I have written a code for gaussian beam propagation in free-space by angular spectrum method.To verify whether the simulation is correct or not, I am propagating the gaussian beam in free-space, and verify the resulted field's beam width with the theoretical formulas. The following is my code, I don't understand what's wrong in it, the beam width is not matching with theoretical beam width, I would really appreciate any guidance. Thank you
Here is my code:
wvl = 1550e-9 # wavelengthwz = 0.05 # beam waistgdim = 1 # spatial extent of the grid;resol = 512 # grid resolutionI = 1 # intensity amplitudezr = (np.pi * wz**2)/wvl # rayleigh rangek = 2*np.pi/wvl# Theoretical beam width at reciever (Lz km) # Gaussian wzt = lambda Lz, wg, lmda: wg * np.sqrt(1 + ((Lz * lmda)/(np.pi * wg**2))**2)wz_ = wzt(0, wz, wvl)z = zr# define griddx = np.sqrt((wvl*z)/resol) #(wvl * np.sqrt(z**2 + gdim**2))/gdimgdim = dx * resolx, y = np.meshgrid(np.arange(-gdim/2, gdim/2, dx), np.arange(-gdim/2, gdim/2, dx))r = np.sqrt(x**2 + y**2)def gaussian(wz, r, I):""" wz: Beam width at z=0; r : Radial coordinates I : Intensity distribution""" Fin = I*np.exp(-2*(r/wz)**2) return Fingbeam = gaussian(wz, r, I)def ft2(g, delta=None):""" Computes the 2D Fourier transform of g with scaling. Parameters: g : numpy.ndarray Input 2D array to transform. delta : float Spacing in the spatial domain. Returns: numpy.ndarray The scaled 2D Fourier transform of g.""" G = np.fft.fftshift(np.fft.fft2(np.fft.ifftshift(g))) return Gdef ang_spec_prop(e, z, resol, dx, wvl): k = (2*np.pi/wvl) fxx = np.fft.fftshift(np.fft.fftfreq(resol, dx)) fxx, fyy = np.meshgrid(fxx, fxx) alfa = k ** 2 - (4 * (np.pi ** 2)) * (fxx ** 2 + fyy ** 2) tmp = np.sqrt(np.abs(alfa)) kz = np.where(alfa >= 0, tmp, 1j*tmp) h1 = np.exp(z * kz * 1j) e_ = ft2(ft2(e)*h1) return e_prop_as = ang_spec_prop(gbeam, z, gbeam.shape[0], dx, wvl)# Calculate the beam widthdef anacal_gbw(ub, r): # Find the intensity where it falls to 1/e^2 of its maximum ub = np.abs(ub)**2 r_flat = r.flatten() imax = ub.max()/(np.exp(1)**2) in_flat = ub.flatten() wg_calc = r_flat[np.abs(in_flat-imax).argmin()] return wg_calcana_w = anacal_gbw(prop_as, r) the_w = wzt(z, wz, wvl)With these parameters, the_w (theoretical beam width) = 0.0707; but ana_w (analytical beam width) = 0.0792