sinus wave with chosen number of variating period

Hi,

I am trying to simulate a refractive index change in a medium, to do that I need to accurately model the evolution of said index with a sinusoidal function with variating period (see picture below for an exemple).

The function is written as n(z)=n0+n1*cos(phi(z)) (n being the index), with phi(z)=alpha/(z+beta), I would expect that fixing beta and calculating alpha for alpha=nT*2*pi*(zmax+beta) (with nT the number of period in the interval from z=0 to z=zmax) would give me a function with nT period but it does not, where did I go wrong?

Thanks

[Mathieu NOE]

hello

can you share the code and maybe the paper or doc you are refering to

[Hugo]

Hello, the code follows the equations :

%%for the figure shared
N=1e6 %increase N for better plot
z=linspace(0,5e-3,N);
n0=1.445;
n1=8e-4;
n=n0+n1*cos(100e-5./(z+1e-6));

%%when trying for a certain amount of periods
N=1000
nT=1000;
z=linspace(0,5e-3,N);
beta=1e-6;
alpha=nT*2*pi*(z(end)+beta);
n=n0+n1*cos(alpha./(z+beta));

I do not get what more I could explain about it, the article will not really be helpful when it comes to answering this question but here it is https://piers.org/pierspublications/PIERS2011SuzhouProceedings04.pdf page 158 of the pdf document, it is focused on the partition integration method for the numerical simulation not on the model of the function applied to z in the cosinus only mentionned once in fig 1.

Answer 1

[Hugo]

Ok not sure that is the best way to do it but it works for me :

define phi(z) as alpha*log(z) and dimension alpha the same way as before.