplot(test)/1000,dp(2,test)*100,'k',...
zplot(test)/1000,abs(d*(zplot(test)-fplot(2))/fplot(2))*100,'k--',...
zplot(test)/1000,4/pi*lambda/d*zplot(test)*100,'k--');
xlabel('z, Distance, km');
ylabel('d, Beam Diameter, cm');
grid on;