Are the lines in the MPB structure due to code issues or display issues?

[niubiworker]

I want to construct a slab of photonic crystal with line defects for band structure calculation using MPB. However, I encountered the issue shown in the image while building the geometry. Does this mean there is an issue with my structure?

import numpy as np
import meep as mp
import meep.mpb as mpb
import matplotlib.pyplot as plt

a=1
ratio=0.3
r=ratio*a
y_num=7
h=0.3
period_a,r,h=a/a,r/a,h/a    
geometry_lattice_base=mp.Lattice(mp.Vector3(1,1),
                            basis1=mp.Vector3(np.sqrt(3) / 2, 0.5),
                            basis2=mp.Vector3(np.sqrt(3) / 2, -0.5),)
geometry_lattice=mp.Lattice(mp.Vector3(1,y_num),
                            basis1=mp.Vector3(np.sqrt(3) / 2, 0.5),
                            basis2=mp.Vector3(np.sqrt(3) / 2, -0.5),)
material_LN=mp.Medium(epsilon=12)
geometry = [mp.Prism(vertices=[mp.cartesian_to_lattice(mp.Vector3(np.sqrt(3)*0.5*period_a,0),geometry_lattice_base),
                                mp.cartesian_to_lattice(mp.Vector3(0,0.5*period_a),geometry_lattice_base),
                                mp.cartesian_to_lattice(mp.Vector3(-np.sqrt(3)*0.5*period_a,0),geometry_lattice_base),
                                mp.cartesian_to_lattice(mp.Vector3(0,-0.5*period_a),geometry_lattice_base),
                                mp.cartesian_to_lattice(mp.Vector3(np.sqrt(3)*0.5*period_a,0),geometry_lattice_base)],
                        height=h,center=mp.Vector3(0,0,0),material=material_LN)]
geometry+=[mp.Cylinder(r, material=mp.Medium(epsilon=1))]
geometry = mp.geometric_objects_lattice_duplicates(geometry_lattice, geometry)
geometry+=[mp.Cylinder(r, material=material_LN,height=h,center=mp.Vector3(0,0,0))]
bloch_lattice=mp.Lattice(mp.Vector3(1,y_num,y_num),
                            basis1=mp.Vector3(np.sqrt(3) / 2, 0.5),
                            basis2=mp.Vector3(np.sqrt(3) / 2, -0.5),)
Gamma = mp.Vector3(0.4)
K_prime = mp.Vector3(0.5)
k_points = mp.interpolate(32, [Gamma, K_prime])
num_band = 20
ms = mpb.ModeSolver(resolution=20,
                    geometry=geometry,
                    geometry_lattice=bloch_lattice,
                    k_points=k_points,
                    num_bands=num_band,)

ms.init_params(reset_fields=True,p=mp.NO_PARITY)
md = mpb.MPBData(rectify=True, periods=1, resolution=200)

eps = ms.get_epsilon()

converted_eps = md.convert(eps)
slice_z = converted_eps[:, :, converted_eps.shape[2] // 2]

plt.figure(figsize=(6, 6))
plt.imshow(slice_z, interpolation='spline36', cmap='binary')
plt.colorbar(label='Epsilon')
plt.title('Slice at Middle Z Plane')
plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.show()

Thank you very much!

[stevengj]

Could be a rounding error? I'm not quite sure what your Prism object is supposed to be.

I would suggest just using the default_material or a Block for the dielectric slab and then add cylinders for the holes.

Also, for this type of line-defect structure it is probably more natural to use a rectangular unit cell rather than bloch_lattice