ring-mode-overlap.py

# Calculating 2d ring-resonator modes, from the Meep tutorial.
import meep as mp


n = 3.4  # index of waveguide
w = 1  # width of waveguide
r = 1  # inner radius of ring

pad = 4  # padding between waveguide and edge of PML
dpml = 2  # thickness of PML

sxy = 2 * (r + w + pad + dpml)  # cell size
cell = mp.Vector3(sxy, sxy)

# Create a ring waveguide by two overlapping cylinders - later objects
# take precedence over earlier objects, so we put the outer cylinder first.
# and the inner (air) cylinder second.
geometry = [
    mp.Cylinder(radius=r + w, height=mp.inf, material=mp.Medium(index=n)),
    mp.Cylinder(radius=r, height=mp.inf, material=mp.air)
]

pml_layers = [mp.PML(dpml)]
resolution = 20

# If we don't want to excite a specific mode symmetry, we can just
# put a single point source at some arbitrary place, pointing in some
# arbitrary direction. We will only look for Ez-polarized modes.

fcen = 0.118  # pulse center frequency
df = 0.010   # pulse width (in frequency)
sources = [mp.Source(src=mp.GaussianSource(fcen, fwidth=df), component=mp.Ez,
                     center=mp.Vector3(r + 0.1))]

# exploit the mirror symmetry in structure+source:
symmetries = [mp.Mirror(mp.Y)]

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

h1 = mp.Harminv(mp.Ez, mp.Vector3(r + 0.1), fcen, df)
sim.run(mp.after_sources(h1), until_after_sources=300)

fields2 = sim.fields
sim.reset_meep()

fcen = 0.236
h2 = mp.Harminv(mp.Ez, mp.Vector3(r + 0.1), fcen, df)
sim.run(mp.after_sources(h2), until_after_sources=300)


def overlap_integral(r, ez1, ez2):
    return ez1.conjugate() * ez2

res = sim.integrate2_field_function(fields2, [mp.Ez], [mp.Ez], overlap_integral)
print("overlap integral of mode at w and 2w: {}".format(abs(res)))