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# 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(f"overlap integral of mode at w and 2w: {abs(res)}")
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