error handling for complex equation

Hey,

My problem is that there is an error message to Laguerrsche, firstly because of a matrix multiplication and secondly that the second input of n over k has to be non negative. However, the input is at most 0, since k runs to pc-1. And all values are scalar, if then possibly the r value would be a vector. I see therefore no solution for the indicated problems and thank you in advance for the answer(s).

% Define the fibre characteristics and wavelength
nCore = 1.434;
nCladding = 1.42;
wavelength = 1.23;    % microns
coreRadius = 25;     % microns(Mü-meter)

 % Calculate fibre V number
    V = (2*pi*coreRadius/wavelength)*sqrt(nCore^2-nCladding^2);

    % Calculate wavenumber 
    k = 2 * pi / wavelength;
     
    % Calculate Fleckradius
    wf = sqrt(2*coreRadius^2/V);
   

iL=1;
pc =3;
r= [0,0.00001,0.005];
 Laguerrsche = symsum(nchoosek(pc-1+iL,pc-1-k)*(-2*r.^2/wf^2)^k/factorial(k), k,0, pc-1);
 YFeld=  sqrt(factorial(pc-1)*pi/factorial(p-1+iL)) *1/wf* Laguerrsche*exp(-x^2/wf^2)*(sqrt(2)*x/coreRadius)^iL;

plot(r,YFeld)

Answer 1

[Alan Stevens]

nchoosek(pc-1+iL,pc-1-k) Your value of pc-1-k isn't a non-negative integer, but it needs to be for nchoosk.

Also why use symsum rather than just sum?

[Anna-Lena Geppert]

I don't understand why pc-1-k is not a negtaive integer. k is defined to run and go to pc-1 at most, and pc is greater than 1 and integer.

As in the picture below, I am just trying to solve this equation for u= 2*r^2/w^2. I used symsum since I am calculating a series.

[Alan Stevens]

You have previously defined k as 2pi/wavelength. Try using a different symbol for this.

[Anna-Lena Geppert]

oh thank you, i see my mistake. :)

but now the variable that runs in the sum is undefined (for k replace variable n). This variable runs with the sum and is therefore also defined, what have I misunderstood?

[Alan Stevens]

How about

% Define the fibre characteristics and wavelength
nCore = 1.434;
nCladding = 1.42;
wavelength = 1.23;    % microns
coreRadius = 25;     % microns(Mü-meter)

 % Calculate fibre V number
    V = (2*pi*coreRadius/wavelength)*sqrt(nCore^2-nCladding^2);

    % Calculate wavenumber 
    k = 2 * pi / wavelength;
     
    % Calculate Fleckradius
    wf = sqrt(2*coreRadius^2/V);
   

iL=1;
pc =3;
r= [0,0.00001,0.005];

Laguerrsche = 0;
for n = 0:pc-1
 Laguerrsche = nchoosek(pc-1+iL,pc-1-n)*(-2*r.^2/wf^2).^n/factorial(n)+Laguerrsche;
end
YFeld=  sqrt(factorial(pc-1)*pi/factorial(pc-1+iL)) *1/wf* Laguerrsche.*exp(-r.^2/wf^2).*(sqrt(2)*r/coreRadius).^iL;

plot(r,YFeld)

Note that in YFeld you had x, which was undefined. I've replaced it by r in the above, though that's just guesswork on my part!

[Anna-Lena Geppert]

okay, thank you. :)