comparison of far fields from near2far and actual DFT fields in near-field regime

cavity_farfield.py

import meep as mp
import numpy as np
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt

resolution = 25                    # pixels/μm                                                                    
fcen = 0.25                        # pulse center frequency                                                       
df = 0.2                           # pulse width (in frequency)                                                   
eps = 13.                          # dielectric constant of waveguide                                             
w = 1.2                            # width of waveguide                                                           
r = 0.36                           # radius of holes                                                              
d = 1.4                            # defect spacing (ordinary spacing = 1)                                        
N = 3                              # number of holes on either side of defect                                     

dpad = 2.                          # padding between last hole and PML edge                                       
dpml = 0.5/(fcen-0.5*df)           # PML thickness (> half the largest wavelength)                                
sx = 2*(dpad+dpml+N) + d - 1       # size of cell in x direction                                                  
d1 = 0.2                           # y-distance from waveguide edge to near2far surface                           
d2 = 1.0                           # y-distance from near2far surface to far-field line                           
sy = w + 2*(d1+d2+dpad+dpml)       # size of cell in y direction (perpendicular to wvg.)                          

cell = mp.Vector3(sx,sy,0)

geometry = [mp.Block(center=mp.Vector3(),
                     size=mp.Vector3(mp.inf,w,mp.inf),
                     material=mp.Medium(epsilon=eps))]

for i in range(N):
    geometry.append(mp.Cylinder(r, center=mp.Vector3(d / 2 + i), height=mp.inf))
    geometry.append(mp.Cylinder(r, center=mp.Vector3(d / -2 - i), height=mp.inf))

pml_layers = mp.PML(dpml)

sources = mp.Source(src=mp.GaussianSource(fcen, fwidth=df),
                    component=mp.Hz,
                    center=mp.Vector3())

symmetries = [mp.Mirror(mp.Y, phase=-1),
              mp.Mirror(mp.X, phase=-1)]

sim = mp.Simulation(cell_size=cell,
                    geometry=geometry,
                    sources=[sources],
                    symmetries=symmetries,
                    boundary_layers=[pml_layers],
                    resolution=resolution)

nearfield = sim.add_near2far(
    fcen, 0, 1,
    mp.Near2FarRegion(mp.Vector3(0, 0.5*w + d1),
                      size=mp.Vector3(sx - 2*dpml)),
    mp.Near2FarRegion(mp.Vector3(-0.5*sx + dpml, 0.5*w + 0.5*d1),
                      size=mp.Vector3(0, d1),
                      weight=-1.0),
    mp.Near2FarRegion(mp.Vector3(0.5*sx - dpml, 0.5*w + 0.5*d1),
                      size=mp.Vector3(0, d1))
)

mon = sim.add_dft_fields([mp.Hz],
                         fcen,
                         0,
                         1,
                         center=mp.Vector3(0, 0.5*w + d1 + d2),
                         size=mp.Vector3(sx - 2*(dpad+dpml), 0))

sim.run(until_after_sources=mp.stop_when_dft_decayed())

sim.plot2D()
if mp.am_master():
    plt.savefig('cavity_farfield_plot2D_{}_{}.png'.format(d1,d2),bbox_inches='tight',dpi=150)

Hz_mon = sim.get_dft_array(mon, mp.Hz, 0)

(x,y,z,w) = sim.get_array_metadata(dft_cell=mon)

ff = []
for xc in x:
    ff_pt = sim.get_farfield(nearfield, mp.Vector3(xc,y[0]))
    ff.append(ff_pt[5])
ff = np.array(ff)

if mp.am_master():
    plt.figure()
    plt.subplot(1,3,1)
    plt.plot(np.real(Hz_mon),'bo-',label='DFT')
    plt.plot(np.real(ff),'ro-',label='N2F')
    plt.legend()
    plt.xlabel('array index')
    plt.ylabel('real(Hz)')

    plt.subplot(1,3,2)
    plt.plot(np.imag(Hz_mon),'bo-',label='DFT')
    plt.plot(np.imag(ff),'ro-',label='N2F')
    plt.legend()
    plt.xlabel('array index')
    plt.ylabel('imag(Hz)')

    plt.subplot(1,3,3)
    plt.plot(np.absolute(Hz_mon),'bo-',label='DFT')
    plt.plot(np.absolute(ff),'ro-',label='N2F')
    plt.legend()
    plt.xlabel('array index')
    plt.ylabel('|Hz|')

    plt.suptitle('comparison of far fields from near2far and\n actual DFT fields in near-field regime ({} and {})\
'.format(d1,d2))
    plt.subplots_adjust(wspace=0.6)
    plt.savefig('farfields_Hz_dft_vs_n2f_res{}_{}_{}.png'.format(resolution,d1,d2),bbox_inches='tight',dpi=150)