refl-angular-kz2d.py

import meep as mp
import math

def refl_planar(theta, kz_2d):
    resolution = 100

    dpml = 1.0
    sx = 10
    sx = 10 + 2*dpml
    cell_size = mp.Vector3(sx)
    pml_layers = [mp.PML(dpml)]

    fcen = 1.0

    # plane of incidence is XZ
    k = mp.Vector3(z=math.sin(theta)).scale(fcen)

    sources = [mp.Source(mp.GaussianSource(fcen,fwidth=0.2*fcen),
                         component=mp.Ey,
                         center=mp.Vector3(-0.5*sx+dpml))]

    sim = mp.Simulation(cell_size=cell_size,
                        boundary_layers=pml_layers,
                        sources=sources,
                        k_point=k,
                        kz_2d=kz_2d,
                        resolution=resolution)

    refl_fr = mp.FluxRegion(center=mp.Vector3(-0.25*sx))
    refl = sim.add_flux(fcen, 0, 1, refl_fr)
    
    sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ey, mp.Vector3(-0.5*sx+dpml), 1e-9))

    input_flux = mp.get_fluxes(refl)
    input_data = sim.get_flux_data(refl)
    sim.reset_meep()

    # add a block with n=3.5 for the air-dielectric interface
    geometry = [mp.Block(size=mp.Vector3(0.5*sx,mp.inf,mp.inf),
                         center=mp.Vector3(0.25*sx),
                         material=mp.Medium(index=3.5))]

    sim = mp.Simulation(cell_size=cell_size,
                        geometry=geometry,
                        boundary_layers=pml_layers,
                        sources=sources,
                        k_point=k,
                        kz_2d=kz_2d,
                        resolution=resolution)

    refl = sim.add_flux(fcen, 0, 1, refl_fr)
    sim.load_minus_flux_data(refl, input_data)

    sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ey, mp.Vector3(-0.5*sx+dpml), 1e-9))

    refl_flux = mp.get_fluxes(refl)
    freqs = mp.get_flux_freqs(refl)

    Rmeep = -refl_flux[0]/input_flux[0]
    return Rmeep


# rotation angle of source: CCW around Y axis, 0 degrees along +X axis
theta_r = math.radians(19.4)

Rmeep_real_imag = refl_planar(theta_r,"real/imag")
Rmeep_complex = refl_planar(theta_r,"complex")
Rmeep_3d = refl_planar(theta_r,"3d")

n1=1
n2=3.5

# compute angle of refracted planewave in medium n2
# for incident planewave in medium n1 at angle theta_in
theta_out = lambda theta_in: math.asin(n1*math.sin(theta_in)/n2)

# compute Fresnel reflectance for S-polarization in medium n2
# for incident planewave in medium n1 at angle theta_in
Rfresnel = lambda theta_in: math.fabs((n2*math.cos(theta_out(theta_in))-n1*math.cos(theta_in))/(n2*math.cos(theta_out(theta_in))+n1*math.cos(theta_in)))**2

print("refl:, {} (real/imag), {} (complex), {} (3d), {} (analytic)".format(Rmeep_real_imag,Rmeep_complex,Rmeep_3d,Rfresnel(theta_r)))