I would like to get the result of Fresnel-Kirchhoff integral in paraxial approximation to the cylindrical diffracted wave and here is a part of my code and if it is solved gonna be carrying the other parts out. It is a Matlab code.
vpa(int(exp(-1i*2*k*(n_cl-n_s)*sqrt(b^2-x_p^2))*exp(1i*k*((x-x_p)^2)/2z),-b,-a))
with respect to x_p. where
b = 62.5*e-6; % cladding radius
a = 4*e-6; % core radius
n_co = 1.473; % core ref index
n_cl = n_co - 0.016; % cladding ref index
n_s = 1.37868e-5; % surrounding ref index
L = 457.9e-9; % wavelength
k = 2*pi/L; % wavenumber
z = 0.4 ;
x =-0.0002;
Which command should be used as an integrator? I've been trying to use int()
instead of quad
since quad
doesn't fulfill the requirement to obtain complex results. In addition to that I've been getting the well-known error of
Explicit integral could not be found
Don't know what to do. Please help me.